%!PS-Adobe-2.0 %%Creator: dvips 5.83 Copyright 1998 Radical Eye Software %%Title: r17lk1.dvi %%CreationDate: Fri Aug 17 11:54:37 2007 %%Pages: 35 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: C:\EMTEX\DVIPS32.EXE -O0.0mm,-8.8mm r17lk1 %DVIPSParameters: dpi=300, compressed %DVIPSSource: TeX output 2007.08.17:1154 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IE 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IE N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IE 256 array N 2 string 0 1 255{IE S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/v{/Ry X /Rx X V}B/V{}B/RV statusdict begin/product where{pop false[(Display) (NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false} ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot} imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{ BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 40258437 52099154 1200 300 300 (/R17/r17lk1.dvi) @start %DVIPSBitmapFont: Fa cmbx6 7.2 1 /Fa 1 81 df80 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmsy8 9.6 1 /Fb 1 84 df83 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmmi5 6 1 /Fc 1 12 df11 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmsy5 6 1 /Fd 1 1 df0 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmbx5 6 4 /Fe 4 81 df<1206123E12FE12CE120EAAEAFFE0A20B107D8F13>49 DI<3801FF08000713F8EA1F80383C0038481318A2481300A3EB0F FFA238780078A27EEA1F803807FFF80001139818117E901D>71 D80 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmbx7 8.4 6 /Ff 6 110 df49 DI77 D80 DI<39FC7E07E09038FF 8FF8393F07F07C393E03E03C003C13C0A939FF0FF0FFA2200F7E8E25>109 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmr5 6 5 /Fg 5 85 df<121FEA3180EA60C0EA4040EAC060A8EA4040EA60C0EA3180EA1F000B107D 8F11>48 D<120C123C12CC120CACEA7FC00A107D8F11>I<123FEA6180EAF0C013E0EA60 60120013E013C0EA0180EA030012065AEA10201220EA7FC012FF0B107D8F11>II<387FFFE0386070600040132000C0133000801310A200001300AAEA07FF 14117E9018>84 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmmi6 7.2 3 /Fh 3 106 df11 D<000813605A481320A2EA4060A3EBC04000C0 13C03840C18038636700EA7E7EEA3C3C130D7F8C17>33 D<1206120712061200A5123812 4CA2128C12981218A2123012321262A21264123808157E940D>105 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmmi8 9.6 5 /Fi 5 118 df<00081306481307A24813035AEB0801131800801302A21330140400C013 0CEBF018B512F0387F9FE0EB1FC0383E0F8018117F901A>33 D<126012F0A212701210A4 1220A212401280040C7C830C>59 D103 D<13C01201A2EA0380A4EA0700EAFFF0EA0700A2120EA45AA4EA3820A31340 EA1880EA0F000C197F980F>116 D<001C13C0EA26011247EB03801287128E120EEB0700 121CA338380E20A21218131E380C26403807C38013117E9019>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr8 9.6 55 /Fj 55 125 df<90387E0F803901C1B0C0390303E1E01207000EEBC0C001011300A6B512 FE380E01C0AF387F87FC1B1C809B19>11 D<133F3801C0C0EA0380380701E0120EEB00C0 1400A5B512E0EA0E00AF387FC7FC161C809B18>II34 D<13401380EA0100120212065A120812185A A312701260A312E0AA1260A312701230A37E1208120C7E12027EEA008013400A287D9D10 >40 D<7E12407E7E12187E120412067EA313801201A313C0AA1380A312031300A3120612 04120C5A12105A5A5A0A287E9D10>I<126012F0A212701210A41220A212401280040C7C 830C>44 DI<126012F0A2126004047C830C>I48 D50 D<13F0EA030CEA0E04EA1C0EEA181E1238EA780CEA7000A212F0EAF3E0EAF438EAF81C13 0E12F0130FA31270A3EA300E1238EA181CEA0C38EA03E0101A7E9915>54 D<1240387FFF801400A2EA4002485A5BA2485A5BA25B13C0A212015BA21203A31207A66C C7FC111B7E9A15>III<13021307A3497EA2EB17C01313A2EB21E0A2EB61F01340A2EB8078A20001137CEBFF FCEB003C00027FA3487FA2000C1480121E39FF807FF81D1B7F9A20>65 DI<90381FC0409038F038C03803800538070003000E13 01481300123C003814401278127000F01400A70070144012781238003C1480121C6CEB01 006C13026C6C5A3800F038EB1FC01A1B7E9A1F>I70 D<90381FC080EBE0313803800B38070007000E13034813015A14001278127000F01400A5 ECFFF0EC0780127012781238A27E7E7E3803800B3800E031EB1FC01C1B7E9A21>I<39FF F1FFE0390F001E00ABEBFFFEEB001EAD39FFF1FFE01B1B7E9A20>I76 D78 D80 D<3807F080EA1C0DEA3003EA70011260EAE000A36C13007E127FEA3FF0EA1FFE6C7E0001 138038000FC01303EB01E013007EA36C13C0EB018012F038CC0600EA83FC131B7E9A18> 83 D<007FB5128038701E030060130100401300A200801440A400001400B0133F3807FF F81A1B7E9A1F>I<39FFF03FE0390F0007001402B36C5B138000035B6C6C5A38007060EB 1F801B1B7E9A20>I<3AFFE1FFC0FF3A1F003E003C001E15186C011E1310A2141FD80780 1420A2EC2780D803C01440A29039E043C0C000011580A29038F081E100001500A2903879 00F2A3013E137CA3011C1338A20118131801081310281B7F9A2B>87 D 92 D97 D<12FC121CAA137E381D8380381E01C0381C00E0 14F014701478A5147014F014E0381E01C03819838038107C00151C7F9B18>IIII<13F8EA018CEA071E1206EA 0E0C1300A6EAFFE0EA0E00AFEA7FE00F1C809B0D>I<3807E380381C3CC038381C801400 EA781EA3EA381CA26C5AEA37E00020C7FC1230A2EA3FF86CB4FC1480EA3003386001C0EA C000A33860018038300300EA1C0EEA07F8121A7F9015>I<12FC121CAA137EEB8380EA1D 01001E13C0121CAC38FF8FF8151C7F9B18>I<1218123CA21218C7FCA712FC121CAFEAFF 80091C7F9B0C>I<12FC121CAAEB0FE0EB0780EB060013085B5B5BEA1DE0EA1EF0EA1C70 7F133C131C7F130F148038FF9FE0131C7F9B16>107 D<12FC121CB3A8EAFF80091C7F9B 0C>I<39FC7E07E0391C838838391D019018001EEBE01C001C13C0AC3AFF8FF8FF802111 7F9024>IIII<3803E080EA0E19EA1C05EA38 07EA7803127012F0A512701278EA3807121CEA0E1BEA03E3EA0003A7EB1FF014197F9016 >III<1204A4120CA2121C123CEAFFE0EA1C00A91310A4120CEA0E20EA03C00C19 7F9810>I<38FC0FC0EA1C01AC1303120CEA060D3803F1F815117F9018>I<38FF07E0383C 0380381C0100A2EA0E02A26C5AA21384EA0388A2EA01D0A213F06C5AA2134013117F9016 >I<39FF3FC3F0393C0701C0001CEB0080A2001E1381000E14001309000713C213191310 380390E4EBA064EBE07C00011378EBC03800001330EB80101C117F901F>I<38FF07E038 3C0380381C0100A2EA0E02A26C5AA21384EA0388A2EA01D0A2EA00F05BA21340A25BA212 F000F1C7FC12F31266123C13197F9016>121 DI< B512F01401808A15>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmbx8 9.6 19 /Fk 19 121 df<127812FCA4127806067C850E>46 D48 D<13E01201121F12FF12E31203B3387FFF80A2111A7D9918>III<13075B5BA25B 5B5B13DFEA019FEA031F1207120E120C12181238127012E0B512F8A238001F00A53803FF F8A2151A7F9918>I<38180180EA1FFF14005B13F813E00018C7FCA4EA1BF8EA1FFE381C 0F80381807C0120014E0A2127012F8A300F013C038600F8038381F00EA1FFEEA07F0131A 7E9918>I<137EEA03FF38078180380E03C0EA1E07123C387C03800078C7FCA2EAF820EA F9FEEAFBFF38FE078038FC03C0A200F813E0A31278A3003C13C0EB0780381E0F00EA0FFE EA03F8131A7E9918>I<1260387FFFE0A214C014801400EAE007EAC00E5B5BC65AA25BA2 12015B1203A31207A76C5A131B7D9A18>III70 D101 D<3803F8F0380FFFF8381E0F 38381C0730003C1380A4001C1300EA1E0FEA0FFEEA13F80010C7FC1218A2EA1FFF14C06C 13E0003F13F0387801F838F00078A3007813F0383E03E0381FFFC03803FE00151B7F9118 >103 D<120C123FA4120CC7FCA5127FA2121FAEEAFFC0A20A1D7F9C0E>105 D107 D114 D<38FF07F8A2EA1F00AC1301EA0F03EB FCFFEA03F818127F911B>117 D<38FFC3FCA2381F80E0380FC1C03807C3803803E700EA 01FE6C5A137C137E13FFEA01DFEB8F80380307C0380603E0380E01F038FF03FEA217127F 911A>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmsy7 8.4 4 /Fl 4 50 df0 D<1203A3EAC30CEAE31CEA7B78EA0FC0EA0300 EA0FC0EA7B78EAE31CEAC30CEA0300A30E0F7D8F14>3 D<120C121EA3123CA31238A212 781270A3126012E0A212C0124007127E920B>48 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmr7 8.4 21 /Fm 21 122 df<1304130EA21317EB37801323EB43C01341EB81E0138048487E14700002 7F0006133C0004131C48131E140E48130F804814801403007FB512C0B612E0A21B187E97 21>1 D11 D<1380EA010012025A120C5AA25AA25AA312E0AA1260A37EA27EA27E12047E 7EEA008009227D9910>40 D<7E12407E7E12187EA27EA27EA31380AA1300A31206A25AA2 5A12105A5A5A09227E9910>I<130CACB61280A2D8000CC7FCAC191A7E951F>43 D48 D<12035AB4FC1207B2EAFFF00C167D9514>III<1330A2137013F0A2EA017012021206120412081210A21220124012C0B5FCEA0070 A5EA07FF10167F9514>I<126012F0A212601200A7126012F0A212701210A31220A21240 128004167D8E0B>59 D<1308131CA3132EA31347A2EB8380A3380101C0A348B47EEA0200 481370A3487FA2001C133C39FF01FF8019187F971D>65 D82 D<387FFFFE38701C0E00401302A200C0130300801301A300001300AF38 03FFE018187F971C>84 D<12FCA212C0B3AD12FCA206237D990B>91 D<12FCA2120CB3AD12FCA2062380990B>93 D97 D<137E130EA8EA07CEEA1C 3EEA380E1270126012E0A512601270EA301EEA1C2E3807CFC012187F9716>100 DI114 D<38FE0F80383C0600EA1C04A2EA1E0CEA0E08A26C5AA2EA03A0A213E06C5AA26C5AA248 C7FCA212E312E212E4127811167F8E15>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmex10 12 28 /Fn 28 119 df<130813101320134013C0EA0180EA0300A21206A25AA2121C12181238A2 12301270A4126012E0AF12601270A412301238A21218121C120CA27EA27EA2EA0180EA00 C013401320131013080D3B798117>0 D<7E12407E7E12187E7EA27EA2EA0180A213C012 0013E0A213601370A413301338AF13301370A4136013E0A213C012011380A2EA0300A212 06A25A5A12105A5A5A0D3B7E8117>II< EAFF80A21201B3B3B312FFA2093B7F8115>I<1303130C1338137013E013C01201B21380 1203EA0700120E123812C01238120E7EEA0380120113C0B2120013E013701338130C1303 103B7A811D>8 D<12C01238120E7EEA0380120113C0B2120013E013701338130C130313 0C1338137013E013C01201B213801203EA0700120E123812C0103B7A811D>I18 D<12C012607E7E7E7E7E7F6C7E12007F13707FA27FA27F130F7F801303801301A2801300 80A214701478A21438143CA3141C141EA4140E140FA7801580B3A315005CA7140E141EA4 141C143CA314381478A2147014F0A25C13015CA213035C130791C7FC5B130E5BA25BA25B 5B5B1201485A90C8FC12065A5A5A5A5A19777F8125>III< 15C0EC0180EC03005C140E140C5C14385C146014E0495AA2495A130791C7FC5B130E131E 131C133C13381378A25BA3485AA3485AA3485AA3120F90C8FCA35AA2121EA3123EA4123C A2127CA8127812F8B3AA1278127CA8123CA2123EA4121EA3121FA27EA37F1207A36C7EA3 6C7EA36C7EA31378A21338133C131C131E130E130F7F8013036D7EA26D7E146014708014 1880140E8080EC0180EC00C01A94758127>32 D<12C012607E12387E120C7E12076C7E12 017F6C7EA2137013781338133C131C131E130E130F7F80A26D7EA36D7EA36D7EA31478A3 147C143CA3143EA2141EA3141FA480A21580A8140715C0B3AA1580140FA81500A25CA414 1EA3143EA2143CA3147C1478A35CA3495AA3495AA3495AA291C7FC5B130E131E131C133C 1338137813705BA2485A5B120348C8FC12065A121C5A12305A5A1A947F8127>III88 D<160FEE1880EE39C0EE33E016731663EEE1C0EEE000A24B5AA315 03A25E1507A393C7FC5DA45D151EA3153EA2153CA2157CA415FC5DA31401A35DA21403A4 4A5AA54A5AA54A5AA54AC8FCA4143EA2147EA3147CA314FC5CA45CA21301A25CA313035C A45C1307A391C9FC5BA2130EA2131E131CA2EA703812F85B1360EA70C0EA2180001FCAFC 2B6F7D7F1C>90 D<1304131FEB7FC0EBF1E03803C078380F001E001C13070070EB01C000 C0EB00601B0980A41C>98 D101 DI<1470EB01F0EB03C0EB0F80EB 1E005BA25B13F85BB3A9485AA2485AA2485A48C7FC123C5A12E012787E120F6C7E6C7EA2 6C7EA26C7EB3A97F13787FA27FEB0F80EB03C0EB01F0EB007014597A8121>110 D<12E012F8123C121FEA07806C7EA26C7E7F1200B3A91378A27FA27F7FEB03C0EB01F0EB 0070EB01E0EB03C0EB0F00131E5BA25BA25BB3A912015B485AA2485A001FC7FC123C12F8 12E014597A8121>I<170CA2171C1718173817301770176017E017C01601178016031700 5E1606160E160C161C1618163816301670166016E05E15015E150393C7FC120200075C48 1406D83780130E0067140C0087141CD803C0131815386C6C133015706C6C136015E05DEB 78015DEB3C0392C8FC6D5A1406140EEB0F0C141CEB079814B8EB03F0A25C13015C13002E 3C7B8132>I<170CA2171C1718A217381730A217701760A217E017C0A316011780A21603 1700A25E1606A2160E160CA2161C1618A216381630A216701660A316E05EA215015EA215 0393C7FCA200025C000714065A48140ED83780130C12670047141C00871418EA03C01538 15306C7EA2157015606C7E15E05D137814015D133C140392C8FCA26D5A1406A2EB0F0E14 0CA2141CEB0798A3EB03F85CA36D5AA36D5AA22E5A7B8132>I<170CA3171C1718A31738 1730A317701760A317E017C0A316011780A416031700A35E1606A3160E160CA3161C1618 A416381630A316701660A316E05EA315015EA3150393C7FCA3120200075C15065A5A150E D82780130CA212470087141C000714186C7EA2153815306C7EA215701560A26C7EA215E0 5D1378A214015DA2133C140392C8FCA36D5A1406A3130F140E140CA3EB079C1498A3EB03 F85CA46D5AA45C1300A22E787B8132>I<170CA3171C1718A417381730A517701760A417 E017C0A416011780A416031700A55E1606A4160E160CA4161C1618A416381630A5167016 60A416E05EA415015EA4150393C7FCA31202A200075C15065AA25A150ED82780130CA212 47A20087141C1518EA03C0A315381530A26C7EA3157015606C7EA315E05DA21378A21401 5DA3133C140392C8FCA3131EA25C1406A3130F140E140CA4EB079C1498A414B8EB03F0A5 13015CA56D5AA32E957B8132>I<1506AB1203A25A7F120FA21217EA13C01223A2EA41E0 A21281C67EA31378A37FA37FA37FA3EB0780A4EB03C0A3EB01E0A3EB00F0A31478A3143C A3141EA3140FA3EC0786A4EC03C6A3EC01E6A3EC00F6A3157EA3153EA3151EA3150EA315 0615041F5B7B8035>I<12C0B3AE02205E8035>I I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmsy10 12 11 /Fo 11 113 df0 D<00C013036C13070070130E6C131C6C1338 6C13706C13E0380381C03801C3803800E700137E133CA2137E13E73801C380380381C038 0700E0000E137048133848131C48130E4813074813031818799727>2 D25 D<166082A282A28282EE0380B812E017C0 C9EA0380EE06005E5EA25EA25E2B127D9432>33 D49 DI83 D<130F1338137013E0EA01C0B1EA0380EA0700 121E12F0121E1207EA0380EA01C0B1EA00E013701338130F10317CA419>102 D<12F0121E1207EA0380EA01C0B1EA00E013701338130F1338137013E0EA01C0B1EA0380 EA0700121E12F010317CA419>I<12C0B3B3AD02317AA40E>106 D<1603A216071606160E 160C161C1618163816301670166016E016C015011680150316005D1506150E150C151C15 18153800061430001E1470002F1460004F14E0D887805B00071301D803C05B140392C7FC 6C6C5A14063800F00E140CEB781C1418EB3C381430EB1E701460EB0FE05C13075C130391 C8FC28327D812A>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmmi7 8.4 21 /Fp 21 119 df11 DI<13F0EA03081206EA0C00A312 0EEA0F80EA07C0EA03E0EA0FF0EA1870EA30301270EA601012E01330A2EAC02013601340 EA6080EA2100121E0D187D9712>14 D28 D<0010131848133C141C48130CA238803008A213601410 143038C0E06038F7FBE0B512C0387E3F80383C1E00160F7E8E19>33 D<126012F0A212701210A31220A212401280040B7C830C>59 D75 DI I97 D<127E120E5AA45AA3EA3BC0EA7C6012701370A212E0A4EAC0E0A2EAC1C013 80EA6300123C0C187D9712>I<12035A7EC7FCA61238124E128EA35AA25AA31271A21272 A2123C09187D970E>105 D<130C131C130C1300A6EA01E0EA023013381204A2EA0070A4 13E0A4EA01C0A4EA03801263EAE70012C612780E1F7F9710>II<123F1207120EA4121CA41238A41270A412E012E4A31268123808187D 970D>I<39383E0F80394CC731C0388F0340008EEB80E0A2391C0701C0A3EC0380EA380E 1588EC0708151039701C032039300C01C01E0F7D8E23>II113 DI< EA03E0EA0C10EA083812181330EA1F0013E0EA0FF01203EA003012E0A2EAC060EA40C0EA 3F000D0F7D8E13>I118 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmmi10 12 40 /Fq 40 121 df<133FEBE180390380C0203907006040000E13705A003C1480A248EB7100 A2147248137A147C1478A21270A2003013B83938033840391C1C18803907E00F001B157E 9420>11 D14 D18 D<0007B51280121F481400 38302080EA4040EA804191C7FCEA00C11381A2EA0183A2EA0303A200077F1206A2120E80 EA1C0100085B19157E941C>25 D<3807FFFC121F4813F8383020001240128013601200A2 5BA412015BA21203A348C7FC7E16157E9416>28 D<000414604814F015F8481478153848 1418A2D840031310A21306A21520EAC004010C134015C090381E018038E07607397FE7FF 005C383F83FC381F01F01D1580941F>33 D<131FEB6180EBC0C0380180E0EA0300000613 F0120EA25AA3383801E0A3EB03C00078138038580700A2EA4C0CEA4638EA83E00080C7FC A57EEAFFF86C7E121FEA0004141F7C941A>37 D<127012F8A3127005057C840E>58 D<127012F812FCA212741204A41208A21210A212201240060F7C840E>I<14C0A2130114 80A213031400A25B1306A2130E130CA2131C1318A213381330A213701360A213E05B1201 5BA2120390C7FCA25A1206A2120E120CA2121C1218A212381230A212701260A212E05AA2 12317DA419>61 D<12E01278121EEA0780EA01E0EA0078131FEB07C0EB00F0143C140FEC 03C0EC00F0153CA215F0EC03C0EC0F00143C14F0EB07C0011FC7FC1378EA01E0EA078000 1EC8FC127812E01E1C7C9927>I64 D<811401811403A21407140BA21413A214231443A2EC83E014 81EB01011302A21304A213081318EB1FFF5B90382001F0EB4000A25B48C7FCA212021206 120E3AFFC00FFF805C21237EA225>I<90B612E0A29038078003150049C71260A21640A2 131E1580A34948C7FCA21407EB3FFF495AEB7806A3EBF0041680A29138000100485A1502 A2150648485BA21538000714F8B6FC5D23227EA125>69 D<027F1340903903FFC0809038 0FC06190381F0013017C130F01F0140048487F485A12074848130690C712025A123E5D48 91C7FCA35AA4EC3FFF5AEC00F0A24A5A7EA21278007C495A123C6C13076C13093907E031 803803FFE0C66CC8FC22247DA227>71 D<9039FFFC3FFFA29039078001E0A290390F0003 C0A4011EEB0780A449EB0F00A3013FB5FC495B903878001EA3495BA448485BA448485BA3 0007130139FFFC3FFFA228227EA129>II<903AFFFC01FF80A2903A0780007800 166049C712804BC7FC15025D011E13105D5D4AC8FCEB3C021406140E142FEB784F148F90 38790780137C496C7E13F0811401EA01E06E7EA21578485AA2810007147E3AFFFC03FFC0 A229227EA12A>75 D<90B5FCA2EB0780A249C7FCA4131EA45BA45BA45B1508A21510485A A21520A24848136015C014030007130FB61280A21D227EA122>II<90B512F815FE903807 801FED0780D90F0013C01503A3011E1307A3168049130F1600151E5D90387801F090387F FFC00178C8FCA25BA4485AA4485AA31207EAFFFCA222227EA120>80 D<90B512F015FC903807803FED0F8090390F0007C01503A3011E1307A3ED0F8049140015 1E1578EC01E0D97FFFC7FC90387803806E7E6E7E5BA281A23801E001A43803C0031620A2 000701011340EAFFFC913800F180C8EA3E0023237EA126>82 D<001FB6FCA2391E00F00F 00381403383001E01220006014021240EB03C01280A33900078000A449C7FCA4131EA45B A45BA313F8387FFFF05C20227EA11D>84 D97 D<133FEBE080380380C0EA0701EA0E03121C003CC7FCA25AA35AA400701340 A23830018038380200EA1C1CEA07E012157E9416>99 D<137CEA03C2EA0701120E121C12 38EA7802EA7004EAFFF800F0C7FCA25AA41480A238700300EA3004EA1838EA0FC011157D 9417>101 D<141EEC638014C71301ECC30014801303A449C7FCA4EBFFF8A2010EC7FCA4 131E131CA55BA55BA4136013E0A35B1270EAF18090C8FC1262123C192D7EA218>I I<13F0EA0FE0A21200A2485AA4485AA448C7FCEB0F80EB30C0EB4060380E8070EA0F0012 0EA24813E0A4383801C0A2EB0380148200701384EB0704A2EB030800E01310386001E017 237DA21D>I<13F0EA0FE0A21200A2485AA4485AA448C7FCEB01F0EB0208EB0438380E08 781310EB2030EB4000EA1D80001EC7FCEA1FC0EA1C70487EA27F141038703820A3EB1840 38E00C803860070015237DA21A>107 D<3A3C07E01F803A46183060C03A47201880603A 87401D0070EB801EA2EB001C000E4913E0A44890387001C0A2ED038016824801E01384ED 0704A2ED0308267001C01310D83000EB01E028157E942C>109 D<383C07E03846183038 4720183887401C1380A21300000E5BA4485BA25C158048EBE100EB01C1A2EB00C24813C4 003013781A157E941E>I<3803C0F83804630CEB74063808780713701580A2EA00E0A439 01C00F00A3141E3803801C5C13C01460380721C0011FC7FC90C8FCA2120EA45AA2EAFFC0 A2191F819419>112 DII<137E138138010080EA0201EA0603140090C7FC120713F8EA03FE6C7EEA003F EB07801303127000F01300A2EAE002EA4004EA3018EA0FE011157E9417>I<136013E0A4 EA01C0A4EA0380EAFFFCA2EA0380EA0700A4120EA45AA31308EA3810A2132012181340EA 07800E1F7F9E12>I<001E131800231338EA438014701283A2EA8700000713E0120EA338 1C01C0A314C2EB0384A21307EA0C09380E11883803E07018157E941D>I<001E13C03823 01E0384381F01380008313701430EA870000071320120EA3481340A21480A2EB0100A213 02EA0C046C5AEA03F015157E9418>I<3801E0F03806310C38081A1C0010133CEA201C14 181400C65AA45BA314083860E01012F0142038E1704038423080383C1F0016157E941C> 120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmr7 6.99719 40 /Fr 40 124 df<12011202120412081210123012201260A2124012C0AA12401260A21220 123012101208120412021201081E7E950D>40 D<12801240122012101208120C12041206 A212021203AA12021206A21204120C12081210122012401280081E7E950D>I<124012E0 12601220A31240A2128003097D8209>44 D<124012E0124003037D8209>46 D<120FEA30C0EA6060A2EA4020EAC030A9EA4020EA6060A2EA30C0EA0F000C137E9211> 48 D<120C121C12EC120CAFEAFFC00A137D9211>I<121FEA60C01360EAF07013301260EA 0070A2136013C012011380EA02005AEA08101210EA2020EA7FE012FF0C137E9211>II54 D<1240EA7FFC13F8EA401012801320EA00401380EA0100A25A12021206A2120EA512040E 147E9311>I<124012E012401200A7124012E01240030D7D8C09>58 D67 DI71 D73 D 80 D82 DI<38FF81FC38 1C00701420AD120C000E13400006138038038300EA00FC16147F9319>85 D<39FF1FF0FC3938038030A2001CEBC020A2001E1460390E04E040A200071480EB0870A2 3903887100EB9039A23801F03EEBE01EA23800C00CA31E147F9321>87 D<127FEAE1C0EAE040EA40601200EA07E0EA3860126012C01364A2EA61E4EA3E380E0D7E 8C11>97 D99 D101 DII<12F01230A6EA33E0EA3430EA38181230A9EAFC7E 0F147F9312>I<1220127012201200A512F01230AB12FC06157F9409>I<12F01230B212FC 06147F9309>108 D<38F3E1F03834321838381C0CEA3018A938FC7E3F180D7F8C1B>IIII114 DI<1210A312301270EAFF80EA3000A71380A3EA1100120E09127F 910D>III120 DI123 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmr10 12 84 /Fs 84 128 df<14201470A214F8A2EB017C143CEB023E141EEB041F8001087F14070110 7F140301207F1401496C7E01C07F4913780001147C90C7123C48143E0002141E0006141F 000480000C158000081407001815C0001014034815E01501007FB612F0A2B712F825237E A22A>1 D<90381FC1F0903870270C9038C07E1E390180FC3E1203390700F81CEC780014 38A7B612E0A23907003800B1397FE1FFC0A21F2380A21D>11 DII<90380FC03F90397031E0C09039E00B80203A01803E00F000 03EB7E013807007CA291383C00E0021C1300A6B712F0A23907001C001670B03A7FF1FFC7 FFA2282380A22A>I<120E12FEA2121E120EAFEAFFC0A20A157F940E>16 D<1207A2120F120E121C12381230126012C0080976A219>19 DI34 D<133C136213C138018080A21203A40181C8FCA21382 1384EA01C8A29039D001FFC013E000009038003C001518D80170131000025C487E00085C D8181C5BEA301E26700E01C7FCEB070200F01382EB0384EB01C8D900F013807E0078EB78 013A3C01FC0300393E070F06390FFE07FC3903F001F822257EA327>38 D<1310132013401380EA01005A12061204120C5AA35AA312701260A312E0AC1260A31270 1230A37EA37E120412067E7EEA00801340132013100C327DA413>40 D<7E12407E7E7E120C7E12021203EA0180A3EA00C0A313E01360A31370AC1360A313E013 C0A3EA0180A3EA0300120212065A12085A5A5A5A0C327DA413>I<497EB0B7FCA2390001 8000B020227D9C27>43 D<127012F812FCA212741204A41208A21210A212201240060F7C 840E>II<127012F8A3127005057C840E>I<14C0A213011480A2 13031400A25B1306A2130E130CA2131C1318A213381330A213701360A213E05B12015BA2 120390C7FCA25A1206A2120E120CA2121C1218A212381230A212701260A212E05AA21231 7DA419>II<1340 EA01C0120712FF12F91201B3A8EA7FFFA210217CA019>I II<1303A25B5BA21317133713 27134713C71387EA0107120312021204120C1208121012301220124012C0B512FCA23800 0700A7EBFFF8A216217FA019>I<00181340381E0380EA1FFF140013FCEA13F00010C7FC A613FCEA130638140380EA1801001013C0C712E0A214F0A3127012F8A314E0EAC0010040 13C0EA600300301380381C0F00EA0FFEEA03F014227EA019>I<133EEBFF803803C0C038 0700E0EA0E01EA1C03A2383801C090C7FC12781270A2EAF0F8EAF306EAF403EB018000F8 13C0EB00E05A14F0A51270A2007813E012381301001C13C0EB0380380F0700EA03FEEA01 F814227EA019>I<12401260387FFFF0A214E03840002000C01340481380EB0100A2EA00 025BA25B131813101330A21370A25BA31201A41203A76C5A14237DA119>II I<127012F8A312701200AB127012F8A3127005157C940E>I<127012F8A312701200AB12 7012F8A312781208A41210A312201240A2051F7C940E>I61 D<497EA3497EA3EB05E0A3EB08F0A3EB1078A3497EA2EB603EEB401EA2EBC01F 497E90B5FC481480EB0007A20002EB03C0A348EB01E0A2120C001E14F039FFC01FFFA220 237EA225>65 DI<903807F00890383FFC18EBFC063901F001383903C000F8 4848137848C71238121E15185AA2007C1408A2127800F81400A81278007C1408A2123CA2 6C1410A26C14206C7E6C6C13403901F001803900FC0700EB3FFCEB07F01D247DA224>I< B512F814FE3907800F80EC03C0EC01E0EC00F01578A2153CA2151EA3151FA9151EA2153E 153CA2157815F0EC01E0EC03C0EC0F80B6120014F820227EA126>III<903807F00890383FFC18EBFC063901F001383903C000F84848137848C71238 121E15185AA2007C1408A2127800F81400A7EC1FFF1278007CEB0078A2123CA27E121F7E 6C7E6C6C13B83801F0013900FC071890383FFC08903807F00020247DA227>I<39FFFC3F FFA239078001E0AD90B5FCA2EB8001AF39FFFC3FFFA220227EA125>II<3807FFF0A238000F00B3A51230127812FCA2130EEAF81E EA401C6C5AEA1870EA07C014237EA11A>I<3AFFFC01FF80A23A0780007800156015405D 4AC7FC14025C5C5C5C5C14C01381EB83E0EB84F01388EB9078EBA03C13C0497E80A26E7E 6E7EA26E7E6E7EA2157815FC3AFFFC03FFC0A222227EA127>III<39 FF8007FF13C00007EB00F8D805E01320EA04F0A21378137C133C7FA27FEB0780A2EB03C0 EB01E0A2EB00F014F81478143CA2141E140FA2EC07A0EC03E0A21401A21400001F1460EA FFE0152020227EA125>I80 DII<3803F810380FFE30EA1E073838 01F0EA70001470481330A21410A36C1300A2127C127FEA3FF0EA1FFE380FFF80000313C0 38003FE0EB03F013001470147814387EA46C133014706C136000F813E038CF03C038C7FF 00EA80FE15247DA21C>I<007FB512FCA2397803C03C0060140C00401404A200C01406A2 00801402A400001400B3A248B51280A21F227EA124>I<39FFFC07FFA239078000F81520 B3A5000314407FA2000114803800E0019038700300EB3C0EEB1FF8EB03F020237EA125> II<3BFFF83FFE03FFA23B0F8003E00078D900011430D807801520A281D803C01540A2 EC0278D801E01580A24A7ED800F0EC0100A2EC081E01F85C01781402EC181FEC100F013C 5CA29138200784011E1488A291384003C8010F14D0A291388001F001075CA291C7FCA26D 5C0102144030237FA133>I<12FEA212C0B3B3A912FEA207317BA40E>91 DI<12FEA21206B3B3A912FEA207317FA40E>I<127012F8A3127005057CA10E>95 D97 D<120E12FEA2121E120EAAEB1F80 EB60E0EB8030380F0038000E131C141E140E140FA7140E141E141C000F1338380C8070EB 60E038081F8018237FA21C>II<1470EB07F0A2 13001470AAEA01F8EA0706EA0E01381C00F04813701278127012F0A71270127812386C13 F0380C01783807067FEA01F818237EA21C>II<133E13E33801C780EA038F130F3807070090C7FCA8EAFFF8A20007C7FCB1 EA7FF8A2112380A20F>I<14783801F08C38071D1CEA0E0E381C0700A2003C1380A4001C 1300A2EA0E0EEA0F1CEA19F00010C7FCA21218121CEA1FFF6C13E014F0383800F8006013 180040131C00C0130CA300601318A200381370380E01C03801FE0016217F9519>I<120E 12FEA2121E120EAAEB1F80EB60E0EB8070380F0038A2120EAE39FFE3FF80A219237FA21C >I<121C123EA3121CC7FCA8120E12FEA2121E120EAFEAFFC0A20A227FA10E>I<13E0EA01 F0A3EA00E01300A813F01207A212001370B3A3127012F813E013C0EA7180EA1F000C2C82 A10F>I<120E12FEA2121E120EAAEB03FCA2EB01E01480EB02005B5B5B133813F8EA0F1C EA0E1E130E7F1480EB03C0130114E014F038FFE3FEA217237FA21A>I<120E12FEA2121E 120EB3ABEAFFE0A20B237FA20E>I<390E1FC07F3AFE60E183809039807201C03A1F003C 00E07E000E1338AE3AFFE3FF8FFEA227157F942A>I<380E1F8038FE60E0EB8070381F00 387E120EAE39FFE3FF80A219157F941C>I<13FC38070380380E01C0381C00E048137000 7813780070133800F0133CA70070133800781378003813706C13E0380E01C03807038038 00FC0016157F9419>I<380E1F8038FE60E0EB8070380F0038000E131C141EA2140FA714 1EA2141C000F1338380E8070EB60E0EB1F8090C7FCA8EAFFE0A2181F7F941C>I<3801F8 2038070460EA0E02EA1C01003813E0EA7800A25AA712701278EA3801121CEA0C02EA070C EA01F0C7FCA8EB0FFEA2171F7E941A>III< 1202A51206A3120E121EEA3FF812FFEA0E00AA1304A6EA07081203EA01F00E1F7F9E13> I<000E133838FE03F8A2381E0078000E1338AC1478A26C13BC3903833F80EA00FC19157F 941C>I<38FFC1FEA2381E0070000E1320A26C1340A238038080A33801C100A2EA00E2A3 1374A21338A3131017157F941A>I<3AFF8FF87F80A23A1E01C01E00D80E00130CECE008 13010007EB6010147090380230303903823820A23901C41840141CA23900E80C80140EA2 D97007C7FCA3EB200221157F9424>I<38FF83FEA2380F01E038070080380381001383EA 01C2EA00E4137813707F133C134E138EEA0187EB0380380201C01206381E00E038FF03FE A217157F941A>I<38FFC1FEA2381E0070000E1320A26C1340A238038080A33801C100A2 EA00E2A31374A21338A31310A25BA3EAF840A25B12B90063C7FC123E171F7F941A>I<38 3FFFC038380380EA300700201300EA600EEA401C133C1338C65A5B12015B38038040EA07 005A000E13C04813805AEA7801EA7007B5FC12157F9416>II127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmti10 12 54 /Ft 54 124 df<91381FC0F8913870718E9138E0F31E903801C0F7ED670C903903800E00 A3EB07005DA45B90B612E016C090390E003800A35B5DA45B5DA45B4A5AA413E04A5AA3D8 01C090C7FC5C3871CE0638F19E0E38F31E1C38620C38383C07E0272D82A21F>11 DI34 D<120E121FA3121D1201A21202A212041208A21210122012C0080F7E840F>44 D<127012F8A212F012E005057B840F>46 D<156015E015C014011580140315005C140614 0E140C141C1418143814301470146014E05C1301495A91C7FC5B1306130E130C131C1318 133813301370136013E05B12015B120390C8FC5A120E120C121C12181238123012701260 12E05A1B317FA419>I<130113031307130E131E133EEA03EE139CEA001CA31338A41370 A413E0A4EA01C0A4EA0380A31207EAFFFCA210217BA019>49 DII<14301470A214E0A314C01301A214 801303A2EB0700A21306130E130C131C131813381330EB6180EBE1C0EBC380EA01831203 130338060700120CEA1F87EA7FE7EAE07E38401FE038000F80EB0E005BA45BA31330142B 7EA019>I54 D<1207EA0F80A21300120EC7FCAB127012F8A25A5A 09157B940F>58 D<14035CA25C1580141FA21437A2146714E714C7EB0187A2EB0307A213 06A2130CA213181338EB3FFF5BEB600701C013C01403EA0180A2EA0300A21206001F1307 39FFC07FFCA21E237DA225>65 D<90387FFFE090B512F8903807803C153E90380F001E15 1FA3011E131E153EA2157C49137815F0EC01E0EC07C090387FFF8090387801E015F01400 5B15F8A3484813F01401A2EC03E0EA03C0EC07C0EC0F800007EB1F00387FFFFCB512F020 227DA123>II<90387FFFF090B57E90380780 3E8149487EED0780A3011E14C01503A215075BA4491480150FA349EB1F00A2151E153E48 48133C5DA25D4848485A4A5AEC0F800007013FC7FC387FFFFCB512E022227DA126>I<01 7FB5FC90B6FC903807801F1507EB0F00A21506A2131EA21403A290383C0600A3141EEB7F FCA2EB781CA2EBF018A44848C7FCA4485AA31207EA7FFE12FF20227DA121>70 DI<90381FFF80A290380078 00A25CA4495AA4495AA4495AA449C7FCA4131EA212381278EAF83CA2485AEAC070EA60E0 EA21C0001FC8FC19237CA11A>74 D<90397FFC1FFC13FF9039078007E0160090380F0006 5D15385D011E5BEC01804AC7FC1406495A5C1438147CEB79FCEB7BBCEB7F1E137C13F849 7EA348487E81A348486C7EA3000780397FFC1FFC00FF133F26227DA126>I77 D<90387FFFE090B512F8903807807C153C90380F001EA4011E133EA3153C49137C157815 F0EC01E090387807C090387FFF000178C7FCA25BA4485AA4485AA31207EA7FFC12FF1F22 7DA122>80 D<90387FFF8090B512E090380780F8157890380F003CA4011E137CA315F849 13F0EC01E0EC03C0EC0F00EB7FF8EB781880140E13F0140FA348485AA448485A1506A200 07EB1F0CEA7FFC00FFEB0F18C7EA03E01F237DA124>82 D<903803E0C090380FF980EB1C 1FEB300FEB700701E0130013C01201A238038006A291C7FC7FA213F0EA01FEEBFFC06C7F EB3FF01307EB00F81478A400301370A31460007013E05CEA7801495AD8EE0FC7FCEAC7FC EA81F81A247CA21C>I<000FB512FCA2903801E03C001C141CEB03C0121800301418A2EB 07801260A3C648C7FCA4131EA45BA45BA45BA31201387FFFC0B5FC1E2278A124>I<393F FE1FFC007F133F3903C003C01580D807801300A4380F0006A4001E5BA4485BA4485BA448 5BA25CA238700180A249C7FCEA380E6C5AEA0FF0EA07C01E2376A125>I<3BFFF07FF83F F817F03B1F000F8007806C01071400020F1306A2021F5BA202375B147702675B02E71370 02C71360D9018713E05E903903078180A201060183C7FCA2010C1386A20118138CA20130 1398A2016013B0A201C013E0A201805BA201005BA2000E91C8FCA22D2376A132>87 D<48138038020100EA0402485A485A485AA2485AA2485AEAB85CEAFC7EA2EAF87CEA7038 110F74A21A>92 D97 DI<137CEA01C2EA 0303EA0707EA0E0F121CEA3C0012381278A35AA41301EA70031306EA301CEA1838EA0FC0 10157B9417>I<1478EB07F0A2EB0070A214E0A4EB01C0A4EB038013F3EA038BEA070F38 0E0700121E121C123CEA380E1278A3485AA214201430EB3860A2EA7078EBD8C038319880 381E0F0015237BA219>I<13F8EA0384EA0E06121C123C1238EA780CEAF038EAFFE0EAF0 00A25AA413021306EA600CEA7038EA3070EA0F800F157A9417>I<147C14CEEB019E1303 148C14005BA4130EA43801FFF0A238001C00A55BA55BA55BA4485AA4485A127300F3C7FC A21266123C172D82A20F>II<13F0EA0FE0A21200A2485AA4485AA448C7FC131EEB6380 13C1380F81C01301120EA2381C0380A438380700A2EB0E08140C00701318131C1430EB0C 2000E013603860078016237DA219>I<13E0A21201EA00C01300A9121E1233EA6380A212 C3EAC700A21207120EA35AA21340EA386013C01270138012311300121E0C227CA10F>I< 13F0EA0FE0A21200A2485AA4485AA448C7FCEB01E0EB0630EB0870380E10F013201460EB 4000EA1D80001EC7FCEA1FC0EA1CE0EA38701330EB3820143038707060A21440EB30C038 E0188038600F0014237DA217>107 DI<391E07C07C393318 61863963B03303D9E03E138038C3C03CA2EB803800079038780700EB0070A3000EEBE00E A2ED1C101618261C01C0133015381660ED18402638038013C0D81801EB0F0026157C9429 >I<381E0780383318E03863B060EBE070EAC3C01380A2380700E0A4380E01C0A2EB0382 1483001C1386EB07065CEB030800381318381801E019157C941C>I<137CEA01C6EA0303 00061380000E13C0121C123C12381278A338F00780A3EB0F00130EEA701E131CEA3038EA 1860EA0F8012157B9419>I<3803C1E038066630380C7C38EB78180018131C1370A23800 E03CA43801C078A31470380380E013C0EBC1C0EBC38038076700133C90C7FCA2120EA45A A2EAFFC0A2161F7F9419>III<1378EA0184EA0306EA020EEA061EA21308EA070013F013F8EA03FCEA00 7C131E130E1270EAF00CA2EAE008EA6010EA3060EA1F800F157D9414>I<136013E0A4EA 01C0A4EA0380EAFFF8A2EA0380EA0700A4120EA45AA213101318EA3830A21360121813C0 EA0F000D1F7C9E11>I<000F133038118070EA21C0006113E012C1EAC380A2380381C0EA 0701A3380E0380A214841486EB070C120C120EEB0B18380613103803E1E018157C941B> I<380F01C0EA11833821C3E0EA61C1EAC1C0EAC380A2000313C0EA0700A3380E0180A3EB 0300A213025B130CEA0618EA01E014157C9417>I<000FEB307039118070F0D821C013F8 0061EBE07800C11438EAC380A2390381C030EA0701A3390E038060A315C0A20107138014 8139060F8300380319863801F0781E157C9421>I<3803C1C0380C663038183C70003013 F0EA2038006013601400C65AA45BA2142014303861C06012F114C000E3138038466300EA 3C3E14157D9417>I<000F133038118070EA21C0006113E012C1EAC380A2380381C0EA07 01A3380E0380A4EB0700120C120E5BEA061EEA03EEEA000EA25B1230EA78381330EA7060 EA60C0EA2180001EC7FC151F7C9418>III E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmbx10 12 61 /Fu 61 125 df5 D<90380FF07F90397FFBFFC03901F83FE33A03F07F87E0EA07E0D80FC01307ED03C06EC7 FCA6B612FCA2260FC03FC7FCB2397FF9FFF0A223237FA221>11 D20 D<383C01E0387E03F038FF07F8A2EB87FCA2EA7F 83383D81EC3801800CA238030018A248133800061330481360001C13E0383801C0002013 0016127EA21E>34 D<123C127E12FFA4127E123C08087C8710>46 D<13FF000313C0380FC3F0381F00F8003E137CA248133EA400FC133FAD007C133EA2007E 137E003E137CA26C13F8380FC3F03803FFC0C6130018207E9F1D>48 D<13381378EA03F812FF12FD1201B3A7387FFFF0A214207C9F1D>II<13FF000713C0380F03F0381E01F8123F14FC13811301121F000C13F81200EB03 F014E0EB0FC0EBFF00A2EB03E0EB01F814FCEB00FEA214FF127CA212FEA214FE387C01FC 1278383C03F0380FFFE00001130018207E9F1D>I<14E013011303A21307130F131F131B 1333137313E3EA01C31383EA03031207120E120C12181238127012E0B6FCA2380007E0A7 48B5FCA218207E9F1D>I<00101330001E13F0381FFFE0A214C014005B13F80018C7FCA4 EA19FE381FFF80381E07E0381C03F0EA1801000013F8A214FCA2127812FCA314F812F838 6003F0003013E0381C0FC0380FFF00EA03FC16207D9F1D>II<1230123C003FB5FCA214FE4813FC14F8A23860007014E038E001C038C003801400C6 5A130E131E131C133CA2137C1378A213F8A31201A86C5A18227DA11D>I<13FF000313E0 380701F0380E00785A143C123C123E123F13C0EBE078381FF8F0EBFFE06C13806C13E06C 13F04813F8381F3FFC383C0FFEEA7803EB01FF38F0007F141F140FA2140E7E0078131C7E 001F13F0380FFFE00001130018207E9F1D>I<13FF000713C0380F83E0381F00F0003E13 F8007E137CA200FE137EA3147FA4007E13FFA2EA3E01001F137FEA0FFEEA03FCC7FC147E A2121E003F13FCA214F8EB01F0381E03E0381C0FC0380FFF00EA03F818207E9F1D>I<14 301478A214FCA3497EA2497E80A29038063F80A2010E7FEB0C1FA2496C7EA201307F1407 01707FEB6003A290B57EA23901C001FEEB8000A248C7127FA248158048143F3AFFF007FF FCA226227EA12B>65 DI<49B41340011FEBC1C090387F80F33901FC001FD803F0130F48481307484813 03121F48481301A2007F140090C8FCA2481500A87E16C07F123F15016C6C1480120F6C6C EB03006C6C1306D801FC131C39007F807890381FFFE0010190C7FC22227DA129>I69 DI<49B41320011FEBE0E090387F8079 3901FC001F48481307D807E0130348481301121F48481300A2007F156090C8FCA2481500 A6913807FFFEA26C9038000FE0A27F123FA26C7E6C7E1207EA03F86C6C131F39007F8073 90381FFFE10101EB806027227DA12D>II I75 DIIIIIII<3801FE023807FFCE381F 01FE383C007E141E48130EA200F81306A27E91C7FCB4FC13F06CB47E6C13E014F86C7F00 077F6C7FEA003F13019038003F80141FA200C0130FA36C1400A26C131E00FC131C38FF80 7838E7FFF038807FC019227DA120>I<007FB612C0A2397E03F80F007814030070140100 60140000E015E0A200C01560A400001500B30003B512F8A223217EA028>I<0002131000 0E13704813E0001813C038300180EA700300601300A2EAC006A200DE13F038FF07F8EB87 FCA2EA7F83A2383F01F8381E00F016127BA21E>92 D97 DII<49B4FCA2EB003FAB13FE3807FFBF38 0FC1FF48C67E003E7F127E127CA212FCA7127C127E123E6C5B380F81FF3907FF3FE0EA01 FC1B237EA220>I<13FE3807FF80380F83E0EA1F01383E00F0127E007C13F812FC1478B5 12F8A200FCC7FCA4127E1418003E13386C1330380F80F03803FFC0C6130015167E951A> II<9038FE0F803903FF9FC0380F83E3381F01F3391E00F000003E7FA5 001E5BEA1F01380F83E0380BFF80D808FEC7FC0018C8FCA2121C381FFFE014FC6C13FF7E 001F1480397C001FC00078130F00F81307A3007CEB0F806CEB1F00381F807E6CB45A0001 13E01A217F951D>II<120EEA3F80127FA4123FEA0E00C7FCA6EAFF80A2121FB2EAFF F0A20C247EA30F>I 107 DI<3AFF03F803F890390FFE0FFE3A1F 183F183F9039201F201F014001C01380A201801380AE3BFFF0FFF0FFF0A22C167D9533> I<38FF03F0EB0FFC381F187EEB203EEB403FA21380AE39FFF1FFE0A21B167D9520>I<13 FF000713E0380F81F0381F00F8003E137C48133EA300FC133FA7007C133E007E137E003E 137C6C13F8380F81F03807FFE0C6130018167E951D>I<38FF87F0EBBFFC381FF07EEBC0 1F9038800F8015C0A2EC07E0A715C0140FA2EC1F8001C01300EBF07EEBBFFCEB8FE00180 C7FCA8EAFFF0A21B207E9520>II<38FF0F80EB1FE0381F33F013631343A2EBC1E0EB8000ADEAFFF8A214167E9518>I< 3807F980EA1FFFEA3807EA7003EAF001A26CC7FCB4FC13F8EA7FFE6C7E6C138012073800 3FC0EAC007130312E0A200F0138038FC0F00EAEFFEEAC3F812167E9517>I<13C0A41201 A212031207120F121FB5FCA2EA0FC0ABEBC180A51207EBE300EA03FEC65A11207F9F16> I<38FF81FFA2381F803FAF5C5C380FC1BF3907FF3FE0EA01FC1B167D9520>I<39FFF01F E0A2390FC007001406EBE00E0007130CEBF01C0003131813F800015BA26C6C5AA2EB7EC0 A2137F6D5AA26DC7FCA2130EA21B167F951E>I<3AFFF3FF87FCA23A1F807C00E0D80FC0 14C0147E9038E03E010007013F1380147FD803F0EB0300ECCF83D801F8138615C6EBFD87 000014CC9038FF03EC017F13F8A2EB7E01013E5BEB3C00011C5B0118136026167F9529> I<39FFF0FFC0A2390FC03C003807E0386D5A00035B6C6C5A3800FD80017FC7FCA27F6D7E 497EEB37E0EB67F013C33801C1F8380380FC48487E48137E39FFC1FFE0A21B167F951E> I<39FFF01FE0A2390FC007001406EBE00E0007130CEBF01C0003131813F800015BA26C6C 5AA2EB7EC0A2137F6D5AA26DC7FCA2130EA2130CA25B1278EAFC3813305BEA69E0EA7F80 001FC8FC1B207F951E>I<387FFFE0A2EA780F38701FC038603F8012E038C07F0013FEA2 EA01FC485AA23807F030EA0FE0A2381FC070EA3F801460387F00E0EAFE03B5FCA214167E 9519>III E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmbx10 17.28 17 /Fv 17 122 df<90391FF0038090B51207000314CF3907F00FFF381FC001903880007F48 C7123F48141F007E140FA200FE1407A26C1403A27F6D90C7FC7F13FC387FFFE014FE6CEB FFC015F06C14FC6C806C8012016C6C1480011F14C013001407020013E0157F153F151F12 E0150FA37E16C07EED1F807EB4EC3F0001C0137E9038FC01FC00F9B55AD8F03F13E0D8E0 0790C7FC23317BB02E>83 D97 D99 D101 D<14FF010713C0011F13F0EB7FC79038FF0FF85A13FE120313FCEC07F0EC01C091C7FCA7 B512F8A3D803FCC7FCB3A8387FFFF0A31D327EB119>I104 DI<2703F007F8EB0FF000FFD93FFFEB7FFE4A6D B5FC903CF1F03FC3E07F803D0FF3C01FE7803FC02607F780EBEF009126000FFEEB1FE001 FE5C495CA2495CB3B500C1B50083B5FCA340207D9F47>109 D<3903F007F800FFEB3FFF 4A7F9039F1F03FC03A0FF3C01FE03807F7804A6C7E13FE5BA25BB3B500C1B51280A32920 7D9F2E>II<3803F03F00FF EBFFC001F113F0EBF3C7390FF78FF80007130F13FEA29038FC07F0EC03E0EC008015005B B1B512E0A31D207E9F22>114 DI<1338A51378A313F8A2120112031207121FB512FEA33807F800B01407A7EBFC0F0003 130EEBFE1E3801FFFC38007FF8EB0FE0182E7EAD20>IIII121 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 300dpi TeXDict begin %%EndSetup %%Page: 27 1 27 0 bop 0 -54 a Fv(Sensitivit)n(y)25 b(of)j(seismic)c(w)n(a)n(v)n(es)h (to)j(the)f(structure)0 60 y Fu(Lud)o(\024)-27 b(ek)19 b(Klime)m(\024)-26 b(s)0 122 y Ft(Dep)m(artment)17 b(of)i(Ge)m (ophysics,)i(F)l(aculty)c(of)h(Mathematics)g(and)h(Physics,)h(Charles)e (University,)0 182 y(Ke)13 b(Karlovu)h(3,)g(121)h(16)e(Pr)m(aha)i(2,)g (Cze)m(ch)e(R)m(epublic,)i(http:/)-8 b(/sw3d.m\013.cuni.cz/)q (sta\013/klimes.h)q(tm)0 313 y Fu(Sum)o(m)m(ary)0 393 y Fs(W)l(e)20 b(study)f(ho)o(w)g(the)g(p)q(erturbations)f(of)i(a)f (generally)g(heterogeneous)f(isotropic)h(or)g(anisotropic)0 453 y(structure)12 b(manifest)h(themselv)o(es)f(in)g(the)h(w)o(a)o(v)o (e\014eld,)g(and)f(whic)o(h)g(p)q(erturbations)f(can)i(b)q(e)g (detected)0 513 y(within)j(a)g(limited)g(ap)q(erture)f(and)h(a)g (limited)g(frequency)g(band.)21 b(A)c(short{duration)c(broad{band)0 573 y(inciden)o(t)24 b(w)o(a)o(v)o(e\014eld)f(with)h(a)h(smo)q(oth)f (frequency)h(sp)q(ectrum)f(is)g(considered.)45 b(In\014nitesimally)0 633 y(small)13 b(p)q(erturbations)f(of)j(elastic)f(mo)q(duli)f(and)g (densit)o(y)h(are)g(decomp)q(osed)f(in)o(to)g(Gab)q(or)h(functions.)0 693 y(The)20 b(w)o(a)o(v)o(e\014eld)e(scattered)h(b)o(y)h(the)g(p)q (erturbations)e(is)h(then)h(comp)q(osed)e(of)i(w)o(a)o(v)o(es)f (scattered)g(b)o(y)0 753 y(individual)h(Gab)q(or)h(functions.)36 b(The)21 b(scattered)h(w)o(a)o(v)o(es)e(are)h(estimated)g(using)f(the)i (\014rst{order)0 813 y(Born)16 b(appro)o(ximation)e(with)j(the)f (paraxial)g(ra)o(y)g(appro)o(ximation.)100 875 y(F)l(or)g(eac)o(h)g (inciden)o(t)g(w)o(a)o(v)o(e,)h(eac)o(h)f(Gab)q(or)h(function)g (generates)f(at)i(most)e(5)h(scattered)g(w)o(a)o(v)o(es,)0 935 y(propagating)10 b(in)h(sp)q(eci\014c)h(directions.)19 b(A)12 b(Gab)q(or)f(function)g(corresp)q(onding)e(to)j(a)g(lo)o(w)f(w)o (a)o(v)o(en)o(um)o(b)q(er)0 995 y(ma)o(y)19 b(generate)h(a)f(single)g (broad{band)e(uncon)o(v)o(erted)h(w)o(a)o(v)o(e)h(scattered)h(in)f (forw)o(ard)f(or)h(narro)o(w{)0 1055 y(angle)f(directions.)28 b(A)19 b(Gab)q(or)f(function)g(corresp)q(onding)f(to)i(a)f(high)g(w)o (a)o(v)o(en)o(um)o(b)q(er)e(usually)i(gen-)0 1115 y(erates)k(0)g(to)h (5)g(narro)o(w{band)c(Gaussian)i(pac)o(k)o(ets)h(scattered)g(in)g(wide) g(angles,)h(but)f(ma)o(y)g(also)0 1175 y(o)q(ccasionally)16 b(generate)g(a)h(narro)o(w{band)d(P)i(to)h(S)f(or)g(S)h(to)g(P)f(con)o (v)o(erted)g(Gaussian)f(pac)o(k)o(et)h(scat-)0 1235 y(tered)k(in)g(a)h (forw)o(ard)e(direction,)h(or)g(a)g(broad{band)e(S)j(to)f(P)h(\(and)f (ev)o(en)g(S)g(to)h(S)f(in)g(a)h(strongly)0 1295 y(anisotropic)15 b(bac)o(kground\))g(con)o(v)o(erted)h(w)o(a)o(v)o(e)f(scattered)i(in)f (wide)g(angles.)100 1358 y(F)l(or)e(a)h(particular)e(source,)h(eac)o(h) h(w)o(a)o(v)o(e)f(scattered)h(b)o(y)g(a)g(Gab)q(or)f(function)h(at)g(a) g(giv)o(en)g(spatial)0 1418 y(lo)q(cation)g(is)f(sensitiv)o(e)g(to)h (just)f(a)h(single)f(linear)f(com)o(bination)g(of)i(22)f(v)m(alues)h (of)g(the)g(elastic)f(mo)q(duli)0 1478 y(and)19 b(densit)o(y)f(corresp) q(onding)f(to)j(the)g(Gab)q(or)e(function.)30 b(This)19 b(information)f(ab)q(out)h(the)h(Gab)q(or)0 1538 y(function)i(is)h (lost)f(if)h(the)g(scattered)g(w)o(a)o(v)o(e)f(do)q(es)h(not)f(fall)h (in)o(to)f(the)h(ap)q(erture)g(co)o(v)o(ered)e(b)o(y)i(the)0 1598 y(receiv)o(ers)16 b(and)f(in)o(to)h(the)h(legible)f(frequency)h (band.)100 1660 y(The)12 b(deriv)o(ed)f(appro)o(ximate)f(solution)h(of) i(the)f(forw)o(ard)e(scattering)i(problem)f(ma)o(y)g(b)q(e)h(utilized)0 1720 y(in)j(designing)f(the)i(migration)f(algorithm)f(based)h(on)g (true)g(linearized)g(in)o(v)o(ersion)e(of)j(the)g(complete)0 1780 y(set)h(of)f(seismograms)e(recorded)i(for)g(all)g(shots.)0 1911 y Fu(Keyw)n(ords)0 1991 y Fs(Elastic)g(w)o(a)o(v)o(es,)g(elastic)h (mo)q(duli,)e(p)q(erturbation,)h(Born)g(appro)o(ximation,)e(paraxial)i (ra)o(y)g(appro)o(xi-)0 2051 y(mation,)g(in)o(v)o(ersion,)e(seismic)h (anisotrop)o(y)l(,)g(heterogeneous)g(media.)p 0 2628 600 2 v 0 2684 a Fr(In:)g(Seismic)c(W)m(a)o(v)o(es)f(in)h(Complex)f (3{D)f(Structures,)i(Rep)q(ort)e(17)g(\(Departmen)o(t)g(of)h(Geoph)o (ysics,)h(Charles)f(Univ)o(ersit)o(y)m(,)i(Prague,)e(2007\),)e(pp.)j (27{61)920 2806 y Fs(27)p eop %%Page: 28 2 28 1 bop 0 -54 a Fu(1.)25 b(In)n(tro)r(duction)0 17 y Fs(W)l(e)19 b(shall)f(study)g(ho)o(w)g(the)h(p)q(erturbations)e(of)i(a) g(generally)f(heterogeneous)g(isotropic)f(or)h(aniso-)0 76 y(tropic)24 b(structure)g(manifest)g(themselv)o(es)g(in)h(the)g(w)o (a)o(v)o(e\014eld,)g(and)f(whic)o(h)g(p)q(erturbations)f(can)0 136 y(b)q(e)i(detected)h(within)e(a)h(limited)f(ap)q(erture)g(and)g(a)h (limited)f(frequency)h(band.)46 b(W)l(e)25 b(consider)0 195 y(a)19 b(smo)q(othly)h(v)m(arying)f(heterogeneous)f(generally)h (anisotropic)f(bac)o(kground)g(medium,)g(with)h(an)0 255 y(isotropic)d(bac)o(kground)f(medium)g(as)h(a)h(sp)q(ecial)g(case.) 23 b(W)l(e)17 b(consider)e(generally)h(anisotropic)g(p)q(er-)0 314 y(turbations)22 b(of)i(the)f(medium.)41 b(W)l(e)23 b(\014rst)g(deriv)o(e)g(the)g(scattered)h(w)o(a)o(v)o(e\014eld)d(in)i (the)h(frequency)0 374 y(domain)14 b(and)h(then)h(in)f(the)h(time)f (domain.)20 b(In)c(the)g(time)f(domain,)f(w)o(e)i(assume)e(a)h (short{duration)0 433 y(broad{band)f(inciden)o(t)i(w)o(a)o(v)o (e\014eld)f(with)h(a)h(smo)q(oth)f(frequency)g(sp)q(ectrum.)100 493 y(In)21 b(Section)g(2,)h(w)o(e)f(decomp)q(ose)g(in\014nitesimally)e (small)i(p)q(erturbations)e(of)j(elastic)f(mo)q(duli)0 552 y(and)15 b(densit)o(y)g(in)o(to)g(Gab)q(or)g(functions.)21 b(The)15 b(w)o(a)o(v)o(e\014eld)f(scattered)i(b)o(y)f(the)h(p)q (erturbations)e(is)h(then)0 612 y(comp)q(osed)j(of)i(w)o(a)o(v)o(es)e (scattered)h(b)o(y)g(individual)e(Gab)q(or)i(functions.)29 b(The)19 b(scattered)g(w)o(a)o(v)o(es)f(are)0 671 y(estimated)h(using)f (the)h(\014rst{order)e(Born)h(appro)o(ximation)f(with)i(the)g(paraxial) f(ra)o(y)h(appro)o(xima-)0 730 y(tion.)27 b(These)18 b(appro)o(ximations)e(are)i(describ)q(ed)f(in)h(Section)g(3.)27 b(Gaussian)17 b(b)q(eams,)h(scattered)g(b)o(y)0 790 y(individual)j(Gab) q(or)i(functions)f(in)g(the)h(time)g(domain,)g(are)g(deriv)o(ed)e(in)i (Section)g(4.)41 b(Gaussian)0 849 y(pac)o(k)o(ets,)17 b(scattered)h(b)o(y)f(individual)e(Gab)q(or)i(functions)g(in)g(the)h (time)f(domain,)g(are)g(then)g(deriv)o(ed)0 909 y(in)c(Section)g(5.)21 b(Sections)13 b(6,)g(7)h(and)e(8)i(are)e(dev)o(oted)i(to)f(the)h (discussion)d(of)i(limited)g(ap)q(erture,)g(to)h(the)0 968 y(application)i(of)i(the)g(deriv)o(ed)f(equations)g(to)h(the)g (linearized)e(in)o(v)o(ersion)g(of)h(scattered)h(w)o(a)o(v)o (e\014elds,)0 1028 y(and)e(to)h(other)f(remarks)f(on)h(applications.)0 1134 y Fu(2.)25 b(Gab)r(or)18 b(represen)n(tation)h(of)f(medium)c(p)r (erturbations)0 1205 y Fs(W)l(e)22 b(consider)e(in\014nitesimally)g (small)h(p)q(erturbations)f Fq(\016)r(c)1117 1212 y Fp(ij)r(k)q(l)1186 1205 y Fs(\()p Fu(x)p Fs(\))j(and)e Fq(\016)r(\045)p Fs(\()p Fu(x)p Fs(\))i(of)f(elastic)f(mo)q(duli)0 1264 y Fq(c)22 1271 y Fp(ij)r(k)q(l)91 1264 y Fs(\()p Fu(x)p Fs(\))d(and)e(densit)o(y)g Fq(\045)p Fs(\()p Fu(x)p Fs(\))h(in)f (elasto)q(dynamic)g(equation)431 1344 y Fq(\045)p Fs(\()p Fu(x)p Fs(\))i(\177)-28 b Fq(u)569 1351 y Fp(i)585 1344 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)e([)p Fq(c)796 1351 y Fp(ij)r(k)q(l)865 1344 y Fs(\()p Fu(x)p Fs(\))18 b Fq(u)980 1351 y Fp(k)q(;l)1029 1344 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\)])1151 1351 y Fp(;j)1196 1344 y Fs(+)i Fq(f)1269 1351 y Fp(i)1286 1344 y Fs(\()p Fu(x)p Fq(;)e(t)p Fs(\))51 b Fq(;)367 b Fs(\(1\))0 1423 y(where)18 b(dot)11 b(_)h(stands)17 b(for)h(the)g(deriv)m(ativ)o(e)h(with)f(resp)q(ect)g (to)h(time,)g(and)e(subscript)1602 1430 y Fp(;j)1653 1423 y Fs(follo)o(wing)g(a)0 1483 y(comma)c(stands)h(for)g(the)g (partial)g(deriv)m(ativ)o(e)g(with)g(resp)q(ect)g(to)h(Cartesian)e (spatial)h(co)q(ordinate)g Fq(x)1855 1490 y Fp(j)1876 1483 y Fs(.)0 1542 y(T)l(erm)i Fq(f)156 1549 y Fp(i)173 1542 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))17 b(represen)o(ts)e(the)i (source)e(of)i(the)g(w)o(a)o(v)o(e\014eld.)100 1602 y(First{order)d(p)q (erturbation)h(\(v)m(ariation\))i Fq(\016)i Fs(of)e(elasto)q(dynamic)f (equation)g(\(1\))h(yields)g(elasto-)0 1661 y(dynamic)f(equation)73 1741 y Fq(\045)p Fs(\()p Fu(x)p Fs(\))198 1728 y(\177)184 1741 y Fq(\016)r(u)237 1748 y Fp(i)253 1741 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)f([)p Fq(c)465 1748 y Fp(ij)r(k)q(l)534 1741 y Fs(\()p Fu(x)p Fs(\))k Fq(\016)r(u)673 1748 y Fp(k)q(;l)721 1741 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\)])843 1748 y Fp(;j)888 1741 y Fo(\000)j Fq(\016)r(\045)p Fs(\()p Fu(x)p Fs(\))21 b(\177)-29 b Fq(u)1102 1748 y Fp(i)1119 1741 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))k(+)f([)p Fq(\016)r(c)1349 1748 y Fp(ij)r(k)q(l)1418 1741 y Fs(\()p Fu(x)p Fs(\))17 b Fq(u)1532 1748 y Fp(k)q(;l)1581 1741 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\)])1703 1748 y Fp(;j)1826 1741 y Fs(\(2\))0 1820 y(for)16 b(w)o(a)o(v)o(e\014eld)f(p)q (erturbation)h Fq(\016)r(u)635 1827 y Fp(k)q(;l)683 1820 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))18 b(due)e(to)h(medium)e(p)q (erturbation)g Fq(\016)r(c)1493 1827 y Fp(ij)r(k)q(l)1563 1820 y Fs(\()p Fu(x)p Fs(\))i(and)f Fq(\016)r(\045)p Fs(\()p Fu(x)p Fs(\).)100 1880 y(The)g(p)q(erturbations)f(are)h(decomp) q(osed)f(in)o(to)h(Gab)q(or)h(functions)e Fq(g)1371 1862 y Fp(\013)1399 1880 y Fs(\()p Fu(x)p Fs(\),)335 1970 y Fq(\016)r(c)381 1977 y Fp(ij)r(k)q(l)450 1970 y Fs(\()p Fu(x)p Fs(\))g(=)578 1922 y Fn(X)597 2027 y Fq(\013)658 1970 y(c)680 1949 y Fp(\013)680 1982 y(ij)r(k)q(l)763 1970 y Fq(g)789 1949 y Fp(\013)817 1970 y Fs(\()p Fu(x)p Fs(\))51 b Fq(;)107 b(\016)r(\045)p Fs(\()p Fu(x)p Fs(\))15 b(=)1235 1922 y Fn(X)1254 2027 y Fq(\013)1315 1970 y(\045)1341 1949 y Fp(\013)1369 1970 y Fq(g)1395 1949 y Fp(\013)1423 1970 y Fs(\()p Fu(x)p Fs(\))50 b Fq(;)271 b Fs(\(3\))0 2092 y(where)16 b(the)h(Gab)q(or)f(functions)341 2171 y Fq(g)367 2151 y Fp(\013)395 2171 y Fs(\()p Fu(x)p Fs(\))e(=)g(exp[i)p Fu(k)664 2151 y Fp(\013)692 2148 y Fm(T)723 2171 y Fs(\()p Fu(x)e Fo(\000)f Fu(x)864 2151 y Fp(\013)892 2171 y Fs(\))h Fo(\000)979 2152 y Fm(1)p 979 2160 20 2 v 979 2188 a(2)1005 2171 y Fs(\()p Fu(x)f Fo(\000)g Fu(x)1145 2151 y Fp(\013)1174 2171 y Fs(\))1193 2151 y Fm(T)1224 2171 y Fu(K)1269 2151 y Fp(\013)1297 2171 y Fs(\()p Fu(x)h Fo(\000)f Fu(x)1438 2151 y Fp(\013)1466 2171 y Fs(\)])327 b(\(4\))0 2251 y(are)19 b(cen)o(tred)g(at)g(v)m(arious)g(spatial)g(p)q(ositions)f Fu(x)908 2233 y Fp(\013)955 2251 y Fs(=)g(\()p Fq(x)1059 2233 y Fp(\013)1059 2263 y Fm(1)1089 2251 y Fq(;)8 b(x)1139 2233 y Fp(\013)1139 2263 y Fm(2)1168 2251 y Fq(;)g(x)1218 2233 y Fp(\013)1218 2263 y Fm(3)1247 2251 y Fs(\))19 b(and)g(ha)o(v)o(e)g(v)m(arious)f(structural)0 2310 y(w)o(a)o(v)o(en)o (um)o(b)q(er)e(v)o(ectors)j Fu(k)491 2292 y Fp(\013)537 2310 y Fs(=)f(\()p Fq(k)641 2292 y Fp(\013)639 2323 y Fm(1)669 2310 y Fq(;)8 b(k)719 2292 y Fp(\013)717 2323 y Fm(2)747 2310 y Fq(;)g(k)797 2292 y Fp(\013)795 2323 y Fm(3)825 2310 y Fs(\).)30 b(F)l(or)18 b(real{v)m(alued)g(p)q (erturbations)f Fq(\016)r(c)1604 2317 y Fp(ij)r(k)q(l)1674 2310 y Fs(\()p Fu(x)p Fs(\))j(of)f(the)0 2370 y(elastic)h(mo)q(duli,)g (w)o(e)g(ma)o(y)g(wish)f(to)i(select)f(matrices)g Fu(K)1101 2352 y Fp(\013)1149 2370 y Fs(and)g Fu(K)1295 2352 y Fp(\014)1342 2370 y Fs(and)f(co)q(e\016cien)o(ts)h Fq(c)1720 2352 y Fp(\013)1720 2384 y(ij)r(k)q(l)1810 2370 y Fs(and)0 2438 y Fq(c)22 2414 y Fp(\014)22 2453 y(ij)r(k)q(l)108 2438 y Fs(corresp)q(onding)14 b(to)j Fq(k)517 2420 y Fp(\013)559 2438 y Fs(=)c Fo(\000)p Fq(k)678 2420 y Fp(\014)721 2438 y Fs(complex{conjugate,)j Fu(K)1209 2420 y Fp(\013)1251 2438 y Fs(=)e(\()p Fu(K)1368 2420 y Fp(\014)1395 2438 y Fs(\))1414 2420 y Fl(\003)1437 2438 y Fs(,)j Fq(c)1490 2420 y Fp(\013)1490 2452 y(ij)r(k)q(l)1573 2438 y Fs(=)c(\()p Fq(c)1666 2414 y Fp(\014)1666 2453 y(ij)r(k)q(l)1736 2438 y Fs(\))1755 2420 y Fl(\003)1778 2438 y Fs(.)100 2497 y(The)19 b(w)o(a)o(v)o(e\014eld)g(scattered)h(b)o(y)g(the)g(p)q (erturbations)e(is)i(then)g(comp)q(osed)f(of)h(w)o(a)o(v)o(es)f Fq(u)1753 2479 y Fp(\013)1753 2510 y(i)1781 2497 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))0 2557 y(scattered)17 b(b)o(y)f(individual)f (Gab)q(or)h(functions,)668 2644 y Fq(\016)r(u)721 2651 y Fp(i)737 2644 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)912 2596 y Fn(X)932 2701 y Fq(\013)993 2644 y(u)1022 2623 y Fp(\013)1022 2656 y(i)1050 2644 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))50 b Fq(;)604 b Fs(\(5\))920 2806 y(28)p eop %%Page: 29 3 29 2 bop 0 -54 a Fs(see)17 b(Figures)d(1,)j(2,)f(3.)p 0 -7 615 2 v 0 556 2 563 v 16 544 a /Figure 1 def 16 544 a @beginspecial 0 @llx 0 @lly 630 @urx 583 @ury 1165 @rwi @setspecial %%BeginDocument: r17lk1/sens1.ps %! %%BoundingBox: 0 0 630 583 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 3 def /wave{ /k1 k1r r div def /k11 k11rr r div r div def /g11 g11rr r div r div def /d r rd div def /h d 2 div def /n1 4.605 g11 div sqrt d div truncate def /C1 c1 angle1 angle2 add 2 div cos radius mul sub def /C2 c2 angle1 angle2 add 2 div sin radius mul sub def n1 neg 1 n1 0.5 add { /x1 exch d mul def k1 k11 x1 mul add x1 mul 57.29578 mul cos 1 add 2 div 2.718282 g11 x1 mul x1 mul neg exp mul dup R 1 sub mul 1 add exch dup G 1 sub mul 1 add exch B 1 sub mul 1 add setrgbcolor newpath C1 C2 radius x1 add h sub angle2 angle1 arcn C1 C2 radius x1 add h add angle1 angle2 arc closepath fill } for }def /packet{ /k1 k1r r div def /k2 k2r r div def /k11 k11rr r div r div def /k12 k12rr r div r div def /k22 k22rr r div r div def /g11 g11rr r div r div def /g12 g12rr r div r div def /g22 g22rr r div r div def /d r rd div def /h d 2 div def /n1 4.605 g11 div sqrt d div truncate def /n2 4.605 g22 div sqrt d div truncate def /X1 {c1 add} def /X2 {c2 add} def n2 neg 1 n2 0.5 add { /x2 exch d mul def n1 neg 1 n1 0.5 add { /x1 exch d mul def k1 k11 x1 mul add k12 x2 mul add x1 mul k2 k12 x1 mul add k22 x2 mul add x2 mul add 57.29578 mul cos 1 add 2 div 2.718282 g11 x1 mul g12 x2 mul add x1 mul g12 x1 mul g22 x2 mul add x2 mul add neg exp mul dup R 1 sub mul 1 add exch dup G 1 sub mul 1 add exch B 1 sub mul 1 add setrgbcolor x1 h sub X1 x2 h sub X2 moveto x1 h add X1 x2 h sub X2 lineto x1 h add X1 x2 h add X2 lineto x1 h sub X1 x2 h add X2 lineto closepath fill } for } for }def % Lengths: /c1 144 def /c2 396 def /r 20 def /radius 800 def % Dimensionless quantities: /angle1 -50 def /angle2 -20 def /k1r 10 def /k11rr 0.00 def /g11rr 6.4 def /rd 25 def % Colour: /R 1.00 def % /R 1.00 def /G 0.00 def % /G 0.90 def /B 0.00 def % /B 0.00 def Figure 2 eq { wave } if % Lengths: /c1 448 60 add def /c2 168 80 add def /radius 1180 def % Dimensionless quantities: /angle1 -45 def /angle2 -15 def Figure 3 eq { wave } if % Lengths: /c1 288 def /c2 288 def /r 50 def % Dimensionless quantities: /k1r -2 def /k2r 14 def /k11rr 0.00 def /k12rr 0.00 def /k22rr 0.00 def /g11rr 1.00 def /g12rr 0.00 def /g22rr 1.00 def /rd 25 def % Colour: /R 0.00 def % /R 1.00 def /G 0.50 def % /G 0.00 def /B 1.00 def % /B 0.00 def packet % Lengths: /c1 432 def /c2 480 def /r 50 def % Dimensionless quantities: /k1r 6 def /k2r 8 def /k11rr 0.64 def /k12rr -0.48 def /k22rr 0.36 def /g11rr 1.00 def /g12rr 0.00 def /g22rr 1.00 def /rd 25 def % Colour: /R 1.00 def % /R 1.00 def /G 0.00 def % /G 0.90 def /B 0.00 def % /B 0.00 def Figure 3 eq { packet } if % Bounding Box: % /X 630 def % /Y 583 def % 0 0 0 setrgbcolor % 0 0 moveto X 0 rlineto 0 Y rlineto X neg 0 rlineto closepath stroke showpage %%EOF %%EndDocument @endspecial 612 556 2 563 v 0 558 615 2 v 0 596 a Fk(Figure)j(1.)25 b Fj(A)16 b(single)f(Gab)q(or)h(func-)0 644 y(tion)e Fi(g)108 629 y Fh(\013)135 644 y Fj(\()p Fk(x)p Fj(\))h(at)g(p)q(oin)o (t)e Fk(x)396 629 y Fh(\013)423 644 y Fj(.)p 638 -7 V 638 556 2 563 v 654 544 a /Figure 2 def 654 544 a @beginspecial 0 @llx 0 @lly 630 @urx 583 @ury 1165 @rwi @setspecial %%BeginDocument: r17lk1/sens1.ps %! %%BoundingBox: 0 0 630 583 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 3 def /wave{ /k1 k1r r div def /k11 k11rr r div r div def /g11 g11rr r div r div def /d r rd div def /h d 2 div def /n1 4.605 g11 div sqrt d div truncate def /C1 c1 angle1 angle2 add 2 div cos radius mul sub def /C2 c2 angle1 angle2 add 2 div sin radius mul sub def n1 neg 1 n1 0.5 add { /x1 exch d mul def k1 k11 x1 mul add x1 mul 57.29578 mul cos 1 add 2 div 2.718282 g11 x1 mul x1 mul neg exp mul dup R 1 sub mul 1 add exch dup G 1 sub mul 1 add exch B 1 sub mul 1 add setrgbcolor newpath C1 C2 radius x1 add h sub angle2 angle1 arcn C1 C2 radius x1 add h add angle1 angle2 arc closepath fill } for }def /packet{ /k1 k1r r div def /k2 k2r r div def /k11 k11rr r div r div def /k12 k12rr r div r div def /k22 k22rr r div r div def /g11 g11rr r div r div def /g12 g12rr r div r div def /g22 g22rr r div r div def /d r rd div def /h d 2 div def /n1 4.605 g11 div sqrt d div truncate def /n2 4.605 g22 div sqrt d div truncate def /X1 {c1 add} def /X2 {c2 add} def n2 neg 1 n2 0.5 add { /x2 exch d mul def n1 neg 1 n1 0.5 add { /x1 exch d mul def k1 k11 x1 mul add k12 x2 mul add x1 mul k2 k12 x1 mul add k22 x2 mul add x2 mul add 57.29578 mul cos 1 add 2 div 2.718282 g11 x1 mul g12 x2 mul add x1 mul g12 x1 mul g22 x2 mul add x2 mul add neg exp mul dup R 1 sub mul 1 add exch dup G 1 sub mul 1 add exch B 1 sub mul 1 add setrgbcolor x1 h sub X1 x2 h sub X2 moveto x1 h add X1 x2 h sub X2 lineto x1 h add X1 x2 h add X2 lineto x1 h sub X1 x2 h add X2 lineto closepath fill } for } for }def % Lengths: /c1 144 def /c2 396 def /r 20 def /radius 800 def % Dimensionless quantities: /angle1 -50 def /angle2 -20 def /k1r 10 def /k11rr 0.00 def /g11rr 6.4 def /rd 25 def % Colour: /R 1.00 def % /R 1.00 def /G 0.00 def % /G 0.90 def /B 0.00 def % /B 0.00 def Figure 2 eq { wave } if % Lengths: /c1 448 60 add def /c2 168 80 add def /radius 1180 def % Dimensionless quantities: /angle1 -45 def /angle2 -15 def Figure 3 eq { wave } if % Lengths: /c1 288 def /c2 288 def /r 50 def % Dimensionless quantities: /k1r -2 def /k2r 14 def /k11rr 0.00 def /k12rr 0.00 def /k22rr 0.00 def /g11rr 1.00 def /g12rr 0.00 def /g22rr 1.00 def /rd 25 def % Colour: /R 0.00 def % /R 1.00 def /G 0.50 def % /G 0.00 def /B 1.00 def % /B 0.00 def packet % Lengths: /c1 432 def /c2 480 def /r 50 def % Dimensionless quantities: /k1r 6 def /k2r 8 def /k11rr 0.64 def /k12rr -0.48 def /k22rr 0.36 def /g11rr 1.00 def /g12rr 0.00 def /g22rr 1.00 def /rd 25 def % Colour: /R 1.00 def % /R 1.00 def /G 0.00 def % /G 0.90 def /B 0.00 def % /B 0.00 def Figure 3 eq { packet } if % Bounding Box: % /X 630 def % /Y 583 def % 0 0 0 setrgbcolor % 0 0 moveto X 0 rlineto 0 Y rlineto X neg 0 rlineto closepath stroke showpage %%EOF %%EndDocument @endspecial 1250 556 2 563 v 638 558 615 2 v 638 596 a Fk(Figure)33 b(2.)62 b Fj(Broad{band)27 b(w)o(a)o(v)o(e)638 644 y Fi(u)663 650 y Fh(i)678 644 y Fj(\()p Fk(x)p Fi(;)7 b(t)p Fj(\))31 b(inciden)o(t)d(at)j(the)f(Gab)q(or)638 691 y(function.)p 1276 -9 V 1276 554 2 563 v 1292 542 a /Figure 3 def 1292 542 a @beginspecial 0 @llx 0 @lly 630 @urx 583 @ury 1165 @rwi @setspecial %%BeginDocument: r17lk1/sens1.ps %! %%BoundingBox: 0 0 630 583 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 3 def /wave{ /k1 k1r r div def /k11 k11rr r div r div def /g11 g11rr r div r div def /d r rd div def /h d 2 div def /n1 4.605 g11 div sqrt d div truncate def /C1 c1 angle1 angle2 add 2 div cos radius mul sub def /C2 c2 angle1 angle2 add 2 div sin radius mul sub def n1 neg 1 n1 0.5 add { /x1 exch d mul def k1 k11 x1 mul add x1 mul 57.29578 mul cos 1 add 2 div 2.718282 g11 x1 mul x1 mul neg exp mul dup R 1 sub mul 1 add exch dup G 1 sub mul 1 add exch B 1 sub mul 1 add setrgbcolor newpath C1 C2 radius x1 add h sub angle2 angle1 arcn C1 C2 radius x1 add h add angle1 angle2 arc closepath fill } for }def /packet{ /k1 k1r r div def /k2 k2r r div def /k11 k11rr r div r div def /k12 k12rr r div r div def /k22 k22rr r div r div def /g11 g11rr r div r div def /g12 g12rr r div r div def /g22 g22rr r div r div def /d r rd div def /h d 2 div def /n1 4.605 g11 div sqrt d div truncate def /n2 4.605 g22 div sqrt d div truncate def /X1 {c1 add} def /X2 {c2 add} def n2 neg 1 n2 0.5 add { /x2 exch d mul def n1 neg 1 n1 0.5 add { /x1 exch d mul def k1 k11 x1 mul add k12 x2 mul add x1 mul k2 k12 x1 mul add k22 x2 mul add x2 mul add 57.29578 mul cos 1 add 2 div 2.718282 g11 x1 mul g12 x2 mul add x1 mul g12 x1 mul g22 x2 mul add x2 mul add neg exp mul dup R 1 sub mul 1 add exch dup G 1 sub mul 1 add exch B 1 sub mul 1 add setrgbcolor x1 h sub X1 x2 h sub X2 moveto x1 h add X1 x2 h sub X2 lineto x1 h add X1 x2 h add X2 lineto x1 h sub X1 x2 h add X2 lineto closepath fill } for } for }def % Lengths: /c1 144 def /c2 396 def /r 20 def /radius 800 def % Dimensionless quantities: /angle1 -50 def /angle2 -20 def /k1r 10 def /k11rr 0.00 def /g11rr 6.4 def /rd 25 def % Colour: /R 1.00 def % /R 1.00 def /G 0.00 def % /G 0.90 def /B 0.00 def % /B 0.00 def Figure 2 eq { wave } if % Lengths: /c1 448 60 add def /c2 168 80 add def /radius 1180 def % Dimensionless quantities: /angle1 -45 def /angle2 -15 def Figure 3 eq { wave } if % Lengths: /c1 288 def /c2 288 def /r 50 def % Dimensionless quantities: /k1r -2 def /k2r 14 def /k11rr 0.00 def /k12rr 0.00 def /k22rr 0.00 def /g11rr 1.00 def /g12rr 0.00 def /g22rr 1.00 def /rd 25 def % Colour: /R 0.00 def % /R 1.00 def /G 0.50 def % /G 0.00 def /B 1.00 def % /B 0.00 def packet % Lengths: /c1 432 def /c2 480 def /r 50 def % Dimensionless quantities: /k1r 6 def /k2r 8 def /k11rr 0.64 def /k12rr -0.48 def /k22rr 0.36 def /g11rr 1.00 def /g12rr 0.00 def /g22rr 1.00 def /rd 25 def % Colour: /R 1.00 def % /R 1.00 def /G 0.00 def % /G 0.90 def /B 0.00 def % /B 0.00 def Figure 3 eq { packet } if % Bounding Box: % /X 630 def % /Y 583 def % 0 0 0 setrgbcolor % 0 0 moveto X 0 rlineto 0 Y rlineto X neg 0 rlineto closepath stroke showpage %%EOF %%EndDocument @endspecial 1888 554 2 563 v 1276 556 615 2 v 1276 596 a Fk(Figure)11 b(3.)17 b Fj(Scattered)9 b(w)o(a)o(v)o(e)f Fi(u)1785 582 y Fh(\013)1787 609 y(i)1804 596 y Fj(\()-5 b Fk(x)p Fi(;t)g Fj(\))n(.)0 834 y Fu(3.)25 b(Applied)c(appro)n (ximations)0 907 y(3.1.)k(First{order)18 b(Born)g(appro)n(xima)o(tion)0 980 y Fs(The)i(\014rst{order)d(sensitivit)o(y)j(of)g(the)g(w)o(a)o(v)o (e\014eld)e(to)i(the)h(in\014nitesimally)d(small)g(structural)h(p)q (er-)0 1040 y(turbations)c(is)h(exactly)i(describ)q(ed)d(b)o(y)h(the)h (\014rst{order)e(Born)h(appro)o(ximation.)100 1099 y(The)26 b Ft(elasto)m(dynamic)k(Gr)m(e)m(en)e(tensor)f Fq(G)899 1106 y Fp(k)q(m)959 1099 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1060 1081 y Fl(0)1075 1099 y Fq(;)g(t)p Fs(\),)30 b(corresp)q(onding)24 b(to)k(elasto)q(dynamic)0 1159 y(equation)16 b(\(1\),)h(is)g(de\014ned) e(b)o(y)h(equation)h(\()817 1146 y(\024)811 1159 y(Cerv)o(en)q(\023)-26 b(y)16 b(2001,)g(eq.)h(2.5.37\))56 1244 y Fq(\045)p Fs(\()p Fu(x)p Fs(\))176 1232 y(\177)164 1244 y Fq(G)203 1251 y Fp(im)255 1244 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)356 1224 y Fl(0)371 1244 y Fq(;)g(t)k Fo(\000)e Fq(t)490 1224 y Fl(0)504 1244 y Fs(\))15 b(=)e([)p Fq(c)626 1251 y Fp(ij)r(k)q(l)695 1244 y Fs(\()p Fu(x)p Fs(\))i Fq(G)817 1251 y Fp(k)q(m;l)902 1244 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1003 1224 y Fl(0)1018 1244 y Fq(;)g(t)j Fo(\000)g Fq(t)1137 1224 y Fl(0)1151 1244 y Fs(\)])1184 1251 y Fp(;j)1228 1244 y Fs(+)g Fq(\016)1300 1251 y Fp(im)1360 1244 y Fq(\016)r Fs(\()p Fu(x)h Fo(\000)f Fu(x)1525 1224 y Fl(0)1539 1244 y Fs(\))d Fq(\016)r Fs(\()p Fq(t)k Fo(\000)f Fq(t)1707 1224 y Fl(0)1721 1244 y Fs(\))17 b Fq(;)55 b Fs(\(6\))0 1330 y(where)22 b(the)h(spatial)f(partial)f(deriv)m(ativ)o (es)i(are)f(related)g(to)h(co)q(ordinates)f Fq(x)1457 1337 y Fp(i)1474 1330 y Fs(.)40 b(The)22 b(corresp)q(ond-)0 1389 y(ing)h(time{harmonic)e(elasto)q(dynamic)h(Green)h(tensor)1090 1377 y Fn(b)1080 1389 y Fq(G)1119 1396 y Fp(k)q(m)1179 1389 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1280 1371 y Fl(0)1295 1389 y Fq(;)g(!)r Fs(\))24 b(is)e(de\014ned)g(b)o(y)h(equation)0 1449 y(\()25 1436 y(\024)19 1449 y(Cerv)o(en)q(\023)-26 b(y)17 b(2001,)f(eq.)h(2.5.38\))189 1541 y Fo(\000)p Fq(!)261 1520 y Fm(2)291 1541 y Fq(\045)p Fs(\()p Fu(x)p Fs(\))410 1528 y Fn(b)400 1541 y Fq(G)439 1548 y Fp(im)491 1541 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)592 1520 y Fl(0)607 1541 y Fq(;)g(!)r Fs(\))14 b(=)f([)p Fq(c)783 1548 y Fp(ij)r(k)q(l)853 1541 y Fs(\()p Fu(x)p Fs(\))945 1528 y Fn(b)936 1541 y Fq(G)975 1548 y Fp(k)q(m;l)1059 1541 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1160 1520 y Fl(0)1175 1541 y Fq(;)g(!)r Fs(\)])1263 1548 y Fp(;j)1307 1541 y Fs(+)j Fq(\016)1379 1548 y Fp(im)1439 1541 y Fq(\016)r Fs(\()p Fu(x)h Fo(\000)f Fu(x)1604 1520 y Fl(0)1618 1541 y Fs(\))50 b Fq(;)125 b Fs(\(7\))0 1626 y(where)20 b(the)g(spatial)g (partial)f(deriv)m(ativ)o(es)h(are)f(again)h(related)g(to)g(co)q (ordinates)f Fq(x)1571 1633 y Fp(i)1589 1626 y Fs(.)32 b(Multiplying)0 1686 y(equation)16 b(\(6\))h(b)o(y)e Fq(f)375 1693 y Fp(i)392 1686 y Fs(\()p Fu(x)441 1668 y Fl(0)456 1686 y Fq(;)8 b(t)496 1668 y Fl(0)510 1686 y Fs(\),)16 b(in)o(tegrating)f(o)o(v)o(er)g Fu(x)948 1668 y Fl(0)978 1686 y Fs(and)h Fq(t)1093 1668 y Fl(0)1107 1686 y Fs(,)g(and)f(comparing)f(the)i(result)g(with)g(\(1\),)0 1745 y(w)o(e)g(see)h(that)425 1818 y Fq(u)454 1825 y Fp(i)470 1818 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)638 1750 y Fn(Z)676 1818 y Fs(d)p Fu(x)734 1797 y Fl(0)731 1750 y Fn(Z)770 1818 y Fs(d)p Fq(t)816 1797 y Fl(0)843 1818 y Fq(G)882 1825 y Fp(im)934 1818 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1035 1797 y Fl(0)1050 1818 y Fq(;)g(t)j Fo(\000)g Fq(t)1169 1797 y Fl(0)1183 1818 y Fs(\))p Fq(f)1226 1825 y Fp(m)1265 1818 y Fs(\()p Fu(x)1314 1797 y Fl(0)1328 1818 y Fq(;)d(t)1368 1797 y Fl(0)1382 1818 y Fs(\))51 b Fq(:)360 b Fs(\(8\))0 1917 y(F)l(or)15 b(equation)i(\(2\),)g(w)o(e)f (analogously)f(obtain)30 2028 y Fq(\016)r(u)83 2035 y Fp(i)99 2028 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)267 1960 y Fn(Z)305 2028 y Fs(d)p Fu(x)363 2007 y Fl(0)360 1960 y Fn(Z)399 2028 y Fs(d)p Fq(t)445 2007 y Fl(0)473 2028 y Fq(G)512 2035 y Fp(im)564 2028 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)665 2007 y Fl(0)680 2028 y Fq(;)g(t)j Fo(\000)g Fq(t)799 2007 y Fl(0)813 2028 y Fs(\))d Fo(f\000)p Fq(\016)r(\045)p Fs(\()p Fu(x)1003 2007 y Fl(0)1018 2028 y Fs(\))s(\177)-28 b Fq(u)1066 2035 y Fp(m)1103 2028 y Fs(\()p Fu(x)1152 2007 y Fl(0)1167 2028 y Fq(;)8 b(t)1207 2007 y Fl(0)1221 2028 y Fs(\))j(+)g([)p Fq(\016)r(c)1361 2035 y Fp(mj)r(k)q(l)1452 2028 y Fs(\()p Fu(x)1501 2007 y Fl(0)1515 2028 y Fs(\))p Fq(u)1563 2035 y Fp(k)q(;l)1612 2028 y Fs(\()p Fu(x)1661 2007 y Fl(0)1676 2028 y Fq(;)d(t)1716 2007 y Fl(0)1730 2028 y Fs(\)])1763 2035 y Fp(;j)1796 2028 y Fo(g)25 b Fq(:)1826 2113 y Fs(\(9\))0 2173 y(W)l(e)f(de\014ne)g(the)g(F)l(ourier) e(transform)i Fn(b)-30 b Fq(u)p Fs(\()p Fq(!)r Fs(\))24 b(of)g(function)g Fq(u)p Fs(\()p Fq(t)p Fs(\))g(according)f(to)1560 2160 y(\024)1554 2173 y(Cerv)o(en)q(\023)-26 b(y)24 b(\(2001,)0 2232 y(eq.)17 b(A.1.2\),)645 2354 y Fn(b)-30 b Fq(u)p Fs(\()p Fq(!)r Fs(\))14 b(=)813 2276 y Fm(+)p Fl(1)812 2286 y Fn(Z)790 2427 y Fl(\0001)856 2354 y Fs(d)p Fq(t)8 b Fs(exp\(i)p Fq(!)r(t)p Fs(\))g Fq(u)p Fs(\()p Fq(t)p Fs(\))51 b Fq(:)554 b Fs(\(10\))0 2489 y(The)16 b(in)o(v)o(erse)f(F)l (ourier)g(transformation)g(then)h(reads)579 2624 y Fq(u)p Fs(\()p Fq(t)p Fs(\))e(=)752 2590 y(1)p 737 2613 56 2 v 737 2658 a(2)p Fq(\031)809 2546 y Fm(+)p Fl(1)808 2556 y Fn(Z)787 2697 y Fl(\0001)852 2624 y Fs(d)p Fq(!)c Fs(exp\()p Fo(\000)p Fs(i)p Fq(!)r(t)p Fs(\))g Fn(b)-30 b Fq(u)p Fs(\()p Fq(!)r Fs(\))50 b Fq(:)490 b Fs(\(11\))920 2806 y(29)p eop %%Page: 30 4 30 3 bop 0 -54 a Fs(If)17 b Fq(u)p Fs(\()p Fq(t)p Fs(\))g(is)f(a)g (real{v)m(alued)g(function,)g(then)737 36 y Fn(b)-30 b Fq(u)p Fs(\()p Fo(\000)p Fq(!)r Fs(\))14 b(=)f([)r Fn(b)-30 b Fq(u)p Fs(\()p Fq(!)r Fs(\)])1068 16 y Fl(\003)1141 36 y Fq(;)646 b Fs(\(12\))0 127 y(and)16 b(\()122 114 y(\024)116 127 y(Cerv)o(en)q(\023)-26 b(y,)16 b(2001,)g(eq.)h(A.1.3\)) 727 217 y Fq(u)p Fs(\()p Fq(t)p Fs(\))d(=)f(Re[)p Fq(u)980 197 y Fm(\()-7 b(A)g(\))1029 217 y Fs(\()p Fq(t)p Fs(\)])50 b Fq(;)638 b Fs(\(13\))0 308 y(where)574 418 y Fq(u)603 397 y Fm(\()-7 b(A)g(\))652 418 y Fs(\()p Fq(t)p Fs(\))14 b(=)784 384 y(1)p 781 406 31 2 v 781 452 a Fq(\031)828 340 y Fm(+)p Fl(1)827 350 y Fn(Z)831 491 y Fm(0)871 418 y Fs(d)p Fq(!)c Fs(exp\()p Fo(\000)p Fs(i)p Fq(!)r(t)p Fs(\))g Fn(b)-30 b Fq(u)p Fs(\()p Fq(!)r Fs(\))535 b(\(14\))0 554 y(is)19 b(the)g(complex{v)m(alued)g(analytical)g(signal)f(corresp)q (onding)f(to)i(real{v)m(alued)g(function)f Fq(u)p Fs(\()p Fq(t)p Fs(\).)31 b(If)0 614 y(w)o(e)16 b(kno)o(w)g(the)h(analytical)g (signal,)e(w)o(e)h(ma)o(y)g(also)g(use)g(F)l(ourier)f(transform)607 764 y Fn(b)-29 b Fq(u)o Fs(\()p Fq(!)r Fs(\))15 b(=)778 744 y Fm(1)p 778 752 20 2 v 778 781 a(2)815 686 y(+)p Fl(1)814 696 y Fn(Z)793 837 y Fl(\0001)858 764 y Fs(d)p Fq(t)8 b Fs(exp\(i)p Fq(!)r(t)p Fs(\))g Fq(u)1128 743 y Fm(\()-7 b(A)g(\))1178 764 y Fs(\()p Fq(t)p Fs(\))567 b(\(15\))0 925 y(\()25 913 y(\024)19 925 y(Cerv)o(en)q(\023)-26 b(y,)21 b(2001,)f(eq.)g(A.3.4\))g(for)f(p)q(ositiv)o(e)h(frequencies,)g (and)f(relation)g(\(12\))h(for)g(negativ)o(e)g(fre-)0 985 y(quencies.)100 1045 y(In)c(this)g(pap)q(er,)g(w)o(e)g(shall)g (assume)f(that)i(the)f(frequency)h(is)f(p)q(ositiv)o(e,)851 1136 y Fq(!)g(>)d Fs(0)50 b Fq(;)762 b Fs(\(16\))0 1226 y(and)19 b(consider)g(F)l(ourier)f(transforms)g(\(10\))j(for)e(a)h (real{v)m(alued)f(function)h(or)g(\(15\))g(for)g(the)g(corre-)0 1286 y(sp)q(onding)15 b(analytical)h(signal,)g(and)f(in)o(v)o(erse)g(F) l(ourier)g(transform)g(\(14\).)100 1346 y(F)l(ourier)22 b(transformation)h(\(10\))i(of)g(equation)f(\(9\))h(yields)g(equation)f (\()1490 1333 y(\024)1484 1346 y(Cerv)o(en)q(\023)-26 b(y)25 b(2001,)h(eq.)0 1406 y(2.6.17\))37 1522 y Fq(\016)t Fn(b)-30 b Fq(u)90 1529 y Fp(i)106 1522 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)289 1454 y Fn(Z)327 1522 y Fs(d)p Fu(x)385 1501 y Fl(0)423 1509 y Fn(b)413 1522 y Fq(G)452 1529 y Fp(im)504 1522 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)605 1501 y Fl(0)620 1522 y Fq(;)g(!)r Fs(\))702 1481 y Fn(\010)731 1522 y Fq(!)764 1501 y Fm(2)795 1522 y Fq(\016)r(\045)p Fs(\()p Fu(x)894 1501 y Fl(0)908 1522 y Fs(\))j Fn(b)-31 b Fq(u)964 1529 y Fp(m)1002 1522 y Fs(\()p Fu(x)1051 1501 y Fl(0)1066 1522 y Fq(;)8 b(!)r Fs(\))j(+)g([)p Fq(\016)r(c)1261 1529 y Fp(mj)r(k)q(l)1351 1522 y Fs(\()p Fu(x)1400 1501 y Fl(0)1415 1522 y Fs(\))r Fn(b)-30 b Fq(u)1463 1529 y Fp(k)q(;l)1512 1522 y Fs(\()p Fu(x)1561 1501 y Fl(0)1576 1522 y Fq(;)8 b(!)r Fs(\)])1664 1529 y Fp(;j)1697 1481 y Fn(\011)1751 1522 y Fq(;)36 b Fs(\(17\))0 1638 y(where)14 b Fn(b)-30 b Fq(u)169 1645 y Fp(k)q(;l)218 1638 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))13 b(is)g(the)f(F)l(ourier)f(transform)g(of)i Fq(u)958 1645 y Fp(k)q(;l)1006 1638 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\),)15 b Fq(\016)t Fn(b)-30 b Fq(u)1196 1645 y Fp(k)q(;l)1244 1638 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))14 b(is)e(the)h(F)l(ourier)e (transform)0 1697 y(of)20 b Fq(\016)r(u)113 1704 y Fp(k)q(;l)161 1697 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\),)22 b(and)d(time{harmonic)e (elasto)q(dynamic)i(Green)g(tensor)g Fq(G)1420 1704 y Fp(im)1472 1697 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1573 1679 y Fl(0)1588 1697 y Fq(;)g(!)r Fs(\))20 b(is)f(de\014ned)0 1757 y(b)o(y)d(equation)h(\(7\).)100 1817 y(F)l(or)e(the)i(medium)e(p)q (erturbation)g(v)m(anishing)h(at)h(the)f(spatial)g(b)q(oundary)g(of)g (the)h(in)o(tegration)0 1877 y(region,)i(w)o(e)h(obtain)e(the)i (\014rst{order)e(w)o(a)o(v)o(e\014eld)g(p)q(erturbation)g(in)h(the)h (form)f(of)h(the)f Ft(\014rst{or)m(der)0 1937 y(Born)f(appr)m(oximatio) q(n)h Fs(for)d(the)h(scattered)g(w)o(a)o(v)o(e\014eld)e(\()1068 1924 y(\024)1062 1937 y(Cerv)o(en)q(\023)-26 b(y)16 b(2001,)g(eq.)h (2.6.18\),)291 2053 y Fq(\016)t Fn(b)-30 b Fq(u)344 2060 y Fp(i)360 2053 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)543 1985 y Fn(Z)581 2053 y Fs(d)p Fu(x)639 2032 y Fl(0)653 2012 y Fn(\002)674 2053 y Fq(!)707 2032 y Fm(2)747 2040 y Fn(b)737 2053 y Fq(G)776 2060 y Fp(im)828 2053 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)929 2032 y Fl(0)944 2053 y Fq(;)g(!)r Fs(\))17 b Fq(\016)r(\045)p Fs(\()p Fu(x)1134 2032 y Fl(0)1148 2053 y Fs(\))i Fn(b)-30 b Fq(u)1213 2060 y Fp(m)1251 2053 y Fs(\()p Fu(x)1300 2032 y Fl(0)1314 2053 y Fq(;)8 b(!)r Fs(\))685 2164 y Fo(\000)744 2152 y Fn(b)734 2164 y Fq(G)773 2171 y Fp(im;j)856 2164 y Fs(\()p Fu(x)p Fq(;)g Fu(x)957 2144 y Fl(0)972 2164 y Fq(;)g(!)r Fs(\))17 b Fq(\016)r(c)1109 2171 y Fp(mj)r(k)q(l)1199 2164 y Fs(\()p Fu(x)1248 2144 y Fl(0)1263 2164 y Fs(\))i Fn(b)-30 b Fq(u)1328 2171 y Fp(k)q(;l)1377 2164 y Fs(\()p Fu(x)1426 2144 y Fl(0)1440 2164 y Fq(;)8 b(!)r Fs(\))1514 2124 y Fn(\003)1585 2164 y Fq(;)202 b Fs(\(18\))0 2255 y(where)17 b(the)i(spatial)e(partial)g(deriv)m(ativ)o(es)h(are)f (related)h(to)g(co)q(ordinates)f Fq(x)1415 2237 y Fl(0)1415 2268 y Fp(i)1432 2255 y Fs(.)27 b(Inserting)17 b(equations)0 2314 y(\(3\))g(and)f(\(5\))h(for)g(the)f(p)q(erturbations,)f(w)o(e)h (arriv)o(e)g(at)h(equation)299 2430 y Fn(b)-30 b Fq(u)326 2410 y Fp(\013)326 2443 y(i)354 2430 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)537 2363 y Fn(Z)575 2430 y Fs(d)p Fu(x)633 2410 y Fl(0)647 2430 y Fq(g)673 2410 y Fp(\013)701 2430 y Fs(\()p Fu(x)750 2410 y Fl(0)764 2430 y Fs(\)[)q Fq(!)831 2410 y Fm(2)871 2418 y Fn(b)861 2430 y Fq(G)900 2437 y Fp(im)952 2430 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1053 2410 y Fl(0)1068 2430 y Fq(;)g(!)r Fs(\))g Fq(\045)1176 2410 y Fp(\013)1215 2430 y Fn(b)-30 b Fq(u)1242 2437 y Fp(m)1280 2430 y Fs(\()p Fu(x)1329 2410 y Fl(0)1343 2430 y Fq(;)8 b(!)r Fs(\))809 2542 y Fo(\000)868 2529 y Fn(b)859 2542 y Fq(G)898 2549 y Fp(im;j)980 2542 y Fs(\()p Fu(x)p Fq(;)g Fu(x)1081 2521 y Fl(0)1096 2542 y Fq(;)g(!)r Fs(\))g Fq(c)1200 2521 y Fp(\013)1200 2554 y(mj)r(k)q(l)1301 2542 y Fn(b)-29 b Fq(u)1329 2549 y Fp(k)q(;l)1377 2542 y Fs(\()p Fu(x)1426 2521 y Fl(0)1441 2542 y Fq(;)8 b(!)r Fs(\)])50 b Fq(;)208 b Fs(\(19\))0 2632 y(where)16 b(the)h(spatial)f(partial)f(deriv)m(ativ)o(es)h(are)h (related)f(to)h(co)q(ordinates)e Fq(x)1402 2614 y Fl(0)1402 2645 y Fp(i)1419 2632 y Fs(.)920 2806 y(30)p eop %%Page: 31 5 31 4 bop 0 -54 a Fu(3.2.)25 b(Ra)n(y{theory)19 b(appro)n(xima)o(tion)0 21 y Fs(The)h(F)l(ourier)e(transform)h(of)i(the)f(inciden)o(t)f(w)o(a)o (v)o(e)h(in)g(the)g(vicinit)o(y)h(of)f(p)q(oin)o(t)g Fu(x)1542 3 y Fp(\013)1591 21 y Fs(is)g(assumed)e(in)0 81 y(form)503 141 y Fn(b)-30 b Fq(u)530 148 y Fp(i)546 141 y Fs(\()p Fu(x)595 121 y Fl(0)609 141 y Fq(;)8 b(!)r Fs(\))15 b Fo(\031)762 129 y Fn(b)750 141 y Fq(A)q Fs(\()p Fu(x)837 121 y Fl(0)851 141 y Fq(;)8 b(!)r Fs(\))p Fq(E)962 148 y Fp(i)979 141 y Fs(\()p Fu(x)1028 121 y Fl(0)1042 141 y Fs(\))g(exp)q([i)p Fq(!)r(T)f Fs(\()p Fu(x)1292 121 y Fl(0)1306 141 y Fs(\)])462 b(\(20\))0 223 y(with)16 b(amplitude)360 210 y Fn(b)349 223 y Fq(A)p Fs(\()p Fu(x)435 205 y Fl(0)450 223 y Fq(;)8 b(!)r Fs(\),)16 b(p)q(olarization)g(v)o (ector)g Fq(E)1016 230 y Fp(i)1033 223 y Fs(\()p Fu(x)1082 205 y Fl(0)1096 223 y Fs(\))h(and)f(tra)o(v)o(el)g(time)h Fq(T)7 b Fs(\()p Fu(x)1568 205 y Fl(0)1582 223 y Fs(\).)100 283 y(Ra)o(y{theory)14 b(appro)o(ximation)e(of)j(the)g(time{harmonic)e (elasto)q(dynamic)h(Green)h(tensor,)f(cor-)0 343 y(resp)q(onding)k(to)j (the)f(elemen)o(tary)f(w)o(a)o(v)o(e)h(with)g(p)q(olarization)f(v)o (ector)h Fq(e)1367 350 y Fp(k)1392 343 y Fs(\()p Fu(x)1441 325 y Fl(0)1455 343 y Fq(;)8 b Fu(x)p Fs(\))21 b(at)g(p)q(oin)o(t)e Fu(x)1775 325 y Fl(0)1810 343 y Fs(and)0 403 y(p)q(olarization)c(v)o (ector)i Fq(e)448 410 y Fp(k)473 403 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)574 385 y Fl(0)589 403 y Fs(\))17 b(at)g(p)q(oin)o(t)f Fu(x)p Fs(,)g(is)g(\()951 390 y(\024)945 403 y(Cerv)o(en)q(\023)-26 b(y)17 b(2001,)f(eq.)h(5.4.24\))227 509 y Fn(b)217 522 y Fq(G)256 529 y Fp(im)308 522 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)409 501 y Fl(0)424 522 y Fq(;)g(!)r Fs(\))14 b Fo(\031)632 488 y Fq(e)655 495 y Fp(i)671 488 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)772 470 y Fl(0)787 488 y Fs(\))15 b Fq(e)844 495 y Fp(m)882 488 y Fs(\()p Fu(x)931 470 y Fl(0)945 488 y Fq(;)8 b Fu(x)p Fs(\))15 b Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1170 470 y Fl(0)1185 488 y Fs(\))p 570 510 696 2 v 570 563 a(4)p Fq(\031)625 520 y Fn(p)p 675 520 408 2 v 43 x Fq(\045)p Fs(\()p Fu(x)p Fs(\))p Fq(v)r Fs(\()p Fu(x)p Fs(\))p Fq(\045)p Fs(\()p Fu(x)938 548 y Fl(0)954 563 y Fs(\))p Fq(v)r Fs(\()p Fu(x)1048 548 y Fl(0)1063 563 y Fs(\))14 b Fq(L)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1231 548 y Fl(0)1246 563 y Fs(\))1297 522 y(exp[i)p Fq(!)r(\034)e Fs(\()p Fu(x)p Fq(;)i Fu(x)1563 501 y Fl(0)1576 522 y Fs(\)])50 b Fq(;)128 b Fs(\(21\))0 651 y(where)19 b Fq(v)r Fs(\()p Fu(x)p Fs(\))h(is)f(the)h(phase)f(v)o (elo)q(cit)o(y)l(,)h Fq(\045)p Fs(\()p Fu(x)p Fs(\))g(is)f(the)h (densit)o(y)l(,)f(and)g Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1422 633 y Fl(0)1437 651 y Fs(\))20 b(is)f(the)g(accum)o(ulated) 0 711 y(recipro)q(cal)d(transmission)e(co)q(e\016cien)o(t)j(describing) e(amplitude)g(losses)h(b)q(et)o(w)o(een)h(p)q(oin)o(ts)f Fu(x)1732 693 y Fl(0)1763 711 y Fs(and)g Fu(x)0 770 y Fs(due)g(to)h(atten)o(uation)f(and)f(due)h(to)h(re\015ections)f(and)f (scattering)h(in)o(to)g(directions)f(leading)h(outside)0 830 y(the)h(vicinit)o(y)f(of)h(p)q(oin)o(t)f Fu(x)p Fs(.)22 b(Here)17 b(the)g Ft(r)m(elative)h(ge)m(ometric)m(al)h(spr)m(e)m(ading) g Fq(L)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1511 812 y Fl(0)1526 830 y Fs(\))17 b(\()1587 818 y(\024)1581 830 y(Cerv)o(en)q(\023)-26 b(y)17 b(2001,)0 890 y(eq.)g(4.14.45\))f(should)f(correctly)i(include)e (p)q(ossible)g(phase)h(shifts)g(due)g(to)h(caustics.)0 1011 y Fu(3.3.)25 b(P)n(araxial)20 b(ra)n(y)g(appro)n(xima)o(tion)0 1086 y Fs(P)o(oin)o(t)12 b Fu(x)160 1068 y Fl(0)188 1086 y Fs(is)h(situated)h(in)f(the)g(vicinit)o(y)h(of)g(p)q(oin)o(t)f Fu(x)948 1068 y Fp(\013)976 1086 y Fs(,)h(and)f(observ)m(ation)g(p)q (oin)o(t)g Fu(x)g Fs(is)h(situated)f(in)g(the)0 1146 y(vicinit)o(y)18 b(of)f(p)q(oin)o(t)h Fu(x)399 1128 y Fm(0)421 1146 y Fs(.)25 b(P)o(oin)o(t)17 b Fu(x)625 1128 y Fm(0)665 1146 y Fs(will)h(b)q(e)g(selected)f(in)h(the)f(direction)g (of)h(maxim)o(um)e(scattering.)0 1206 y(W)l(e)c(shall)f(apply)h(the)g Ft(p)m(ar)m(axial)k(r)m(ay)f(appr)m(oximation)g Fs(to)e(b)q(oth)f (inciden)o(t)f(w)o(a)o(v)o(e)g Fq(u)1494 1213 y Fp(k)1518 1206 y Fs(\()p Fu(x)1567 1188 y Fl(0)1582 1206 y Fq(;)d(t)1622 1188 y Fl(0)1636 1206 y Fs(\))k(and)f(Green)0 1266 y(tensor)h Fq(G)185 1273 y Fp(im;j)268 1266 y Fs(\()p Fu(x)p Fq(;)c Fu(x)369 1248 y Fl(0)383 1266 y Fq(;)g(t)p Fs(\))14 b(from)e(p)q(oin)o (t)g Fu(x)726 1248 y Fp(\013)768 1266 y Fs(to)h(p)q(oin)o(t)f Fu(x)981 1248 y Fl(0)995 1266 y Fs(.)21 b(W)l(e)13 b(shall)f(also)g (use)g(the)h(t)o(w)o(o{p)q(oin)o(t)f(paraxial)0 1326 y(appro)o(ximation)h(of)j(Green)f(tensor)g Fq(G)721 1333 y Fp(im;j)804 1326 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)905 1308 y Fl(0)920 1326 y Fq(;)g(t)p Fs(\))16 b(from)f(p)q(oin)o(t)g Fu(x)1271 1308 y Fp(\013)1315 1326 y Fs(to)h(p)q(oin)o(t)f Fu(x)1534 1308 y Fl(0)1564 1326 y Fs(and)g(from)g(p)q(oin)o(t)0 1385 y Fu(x)30 1367 y Fm(0)69 1385 y Fs(to)h(p)q(oin)o(t)g Fu(x)p Fs(.)22 b(The)15 b(paraxial)g(ra)o(y)h(appro)o(ximation)e (consists)g(in)i(a)g(constan)o(t)f(amplitude)g(and)g(in)0 1445 y(the)i(second{order)d(T)l(a)o(ylor)i(expansion)f(of)i(tra)o(v)o (el)f(time)g(at)h(p)q(oin)o(ts)f Fu(x)1324 1427 y Fp(\013)1369 1445 y Fs(and)g Fu(x)1496 1427 y Fm(0)1518 1445 y Fs(.)100 1505 y(A)h(\\constan)o(t)e(amplitude")h(means)f(that)i(w)o(e)f(shall)g (apply)g(appro)o(ximations)709 1583 y Fn(b)698 1596 y Fq(A)p Fs(\()p Fu(x)784 1575 y Fl(0)798 1596 y Fq(;)8 b(!)r Fs(\))15 b Fo(\031)951 1583 y Fn(b)939 1596 y Fq(A)q Fs(\()p Fu(x)1026 1575 y Fp(\013)1055 1596 y Fq(;)8 b(!)r Fs(\))50 b Fq(;)608 b Fs(\(22\))736 1686 y Fq(E)773 1693 y Fp(i)790 1686 y Fs(\()p Fu(x)839 1666 y Fl(0)853 1686 y Fs(\))15 b Fo(\031)e Fq(E)976 1693 y Fp(i)993 1686 y Fs(\()p Fu(x)1042 1666 y Fp(\013)1071 1686 y Fs(\))50 b Fq(;)647 b Fs(\(23\))698 1762 y Fq(e)721 1769 y Fp(i)737 1762 y Fs(\()p Fu(x)786 1742 y Fl(0)801 1762 y Fq(;)8 b Fu(x)p Fs(\))15 b Fo(\031)e Fq(e)962 1769 y Fp(i)979 1762 y Fs(\()p Fu(x)1028 1742 y Fp(\013)1057 1762 y Fq(;)8 b Fu(x)p Fs(\))51 b Fq(;)608 b Fs(\(24\))698 1838 y Fq(e)721 1845 y Fp(i)737 1838 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)838 1818 y Fl(0)853 1838 y Fs(\))15 b Fo(\031)e Fq(e)962 1845 y Fp(i)979 1838 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1080 1818 y Fp(\013)1109 1838 y Fs(\))51 b Fq(;)608 b Fs(\(25\))764 1914 y Fq(\045)p Fs(\()p Fu(x)839 1894 y Fl(0)853 1914 y Fs(\))15 b Fo(\031)e Fq(\045)p Fs(\()p Fu(x)1014 1894 y Fp(\013)1043 1914 y Fs(\))50 b Fq(;)675 b Fs(\(26\))764 1990 y Fq(v)r Fs(\()p Fu(x)839 1969 y Fl(0)853 1990 y Fs(\))15 b Fo(\031)e Fq(v)r Fs(\()p Fu(x)1014 1969 y Fp(\013)1043 1990 y Fs(\))50 b Fq(;)675 b Fs(\(27\))699 2066 y Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)838 2045 y Fl(0)853 2066 y Fs(\))15 b Fo(\031)e Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1078 2045 y Fp(\013)1108 2066 y Fs(\))50 b Fq(;)610 b Fs(\(28\))679 2142 y Fu(Q)722 2149 y Fm(2)744 2142 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)845 2121 y Fl(0)860 2142 y Fs(\))15 b Fo(\031)e Fu(Q)989 2149 y Fm(2)1011 2142 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1112 2121 y Fp(\013)1142 2142 y Fs(\))640 b(\(29\))0 2217 y(in)16 b(the)h(vicinit)o(y)f(of)h(p)q (oin)o(t)f Fu(x)539 2199 y Fp(\013)568 2217 y Fs(.)100 2277 y(W)l(e)g(ma)o(y)g(also)g(apply)g(appro)o(ximations)679 2368 y Fq(e)702 2375 y Fp(i)719 2368 y Fs(\()p Fu(x)768 2347 y Fp(\013)797 2368 y Fq(;)8 b Fu(x)p Fs(\))15 b Fo(\031)e Fq(e)958 2375 y Fp(i)975 2368 y Fs(\()p Fu(x)1024 2347 y Fp(\013)1053 2368 y Fq(;)8 b Fu(x)1105 2347 y Fm(0)1128 2368 y Fs(\))50 b Fq(;)590 b Fs(\(30\))679 2458 y Fq(e)702 2465 y Fp(i)719 2458 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)820 2438 y Fp(\013)849 2458 y Fs(\))15 b Fo(\031)e Fq(e)958 2465 y Fp(i)975 2458 y Fs(\()p Fu(x)1024 2438 y Fm(0)1047 2458 y Fq(;)8 b Fu(x)1099 2438 y Fp(\013)1128 2458 y Fs(\))50 b Fq(;)590 b Fs(\(31\))774 2534 y Fq(\045)p Fs(\()p Fu(x)p Fs(\))15 b Fo(\031)e Fq(\045)p Fs(\()p Fu(x)1010 2514 y Fm(0)1033 2534 y Fs(\))50 b Fq(;)685 b Fs(\(32\))774 2610 y Fq(v)r Fs(\()p Fu(x)p Fs(\))15 b Fo(\031)e Fq(v)r Fs(\()p Fu(x)1010 2590 y Fm(0)1033 2610 y Fs(\))50 b Fq(;)685 b Fs(\(33\))681 2686 y Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)820 2665 y Fp(\013)849 2686 y Fs(\))15 b Fo(\031)e Fq(R)p Fs(\()p Fu(x)1022 2665 y Fm(0)1045 2686 y Fq(;)8 b Fu(x)1097 2665 y Fp(\013)1126 2686 y Fs(\))50 b Fq(;)592 b Fs(\(34\))920 2806 y(31)p eop %%Page: 32 6 32 5 bop 661 -54 a Fu(Q)704 -47 y Fm(2)726 -54 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)827 -75 y Fp(\013)856 -54 y Fs(\))15 b Fo(\031)e Fu(Q)985 -47 y Fm(2)1008 -54 y Fs(\()p Fu(x)1057 -75 y Fm(0)1079 -54 y Fq(;)8 b Fu(x)1131 -75 y Fp(\013)1160 -54 y Fs(\))622 b(\(35\))0 23 y(in)16 b(the)h(vicinit)o(y)f(of)h(p)q (oin)o(t)f Fu(x)539 5 y Fm(0)562 23 y Fs(,)g(e.g.,)g(in)h(Sections)e (4.4.3)h(or)h(5.3.)100 84 y(F)l(or)h(tra)o(v)o(el)g(time)h Fq(T)7 b Fs(\()p Fu(x)535 66 y Fl(0)550 84 y Fs(\))19 b(of)g(the)h(inciden)o(t)e(w)o(a)o(v)o(e)g(at)i(p)q(oin)o(t)e Fu(x)1278 66 y Fl(0)1292 84 y Fs(,)i(situated)f(in)f(the)i(vicinit)o(y) f(of)0 144 y(p)q(oin)o(t)d Fu(x)160 126 y Fp(\013)189 144 y Fs(,)g(w)o(e)g(denote)781 206 y Fq(T)817 186 y Fp(\013)859 206 y Fs(=)e Fq(T)7 b Fs(\()p Fu(x)997 186 y Fp(\013)1026 206 y Fs(\))50 b Fq(;)692 b Fs(\(36\))760 315 y Fq(T)796 294 y Fp(\013)789 327 y(;i)839 315 y Fs(=)897 281 y Fq(@)s(T)7 b Fs(\()p Fu(x)1011 263 y Fp(\013)1041 281 y Fs(\))p 897 303 163 2 v 936 349 a Fq(@)s(x)993 332 y Fp(\013)993 363 y(i)1116 315 y Fq(;)671 b Fs(\(37\))744 461 y Fq(T)780 441 y Fp(\013)773 474 y(;ij)833 461 y Fs(=)892 428 y Fq(@)921 410 y Fm(2)943 428 y Fq(T)7 b Fs(\()p Fu(x)1028 410 y Fp(\013)1057 428 y Fs(\))p 892 450 185 2 v 898 496 a Fq(@)s(x)955 478 y Fp(\013)955 510 y(i)984 496 y Fq(@)s(x)1041 478 y Fp(\013)1041 510 y(j)1133 461 y Fq(:)654 b Fs(\(38\))0 573 y(The)16 b(slo)o(wness)f(v)o (ector)i(of)f(the)h(inciden)o(t)f(w)o(a)o(v)o(e)g(at)g(p)q(oin)o(t)g Fu(x)1125 555 y Fp(\013)1171 573 y Fs(is)823 665 y Fq(P)855 672 y Fp(i)886 665 y Fs(=)d Fq(T)974 645 y Fp(\013)967 678 y(;i)1053 665 y Fq(:)734 b Fs(\(39\))0 758 y(The)16 b(second{order)f(T)l(a)o(ylor)g(expansion)h(of)g(tra)o(v)o(el)g(time)h (of)f(the)h(inciden)o(t)f(w)o(a)o(v)o(e)g(at)h(p)q(oin)o(t)f Fu(x)1775 739 y Fp(\013)1820 758 y Fs(is)517 850 y Fq(T)7 b Fs(\()p Fu(x)602 829 y Fl(0)617 850 y Fs(\))14 b Fo(\031)g Fq(T)739 829 y Fp(\013)778 850 y Fs(+)d Fq(P)860 857 y Fp(i)876 850 y Fs(\001)p Fq(x)946 829 y Fl(0)946 862 y Fp(i)974 850 y Fs(+)1030 830 y Fm(1)p 1030 838 20 2 v 1030 867 a(2)1056 850 y Fq(T)1092 829 y Fp(\013)1085 862 y(;ij)1132 850 y Fs(\001)p Fq(x)1202 829 y Fl(0)1202 862 y Fp(i)1218 850 y Fs(\001)p Fq(x)1288 829 y Fl(0)1288 862 y Fp(j)1359 850 y Fq(;)428 b Fs(\(40\))0 942 y(where)755 1004 y(\001)p Fq(x)825 984 y Fl(0)825 1016 y Fp(i)856 1004 y Fs(=)13 b Fq(x)936 984 y Fl(0)936 1016 y Fp(i)964 1004 y Fo(\000)e Fq(x)1042 984 y Fp(\013)1042 1016 y(i)1121 1004 y Fq(:)666 b Fs(\(41\))0 1081 y(W)l(e)20 b(denote)g(the)g(spatial) f(deriv)m(ativ)o(es)g(of)h(tra)o(v)o(el)f(time)h Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1206 1063 y Fl(0)1220 1081 y Fs(\))20 b(from)f(p)q(oin)o(t)h Fu(x)1544 1063 y Fl(0)1578 1081 y Fs(to)g(observ)m(ation)0 1141 y(p)q(oin)o(t)c Fu(x)h Fs(as)685 1229 y Fq(\034)707 1236 y Fp(;i)735 1229 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)836 1209 y Fl(0)851 1229 y Fs(\))15 b(=)943 1196 y Fq(@)s(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1101 1178 y Fl(0)1116 1196 y Fs(\))p 943 1218 192 2 v 1002 1264 a Fq(@)s(x)1059 1271 y Fp(i)1191 1229 y Fq(;)596 b Fs(\(42\))685 1367 y Fq(\034)713 1346 y Fl(0)707 1379 y Fp(;i)735 1367 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)836 1346 y Fl(0)851 1367 y Fs(\))15 b(=)943 1333 y Fq(@)s(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1101 1315 y Fl(0)1116 1333 y Fs(\))p 943 1355 V 1002 1401 a Fq(@)s(x)1059 1384 y Fl(0)1059 1415 y Fp(i)1191 1367 y Fq(;)596 b Fs(\(43\))665 1514 y Fq(\034)687 1521 y Fp(;ij)734 1514 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)835 1493 y Fl(0)849 1514 y Fs(\))15 b(=)941 1480 y Fq(@)970 1462 y Fm(2)993 1480 y Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1122 1462 y Fl(0)1136 1480 y Fs(\))p 941 1502 215 2 v 972 1548 a Fq(@)s(x)1029 1555 y Fp(i)1046 1548 y Fq(@)s(x)1103 1555 y Fp(j)1211 1514 y Fq(;)576 b Fs(\(44\))665 1661 y Fq(\034)693 1641 y Fl(0)687 1673 y Fp(;ij)734 1661 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)835 1641 y Fl(0)849 1661 y Fs(\))15 b(=)941 1627 y Fq(@)970 1609 y Fm(2)993 1627 y Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1122 1609 y Fl(0)1136 1627 y Fs(\))p 941 1650 V 972 1695 a Fq(@)s(x)1029 1702 y Fp(i)1046 1695 y Fq(@)s(x)1103 1678 y Fl(0)1103 1709 y Fp(j)1211 1661 y Fq(;)576 b Fs(\(45\))665 1815 y Fq(\034)693 1794 y Fl(00)687 1827 y Fp(;ij)734 1815 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)835 1794 y Fl(0)849 1815 y Fs(\))15 b(=)941 1781 y Fq(@)970 1763 y Fm(2)993 1781 y Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1122 1763 y Fl(0)1136 1781 y Fs(\))p 941 1803 V 972 1849 a Fq(@)s(x)1029 1832 y Fl(0)1029 1863 y Fp(i)1046 1849 y Fq(@)s(x)1103 1832 y Fl(0)1103 1863 y Fp(j)1211 1815 y Fq(:)576 b Fs(\(46\))0 1927 y(A)o(t)17 b(p)q(oin)o(t)f Fu(x)232 1909 y Fp(\013)261 1927 y Fs(,)g(w)o(e)g(denote)729 1989 y Fq(\034)757 1968 y Fp(\013)785 1989 y Fs(\()p Fu(x)p Fs(\))f(=)e Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1049 1968 y Fp(\013)1078 1989 y Fs(\))50 b Fq(;)640 b Fs(\(47\))712 2068 y Fq(\034)740 2048 y Fp(\013)p Fl(0)734 2081 y Fp(;i)779 2068 y Fs(\()p Fu(x)p Fs(\))15 b(=)f Fq(\034)943 2048 y Fl(0)937 2081 y Fp(;i)965 2068 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1066 2048 y Fp(\013)1095 2068 y Fs(\))50 b Fq(;)623 b Fs(\(48\))697 2148 y Fq(\034)725 2128 y Fp(\013)p Fl(00)719 2160 y Fp(;ij)776 2148 y Fs(\()p Fu(x)p Fs(\))14 b(=)g Fq(\034)939 2128 y Fl(00)933 2160 y Fp(;ij)980 2148 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1081 2128 y Fp(\013)1110 2148 y Fs(\))50 b Fq(:)608 b Fs(\(49\))0 2225 y(Slo)o(wness)15 b(v)o(ector)h(at)h(p)q (oin)o(t)f Fu(x)577 2207 y Fp(\013)622 2225 y Fs(p)q(oin)o(ting)g(to)o (w)o(ards)f(observ)m(ation)g(p)q(oin)o(t)i Fu(x)f Fs(is)737 2317 y Fq(p)762 2324 y Fp(i)779 2317 y Fs(\()p Fu(x)p Fs(\))f(=)e Fo(\000)p Fq(\034)981 2297 y Fp(\013)p Fl(0)975 2330 y Fp(;i)1020 2317 y Fs(\()p Fu(x)p Fs(\))51 b Fq(:)648 b Fs(\(50\))0 2410 y(The)16 b(second{order)f(T)l(a)o(ylor)g(expansion)h (of)g(tra)o(v)o(el)g(time)h Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1229 2392 y Fl(0)1243 2410 y Fs(\))17 b(at)g(p)q(oin)o(t)f Fu(x)1500 2392 y Fp(\013)1545 2410 y Fs(is)385 2502 y Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)514 2481 y Fl(0)529 2502 y Fs(\))14 b Fo(\031)g Fq(\034)643 2481 y Fp(\013)670 2502 y Fs(\()p Fu(x)p Fs(\))e(+)f Fq(\034)828 2481 y Fp(\013)p Fl(0)822 2514 y Fp(;i)867 2502 y Fs(\()p Fu(x)p Fs(\)\001)p Fq(x)1005 2481 y Fl(0)1005 2514 y Fp(i)1034 2502 y Fs(+)1090 2482 y Fm(1)p 1090 2490 20 2 v 1090 2519 a(2)1116 2502 y Fq(\034)1144 2481 y Fp(\013)p Fl(00)1138 2514 y Fp(;ij)1194 2502 y Fs(\()p Fu(x)p Fs(\)\001)p Fq(x)1332 2481 y Fl(0)1332 2514 y Fp(i)1350 2502 y Fs(\001)p Fq(x)1420 2481 y Fl(0)1420 2514 y Fp(j)1491 2502 y Fq(;)296 b Fs(\(51\))0 2594 y(or,)16 b(in)g(terms)g(of)g(the)h(slo)o(wness)e(v)o (ector,)398 2686 y Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)527 2665 y Fl(0)542 2686 y Fs(\))14 b Fo(\031)f Fq(\034)655 2665 y Fp(\013)683 2686 y Fs(\()p Fu(x)p Fs(\))f Fo(\000)f Fq(p)838 2693 y Fp(i)855 2686 y Fs(\()p Fu(x)p Fs(\)\001)p Fq(x)993 2665 y Fl(0)993 2698 y Fp(i)1021 2686 y Fs(+)1077 2666 y Fm(1)p 1077 2675 V 1077 2703 a(2)1103 2686 y Fq(\034)1131 2665 y Fp(\013)p Fl(00)1125 2698 y Fp(;ij)1182 2686 y Fs(\()p Fu(x)p Fs(\)\001)p Fq(x)1320 2665 y Fl(0)1320 2698 y Fp(i)1337 2686 y Fs(\001)p Fq(x)1407 2665 y Fl(0)1407 2698 y Fp(j)1478 2686 y Fq(:)309 b Fs(\(52\))920 2806 y(32)p eop %%Page: 33 7 33 6 bop 0 -54 a Fs(A)o(t)17 b(p)q(oin)o(t)f Fu(x)232 -72 y Fm(0)255 -54 y Fs(,)g(w)o(e)g(denote)755 11 y Fq(\034)783 -9 y Fm(0)819 11 y Fs(=)e Fq(\034)6 b Fs(\()p Fu(x)949 -9 y Fm(0)971 11 y Fq(;)i Fu(x)1023 -9 y Fp(\013)1052 11 y Fs(\))50 b Fq(;)666 b Fs(\(53\))744 97 y Fq(\034)772 76 y Fm(0)766 109 y Fp(;i)808 97 y Fs(=)13 b Fq(\034)882 104 y Fp(;i)911 97 y Fs(\()p Fu(x)960 76 y Fm(0)982 97 y Fq(;)8 b Fu(x)1034 76 y Fp(\013)1063 97 y Fs(\))50 b Fq(;)655 b Fs(\(54\))738 190 y Fq(\034)766 169 y Fm(0)p Fl(0)760 202 y Fp(;i)813 190 y Fs(=)14 b Fq(\034)894 169 y Fl(0)888 202 y Fp(;i)916 190 y Fs(\()p Fu(x)965 169 y Fm(0)988 190 y Fq(;)8 b Fu(x)1040 169 y Fp(\013)1069 190 y Fs(\))50 b Fq(;)649 b Fs(\(55\))725 282 y Fq(\034)753 262 y Fm(0)747 295 y Fp(;ij)808 282 y Fs(=)13 b Fq(\034)882 289 y Fp(;ij)929 282 y Fs(\()p Fu(x)978 262 y Fm(0)1001 282 y Fq(;)8 b Fu(x)1053 262 y Fp(\013)1082 282 y Fs(\))50 b Fq(;)636 b Fs(\(56\))725 375 y Fq(\034)753 354 y Fm(0)p Fl(0)747 387 y Fp(;ij)808 375 y Fs(=)13 b Fq(\034)888 354 y Fl(0)882 387 y Fp(;ij)929 375 y Fs(\()p Fu(x)978 354 y Fm(0)1001 375 y Fq(;)8 b Fu(x)1053 354 y Fp(\013)1082 375 y Fs(\))50 b Fq(;)636 b Fs(\(57\))723 468 y Fq(\034)751 447 y Fm(0)p Fl(00)745 480 y Fp(;ij)810 468 y Fs(=)13 b Fq(\034)890 447 y Fl(00)884 480 y Fp(;ij)931 468 y Fs(\()p Fu(x)980 447 y Fm(0)1003 468 y Fq(;)8 b Fu(x)1055 447 y Fp(\013)1084 468 y Fs(\))50 b Fq(:)634 b Fs(\(58\))0 548 y(Slo)o(wness)15 b(v)o(ector)h(at)h(p)q(oin)o(t)f Fu(x)577 530 y Fp(\013)622 548 y Fs(p)q(oin)o(ting)g(to)o(w)o(ards)f(p) q(oin)o(t)h Fu(x)1165 530 y Fm(0)1204 548 y Fs(is)707 643 y Fq(p)732 623 y Fm(0)732 656 y Fp(i)768 643 y Fs(=)d Fq(p)845 650 y Fp(i)862 643 y Fs(\()p Fu(x)911 623 y Fm(0)934 643 y Fs(\))h(=)g Fo(\000)p Fq(\034)1087 623 y Fm(0)p Fl(0)1081 656 y Fp(;i)1170 643 y Fq(:)617 b Fs(\(59\))0 738 y(The)16 b(second{order)f(T)l(a)o(ylor)g(expansion)h (of)g(tra)o(v)o(el)g(time)h(\(47\))g(at)g(p)q(oin)o(t)f Fu(x)1426 720 y Fm(0)1465 738 y Fs(is)524 834 y Fq(\034)552 813 y Fp(\013)580 834 y Fs(\()p Fu(x)p Fs(\))f Fo(\031)f Fq(\034)744 813 y Fm(0)776 834 y Fs(+)d Fq(\034)854 813 y Fm(0)848 846 y Fp(;i)876 834 y Fs(\001)p Fq(x)946 841 y Fp(i)974 834 y Fs(+)1030 814 y Fm(1)p 1030 822 20 2 v 1030 851 a(2)1056 834 y Fq(\034)1084 813 y Fm(0)1078 846 y Fp(;ij)1124 834 y Fs(\001)p Fq(x)1194 841 y Fp(i)1211 834 y Fs(\001)p Fq(x)1281 841 y Fp(j)1352 834 y Fq(;)435 b Fs(\(60\))0 929 y(where)758 994 y(\001)p Fq(x)828 1001 y Fp(i)859 994 y Fs(=)13 b Fq(x)939 1001 y Fp(i)967 994 y Fo(\000)e Fq(x)1045 974 y Fm(0)1045 1007 y Fp(i)1118 994 y Fq(:)669 b Fs(\(61\))0 1075 y(The)18 b(corresp)q(onding)e(T)l(a)o (ylor)h(expansions)g(of)h(tra)o(v)o(el)g(time)g(deriv)m(ativ)o(es)g (\(48\))h(and)e(\(49\))i(at)g(p)q(oin)o(t)0 1135 y Fu(x)30 1117 y Fm(0)69 1135 y Fs(are)671 1200 y Fq(\034)699 1179 y Fp(\013)p Fl(0)693 1212 y Fp(;i)738 1200 y Fs(\()p Fu(x)p Fs(\))c Fo(\031)f Fq(\034)902 1179 y Fm(0)p Fl(0)896 1212 y Fp(;i)946 1200 y Fs(+)d Fq(\034)1024 1179 y Fm(0)p Fl(0)1018 1212 y Fp(;j)r(i)1064 1200 y Fs(\001)p Fq(x)1134 1207 y Fp(j)1205 1200 y Fq(;)582 b Fs(\(62\))770 1293 y Fq(\034)798 1272 y Fp(\013)p Fl(00)792 1305 y Fp(;ij)848 1293 y Fs(\()p Fu(x)p Fs(\))15 b Fo(\031)f Fq(\034)1012 1272 y Fm(0)p Fl(00)1006 1305 y Fp(;ij)1106 1293 y Fq(:)681 b Fs(\(63\))0 1446 y Fu(3.4.)25 b(High{frequency)19 b(appro)n(ximation) d(of)j(spatial)h(deriv)m(ativ)n(es)0 1526 y Fs(W)l(e)d(use)f(the)h Ft(high{fr)m(e)m(quency)j(appr)m(oximation)h(of)d(sp)m(atial)i (derivatives)p Fs(,)185 1645 y Fq(u)214 1652 y Fp(i;k)264 1645 y Fs(\()p Fu(x)313 1624 y Fl(0)327 1645 y Fq(;)8 b(t)p Fs(\))15 b Fo(\031)e(\000)c Fs(_)-23 b Fq(u)521 1652 y Fp(i)537 1645 y Fs(\()p Fu(x)586 1624 y Fl(0)601 1645 y Fq(;)8 b(t)p Fs(\))14 b Fq(P)706 1652 y Fp(k)780 1645 y Fq(;)908 1611 y(@)s(G)976 1618 y Fp(ij)p 908 1633 104 2 v 919 1679 a Fq(@)s(x)976 1662 y Fl(0)976 1694 y Fp(k)1018 1645 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1119 1624 y Fl(0)1133 1645 y Fq(;)g(t)p Fs(\))15 b Fo(\031)1276 1632 y Fs(_)1259 1645 y Fq(G)1298 1652 y Fp(ij)1334 1645 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1435 1624 y Fl(0)1450 1645 y Fq(;)g(t)p Fs(\))14 b Fq(p)1548 1652 y Fp(k)1573 1645 y Fs(\()p Fu(x)p Fs(\))50 b Fq(;)96 b Fs(\(64\))0 1769 y(and)58 1891 y Fn(b)-30 b Fq(u)85 1898 y Fp(i;k)135 1891 y Fs(\()p Fu(x)184 1870 y Fl(0)199 1891 y Fq(;)8 b(!)r Fs(\))14 b Fo(\031)f Fs(i)p Fq(!)f Fn(b)-30 b Fq(u)423 1898 y Fp(i)439 1891 y Fs(\()p Fu(x)488 1870 y Fl(0)503 1891 y Fq(;)8 b(!)r Fs(\))14 b Fq(P)623 1898 y Fp(k)697 1891 y Fq(;)825 1857 y(@)864 1845 y Fn(b)854 1857 y Fq(G)893 1864 y Fp(ij)p 825 1880 V 836 1925 a Fq(@)s(x)893 1908 y Fl(0)893 1940 y Fp(k)935 1891 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1036 1870 y Fl(0)1050 1891 y Fq(;)g(!)r Fs(\))15 b Fo(\031)e(\000)p Fs(i)p Fq(!)1295 1878 y Fn(b)1285 1891 y Fq(G)1324 1898 y Fp(ij)1359 1891 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1460 1870 y Fl(0)1475 1891 y Fq(;)g(!)r Fs(\))14 b Fq(p)1588 1898 y Fp(k)1613 1891 y Fs(\()p Fu(x)p Fs(\))51 b Fq(;)k Fs(\(65\))0 2018 y(where)16 b Fq(P)176 2025 y Fp(i)209 2018 y Fs(de\014ned)f(b)o(y)h(\(39\))h(is)f (the)g(slo)o(wness)f(v)o(ector)h(of)g(the)h(inciden)o(t)e(w)o(a)o(v)o (e,)h(and)f Fq(p)1625 2025 y Fp(k)1650 2018 y Fs(\()p Fu(x)p Fs(\))i(de\014ned)0 2078 y(b)o(y)f(\(50\))h(is)f(the)h(slo)o (wness)e(v)o(ector)i(determining)d(the)j(ra)o(y)f(leading)g(from)f(p)q (oin)o(t)i Fu(x)1557 2060 y Fp(\013)1602 2078 y Fs(to)g(p)q(oin)o(t)f Fu(x)p Fs(.)920 2806 y(33)p eop %%Page: 34 8 34 7 bop 0 -54 a Fu(4.)25 b(Scattering)20 b(in)g(the)f(frequency)h(dom) o(ain)c(|)k(Gaussian)e(b)r(eams)0 20 y Fs(A)d Ft(br)m(o)m(ad{b)m(a)q (nd)k(incident)e(wave\014eld)e Fs(\(20\))g(ha)o(ving)f(a)h Ft(smo)m(oth)i(fr)m(e)m(quency)g(sp)m(e)m(ctrum)f Fs(is)e(considered,)0 79 y(with)h(a)f(frequency)h(band)f(limited)g(b)o(y)h(the)g(minim)o(um)d (frequency)i(and)h(the)g(maxim)o(um)d(frequency)l(.)0 195 y Fu(4.1.)25 b(Born)17 b(appro)n(ximation)g(with)k(paraxial)f(ra)n (y)f(appro)n(ximation)d(at)k(p)r(oin)n(t)f(x)1720 177 y Fp(\013)0 268 y Fs(Inserting)11 b(appro)o(ximations)e(\(20\){\(29\))j (and)f(\(65\))i(in)o(to)e(the)h(Born)f(appro)o(ximation)f(\(19\),)j(w)o (e)e(arriv)o(e)0 328 y(at)222 416 y Fn(b)-30 b Fq(u)249 396 y Fp(\013)249 429 y(i)277 416 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)474 383 y Fq(!)507 365 y Fm(2)p 474 405 56 2 v 474 450 a Fs(2)p Fq(\031)541 382 y(e)564 389 y Fp(i)581 382 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)682 364 y Fp(\013)711 382 y Fs(\))14 b Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)883 364 y Fp(\013)913 382 y Fs(\))958 369 y Fn(b)946 382 y Fq(A)p Fs(\()p Fu(x)1032 364 y Fp(\013)1061 382 y Fq(;)g(!)r Fs(\))1149 339 y Fn(p)p 1199 339 124 2 v 43 x Fq(\045)p Fs(\()p Fu(x)1274 367 y Fp(\013)1303 382 y Fs(\))p 541 405 782 2 v 658 415 a Fn(p)p 708 415 313 2 v 42 x Fq(\045)p Fs(\()p Fu(x)p Fs(\))p Fq(v)r Fs(\()p Fu(x)p Fs(\))p Fq(v)r Fs(\()p Fu(x)971 443 y Fp(\013)1002 457 y Fs(\))p Fq(L)p Fs(\()p Fu(x)p Fq(;)g Fu(x)1156 443 y Fp(\013)1185 457 y Fs(\))1345 416 y Fq(r)1368 396 y Fp(\013)1397 416 y Fs(\()p Fu(x)p Fs(\))18 b Fq(I)1509 396 y Fp(\013)1537 416 y Fs(\()p Fu(x)p Fs(\))51 b Fq(;)131 b Fs(\(66\))0 526 y(where)16 b(in)o(tegral)438 609 y Fq(I)464 588 y Fp(\013)493 609 y Fs(\()p Fu(x)p Fs(\))e(=)620 541 y Fn(Z)658 609 y Fs(d)p Fu(x)716 588 y Fl(0)730 609 y Fq(g)756 588 y Fp(\013)784 609 y Fs(\()p Fu(x)833 588 y Fl(0)848 609 y Fs(\))j(exp)p Fo(f)p Fs(i)p Fq(!)r Fs([)p Fq(T)7 b Fs(\()p Fu(x)1131 588 y Fl(0)1145 609 y Fs(\))k(+)g Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)1354 588 y Fl(0)1369 609 y Fs(\)])399 b(\(67\))0 708 y(accoun)o(ts)16 b(for)g(the)h (directional)e(prop)q(erties)h(of)g(scattered)h(time{harmonic)d(w)o(a)o (v)o(e)k Fn(b)-30 b Fq(u)1608 690 y Fp(\013)1608 721 y(i)1636 708 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\).)100 768 y(Here)16 b Fq(r)240 749 y Fp(\013)270 768 y Fs(\()p Fu(x)p Fs(\))h(is)f(the)h(\\re\015ectivit)o(y)g(function",)p 0 811 1890 2 v 0 971 2 160 v 260 906 a Fq(r)283 885 y Fp(\013)312 906 y Fs(\()p Fu(x)p Fs(\))e(=)453 866 y Fq(\045)479 848 y Fp(\013)507 866 y Fq(E)544 873 y Fp(m)582 866 y Fs(\()p Fu(x)631 848 y Fp(\013)660 866 y Fs(\))p Fq(e)702 873 y Fp(m)740 866 y Fs(\()p Fu(x)789 848 y Fp(\013)818 866 y Fq(;)8 b Fu(x)p Fs(\))k Fo(\000)f Fq(c)973 848 y Fp(\013)973 880 y(ij)r(k)q(l)1042 866 y Fq(E)1079 873 y Fp(i)1096 866 y Fs(\()p Fu(x)1145 848 y Fp(\013)1174 866 y Fs(\))p Fq(P)1225 873 y Fp(j)1246 866 y Fq(e)1269 873 y Fp(k)1294 866 y Fs(\()p Fu(x)1343 848 y Fp(\013)1372 866 y Fq(;)d Fu(x)p Fs(\))p Fq(p)1468 873 y Fp(l)1484 866 y Fs(\()p Fu(x)p Fs(\))p 453 894 1100 2 v 921 940 a(2)16 b Fq(\045)p Fs(\()p Fu(x)1037 926 y Fp(\013)1066 940 y Fs(\))1609 906 y Fq(;)169 b Fs(\(68\))p 1888 971 2 160 v 0 973 1890 2 v 0 1038 a(where)12 b Fq(P)172 1045 y Fp(i)201 1038 y Fs(and)g Fq(E)331 1045 y Fp(i)359 1038 y Fs(are)h(the)f(slo)o(wness)f(v)o(ector)h(and)g(the)h(p)q(olarization) e(v)o(ector)h(of)h(the)g(inciden)o(t)e(w)o(a)o(v)o(e,)0 1097 y Fq(p)25 1104 y Fp(i)60 1097 y Fs(and)18 b Fq(e)182 1104 y Fp(i)218 1097 y Fs(are)g(the)h(slo)o(wness)e(v)o(ector)h(and)g (the)h(p)q(olarization)f(v)o(ector)h(of)f(the)h(w)o(a)o(v)o(e)f (scattered)h(at)0 1157 y(p)q(oin)o(t)k Fu(x)167 1139 y Fp(\013)219 1157 y Fs(and)g(propagating)e(to)o(w)o(ards)h(p)q(oin)o (t)h Fu(x)p Fs(.)42 b(Densit)o(y)23 b Fq(\045)i Fs(=)g Fq(\045)p Fs(\()p Fu(x)1401 1139 y Fp(\013)1430 1157 y Fs(\))f(corresp)q(onds)d(to)j(the)0 1217 y(bac)o(kground.)100 1276 y(W)l(e)16 b(no)o(w)g(in)o(tro)q(duce)g(tra)o(v)o(el)g(time)636 1363 y Fq(\022)q Fs(\()p Fu(x)p Fq(;)8 b Fu(x)761 1343 y Fl(0)776 1363 y Fs(\))14 b(=)g Fq(\034)6 b Fs(\()p Fu(x)p Fq(;)i Fu(x)991 1343 y Fl(0)1005 1363 y Fs(\))k(+)f Fq(T)c Fs(\()p Fu(x)1171 1343 y Fl(0)1185 1363 y Fs(\))597 b(\(69\))0 1450 y(through)15 b(p)q(oin)o(t)h Fu(x)348 1432 y Fl(0)379 1450 y Fs(to)h(observ)m(ation)f(p)q(oin)o(t)g Fu(x)p Fs(,)h(and)e(its)i(second{order)d(T)l(a)o(ylor)i(expansion)391 1536 y Fq(\022)q Fs(\()p Fu(x)p Fq(;)8 b Fu(x)516 1516 y Fl(0)531 1536 y Fs(\))15 b Fo(\031)e Fq(\022)641 1516 y Fp(\013)670 1536 y Fs(\()p Fu(x)p Fs(\))f(+)f Fq(\022)824 1516 y Fp(\013)p Fl(0)823 1549 y Fp(;i)865 1536 y Fs(\()p Fu(x)p Fs(\)\001)p Fq(x)1003 1516 y Fl(0)1003 1549 y Fp(i)1031 1536 y Fs(+)1087 1517 y Fm(1)p 1087 1525 20 2 v 1087 1554 a(2)1113 1536 y Fq(\022)1137 1516 y Fp(\013)p Fl(00)1136 1549 y Fp(;ij)1189 1536 y Fs(\()p Fu(x)p Fs(\)\001)p Fq(x)1327 1516 y Fl(0)1327 1549 y Fp(i)1345 1536 y Fs(\001)p Fq(x)1415 1516 y Fl(0)1415 1549 y Fp(j)1486 1536 y Fq(;)301 b Fs(\(70\))0 1623 y(where)694 1683 y Fq(\022)718 1662 y Fp(\013)747 1683 y Fs(\()p Fu(x)p Fs(\))15 b(=)e Fq(T)918 1662 y Fp(\013)958 1683 y Fs(+)e Fq(\034)1036 1662 y Fp(\013)1064 1683 y Fs(\()p Fu(x)p Fs(\))50 b Fq(;)605 b Fs(\(71\))682 1756 y Fq(\022)706 1736 y Fp(\013)p Fl(0)705 1769 y Fp(;i)747 1756 y Fs(\()p Fu(x)p Fs(\))15 b(=)e Fq(T)918 1736 y Fp(\013)911 1769 y(;i)958 1756 y Fs(+)e Fq(\034)1036 1736 y Fp(\013)p Fl(0)1030 1769 y Fp(;i)1075 1756 y Fs(\()p Fu(x)p Fs(\))51 b Fq(;)593 b Fs(\(72\))665 1830 y Fq(\022)689 1810 y Fp(\013)p Fl(00)688 1842 y Fp(;ij)741 1830 y Fs(\()p Fu(x)p Fs(\))15 b(=)f Fq(T)913 1810 y Fp(\013)906 1842 y(;ij)964 1830 y Fs(+)d Fq(\034)1042 1810 y Fp(\013)p Fl(00)1036 1842 y Fp(;ij)1092 1830 y Fs(\()p Fu(x)p Fs(\))51 b Fq(;)576 b Fs(\(73\))0 1904 y(see)17 b(\(36\){\(38\))g(and)f(\(47\){\(49\).)23 b(Equation)16 b(\(72\))h(ma)o(y)f(also)g(b)q(e)h(expressed)e(in)i(form)703 1990 y Fq(\022)727 1970 y Fp(\013)p Fl(0)726 2003 y Fp(;i)768 1990 y Fs(\()p Fu(x)p Fs(\))e(=)e Fq(P)935 1997 y Fp(i)963 1990 y Fo(\000)e Fq(p)1038 1997 y Fp(i)1054 1990 y Fs(\()p Fu(x)p Fs(\))51 b Fq(;)614 b Fs(\(74\))0 2077 y(see)17 b(equations)f(\(39\))h(and)f(\(50\).)100 2137 y(In)o(tegral)f(\(67\))i (with)g(\(4\))g(and)f(\(70\))h(reads)51 2249 y Fq(I)77 2228 y Fp(\013)119 2249 y Fo(\031)164 2181 y Fn(Z)202 2249 y Fs(d\001)p Fu(x)302 2228 y Fl(0)324 2249 y Fs(exp)408 2209 y Fn(\002)429 2249 y Fs(i)p Fq(k)471 2228 y Fp(\013)469 2261 y(i)507 2249 y Fs(\001)p Fq(x)577 2228 y Fl(0)577 2261 y Fp(i)605 2249 y Fo(\000)660 2229 y Fm(1)p 660 2238 V 660 2266 a(2)686 2249 y Fq(K)732 2228 y Fp(\013)728 2261 y(ij)764 2249 y Fs(\001)p Fq(x)834 2228 y Fl(0)834 2261 y Fp(i)850 2249 y Fs(\001)p Fq(x)920 2228 y Fl(0)920 2261 y Fp(j)952 2249 y Fs(+)11 b(i)p Fq(!)r Fs(\()p Fq(\022)1092 2228 y Fp(\013)1132 2249 y Fs(+)g Fq(\022)1206 2228 y Fp(\013)p Fl(0)1205 2261 y Fp(;i)1247 2249 y Fs(\001)p Fq(x)1317 2228 y Fl(0)1317 2261 y Fp(i)1344 2249 y Fs(+)1400 2229 y Fm(1)p 1400 2238 V 1400 2266 a(2)1426 2249 y Fq(\022)1450 2228 y Fp(\013)p Fl(00)1449 2261 y Fp(;ij)1502 2249 y Fs(\001)p Fq(x)1572 2228 y Fl(0)1572 2261 y Fp(i)1589 2249 y Fs(\001)p Fq(x)1659 2228 y Fl(0)1659 2261 y Fp(j)1680 2249 y Fs(\))1699 2209 y Fn(\003)1736 2249 y Fq(:)51 b Fs(\(75\))0 2359 y(W)l(e)17 b(rearrange)e(the)h(exp)q(onen)o(t)h(of)g (the)f(in)o(tegrand,)110 2468 y Fq(I)136 2447 y Fp(\013)178 2468 y Fo(\031)223 2400 y Fn(Z)261 2468 y Fs(d\001)p Fu(x)361 2447 y Fl(0)382 2468 y Fs(exp)458 2413 y Fn(n)492 2468 y Fs(i)p Fq(!)r(\022)563 2447 y Fp(\013)603 2468 y Fo(\000)658 2448 y Fm(1)p 658 2457 V 658 2485 a(2)684 2468 y Fs(\()p Fq(K)749 2447 y Fp(\013)745 2480 y(ij)792 2468 y Fo(\000)11 b Fs(i)p Fq(!)r(\022)913 2447 y Fp(\013)p Fl(00)912 2480 y Fp(;ij)965 2468 y Fs(\)[\001)p Fq(x)1068 2447 y Fl(0)1068 2480 y Fp(i)1095 2468 y Fo(\000)g Fs(i\()p Fq(K)1224 2447 y Fp(\013)1264 2468 y Fo(\000)g Fs(i)p Fq(!)r(\022)1385 2447 y Fp(\013)p Fl(00)1436 2468 y Fs(\))1455 2447 y Fl(\000)p Fm(1)1455 2483 y Fp(ik)1509 2468 y Fs(\()p Fq(k)1556 2447 y Fp(\013)1554 2480 y(k)1596 2468 y Fs(+)f Fq(!)r(\022)1702 2447 y Fp(\013)p Fl(0)1701 2480 y Fp(;k)1743 2468 y Fs(\)])945 2575 y Fo(\002)p Fs([\001)p Fq(x)1068 2554 y Fl(0)1068 2587 y Fp(j)1100 2575 y Fo(\000)h Fs(i\()p Fq(K)1229 2554 y Fp(\013)1268 2575 y Fo(\000)g Fs(i)p Fq(!)r(\022)1389 2554 y Fp(\013)p Fl(00)1441 2575 y Fs(\))1460 2553 y Fl(\000)p Fm(1)1460 2590 y Fp(j)r(l)1514 2575 y Fs(\()p Fq(k)1561 2554 y Fp(\013)1559 2587 y(l)1600 2575 y Fs(+)g Fq(!)r(\022)1707 2554 y Fp(\013)p Fl(0)1706 2587 y Fp(;l)1747 2575 y Fs(\)])563 2674 y Fo(\000)608 2654 y Fm(1)p 608 2662 V 608 2691 a(2)634 2674 y Fs(\()p Fq(K)699 2653 y Fp(\013)739 2674 y Fo(\000)f Fs(i)p Fq(!)r(\022)859 2653 y Fp(\013)p Fl(00)911 2674 y Fs(\))930 2652 y Fl(\000)p Fm(1)930 2687 y Fp(ij)984 2674 y Fs([)p Fq(k)1026 2653 y Fp(\013)1024 2686 y(i)1065 2674 y Fs(+)h Fq(!)r(\022)1172 2653 y Fp(\013)p Fl(0)1171 2686 y Fp(;i)1212 2674 y Fs(][)p Fq(k)1268 2653 y Fp(\013)1266 2686 y(j)1307 2674 y Fs(+)f Fq(!)r(\022)1413 2653 y Fp(\013)p Fl(0)1412 2686 y Fp(;j)1454 2674 y Fs(])1468 2618 y Fn(o)1551 2674 y Fq(;)236 b Fs(\(76\))920 2806 y(34)p eop %%Page: 35 9 35 8 bop 0 -54 a Fs(where)14 b(\()p Fq(K)207 -72 y Fp(\013)243 -54 y Fo(\000)7 b Fs(i)p Fq(!)r(\022)360 -72 y Fp(\013)p Fl(00)412 -54 y Fs(\))431 -75 y Fl(\000)p Fm(1)431 -40 y Fp(ij)500 -54 y Fs(stands)14 b(for)g(the)h(comp)q(onen)o(ts)f(of)h (the)g(matrix)f(in)o(v)o(erse)f(to)i(matrix)f Fq(K)1812 -72 y Fp(\013)1808 -41 y(ij)1851 -54 y Fo(\000)0 6 y Fs(i)p Fq(!)r(\022)71 -13 y Fp(\013)p Fl(00)70 19 y Fp(;ij)123 6 y Fs(.)22 b(W)l(e)17 b(no)o(w)e(in)o(tegrate)h(\(76\))i(and)d(arriv)o (e)h(at)25 147 y Fq(I)51 126 y Fp(\013)93 147 y Fo(\031)146 61 y Fn(s)p 195 61 381 2 v 328 113 a Fs(\(2)p Fq(\031)r Fs(\))421 99 y Fm(3)p 201 135 369 2 v 201 181 a Fs(det\()p Fq(K)335 164 y Fp(\013)331 195 y(ij)378 181 y Fo(\000)11 b Fs(i)p Fq(!)r(\022)499 164 y Fp(\013)p Fl(00)498 195 y Fp(;ij)551 181 y Fs(\))600 147 y(exp)676 91 y Fn(n)709 147 y Fs(i)p Fq(!)r(\022)780 126 y Fp(\013)817 147 y Fo(\000)870 127 y Fm(1)p 870 135 20 2 v 870 164 a(2)896 147 y Fs(\()p Fq(K)961 126 y Fp(\013)998 147 y Fo(\000)d Fs(i)p Fq(!)r(\022)1116 126 y Fp(\013)p Fl(00)1168 147 y Fs(\))1187 125 y Fl(\000)p Fm(1)1187 161 y Fp(ij)1241 147 y Fs([)p Fq(k)1283 126 y Fp(\013)1281 159 y(i)1319 147 y Fs(+)g Fq(!)r(\022)1423 126 y Fp(\013)p Fl(0)1422 159 y Fp(;i)1464 147 y Fs(][)p Fq(k)1520 126 y Fp(\013)1518 159 y(j)1556 147 y Fs(+)g Fq(!)r(\022)1660 126 y Fp(\013)p Fl(0)1659 159 y Fp(;j)1700 147 y Fs(])1714 91 y Fn(o)1763 147 y Fq(:)24 b Fs(\(77\))0 275 y(In)13 b(this)g(pap)q(er,)g(the)g (square)g(ro)q(ot)g(of)h(the)f(determinan)o(t)f(of)i(a)f(symmetric)f (complex{v)m(alued)h(matrix)0 335 y(is)i(de\014ned)g(as)g(the)h(pro)q (duct)f(of)h(the)g(square)f(ro)q(ots)h(of)g(its)f(eigen)o(v)m(alues.)21 b(The)16 b(square)f(ro)q(ot)h(of)g(eac)o(h)0 395 y(eigen)o(v)m(alue)g (is)g(tak)o(en)h(with)f(the)h(p)q(ositiv)o(e)f(real)g(part.)100 454 y(Insertion)f(of)i(\(77\))g(in)o(to)f(\(66\))h(yields)p 0 498 1890 2 v 0 601 2 103 v 460 570 a Fn(b)-29 b Fq(u)488 549 y Fp(\013)488 582 y(i)516 570 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))14 b(=)g Fq(e)729 577 y Fp(i)746 570 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)847 549 y Fp(\013)876 570 y Fs(\))14 b Fn(b)-28 b Fq(a)q Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))17 b(exp[i)p Fq(!)r(T)1249 549 y Fp(\013)1242 582 y(!)1277 570 y Fs(\()p Fu(x)p Fs(\)])51 b Fq(;)368 b Fs(\(78\))p 1888 601 V 0 603 1890 2 v 0 667 a(where)96 793 y Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)f Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)453 772 y Fp(\013)482 793 y Fs(\))509 703 y Fn(s)p 560 703 251 2 v 558 759 a Fq(\045)p Fs(\()p Fu(x)633 745 y Fp(\013)661 759 y Fs(\))p Fq(v)r Fs(\()p Fu(x)755 745 y Fp(\013)785 759 y Fs(\))p 558 781 247 2 v 586 827 a Fq(\045)p Fs(\()p Fu(x)p Fs(\))p Fq(v)r Fs(\()p Fu(x)p Fs(\))832 759 y Fq(!)865 741 y Fm(2)899 746 y Fn(b)888 759 y Fq(A)p Fs(\()p Fu(x)974 741 y Fp(\013)1003 759 y Fq(;)g(!)r Fs(\))14 b Fq(r)1114 741 y Fp(\013)1143 759 y Fs(\()p Fu(x)p Fs(\))p 824 781 389 2 v 865 827 a Fq(v)r Fs(\()p Fu(x)940 812 y Fp(\013)969 827 y Fs(\))p Fq(L)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1123 812 y Fp(\013)1152 827 y Fs(\))1385 718 y Fo(p)p 1427 718 56 2 v 41 x Fs(2)p Fq(\031)p 1233 781 403 2 v 1233 791 a Fn(q)p 1282 791 353 2 v 1282 845 a Fs(det)q(\()p Fq(K)1417 827 y Fp(\013)1413 859 y(ij)1451 845 y Fo(\000)s Fs(i)p Fq(!)r(\022)1564 827 y Fp(\013)p Fl(00)1563 859 y Fp(;ij)1615 845 y Fs(\))1691 793 y Fq(;)96 b Fs(\(79\))0 945 y(and)100 1032 y(i)p Fq(!)r(T)183 1011 y Fp(\013)176 1044 y(!)211 1032 y Fs(\()p Fu(x)p Fs(\))15 b(=)f(i)p Fq(!)r(\022)418 1011 y Fp(\013)446 1032 y Fs(\()p Fu(x)p Fs(\))e Fo(\000)582 1012 y Fm(1)p 582 1021 20 2 v 582 1049 a(2)608 1032 y Fs([)p Fq(K)668 1011 y Fp(\013)707 1032 y Fo(\000)f Fs(i)p Fq(!)r(\022)828 1011 y Fp(\013)p Fl(00)880 1032 y Fs(\()p Fu(x)p Fs(\)])962 1011 y Fl(\000)p Fm(1)962 1046 y Fp(ij)1016 1032 y Fs([)p Fq(k)1058 1011 y Fp(\013)1056 1044 y(i)1097 1032 y Fs(+)g Fq(!)r(\022)1204 1011 y Fp(\013)p Fl(0)1203 1044 y Fp(;i)1244 1032 y Fs(\()p Fu(x)p Fs(\)][)p Fq(k)1368 1011 y Fp(\013)1366 1044 y(j)1408 1032 y Fs(+)f Fq(!)r(\022)1514 1011 y Fp(\013)p Fl(0)1513 1044 y Fp(;j)1555 1032 y Fs(\()p Fu(x)p Fs(\)])51 b Fq(:)99 b Fs(\(80\))0 1119 y(F)l(or)22 b(giv)o(en)h(frequency)h Fq(!)h Fs(and)e(giv)o(en)g(slo)o(wness)f(v)o(ector)h Fq(p)1150 1126 y Fp(i)1167 1119 y Fs(\()p Fu(x)p Fs(\),)j(Gab)q(or)d (function)g Fq(g)1664 1101 y Fp(\013)1692 1119 y Fs(\()p Fu(x)1741 1101 y Fl(0)1756 1119 y Fs(\))h(con-)0 1178 y(cen)o(trated)c(at)h(p)q(oin)o(t)e Fu(x)452 1160 y Fp(\013)501 1178 y Fs(in\015uence)h(the)g(seismogram)e(for)i(structural)f(w)o(a)o (v)o(en)o(um)o(b)q(ers)e(from)j(the)0 1238 y(vicinit)o(y)c(of)h(the)g (\\w)o(a)o(v)o(en)o(um)o(b)q(er)c(surface")j(parametrized)f(b)o(y)h Fq(p)1221 1245 y Fp(i)1238 1238 y Fs(\()p Fu(x)p Fs(\))i(and)d (de\014ned)h(b)o(y)g(equation)572 1325 y Fq(k)600 1304 y Fp(\013)598 1337 y(i)642 1325 y Fs(=)d Fo(\000)p Fq(!)r(\022)790 1304 y Fp(\013)p Fl(0)789 1337 y Fp(;i)830 1325 y Fs(\()p Fu(x)p Fs(\))i(=)f Fq(!)c Fs([)p Fq(p)1046 1332 y Fp(i)1062 1325 y Fs(\()p Fu(x)p Fs(\))i Fo(\000)f Fq(P)1224 1332 y Fp(i)1241 1325 y Fs(])49 b Fq(:)483 b Fs(\(81\))0 1411 y(F)l(or)15 b(illustration,)g(refer)h(to)h(transform)e(\(209\))i(and)f (to)h(Figures)e(4,)h(5)h(and)e(6.)0 1527 y Fu(4.2.)25 b(P)n(araxial)20 b(ra)n(y)g(appro)n(xima)o(tion)d(at)i(p)r(oin)n(t)h(x) 1070 1509 y Fm(0)0 1600 y Fs(Inserting)c(T)l(a)o(ylor)g(expansions)g (\(60\),)h(\(62\))h(and)f(\(63\))g(in)o(to)g(de\014nitions)f(\(71\),)h (\(72\))h(and)f(\(73\),)g(w)o(e)0 1660 y(obtain)f(T)l(a)o(ylor)f (expansions)463 1747 y Fq(\022)487 1726 y Fp(\013)516 1747 y Fs(\()p Fu(x)p Fs(\))g(=)f Fq(T)688 1726 y Fp(\013)727 1747 y Fs(+)d Fq(\034)805 1726 y Fm(0)838 1747 y Fs(+)g Fq(\034)916 1726 y Fm(0)910 1759 y Fp(;i)938 1747 y Fs(\001)p Fq(x)1008 1754 y Fp(i)1035 1747 y Fs(+)1091 1727 y Fm(1)p 1091 1735 V 1091 1764 a(2)1117 1747 y Fq(\034)1145 1726 y Fm(0)1139 1759 y Fp(;ij)1186 1747 y Fs(\001)p Fq(x)1256 1754 y Fp(i)1272 1747 y Fs(\001)p Fq(x)1342 1754 y Fp(j)1413 1747 y Fq(;)374 b Fs(\(82\))610 1841 y Fq(\022)634 1820 y Fp(\013)p Fl(0)633 1853 y Fp(;i)674 1841 y Fs(\()p Fu(x)p Fs(\))15 b(=)f Fq(T)846 1820 y Fp(\013)839 1853 y(;i)885 1841 y Fs(+)d Fq(\034)963 1820 y Fm(0)p Fl(0)957 1853 y Fp(;i)1007 1841 y Fs(+)g Fq(\034)1085 1820 y Fm(0)p Fl(0)1079 1853 y Fp(;j)r(i)1126 1841 y Fs(\001)p Fq(x)1196 1848 y Fp(j)1267 1841 y Fq(;)520 b Fs(\(83\))772 1922 y Fq(\022)796 1901 y Fp(\013)p Fl(00)795 1934 y Fp(;ij)848 1922 y Fs(\()p Fu(x)p Fs(\))15 b(=)f Fq(\022)1008 1901 y Fm(0)p Fl(00)1007 1934 y Fp(;ij)1104 1922 y Fq(;)683 b Fs(\(84\))0 1995 y(where)740 2055 y Fq(\022)764 2034 y Fm(0)p Fl(00)763 2067 y Fp(;ij)824 2055 y Fs(=)14 b Fq(T)913 2034 y Fp(\013)906 2067 y(;ij)964 2055 y Fs(+)d Fq(\034)1042 2034 y Fm(0)p Fl(00)1036 2067 y Fp(;ij)1136 2055 y Fq(:)651 b Fs(\(85\))0 2129 y(The)16 b(T)l(a)o(ylor)g(expansion) f(of)i(\(80\))g(in)f(the)h(vicinit)o(y)g(of)f(p)q(oin)o(t)g Fu(x)1191 2111 y Fm(0)1231 2129 y Fs(then)g(reads)429 2215 y(i)p Fq(!)r(T)512 2195 y Fp(\013)505 2228 y(!)540 2215 y Fs(\()p Fu(x)p Fs(\))f(=)e(i)p Fq(!)r Fs([)p Fq(T)772 2195 y Fp(\013)811 2215 y Fs(+)e Fq(\034)889 2195 y Fm(0)922 2215 y Fs(+)g Fq(\034)1000 2195 y Fm(0)994 2228 y Fp(;i)1022 2215 y Fs(\001)p Fq(x)1092 2222 y Fp(i)1119 2215 y Fs(+)1175 2196 y Fm(1)p 1175 2204 V 1175 2232 a(2)1201 2215 y Fq(\034)1229 2195 y Fm(0)1223 2228 y Fp(;ij)1270 2215 y Fs(\001)p Fq(x)1340 2222 y Fp(i)1356 2215 y Fs(\001)p Fq(x)1426 2222 y Fp(j)1447 2215 y Fs(])30 2310 y Fo(\000)75 2290 y Fm(1)p 75 2299 V 75 2327 a(2)100 2310 y Fs(\()p Fq(K)165 2290 y Fp(\013)205 2310 y Fo(\000)g Fs(i)p Fq(!)r(\022)326 2290 y Fm(0)p Fl(00)372 2310 y Fs(\))391 2289 y Fl(\000)p Fm(1)391 2324 y Fp(ij)445 2310 y Fs([)p Fq(k)487 2290 y Fp(\013)485 2322 y(i)525 2310 y Fs(+)g Fq(!)r Fs(\()p Fq(T)663 2290 y Fp(\013)656 2322 y(;i)703 2310 y Fs(+)g Fq(\034)781 2290 y Fm(0)p Fl(0)775 2322 y Fp(;i)825 2310 y Fs(+)g Fq(\034)903 2290 y Fm(0)p Fl(0)897 2322 y Fp(;mi)960 2310 y Fs(\001)p Fq(x)1030 2317 y Fp(m)1068 2310 y Fs(\)][)p Fq(k)1143 2290 y Fp(\013)1141 2322 y(j)1182 2310 y Fs(+)g Fq(!)r Fs(\()p Fq(T)1320 2290 y Fp(\013)1313 2322 y(;j)1360 2310 y Fs(+)f Fq(\034)1437 2290 y Fm(0)p Fl(0)1431 2322 y Fp(;j)1482 2310 y Fs(+)h Fq(\034)1560 2290 y Fm(0)p Fl(0)1554 2322 y Fp(;nj)1611 2310 y Fs(\001)p Fq(x)1681 2317 y Fp(n)1708 2310 y Fs(\)])17 b Fq(:)29 b Fs(\(86\))0 2393 y(Since)11 b(the)h(real)e(part)h(of)h(matrix)f(\()p Fq(K)674 2375 y Fp(\013)703 2393 y Fo(\000)q Fs(i)p Fq(!)r(\022)814 2375 y Fm(0)p Fl(00)860 2393 y Fs(\))879 2372 y Fl(\000)p Fm(1)879 2407 y Fp(ij)944 2393 y Fs(is)g(p)q(ositiv)o(e{de\014nite,)g (the)h(maxim)o(um)d(scattering)0 2453 y(\(extreme)17 b(of)g(real)f(part)g(of)h(i)p Fq(!)r(T)611 2435 y Fp(\013)604 2465 y(!)639 2453 y Fs(\()p Fu(x)p Fs(\)\))h(at)e(the)h(axial)g(ra)o(y) f(\001)p Fq(x)d Fs(=)h(0)i(o)q(ccurs)h(if)676 2540 y Fq(k)704 2519 y Fp(\013)702 2552 y(i)743 2540 y Fs(+)11 b Fq(!)f Fs(\()p Fq(T)889 2519 y Fp(\013)882 2552 y(;i)929 2540 y Fs(+)g Fq(\034)1006 2519 y Fm(0)p Fl(0)1000 2552 y Fp(;i)1040 2540 y Fs(\))k(=)g(0)49 b Fq(;)587 b Fs(\(87\))0 2626 y(i.e.,)16 b(if)730 2686 y Fq(p)755 2665 y Fm(0)755 2698 y Fp(i)792 2686 y Fs(=)d Fq(P)876 2693 y Fp(i)904 2686 y Fs(+)e Fq(!)987 2665 y Fl(\000)p Fm(1)1040 2686 y Fq(k)1068 2665 y Fp(\013)1066 2698 y(i)1146 2686 y Fq(;)641 b Fs(\(88\))920 2806 y(35)p eop %%Page: 36 10 36 9 bop 0 -54 a Fs(see)23 b(equations)g(\(39\))h(and)e(\(59\).)42 b(Inserting)22 b(\(88\))i(in)o(to)f(existence)g(condition)f(\()1580 -67 y(\024)1574 -54 y(Cerv)o(en)q(\023)-26 b(y)24 b(2001,)0 6 y(eq.)17 b(2.2.36\))555 69 y(det[)p Fq(c)660 76 y Fp(ij)r(k)q(l)729 69 y Fs(\()p Fu(x)778 49 y Fp(\013)807 69 y Fs(\))p Fq(p)851 49 y Fm(0)851 81 y Fp(j)874 69 y Fq(p)899 49 y Fm(0)899 81 y Fp(l)933 69 y Fo(\000)10 b Fq(\045)p Fs(\()p Fu(x)1057 49 y Fp(\013)1086 69 y Fs(\))p Fq(\016)1127 76 y Fp(ik)1166 69 y Fs(])k(=)g(0)49 b Fq(;)466 b Fs(\(89\))0 147 y(w)o(e)16 b(obtain)g(the)h(sixth{order)e(p)q(olynomial)h(equation)258 240 y(det)q Fo(f)p Fq(c)375 247 y Fp(ij)r(k)q(l)444 240 y Fs(\()p Fu(x)493 220 y Fp(\013)522 240 y Fs(\)[)p Fq(P)587 247 y Fp(i)615 240 y Fs(+)11 b(\()p Fq(!)717 220 y Fm(0)739 240 y Fs(\))758 220 y Fl(\000)p Fm(1)812 240 y Fq(k)840 220 y Fp(\013)838 253 y(i)868 240 y Fs(][)p Fq(P)928 247 y Fp(l)954 240 y Fs(+)g(\()p Fq(!)1056 220 y Fm(0)1078 240 y Fs(\))1097 220 y Fl(\000)p Fm(1)1151 240 y Fq(k)1179 220 y Fp(\013)1177 253 y(l)1207 240 y Fs(])g Fo(\000)g Fq(\045)p Fs(\()p Fu(x)1357 220 y Fp(\013)1385 240 y Fs(\))p Fq(\016)1426 247 y Fp(ik)1466 240 y Fo(g)i Fs(=)h(0)219 b(\(90\))0 334 y(for)15 b(frequencies)g Fq(!)h Fs(=)d Fq(!)461 315 y Fm(0)499 334 y Fs(corresp)q(onding)g(to)j(maxim)o(um)d (scattering)i(b)o(y)g(Gab)q(or)g(function)g Fq(g)1779 315 y Fp(\013)1807 334 y Fs(\()p Fu(x)p Fs(\).)0 393 y(Because)22 b(slo)o(wness)d(v)o(ector)j Fq(P)586 400 y Fp(i)624 393 y Fs(of)g(the)g(inciden)o(t)f(w)o(a)o(v)o(e)f (satis\014es)h(the)h(c)o(haracteristic)e(equation,)0 453 y(equation)h(\(90\))g(has)f(a)h(trivial)f(solution)g(\()p Fq(!)853 435 y Fm(0)875 453 y Fs(\))894 435 y Fl(\000)p Fm(1)969 453 y Fs(=)g(0)h(corresp)q(onding)d(to)j(the)g(forw)o(ard)e (broad{)0 513 y(band)k(scattering.)44 b(The)24 b(zero)g(to)h(\014v)o(e) f Ft(p)m(ositive)i Fs(solutions)c(of)j(equation)f(\(90\))g(corresp)q (ond)f(to)0 573 y(wide{angle)16 b(scattering.)100 635 y(F)l(or)f(p)q(ositiv)o(e)h Fq(!)406 617 y Fm(0)445 635 y Fs(satisfying)g(equation)g(\(90\),)h(w)o(e)g(c)o(ho)q(ose)p 0 685 1890 2 v 0 788 2 103 v 696 757 a Fq(p)721 736 y Fm(0)721 769 y Fp(i)757 757 y Fs(=)d Fq(P)842 764 y Fp(i)869 757 y Fs(+)d(\()p Fq(!)971 736 y Fm(0)994 757 y Fs(\))1013 736 y Fl(\000)p Fm(1)1067 757 y Fq(k)1095 736 y Fp(\013)1093 769 y(i)1172 757 y Fq(:)606 b Fs(\(91\))p 1888 788 V 0 790 1890 2 v 0 861 a(W)l(e)19 b(assume)f(that)i(p)q(oin)o(t)f Fu(x)537 843 y Fm(0)579 861 y Fs(is)f(situated)h(on)g(the)h(ra)o(y)e (determined)g(b)o(y)h(initial)g(slo)o(wness)e(v)o(ector)0 921 y Fq(p)25 903 y Fm(0)25 934 y Fp(i)47 921 y Fs(,)g(see)f(\(59\).)23 b(Then)351 1040 y Fq(k)379 1019 y Fp(\013)377 1052 y(i)418 1040 y Fs(+)11 b Fq(!)r Fs(\()p Fq(T)556 1019 y Fp(\013)549 1052 y(;i)595 1040 y Fs(+)g Fq(\034)673 1019 y Fm(0)p Fl(0)667 1052 y Fp(;i)717 1040 y Fs(+)g Fq(\034)795 1019 y Fm(0)p Fl(0)789 1052 y Fp(;mi)853 1040 y Fs(\001)p Fq(x)923 1047 y Fp(m)961 1040 y Fs(\))j(=)f Fq(!)r(\034)1107 1019 y Fm(0)p Fl(0)1101 1052 y Fp(;mi)1165 1040 y Fs(\001)p Fq(x)1235 1047 y Fp(m)1284 1040 y Fo(\000)1339 1006 y Fs(\001)p Fq(!)p 1339 1028 75 2 v 1349 1074 a(!)1382 1059 y Fm(0)1420 1040 y Fq(k)1448 1019 y Fp(\013)1446 1052 y(i)1525 1040 y Fq(;)262 b Fs(\(92\))0 1146 y(where)768 1210 y(\001)p Fq(!)16 b Fs(=)d Fq(!)g Fo(\000)e Fq(!)1036 1189 y Fm(0)1108 1210 y Fq(:)679 b Fs(\(93\))0 1288 y(W)l(e)17 b(insert)f(\(92\))h(in)o(to)f(\(86\),)96 1381 y Fq(T)132 1361 y Fp(\013)125 1393 y(!)160 1381 y Fs(\()p Fu(x)p Fs(\))f(=)p Fq(T)318 1361 y Fp(\013)358 1381 y Fs(+)10 b Fq(\034)435 1361 y Fm(0)468 1381 y Fs(+)h Fq(\034)546 1361 y Fm(0)540 1393 y Fp(;i)568 1381 y Fs(\001)p Fq(x)638 1388 y Fp(i)666 1381 y Fs(+)722 1361 y Fm(1)p 722 1370 20 2 v 722 1398 a(2)747 1381 y Fq(\034)775 1361 y Fm(0)769 1393 y Fp(;ij)816 1381 y Fs(\001)p Fq(x)886 1388 y Fp(i)903 1381 y Fs(\001)p Fq(x)973 1388 y Fp(j)293 1488 y Fo(\000)349 1468 y Fm(1)p 349 1476 V 349 1505 a(2)375 1488 y Fs(\()p Fq(\022)418 1467 y Fm(0)p Fl(00)475 1488 y Fs(+)g(i)p Fq(!)572 1467 y Fl(\000)p Fm(1)625 1488 y Fq(K)671 1467 y Fp(\013)699 1488 y Fs(\))718 1467 y Fl(\000)p Fm(1)718 1502 y Fp(ij)772 1488 y Fs([)p Fq(\034)814 1467 y Fm(0)p Fl(0)808 1500 y Fp(;mi)872 1488 y Fs(\001)p Fq(x)942 1495 y Fp(m)991 1488 y Fo(\000)1053 1454 y Fs(\001)p Fq(!)p 1046 1476 88 2 v 1046 1522 a(!)1079 1508 y Fm(0)1101 1522 y Fq(!)1140 1488 y(k)1168 1467 y Fp(\013)1166 1500 y(i)1196 1488 y Fs(][)p Fq(\034)1252 1467 y Fm(0)p Fl(0)1246 1500 y Fp(;nj)1303 1488 y Fs(\001)p Fq(x)1373 1495 y Fp(n)1411 1488 y Fo(\000)1474 1454 y Fs(\001)p Fq(!)p 1467 1476 V 1467 1522 a(!)1500 1508 y Fm(0)1522 1522 y Fq(!)1561 1488 y(k)1589 1467 y Fp(\013)1587 1500 y(j)1617 1488 y Fs(])49 b Fq(:)107 b Fs(\(94\))0 1601 y(F)l(or)15 b Fq(!)h Fs(=)e Fq(!)222 1583 y Fm(0)260 1601 y Fs(equation)j(\(94\))g (yields)92 1694 y Fq(T)128 1673 y Fp(\013)121 1707 y(!)147 1697 y Fg(0)169 1694 y Fs(\()p Fu(x)p Fs(\))e(=)f Fq(T)341 1673 y Fp(\013)380 1694 y Fs(+)d Fq(\034)458 1673 y Fm(0)491 1694 y Fs(+)g Fq(\034)569 1673 y Fm(0)563 1706 y Fp(;i)591 1694 y Fs(\001)p Fq(x)661 1701 y Fp(i)689 1694 y Fs(+)744 1674 y Fm(1)p 744 1682 20 2 v 744 1711 a(2)770 1694 y Fs([)p Fq(\034)812 1673 y Fm(0)806 1706 y Fp(;ij)864 1694 y Fo(\000)g Fq(\034)942 1673 y Fm(0)p Fl(0)936 1706 y Fp(;ir)983 1694 y Fs(\()p Fq(\022)1026 1673 y Fm(0)p Fl(00)1084 1694 y Fs(+)g(i)p Fq(!)1181 1673 y Fl(\000)p Fm(1)1234 1694 y Fq(K)1280 1673 y Fp(\013)1308 1694 y Fs(\))1327 1673 y Fl(\000)p Fm(1)1327 1706 y Fp(r)q(s)1381 1694 y Fq(\034)1409 1673 y Fm(0)p Fl(0)1403 1706 y Fp(;j)r(s)1454 1694 y Fs(]\001)p Fq(x)1538 1701 y Fp(i)1555 1694 y Fs(\001)p Fq(x)1625 1701 y Fp(j)1696 1694 y Fq(:)91 b Fs(\(95\))0 1787 y(Equation)16 b(\(94\))h(then)g(reads)0 1920 y Fq(T)36 1899 y Fp(\013)29 1932 y(!)64 1920 y Fs(\()p Fu(x)p Fs(\))e(=)f Fq(T)236 1899 y Fp(\013)229 1933 y(!)255 1923 y Fg(0)277 1920 y Fs(\()p Fu(x)p Fs(\))6 b(+)g Fq(\034)424 1899 y Fm(0)p Fl(0)418 1932 y Fp(;ir)466 1920 y Fs(\()p Fq(\022)509 1899 y Fm(0)p Fl(00)561 1920 y Fs(+)g(i)p Fq(!)653 1899 y Fl(\000)p Fm(1)706 1920 y Fq(K)752 1899 y Fp(\013)780 1920 y Fs(\))799 1899 y Fl(\000)p Fm(1)799 1932 y Fp(r)q(s)853 1920 y Fq(k)881 1899 y Fp(\013)879 1932 y(s)909 1920 y Fs(\001)p Fq(x)979 1927 y Fp(i)1008 1886 y Fs(\001)p Fq(!)p 1001 1909 88 2 v 1001 1954 a(!)1034 1940 y Fm(0)1056 1954 y Fq(!)1101 1920 y Fo(\000)1151 1886 y Fs(1)p 1151 1909 25 2 v 1151 1954 a(2)1182 1920 y Fq(k)1210 1899 y Fp(\013)1208 1932 y(r)1238 1920 y Fs(\()p Fq(\022)1281 1899 y Fm(0)p Fl(00)1333 1920 y Fs(+)g(i)p Fq(!)1425 1899 y Fl(\000)p Fm(1)1477 1920 y Fq(K)1523 1899 y Fp(\013)1552 1920 y Fs(\))1571 1899 y Fl(\000)p Fm(1)1571 1932 y Fp(r)q(s)1624 1920 y Fq(k)1652 1899 y Fp(\013)1650 1932 y(s)1680 1850 y Fn(\022)1730 1886 y Fs(\001)p Fq(!)p 1723 1909 88 2 v 1723 1954 a(!)1756 1940 y Fm(0)1778 1954 y Fq(!)1817 1850 y Fn(\023)1840 1860 y Fm(2)1876 1920 y Fq(:)1801 2010 y Fs(\(96\))0 2070 y(Equation)18 b(\(95\))i(represen)o(ts)c(the)j (paraxial)f(expansion)f(of)i(the)g(complex{v)m(alued)f(tra)o(v)o (el{time)g(of)0 2130 y(the)24 b(time{harmonic)e(Gaussian)h(b)q(eam)g (scattered)h(b)o(y)g(Gab)q(or)f(function)h Fq(g)1492 2111 y Fp(\013)1520 2130 y Fs(\()p Fu(x)p Fs(\))h(at)f(frequency)0 2190 y Fq(!)33 2171 y Fm(0)55 2190 y Fs(.)37 b(Equation)21 b(\(96\))i(describ)q(es)d(the)i(appro)o(ximate)e(frequency)h(dep)q (endence)h(of)f(the)h(scattered)0 2249 y(Gaussian)15 b(b)q(eam.)100 2311 y(T)l(o)g(deriv)o(e)h(the)g(explicit)g(ev)o (olution)f(equations)h(with)g(corresp)q(onding)d(initial)j(conditions)e (for)0 2371 y(scattered)k(Gaussian)e(b)q(eam)h(\(78\))i(with)e (amplitude)g(\(79\))h(and)f(tra)o(v)o(el)g(time)h(\(96\),)g(w)o(e)g (transform)0 2431 y(all)f(quan)o(tities)g(in)o(to)f(the)i(ra)o(y{cen)o (tered)e(co)q(ordinates)g(attac)o(hed)h(to)h(the)f(ra)o(y)g(leading)f (from)h(p)q(oin)o(t)0 2491 y Fu(x)30 2473 y Fp(\013)75 2491 y Fs(to)g(p)q(oin)o(t)f Fu(x)296 2473 y Fm(0)319 2491 y Fs(.)920 2806 y(36)p eop %%Page: 37 11 37 10 bop 0 -54 a Fu(4.3.)25 b(Ra)n(y{cen)n(tred)20 b(co)r(ordinate)f (system)0 26 y Fs(The)f Fq(q)126 33 y Fm(3)148 26 y Fs({co)q(ordinate)f (line)h(of)f(ra)o(y{cen)o(tred)g(co)q(ordinates)g Fq(q)1132 33 y Fp(m)1187 26 y Fs(is)h(the)g(axial)f(ra)o(y)g(parametrized)f(b)o (y)0 86 y(an)o(y)e(parameter)f Fq(q)350 93 y Fm(3)387 86 y Fs(increasing)g(along)h(the)g(axial)h(ra)o(y)l(.)20 b(The)14 b(Cartesian)g(co)q(ordinates)f(corresp)q(ond-)0 146 y(ing)j(to)h Fq(q)166 153 y Fp(m)221 146 y Fs(are)637 210 y Fq(x)665 217 y Fp(i)696 210 y Fs(=)d Fq(x)777 190 y Fm(R)777 223 y Fp(i)808 210 y Fs(\()p Fq(q)849 217 y Fm(3)872 210 y Fs(\))e(+)f Fq(h)982 190 y Fp(i)982 223 y(M)1026 210 y Fs(\()p Fq(q)1067 217 y Fm(3)1090 210 y Fs(\))j Fq(q)1145 217 y Fp(M)1239 210 y Fq(;)548 b Fs(\(97\))0 290 y(where)16 b Fq(x)172 272 y Fm(R)172 303 y Fp(i)204 290 y Fs(\()p Fq(q)245 297 y Fm(3)268 290 y Fs(\))h(are)g(p)q(oin)o(ts)f(of)h(the)g(axial)g(ra)o(y)l(.)k (This)16 b(is)h(b)q(oth)g(the)g(de\014nition)e(of)i(the)h(ra)o(y{cen)o (tred)0 350 y(co)q(ordinates,)g(and)f(the)i(transformation)d(equation)i (from)f(the)i(ra)o(y{cen)o(tred)e(to)h(Cartesian)g(co)q(or-)0 410 y(dinates.)j(The)c(transformation)d(matrices,)i(tak)o(en)g(at)h (the)g(cen)o(tral)f(ra)o(y)l(,)f(are)593 528 y Fq(h)622 507 y Fp(i)622 540 y(m)674 528 y Fs(=)740 494 y Fq(@)s(x)797 501 y Fp(i)p 732 516 90 2 v 732 562 a Fq(@)s(q)783 569 y Fp(m)877 528 y Fq(;)998 515 y Fn(b)999 528 y Fq(h)1028 507 y Fp(m)1028 540 y(i)1079 528 y Fs(=)1138 494 y Fq(@)s(q)1189 501 y Fp(m)p 1138 516 V 1145 562 a Fq(@)s(x)1202 569 y Fp(i)1283 528 y Fq(:)504 b Fs(\(98\))0 660 y(The)18 b(\\con)o(tra)o(v)m(arian)o(t)f(basis)g(v)o(ectors")h Fq(h)785 642 y Fp(i)785 673 y Fm(1)807 660 y Fs(,)h Fq(h)869 642 y Fp(i)869 673 y Fm(2)891 660 y Fs(,)g Fq(h)953 642 y Fp(i)953 673 y Fm(3)993 660 y Fs(and)f(the)h(\\co)o(v)m(arian)o(t)e (basis)g(v)o(ectors")1740 647 y Fn(b)1741 660 y Fq(h)1770 642 y Fm(1)1770 673 y Fp(i)1792 660 y Fs(,)1824 647 y Fn(b)1825 660 y Fq(h)1854 642 y Fm(2)1854 673 y Fp(i)1876 660 y Fs(,)-1 714 y Fn(b)0 728 y Fq(h)29 709 y Fm(3)29 741 y Fp(i)68 728 y Fs(of)f(the)h(ra)o(y{cen)o(tred)e(co)q(ordinate)h (system)h(are)f(de\014ned)f(b)o(y)h(equations)775 848 y Fq(h)804 828 y Fp(i)804 861 y Fm(3)840 848 y Fs(=)e Fq(H)938 828 y Fp(;i)981 815 y Fs(d)p Fq(\034)p 973 837 73 2 v 973 883 a Fs(d)p Fq(q)1023 890 y Fm(3)1101 848 y Fq(;)686 b Fs(\(99\))791 992 y Fn(b)792 1005 y Fq(h)821 985 y Fm(3)821 1017 y Fp(i)856 1005 y Fs(=)14 b Fq(p)934 1012 y Fp(i)957 971 y Fs(d)p Fq(q)1007 978 y Fm(3)p 957 994 V 965 1039 a Fs(d)p Fq(\034)1085 1005 y(;)678 b Fs(\(100\))806 1118 y Fq(h)835 1097 y Fp(i)835 1130 y(a)858 1105 y Fn(b)859 1118 y Fq(h)888 1097 y Fp(b)888 1130 y(i)921 1118 y Fs(=)14 b Fq(\016)998 1097 y Fp(b)996 1130 y(a)1070 1118 y Fq(:)693 b Fs(\(101\))0 1198 y(Here)609 1276 y Fq(H)650 1283 y Fp(;i)693 1276 y Fs(=)752 1242 y Fq(@)s(H)p 752 1264 75 2 v 752 1310 a(@)s(x)809 1317 y Fp(i)882 1276 y Fq(;)108 b(H)1049 1255 y Fp(;i)1092 1276 y Fs(=)1150 1242 y Fq(@)s(H)p 1150 1264 V 1152 1310 a(@)s(p)1206 1317 y Fp(i)1777 1276 y Fs(\(102\))0 1382 y(are)20 b(the)g(phase{space)f(deriv)m(ativ)o(es)h (of)h(Hamiltonian)e Fq(H)24 b Fs(=)c Fq(H)t Fs(\()p Fq(x)1279 1389 y Fp(m)1318 1382 y Fq(;)8 b(p)1365 1389 y Fp(n)1393 1382 y Fs(\))20 b(corresp)q(onding)e(to)j(the)0 1442 y(Gaussian)c(b)q(eam)h(scattered)g(at)h(p)q(oin)o(t)e Fu(x)791 1424 y Fp(\013)820 1442 y Fs(.)27 b(W)l(e)19 b(assume)e(in)g(this)h(pap)q(er)g(that)h(the)f(Hamiltonian)0 1502 y(is)g(a)h(homogeneous)e(function)h(of)h(an)g(arbitrary)e(degree)i (with)f(resp)q(ect)h(to)g(the)g(slo)o(wness)e(v)o(ector.)0 1562 y(Then)f Fq(H)175 1544 y Fp(;i)221 1562 y Fs(is)g(the)g(ra)o(y{v)o (elo)q(cit)o(y)h(v)o(ector.)100 1624 y(The)11 b(\014rst)g(t)o(w)o(o)g (con)o(tra)o(v)m(arian)o(t)e(basis)h(v)o(ectors)h Fq(h)993 1606 y Fp(i)993 1636 y Fm(1)1015 1624 y Fs(,)i Fq(h)1071 1606 y Fp(i)1071 1636 y Fm(2)1104 1624 y Fs(of)f(the)g(ra)o(y{cen)o (tred)d(co)q(ordinate)i(system)0 1684 y(are)18 b(tangen)o(t)f(to)i(the) f(w)o(a)o(v)o(efron)o(t,)f(the)h(third)g(con)o(tra)o(v)m(arian)o(t)e (basis)h(v)o(ector)h Fq(h)1484 1666 y Fp(i)1484 1696 y Fm(3)1524 1684 y Fs(is)g(tangen)o(t)f(to)i(the)0 1751 y(ra)o(y)l(.)27 b(The)18 b(\014rst)g(t)o(w)o(o)f(co)o(v)m(arian)o(t)h (basis)f(v)o(ectors)922 1737 y Fn(b)923 1751 y Fq(h)952 1732 y Fm(1)952 1763 y Fp(i)974 1751 y Fs(,)1006 1737 y Fn(b)1007 1751 y Fq(h)1036 1732 y Fm(2)1036 1763 y Fp(i)1076 1751 y Fs(of)i(the)g(ra)o(y{cen)o(tred)e(co)q(ordinate)g (system)0 1818 y(are)e(p)q(erp)q(endicular)f(to)i(the)g(ra)o(y)l(,)f (the)h(third)f(co)o(v)m(arian)o(t)g(basis)f(v)o(ector)1329 1804 y Fn(b)1330 1818 y Fq(h)1359 1800 y Fm(3)1359 1831 y Fp(i)1397 1818 y Fs(is)h(p)q(erp)q(endicular)f(to)i(the)0 1885 y(w)o(a)o(v)o(efron)o(t.)k(Whereas)15 b(basis)f(v)o(ectors)i Fq(h)768 1867 y Fp(i)768 1897 y Fm(3)806 1885 y Fs(and)901 1872 y Fn(b)902 1885 y Fq(h)931 1867 y Fm(3)931 1898 y Fp(i)968 1885 y Fs(are)g(uniquely)f(determined)f(b)o(y)h(equations)g (\(99\))0 1945 y(and)f(\(100\),)h(w)o(e)g(ma)o(y)f(either)g(c)o(ho)q (ose)g(the)h(con)o(tra)o(v)m(arian)o(t)e(basis)g(v)o(ectors)h Fq(h)1413 1927 y Fp(i)1413 1957 y Fm(1)1450 1945 y Fs(and)g Fq(h)1574 1927 y Fp(i)1574 1957 y Fm(2)1611 1945 y Fs(arbitrarily)e(in) 0 2011 y(the)j(w)o(a)o(v)o(efron)o(t)f(tangen)o(t)h(plane,)g(or)f(c)o (ho)q(ose)h(the)h(co)o(v)m(arian)o(t)e(basis)g(v)o(ectors)1438 1998 y Fn(b)1439 2011 y Fq(h)1468 1993 y Fm(1)1468 2024 y Fp(i)1505 2011 y Fs(and)1600 1998 y Fn(b)1600 2011 y Fq(h)1629 1993 y Fm(2)1629 2024 y Fp(i)1667 2011 y Fs(arbitrarily)0 2071 y(in)i(the)h(plane)f(p)q(erp)q(endicular)f(to)h (the)h(ra)o(y)f(v)o(elo)q(cit)o(y)h(v)o(ector)g Fq(h)1188 2053 y Fp(i)1188 2084 y Fm(3)1210 2071 y Fs(.)100 2134 y(W)l(e)f(de\014ne)g(the)h(Jacobian)785 2198 y Fq(h)d Fs(=)f(det)q(\()p Fq(h)998 2178 y Fp(i)998 2211 y(m)1036 2198 y Fs(\))722 b(\(103\))0 2278 y(of)15 b(the)f(transformation)f (from)g(ra)o(y{cen)o(tred)g(co)q(ordinates)h Fq(q)1144 2285 y Fp(m)1197 2278 y Fs(to)g(Cartesian)g(co)q(ordinates)f Fq(x)1768 2285 y Fp(i)1786 2278 y Fs(.)21 b(W)l(e)0 2338 y(shall)16 b(use)g(notation)805 2420 y Fu(q)e Fs(=)901 2350 y Fn(\022)946 2390 y Fq(q)968 2397 y Fm(1)946 2450 y Fq(q)968 2457 y Fm(2)999 2350 y Fn(\023)1777 2420 y Fs(\(104\))0 2527 y(for)i(the)h(\014rst)f(t)o(w)o(o)g(ra)o(y{cen)o (tred)f(co)q(ordinates,)h(and)760 2654 y Fu(p)792 2633 y Fm(\()p Fp(q)q Fm(\))859 2654 y Fs(=)912 2583 y Fn(\022)957 2623 y Fq(p)982 2597 y Fm(\()p Fp(q)q Fm(\))982 2637 y(1)957 2694 y Fq(p)982 2668 y Fm(\()p Fp(q)q Fm(\))982 2707 y(2)1043 2583 y Fn(\023)1777 2654 y Fs(\(105\))920 2806 y(37)p eop %%Page: 38 12 38 11 bop 0 -54 a Fs(for)16 b(the)h(\014rst)f(t)o(w)o(o)g(ra)o(y{cen)o (tred)f(comp)q(onen)o(ts)793 46 y Fq(p)818 20 y Fm(\()p Fp(q)q Fm(\))818 61 y Fp(K)885 46 y Fs(=)f Fq(h)967 26 y Fp(i)967 58 y(K)1005 46 y Fq(p)1030 53 y Fp(i)1777 46 y Fs(\(106\))0 140 y(of)j(the)g(slo)o(wness)d(v)o(ector.)0 268 y Fu(4.3.1.)38 b(P)n(araxial{ra)n(y)25 b(propagator)c(matrix)g(and) i(the)h(second)g(deriv)m(ativ)n(es)h(of)e(t)n(w)n(o{)0 328 y(p)r(oin)n(t)d(tra)n(v)n(el)h(time)0 407 y Fs(Di\013eren)o (tiating)16 b(the)g(eik)o(onal)g(equation)h(\(stationary)f (Hamilton{Jacobi)f(equation\))758 500 y Fq(H)t Fs(\()p Fq(x)850 507 y Fp(m)889 500 y Fq(;)8 b(\034)933 507 y Fp(;n)972 500 y Fs(\))14 b(=)g(0)694 b(\(107\))0 594 y(with)16 b(resp)q(ect)h(to)g Fq(x)373 601 y Fp(i)390 594 y Fs(,)f(w)o(e)h(obtain)725 687 y Fq(H)766 694 y Fp(;i)806 687 y Fs(+)11 b Fq(H)901 667 y Fp(;k)938 687 y Fq(\034)960 694 y Fp(;k)q(i)1024 687 y Fs(=)i(0)50 b Fq(:)612 b Fs(\(108\))0 781 y(Multiplying)15 b(\(108\))i(b)o(y)f Fq(h)499 763 y Fp(i)499 793 y(a)537 761 y Fm(d)p Fp(\034)p 529 769 60 2 v 529 798 a Fm(d)p Fp(q)569 803 y Fg(3)612 781 y Fs(and)f(considering)g(\(99\),)i(w)o(e)f(arriv)o(e)g(at)h (expression)680 890 y Fq(h)709 870 y Fp(i)709 903 y(a)733 890 y Fq(\034)755 897 y Fp(;ij)801 890 y Fq(h)830 866 y Fp(j)830 904 y Fm(3)866 890 y Fs(=)d Fo(\000)p Fq(h)987 870 y Fp(i)987 903 y(a)1010 890 y Fq(H)1051 897 y Fp(;i)1102 871 y Fm(d)p Fp(\034)p 1095 879 V 1095 908 a Fm(d)p Fp(q)1135 913 y Fg(3)1777 890 y Fs(\(109\))0 984 y(for)i(the)h(second)f(tra)o(v)o (el{time)f(deriv)m(ativ)o(es)i(in)f(the)g(ra)o(y{cen)o(tred)g(co)q (ordinates.)21 b(W)l(e)16 b(denote)h(b)o(y)650 1034 y Fn(\022)699 1074 y Fu(M)753 1056 y Fp(\013)753 1087 y Fm(3)695 1134 y Fq(M)748 1116 y Fp(\013)743 1147 y Fm(33)793 1034 y Fn(\023)888 1104 y Fq(;)1010 1034 y Fn(\022)1062 1074 y Fu(M)1116 1081 y Fm(3)1055 1134 y Fq(M)1103 1141 y Fm(33)1154 1034 y Fn(\023)1777 1104 y Fs(\(110\))0 1231 y(the)g(righ)o(t{hand)d(sides)i(of)g(equation)h(\(109\))g(at)g(p)q (oin)o(ts)f Fu(x)1090 1213 y Fp(\013)1135 1231 y Fs(and)g Fu(x)1262 1213 y Fm(0)1284 1231 y Fs(,)h(resp)q(ectiv)o(ely)l(,)506 1324 y Fq(M)559 1304 y Fp(\013)554 1337 y(a)p Fm(3)612 1324 y Fs(=)d Fo(\000)p Fq(h)733 1304 y Fp(i)733 1337 y(a)756 1324 y Fs(\()p Fu(x)805 1304 y Fp(\013)834 1324 y Fs(\))p Fq(H)894 1331 y Fp(;i)923 1324 y Fs(\()p Fu(x)972 1304 y Fp(\013)1001 1324 y Fq(;)8 b Fo(\000)p Fq(\034)1090 1304 y Fm(0)p Fl(0)1084 1337 y Fp(k)1124 1324 y Fs(\))1165 1305 y Fm(d)p Fp(\034)p 1157 1313 V 1157 1341 a Fm(d)p Fp(q)1197 1346 y Fg(3)1223 1324 y Fs(\()p Fu(x)1272 1304 y Fp(\013)1301 1324 y Fs(\))50 b Fq(;)393 b Fs(\(111\))540 1434 y Fq(M)588 1441 y Fp(a)p Fm(3)646 1434 y Fs(=)14 b Fo(\000)p Fq(h)767 1414 y Fp(i)767 1447 y(a)790 1434 y Fs(\()p Fu(x)839 1414 y Fm(0)862 1434 y Fs(\))p Fq(H)922 1441 y Fp(;i)952 1434 y Fs(\()p Fu(x)1001 1414 y Fm(0)1024 1434 y Fq(;)8 b(\034)1074 1414 y Fm(0)1068 1447 y Fp(k)1095 1434 y Fs(\))1137 1415 y Fm(d)p Fp(\034)p 1129 1423 V 1129 1451 a Fm(d)p Fp(q)1169 1456 y Fg(3)1195 1434 y Fs(\()p Fu(x)1244 1414 y Fm(0)1267 1434 y Fs(\))50 b Fq(:)427 b Fs(\(112\))0 1519 y(Note)17 b(that)g(in)f(an)h(isotropic)e (medium,)g(\(111\))i(and)f(\(112\))h(are)f(the)h(slo)o(wness)d(gradien) o(ts.)100 1581 y(Denote)21 b(b)o(y)f Fu(Q)391 1588 y Ff(1)417 1581 y Fs(,)h Fu(Q)495 1588 y Ff(2)521 1581 y Fs(,)h Fu(P)596 1588 y Ff(1)642 1581 y Fs(and)e Fu(P)782 1588 y Ff(2)828 1581 y Fs(the)h(2)14 b Fo(\002)g Fs(2)21 b(submatrices)e(of)i(the)g(4)14 b Fo(\002)g Fs(4)21 b(paraxial)f(ra)o (y)0 1641 y(propagator)15 b(matrix)640 1731 y Fu(\005)p Fs(\()p Fu(x)734 1711 y Fm(0)757 1731 y Fq(;)8 b Fu(x)809 1711 y Fp(\013)838 1731 y Fs(\))14 b(=)924 1661 y Fn(\022)969 1701 y Fu(Q)1012 1708 y Ff(1)1087 1701 y Fu(Q)1130 1708 y Ff(2)971 1761 y Fu(P)1010 1768 y Ff(1)1089 1761 y Fu(P)1128 1768 y Ff(2)1163 1661 y Fn(\023)1777 1731 y Fs(\(113\))0 1843 y(from)i(p)q(oin)o(t)g Fu(x)278 1825 y Fp(\013)323 1843 y Fs(to)h(p)q(oin)o(t)f Fu(x)544 1825 y Fm(0)583 1843 y Fs(in)g(ra)o(y{cen)o(tred)f(co)q(ordinates.)100 1905 y(The)e(matrices)f Fq(\034)423 1887 y Fm(0)p Fl(00)417 1918 y Fp(;ij)468 1905 y Fs(,)h Fq(\034)523 1887 y Fm(0)p Fl(0)517 1918 y Fp(;ij)564 1905 y Fs(,)h Fq(\034)620 1887 y Fm(0)614 1918 y Fp(;ij)660 1905 y Fs(,)g(co)o(v)m(arian)o(tly)f (transformed)e(in)o(to)h(the)i(ra)o(y{cen)o(tred)e(co)q(ordinate)0 1965 y(system,)625 2035 y Fq(\034)653 2009 y Fm(0)p Fl(00)p Fm(\()p Fp(q)q Fm(\))647 2050 y(;)p Fp(ab)762 2035 y Fs(=)i Fq(h)844 2014 y Fp(i)844 2047 y(a)868 2035 y Fs(\()p Fu(x)917 2014 y Fp(\013)946 2035 y Fs(\))8 b Fq(\034)1001 2014 y Fm(0)p Fl(00)995 2047 y Fp(;ij)1054 2035 y Fq(h)1083 2011 y Fp(j)1083 2050 y(b)1104 2035 y Fs(\()p Fu(x)1153 2014 y Fp(\013)1182 2035 y Fs(\))50 b Fq(;)512 b Fs(\(114\))636 2136 y Fq(\034)664 2110 y Fm(0)p Fl(0)p Fm(\()p Fp(q)q Fm(\))658 2151 y(;)p Fp(ab)762 2136 y Fs(=)13 b Fq(h)843 2115 y Fp(i)843 2148 y(a)867 2136 y Fs(\()p Fu(x)916 2115 y Fm(0)939 2136 y Fs(\))8 b Fq(\034)994 2115 y Fm(0)p Fl(0)988 2148 y Fp(;ij)1044 2136 y Fq(h)1073 2112 y Fp(j)1073 2151 y(b)1093 2136 y Fs(\()p Fu(x)1142 2115 y Fp(\013)1171 2136 y Fs(\))50 b Fq(;)523 b Fs(\(115\))645 2237 y Fq(\034)673 2211 y Fm(0\()p Fp(q)q Fm(\))667 2252 y(;)p Fp(ab)759 2237 y Fs(=)13 b Fq(h)840 2216 y Fp(i)840 2249 y(a)864 2237 y Fs(\()p Fu(x)913 2216 y Fm(0)936 2237 y Fs(\))8 b Fq(\034)991 2216 y Fm(0)985 2249 y Fp(;ij)1041 2237 y Fq(h)1070 2213 y Fp(j)1070 2252 y(b)1090 2237 y Fs(\()p Fu(x)1139 2216 y Fm(0)1162 2237 y Fs(\))51 b Fq(;)531 b Fs(\(116\))0 2316 y(represen)o(t)22 b(the)h(second)f(co)o(v)m(arian)o (t)g(deriv)m(ativ)o(es)h(of)g(tra)o(v)o(el)g(time)g(in)f(ra)o(y{cen)o (tred)g(co)q(ordinates.)0 2376 y(This)e(means)g(that)h(they)g(represen) o(t)f(the)h(partial)f(deriv)m(ativ)o(es)g(of)h(tra)o(v)o(el)f(time)h (with)g(resp)q(ect)g(to)0 2435 y(lo)q(cal)c(Cartesian)e(co)q(ordinates) 473 2529 y(\001)p Fq(x)543 2508 y Fm(\()p Fp(q)q Fm(\))p Fl(0)543 2541 y Fp(m)621 2529 y Fs(=)673 2516 y Fn(b)674 2529 y Fq(h)703 2508 y Fp(m)703 2541 y(i)740 2529 y Fs(\()p Fu(x)789 2508 y Fp(\013)818 2529 y Fs(\))8 b(\001)p Fq(x)915 2508 y Fl(0)915 2541 y Fp(i)947 2529 y Fs(=)998 2516 y Fn(b)999 2529 y Fq(h)1028 2508 y Fp(m)1028 2541 y(i)1066 2529 y Fs(\()p Fu(x)1115 2508 y Fp(\013)1144 2529 y Fs(\))14 b([)p Fq(x)1219 2508 y Fl(0)1219 2541 y Fp(i)1247 2529 y Fo(\000)d Fq(x)1325 2508 y Fp(\013)1325 2541 y(i)1353 2529 y Fs(])410 b(\(117\))0 2622 y(and)481 2686 y(\001)p Fq(x)551 2665 y Fm(\()p Fp(q)q Fm(\))551 2698 y Fp(m)618 2686 y Fs(=)669 2673 y Fn(b)670 2686 y Fq(h)699 2665 y Fp(m)699 2698 y(i)737 2686 y Fs(\()p Fu(x)786 2665 y Fm(0)809 2686 y Fs(\))8 b(\001)p Fq(x)906 2693 y Fp(i)937 2686 y Fs(=)989 2673 y Fn(b)989 2686 y Fq(h)1018 2665 y Fp(m)1018 2698 y(i)1056 2686 y Fs(\()p Fu(x)1105 2665 y Fm(0)1128 2686 y Fs(\))14 b([)p Fq(x)1203 2693 y Fp(i)1231 2686 y Fo(\000)d Fq(x)1309 2665 y Fm(0)1309 2698 y Fp(i)1332 2686 y Fs(])49 b Fq(:)368 b Fs(\(118\))920 2806 y(38)p eop %%Page: 39 13 39 12 bop 0 -54 a Fs(The)16 b(matrices)g Fq(\034)330 -80 y Fm(0)p Fl(00)p Fm(\()p Fp(q)q Fm(\))324 -39 y(;)p Fp(ab)442 -54 y Fq(\034)470 -80 y Fm(0)p Fl(0)p Fm(\()p Fp(q)q Fm(\))464 -39 y(;)p Fp(ab)571 -54 y Fs(and)f Fq(\034)695 -80 y Fm(0\()p Fp(q)q Fm(\))689 -39 y(;)p Fp(ab)784 -54 y Fs(read)h(\()920 -67 y(\024)914 -54 y(Cerv)o(en)q(\023)-26 b(y,)17 b(Klime)m(\024)-22 b(s)15 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)16 b(1984,)g(eq.)h(22\))680 -4 y Fn(\022)725 36 y Fu(Q)768 43 y Ff(2)793 14 y Fl(\000)p Fm(1)846 36 y Fu(Q)889 43 y Ff(1)968 36 y Fo(\000)p Fu(M)1061 18 y Fp(\013)1061 49 y Fm(3)743 96 y Fo(\000)p Fu(M)836 78 y Fp(\013)836 108 y Fm(3)865 74 y(T)964 96 y Fo(\000)p Fq(M)1056 78 y Fp(\013)1051 108 y Fm(33)1102 -4 y Fn(\023)1196 66 y Fq(;)567 b Fs(\(119\))740 153 y Fn(\022)785 200 y Fo(\000)p Fu(Q)867 207 y Ff(2)892 178 y Fl(\000)p Fm(1)946 168 y(T)1026 200 y Fu(0)851 260 y(0)880 242 y Fm(T)1028 260 y Fs(0)1063 153 y Fn(\023)1777 223 y Fs(\(120\))0 328 y(and)701 335 y Fn(\022)746 376 y Fu(P)785 383 y Ff(2)810 376 y Fu(Q)853 383 y Ff(2)878 354 y Fl(\000)p Fm(1)988 376 y Fu(M)1042 383 y Fm(3)785 435 y Fu(M)839 442 y Fm(3)862 413 y(T)982 435 y Fq(M)1030 442 y Fm(33)1080 335 y Fn(\023)1175 405 y Fq(;)588 b Fs(\(121\))0 508 y(resp)q(ectiv)o(ely)l(.)100 575 y(Note)20 b(that)g(the)g(matrices)f Fq(\034)654 549 y Fm(0)p Fl(00)p Fm(\()p Fp(q)q Fm(\))648 590 y Fp(;ab)770 575 y Fq(\034)798 549 y Fm(0)p Fl(0)p Fm(\()p Fp(q)q Fm(\))792 590 y Fp(;ab)901 575 y Fs(and)g Fq(\034)1029 549 y Fm(0\()p Fp(q)q Fm(\))1023 590 y Fp(;ab)1122 575 y Fs(of)h(the)g(second)f(partial)g(deriv)m(ativ)o(es)g(of)0 635 y(tra)o(v)o(el)j(time)h(in)g(ra)o(y{cen)o(tred)f(co)q(ordinates)g (ha)o(v)o(e)g(the)i(form)e(analogous)g(to)h(\(119\),)i(\(120\))f(and)0 694 y(\(121\),)17 b(but)f(with)h(zero)f Fu(M)508 676 y Fp(\013)508 707 y Fm(3)553 694 y Fs(and)g Fu(M)704 701 y Fm(3)727 694 y Fs(.)0 816 y Fu(4.3.2.)24 b(Other)19 b(matrices)e(and)i(v)n(ectors)g(app)r(earing)f(in)i(equations)g Fs(\(95\))f Fu(and)g Fs(\(96\))0 891 y(Denote)e(b)o(y)739 908 y Fn( )802 957 y Fu(T)842 939 y Fm(\()p Fp(q)q Fm(\))960 957 y Fu(T)1000 931 y Fm(\()p Fp(q)q Fm(\))1000 971 y(3)787 1039 y Fu(T)827 1013 y Fm(\()p Fp(q)q Fm(\))827 1052 y(3)880 999 y(T)962 1039 y Fq(T)998 1013 y Fm(\()p Fp(q)q Fm(\))991 1052 y(;33)1062 908 y Fn(!)1777 993 y Fs(\(122\))0 1111 y(matrix)f Fq(T)198 1093 y Fp(\013)191 1124 y(;ij)255 1111 y Fs(in)g(the)h(ra)o(y{cen)o(tred)e(co)q(ordinate)h(system,)640 1218 y Fq(T)676 1192 y Fm(\()p Fp(q)q Fm(\))669 1233 y(;)p Fp(ab)743 1218 y Fs(=)e Fq(h)825 1197 y Fp(i)825 1230 y(a)849 1218 y Fs(\()p Fu(x)898 1197 y Fp(\013)927 1218 y Fs(\))8 b Fq(T)990 1197 y Fp(\013)983 1230 y(;ij)1039 1218 y Fq(h)1068 1194 y Fp(j)1068 1233 y(b)1089 1218 y Fs(\()p Fu(x)1138 1197 y Fp(\013)1167 1218 y Fs(\))50 b Fq(;)527 b Fs(\(123\))0 1308 y(and)16 b(b)o(y)733 1325 y Fn( )797 1375 y Fu(K)842 1357 y Fm(\()p Fp(q)q Fm(\))960 1375 y Fu(K)1005 1349 y Fm(\()p Fp(q)q Fm(\))1005 1388 y(3)781 1456 y Fu(K)826 1431 y Fm(\()p Fp(q)q Fm(\))826 1470 y(3)879 1417 y(T)960 1456 y Fq(K)1006 1431 y Fm(\()p Fp(q)q Fm(\))1002 1470 y(33)1067 1325 y Fn(!)1777 1411 y Fs(\(124\))0 1528 y(matrix)g Fq(K)208 1510 y Fp(\013)204 1541 y(ij)256 1528 y Fs(in)g(the)h(ra)o(y{cen)o(tred)e(co)q(ordinate)h (system,)635 1635 y Fq(K)681 1609 y Fm(\()p Fp(q)q Fm(\))677 1650 y Fp(ab)748 1635 y Fs(=)d Fq(h)829 1615 y Fp(i)829 1648 y(a)853 1635 y Fs(\()p Fu(x)902 1615 y Fp(\013)931 1635 y Fs(\))8 b Fq(K)1004 1615 y Fp(\013)1000 1648 y(ij)1044 1635 y Fq(h)1073 1611 y Fp(j)1073 1650 y(b)1094 1635 y Fs(\()p Fu(x)1143 1615 y Fp(\013)1172 1635 y Fs(\))50 b Fq(:)522 b Fs(\(125\))100 1726 y(Then)10 b(matrix)h Fq(\022)405 1708 y Fm(0)p Fl(00)404 1740 y Fp(;k)q(l)454 1726 y Fs(+)q(i)p Fq(!)541 1708 y Fl(\000)p Fm(1)594 1726 y Fq(K)640 1708 y Fp(\013)636 1739 y(ij)671 1726 y Fs(,)h(co)o(v)m(arian)o(tly)f(transformed)e(in)o(to)i(the)h(ra)o (y{cen)o(tred)e(co)q(ordinate)0 1786 y(system,)16 b(is)514 1803 y Fn(\022)559 1843 y Fu(T)599 1825 y Fm(\()p Fp(q)q Fm(\))663 1843 y Fs(+)11 b Fu(Q)756 1850 y Ff(2)781 1821 y Fl(\000)p Fm(1)834 1843 y Fu(Q)877 1850 y Ff(1)914 1843 y Fs(+)f(i)p Fq(!)1010 1825 y Fl(\000)p Fm(1)1063 1843 y Fu(K)1108 1825 y Fm(\()p Fp(q)q Fm(\))1211 1843 y Fu(m)821 1903 y(m)872 1885 y Fm(T)1213 1903 y Fq(m)1267 1803 y Fn(\023)1362 1873 y Fq(;)401 b Fs(\(126\))0 1976 y(where)615 2036 y Fu(m)11 b Fs(=)i Fu(T)769 2010 y Fm(\()p Fp(q)q Fm(\))769 2049 y(3)833 2036 y Fo(\000)e Fu(M)937 2015 y Fp(\013)937 2048 y Fm(3)977 2036 y Fs(+)g(i)p Fq(!)1074 2015 y Fl(\000)p Fm(1)1127 2036 y Fu(K)1172 2010 y Fm(\()p Fp(q)q Fm(\))1172 2049 y(3)1777 2036 y Fs(\(127\))0 2111 y(and)608 2172 y Fq(m)i Fs(=)h Fq(T)754 2146 y Fm(\()p Fp(q)q Fm(\))747 2185 y(;33)818 2172 y Fo(\000)d Fq(M)921 2151 y Fp(\013)916 2184 y Fm(33)970 2172 y Fs(+)f(i)p Fq(!)1066 2151 y Fl(\000)p Fm(1)1120 2172 y Fq(K)1166 2146 y Fm(\()p Fp(q)q Fm(\))1162 2185 y(33)1268 2172 y Fq(:)495 b Fs(\(128\))0 2256 y(In)o(v)o(erse)14 b(matrix)h(\()p Fq(\022)372 2238 y Fm(0)p Fl(00)427 2256 y Fs(+)9 b(i)p Fq(!)522 2238 y Fl(\000)p Fm(1)575 2256 y Fq(K)621 2238 y Fp(\013)649 2256 y Fs(\))668 2235 y Fl(\000)p Fm(1)668 2271 y Fp(k)q(l)722 2256 y Fs(,)16 b(also)f(expressed)f(in)h(the)h(ra)o(y{cen)o(tred)e(co)q(ordinate)h (system,)0 2316 y(is)345 2323 y Fn( )404 2376 y Fs([)p Fu(Q)461 2383 y Ff(2)486 2354 y Fl(\000)p Fm(1)540 2376 y Fu(Q)583 2383 y Ff(1)619 2376 y Fs(+)c Fu(M)723 2358 y Fp(\013)751 2376 y Fs(])765 2358 y Fl(\000)p Fm(1)947 2376 y Fo(\000)992 2352 y Fm([)p Ff(Q)1037 2357 y Fe(2)1058 2337 y Fd(\000)p Fg(1)1105 2352 y Ff(Q)1139 2357 y Fe(1)1160 2352 y Fm(+)p Ff(M)1233 2337 y Fc(\013)1258 2352 y Fm(])1269 2337 y Fd(\000)p Fg(1)1316 2352 y Ff(m)p 992 2365 362 2 v 1155 2393 a Fp(m)392 2455 y Fo(\000)437 2430 y Ff(m)474 2415 y Fg(T)501 2430 y Fm([)p Ff(Q)546 2435 y Fe(2)567 2415 y Fd(\000)p Fg(1)614 2430 y Ff(Q)648 2435 y Fe(1)669 2430 y Fm(+)p Ff(M)742 2415 y Fc(\013)767 2430 y Fm(])778 2415 y Fd(\000)p Fg(1)p 437 2443 388 2 v 613 2472 a Fp(m)894 2435 y Fm(1)p 886 2443 36 2 v 886 2472 a Fp(m)939 2455 y Fs(+)995 2430 y Ff(m)1032 2415 y Fg(T)1058 2430 y Fm([)p Ff(Q)1103 2435 y Fe(2)1125 2415 y Fd(\000)p Fg(1)1171 2430 y Ff(Q)1205 2435 y Fe(1)1226 2430 y Fm(+)p Ff(M)1299 2415 y Fc(\013)1325 2430 y Fm(])1336 2415 y Fd(\000)p Fg(1)1382 2430 y Ff(m)p 995 2443 426 2 v 1180 2472 a Fp(m)1215 2462 y Fg(2)1434 2323 y Fn(!)1532 2409 y Fq(;)231 b Fs(\(129\))0 2526 y(where)p 0 2561 1890 2 v 0 2706 2 146 v 552 2653 a Fu(M)606 2633 y Fp(\013)649 2653 y Fs(=)13 b Fu(T)741 2633 y Fm(\()p Fp(q)q Fm(\))805 2653 y Fs(+)e(i)p Fq(!)902 2633 y Fl(\000)p Fm(1)955 2653 y Fu(K)1000 2633 y Fm(\()p Fp(q)q Fm(\))1064 2653 y Fo(\000)1120 2620 y Fu(m)g(m)1232 2602 y Fm(T)p 1120 2642 141 2 v 1168 2688 a Fq(m)1316 2653 y(:)437 b Fs(\(130\))p 1888 2706 2 146 v 0 2708 1890 2 v 920 2806 a(39)p eop %%Page: 40 14 40 13 bop 0 -54 a Fs(W)l(e)23 b(shall)f(see)h(later)f(that)i(matrix)e Fu(M)761 -72 y Fp(\013)813 -54 y Fs(describ)q(es)f(the)j(initial)e (conditions)f(for)i(the)g(scattered)0 6 y(Gaussian)15 b(b)q(eam)h(at)h(p)q(oin)o(t)f Fu(x)569 -13 y Fp(\013)598 6 y Fs(.)100 65 y(W)l(e)g(also)g(denote)h(b)o(y)833 82 y Fn(\022)878 122 y Fu(k)908 104 y Fm(\()p Fp(q)q Fm(\))880 182 y Fq(k)908 156 y Fm(\()p Fp(q)q Fm(\))906 195 y(3)970 82 y Fn(\023)1777 152 y Fs(\(131\))0 253 y(v)o(ector)g Fq(k)178 235 y Fp(\013)176 266 y(i)222 253 y Fs(co)o(v)m(arian)o(tly)f (transformed)e(in)o(to)i(the)h(ra)o(y{cen)o(tred)e(co)q(ordinate)h (system,)785 339 y Fq(k)813 319 y Fm(\()p Fp(q)q Fm(\))811 352 y Fp(a)880 339 y Fs(=)d Fq(h)961 319 y Fp(i)961 352 y(a)985 339 y Fq(k)1013 319 y Fp(\013)1011 352 y(i)1091 339 y Fq(:)672 b Fs(\(132\))0 481 y Fu(4.4.)25 b(Gaussian)18 b(b)r(eam)o(s)0 555 y(4.4.1.)24 b(Complex{v)m(alued)18 b(tra)n(v)n(el)j(time)c(of)h(the)i(Gaussian)e(b)r(eam)d(at)20 b(frequency)f Fq(!)1811 537 y Fm(0)0 628 y Fs(W)l(e)e(denote)f(b)o(y) 751 645 y Fn(\022)823 685 y Fu(M)83 b(M)1014 692 y Fm(3)796 745 y Fu(M)850 752 y Fm(3)873 723 y(T)954 745 y Fq(M)1002 752 y Fm(33)1052 645 y Fn(\023)1777 715 y Fs(\(133\))0 825 y(matrix)22 b Fq(\034)196 807 y Fm(0)190 838 y Fp(;ij)252 825 y Fo(\000)15 b Fq(\034)334 807 y Fm(0)p Fl(0)328 839 y Fp(;ik)378 825 y Fs(\()p Fq(\022)421 807 y Fm(0)p Fl(00)483 825 y Fs(+)g(i)p Fq(!)584 807 y Fl(\000)p Fm(1)637 825 y Fq(K)683 807 y Fp(\013)712 825 y Fs(\))731 804 y Fl(\000)p Fm(1)731 840 y Fp(k)q(l)784 825 y Fq(\034)812 807 y Fm(0)p Fl(0)806 839 y Fp(;j)r(l)875 825 y Fs(in)22 b(\(95\))h(co)o(v)m(arian)o(tly)f(transformed)f(in)o(to)i(the)g(ra)o (y{)0 885 y(cen)o(tred)16 b(co)q(ordinate)g(system,)337 971 y Fq(M)385 978 y Fp(ab)441 971 y Fs(=)d Fq(h)522 951 y Fp(i)522 983 y(a)546 971 y Fs(\()p Fu(x)595 951 y Fm(0)618 971 y Fs(\))8 b([)p Fq(\034)687 951 y Fm(0)681 983 y Fp(;ij)739 971 y Fo(\000)j Fq(\034)817 951 y Fm(0)p Fl(0)811 983 y Fp(;ik)861 971 y Fs(\()p Fq(\022)904 951 y Fm(0)p Fl(00)962 971 y Fs(+)g(i)p Fq(!)1059 951 y Fl(\000)p Fm(1)1112 971 y Fq(K)1158 951 y Fp(\013)1186 971 y Fs(\))1205 950 y Fl(\000)p Fm(1)1205 986 y Fp(k)q(l)1259 971 y Fq(\034)1287 951 y Fm(0)p Fl(0)1281 983 y Fp(;j)r(l)1326 971 y Fs(])d Fq(h)1377 947 y Fp(j)1377 986 y(b)1398 971 y Fs(\()p Fu(x)1447 951 y Fm(0)1470 971 y Fs(\))50 b Fq(:)224 b Fs(\(134\))0 1058 y(Matrix)18 b(\(133\))g(can)g(simply)f(b)q(e)i (calculated)f(using)f(matrices)g(\(120\),)i(\(121\))f(and)g(\(129\).)27 b(Its)18 b(sub-)0 1117 y(matrices)g Fu(M)256 1124 y Fm(3)297 1117 y Fs(and)g Fq(M)444 1124 y Fm(33)506 1117 y Fs(come)g(directly)h (from)f(\(121\),)h(and)f(are)h(de\014ned)e(b)o(y)i(\(110\))g(with)g (\(112\).)0 1177 y(The)d(2)s Fo(\002)s Fs(2)g(submatrix)f(reads)385 1269 y Fu(M)f Fs(=)g Fu(P)545 1276 y Ff(2)570 1269 y Fu(Q)613 1276 y Ff(2)638 1247 y Fl(\000)p Fm(1)703 1269 y Fo(\000)d Fu(Q)796 1276 y Ff(2)821 1247 y Fl(\000)p Fm(1)874 1237 y(T)905 1269 y Fs([)p Fu(Q)962 1276 y Ff(2)987 1247 y Fl(\000)p Fm(1)1041 1269 y Fu(Q)1084 1276 y Ff(1)1120 1269 y Fs(+)g Fu(M)1224 1248 y Fp(\013)1252 1269 y Fs(])1266 1248 y Fl(\000)p Fm(1)1320 1269 y Fu(Q)1363 1276 y Ff(2)1388 1247 y Fl(\000)p Fm(1)1491 1269 y Fq(:)272 b Fs(\(135\))0 1355 y(Considering)14 b(the)j(symmetry)f(of)h Fu(P)689 1362 y Ff(2)714 1355 y Fu(Q)757 1362 y Ff(2)782 1333 y Fl(\000)p Fm(1)836 1355 y Fs(,)f(\(135\))h(can)f(b)q(e)h(expressed)f (as)331 1455 y Fu(M)e Fs(=)f Fu(Q)494 1462 y Ff(2)519 1433 y Fl(\000)p Fm(1)573 1423 y(T)604 1455 y Fs([)p Fu(P)657 1462 y Ff(2)682 1433 y Fm(T)713 1455 y Fs(\()p Fu(Q)775 1462 y Ff(1)811 1455 y Fs(+)e Fu(Q)904 1462 y Ff(2)929 1455 y Fu(M)983 1434 y Fp(\013)1012 1455 y Fs(\))g Fo(\000)g Fu(1)p Fs(][)p Fu(Q)1192 1462 y Ff(1)1228 1455 y Fs(+)g Fu(Q)1321 1462 y Ff(2)1346 1455 y Fu(M)1400 1434 y Fp(\013)1428 1455 y Fs(])1442 1434 y Fl(\000)p Fm(1)1546 1455 y Fq(:)217 b Fs(\(136\))0 1541 y(W)l(e)19 b(apply)f(the)g(symplectic)h(prop)q(ert)o(y)e(of)i(paraxial)e(ra)o(y)h (propagator)f(matrix)h(\(113\),)i Fu(P)1715 1548 y Ff(2)1740 1519 y Fm(T)1771 1541 y Fu(Q)1814 1548 y Ff(1)1851 1541 y Fo(\000)0 1601 y Fu(Q)43 1608 y Ff(2)68 1579 y Fm(T)99 1601 y Fu(P)138 1608 y Ff(1)177 1601 y Fs(=)14 b Fu(1)i Fs(and)g Fu(P)411 1608 y Ff(2)436 1579 y Fm(T)467 1601 y Fu(Q)510 1608 y Ff(2)546 1601 y Fo(\000)11 b Fu(Q)639 1608 y Ff(2)664 1579 y Fm(T)695 1601 y Fu(P)734 1608 y Ff(2)773 1601 y Fs(=)j Fu(0)p Fs(,)397 1698 y Fu(M)g Fs(=)f Fu(Q)560 1705 y Ff(2)586 1676 y Fl(\000)p Fm(1)639 1666 y(T)670 1698 y Fu(Q)713 1705 y Ff(2)738 1676 y Fm(T)769 1698 y Fs([)p Fu(P)822 1705 y Ff(1)858 1698 y Fs(+)e Fu(P)947 1705 y Ff(2)972 1698 y Fu(M)1026 1678 y Fp(\013)1055 1698 y Fs(][)p Fu(Q)1126 1705 y Ff(1)1162 1698 y Fs(+)g Fu(Q)1255 1705 y Ff(2)1280 1698 y Fu(M)1334 1678 y Fp(\013)1362 1698 y Fs(])1376 1678 y Fl(\000)p Fm(1)1480 1698 y Fq(;)283 b Fs(\(137\))0 1784 y(and)16 b(arriv)o(e)f(at)522 1844 y Fu(M)g Fs(=)e([)p Fu(P)696 1851 y Ff(1)732 1844 y Fs(+)e Fu(P)821 1851 y Ff(2)846 1844 y Fu(M)900 1824 y Fp(\013)929 1844 y Fs(][)p Fu(Q)1000 1851 y Ff(1)1036 1844 y Fs(+)g Fu(Q)1129 1851 y Ff(2)1154 1844 y Fu(M)1208 1824 y Fp(\013)1237 1844 y Fs(])1251 1824 y Fl(\000)p Fm(1)1354 1844 y Fq(;)409 b Fs(\(138\))0 1918 y(whic)o(h)16 b(describ)q(es)f(the)i(Gaussian)e(b)q (eam)h(giv)o(en)g(b)o(y)g(initial)g(conditions)818 2004 y Fu(M)f Fs(=)e Fu(M)993 1984 y Fp(\013)1777 2004 y Fs(\(139\))0 2090 y(at)j(p)q(oin)o(t)f Fu(x)219 2072 y Fp(\013)263 2090 y Fs(\(Klime)m(\024)-22 b(s,)15 b(2004,)g(eq.)h(50;)754 2078 y(\024)748 2090 y(Cerv)o(en)q(\023)-26 b(y,)16 b(Klime)m(\024)-22 b(s)14 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)15 b(2007,)h(eq.)f(135\).)22 b(De\014ning)0 2150 y(the)17 b(matrix)p 0 2181 1890 2 v 0 2284 2 103 v 724 2253 a Fu(Q)d Fs(=)g Fu(Q)877 2260 y Fm(1)910 2253 y Fs(+)d Fu(Q)1003 2260 y Fm(2)1025 2253 y Fu(M)1079 2232 y Fp(\013)1767 2253 y Fs(\(140\))p 1888 2284 V 0 2286 1890 2 v 0 2350 a(of)17 b(geometrical)f(spreading)e(of)j(the)g (Gaussian)e(b)q(eam,)h(and)g(matrix)p 0 2391 V 0 2494 2 103 v 723 2463 a Fu(P)e Fs(=)g Fu(P)868 2470 y Fm(1)901 2463 y Fs(+)d Fu(P)990 2470 y Fm(2)1013 2463 y Fu(M)1067 2442 y Fp(\013)1145 2463 y Fq(;)608 b Fs(\(141\))p 1888 2494 V 0 2496 1890 2 v 0 2560 a(equation)16 b(\(138\))h(ma)o(y)f(b)q(e) h(expressed)f(in)g(the)h(form)p 0 2604 V 0 2706 2 103 v 781 2675 a Fu(M)d Fs(=)g Fu(PQ)984 2655 y Fl(\000)p Fm(1)1087 2675 y Fq(:)666 b Fs(\(142\))p 1888 2706 V 0 2708 1890 2 v 920 2806 a(40)p eop %%Page: 41 15 41 14 bop 0 -54 a Fs(The)19 b(paraxial)g(expansion)f(\(95\))i(of)f(the) h(complex{v)m(alued)e(tra)o(v)o(el{time)h(of)g(the)h(time{harmonic)0 6 y(Gaussian)11 b(b)q(eam)g(scattered)h(b)o(y)g(Gab)q(or)g(function)g Fq(g)980 -12 y Fp(\013)1008 6 y Fs(\()p Fu(x)p Fs(\))h(at)f(frequency)g Fq(!)1399 -12 y Fm(0)1434 6 y Fs(in)f(the)i(lo)q(cal)f(Cartesian)0 66 y(co)q(ordinates)k(reads)p 0 102 1890 2 v 0 217 2 115 v 376 174 a Fq(T)412 154 y Fp(\013)405 187 y(!)431 178 y Fg(0)454 174 y Fs(\()p Fu(x)p Fs(\))f(=)e Fq(T)625 154 y Fp(\013)665 174 y Fs(+)d Fq(\034)742 154 y Fm(0)775 174 y Fs(+)839 154 y Fm(d)p Fp(\034)p 831 163 60 2 v 831 191 a Fm(d)p Fp(q)871 196 y Fg(3)897 174 y Fs(\001)p Fq(x)967 148 y Fm(\()p Fp(q)q Fm(\))967 187 y(3)1031 174 y Fs(+)1087 154 y Fm(1)p 1087 163 20 2 v 1087 191 a(2)1113 174 y Fs(\001)p Fq(x)1183 148 y Fm(\()p Fp(q)q Fm(\))1183 188 y Fp(i)1236 174 y Fq(M)1284 181 y Fp(ij)1319 174 y Fs(\001)p Fq(x)1389 148 y Fm(\()p Fp(q)q Fm(\))1389 188 y Fp(j)1492 174 y Fq(:)261 b Fs(\(143\))p 1888 217 2 115 v 0 219 1890 2 v 0 289 a(Matrix)12 b Fq(M)210 296 y Fp(ij)259 289 y Fs(is)g(giv)o(en)g(b)o(y)h(\(112\))g(and)f(\(142\).) 21 b(Note)14 b(that)f(\(143\))g(can)g(b)q(e)g(expressed)e(in)i(ra)o (y{cen)o(tred)0 349 y(co)q(ordinates)j(as)505 411 y Fq(T)541 390 y Fp(\013)534 424 y(!)560 414 y Fg(0)583 411 y Fs(\()p Fu(x)p Fs(\))e(=)g Fq(T)754 390 y Fp(\013)793 411 y Fs(+)d Fq(\034)871 390 y Fp(\013)899 411 y Fs(\()p Fu(x)948 390 y Fm(R)980 411 y Fs(\()p Fq(q)1021 418 y Fm(3)1044 411 y Fs(\)\))h(+)1150 391 y Fm(1)p 1150 400 20 2 v 1150 428 a(2)1175 411 y Fu(q)1205 390 y Fm(T)1237 411 y Fu(Mq)50 b Fq(:)392 b Fs(\(144\))0 554 y Fu(4.4.2.)24 b(Complex{v)m(alued)18 b(tra)n(v)n(el)j(time)c(of)h(the)i(Gaussian)e(b)r(eam)d(at)20 b(frequency)f Fq(!)0 631 y Fs(W)l(e)i(m)o(ultiply)f(matrix)g(\(129\))i (b)o(y)e(v)o(ector)h(\(131\).)35 b(The)21 b(\014rst)f(t)o(w)o(o)h(ra)o (y{cen)o(tred)e(comp)q(onen)o(ts)h(of)0 691 y(v)o(ector)d(\()p Fq(!)202 673 y Fm(0)224 691 y Fs(\))243 673 y Fl(\000)p Fm(1)297 691 y Fs(\()p Fq(\022)340 673 y Fm(0)p Fl(00)397 691 y Fs(+)11 b(i)p Fq(!)494 673 y Fl(\000)p Fm(1)547 691 y Fq(K)593 673 y Fp(\013)622 691 y Fs(\))641 670 y Fl(\000)p Fm(1)641 705 y Fp(ij)695 691 y Fq(k)723 673 y Fp(\013)721 704 y(j)767 691 y Fs(app)q(earing)k(in)h(equation)h (\(96\))g(then)f(are)645 794 y Fo(\000)p Fs([)p Fu(Q)741 801 y Ff(2)766 772 y Fl(\000)p Fm(1)819 794 y Fu(Q)862 801 y Ff(1)898 794 y Fs(+)11 b Fu(M)1002 773 y Fp(\013)1031 794 y Fs(])1045 773 y Fl(\000)p Fm(1)1098 794 y Fu(M)1152 773 y Fp(\013)1152 806 y Fm(4)1231 794 y Fq(;)532 b Fs(\(145\))0 886 y(where)p 0 923 1890 2 v 0 1108 2 186 v 552 1027 a Fu(M)606 1006 y Fp(\013)606 1039 y Fm(4)648 1027 y Fs(=)14 b Fo(\000)p Fs(\()p Fq(!)792 1006 y Fm(0)814 1027 y Fs(\))833 1006 y Fl(\000)p Fm(1)895 941 y Fn( )935 1027 y Fu(k)965 1006 y Fm(\()p Fp(q)q Fm(\))1029 1027 y Fo(\000)1085 993 y Fu(m)p Fq(k)1163 967 y Fm(\()p Fp(q)q Fm(\))1162 1006 y(3)p 1085 1015 129 2 v 1127 1061 a Fq(m)1219 941 y Fn(!)1317 1027 y Fq(:)436 b Fs(\(146\))p 1888 1108 2 186 v 0 1110 1890 2 v 0 1180 a(The)16 b(third)g(ra)o(y{cen)o(tred)f (comp)q(onen)o(t)h(of)g(v)o(ector)h(\()p Fq(!)1010 1162 y Fm(0)1033 1180 y Fs(\))1052 1162 y Fl(\000)p Fm(1)1105 1180 y Fs(\()p Fq(\022)1148 1162 y Fm(0)p Fl(00)1206 1180 y Fs(+)11 b(i)p Fq(!)1303 1162 y Fl(\000)p Fm(1)1356 1180 y Fq(K)1402 1162 y Fp(\013)1430 1180 y Fs(\))1449 1158 y Fl(\000)p Fm(1)1449 1193 y Fp(ij)1503 1180 y Fq(k)1531 1162 y Fp(\013)1529 1193 y(j)1575 1180 y Fs(is)481 1290 y(\()p Fq(!)533 1272 y Fm(0)555 1290 y Fs(\))574 1272 y Fl(\000)p Fm(1)628 1290 y Fq(k)656 1264 y Fm(\()p Fp(q)q Fm(\))654 1303 y(3)720 1290 y Fs(+)g Fu(m)820 1272 y Fm(T)848 1290 y Fs([)p Fu(Q)905 1297 y Ff(2)930 1268 y Fl(\000)p Fm(1)984 1290 y Fu(Q)1027 1297 y Ff(1)1063 1290 y Fs(+)g Fu(M)1167 1272 y Fp(\013)1195 1290 y Fs(])1209 1272 y Fl(\000)p Fm(1)1263 1290 y Fu(M)1317 1272 y Fp(\013)1317 1302 y Fm(4)p 481 1312 865 2 v 891 1357 a Fq(m)1401 1323 y(:)362 b Fs(\(147\))0 1439 y(The)11 b(\014rst)g(t)o(w)o(o)g(ra)o (y{cen)o(tred)f(comp)q(onen)o(ts)g(of)i(v)o(ector)g(\()p Fq(!)1067 1420 y Fm(0)1089 1439 y Fs(\))1108 1420 y Fl(\000)p Fm(1)1162 1439 y Fq(\034)1190 1420 y Fm(0)p Fl(0)1184 1452 y Fp(;ij)1231 1439 y Fs(\()p Fq(\022)1274 1420 y Fm(0)p Fl(00)1321 1439 y Fs(+)q(i)p Fq(!)1408 1420 y Fl(\000)p Fm(1)1461 1439 y Fq(K)1507 1420 y Fp(\013)1535 1439 y Fs(\))1554 1417 y Fl(\000)p Fm(1)1554 1454 y Fp(j)r(k)1608 1439 y Fq(k)1636 1420 y Fp(\013)1634 1453 y(k)1675 1439 y Fs(app)q(earing)0 1498 y(in)k(equation)h(\(96\))g(can)f(b)q(e)h (obtained)f(from)f(\(120\))i(and)f(\(145\).)23 b(They)16 b(read)517 1604 y Fu(M)571 1611 y Fm(4)607 1604 y Fs(=)e Fu(Q)703 1611 y Ff(2)728 1582 y Fl(\000)p Fm(1)781 1572 y(T)812 1604 y Fs([)p Fu(Q)869 1611 y Ff(2)894 1582 y Fl(\000)p Fm(1)948 1604 y Fu(Q)991 1611 y Ff(1)1027 1604 y Fs(+)d Fu(M)1131 1584 y Fp(\013)1160 1604 y Fs(])1174 1584 y Fl(\000)p Fm(1)1227 1604 y Fu(M)1281 1584 y Fp(\013)1281 1616 y Fm(4)1359 1604 y Fq(;)404 b Fs(\(148\))0 1696 y(i.e.,)604 1768 y Fu(M)658 1775 y Fm(4)695 1768 y Fs(=)13 b([)p Fu(Q)804 1775 y Ff(1)840 1768 y Fs(+)e Fu(Q)933 1775 y Ff(2)958 1768 y Fu(M)1012 1747 y Fp(\013)1041 1768 y Fs(])1055 1747 y Fl(\000)p Fm(1)1108 1737 y(T)1139 1768 y Fu(M)1193 1747 y Fp(\013)1193 1780 y Fm(4)1272 1768 y Fq(:)491 b Fs(\(149\))0 1845 y(The)26 b(third)f(comp)q(onen)o(t) g(is)g(zero.)49 b(It)27 b(is)e(in)o(teresting)g(that)h(equation)g (\(149\))g(for)g(the)g(space{)0 1905 y(frequency)18 b(dep)q(endence)e (of)i(the)g(scattered)f(Gaussian)f(b)q(eam)h(has)g(the)g(same)g(form)g (as)g(the)g(equa-)0 1965 y(tion)c(for)f(the)h(space{time)f(dep)q (endence)h(of)g(a)f(Gaussian)f(pac)o(k)o(et)i(\(Klime)m(\024)-22 b(s,)13 b(2004,)g(eq.)g(74;)1703 1952 y(\024)1698 1965 y(Cerv)o(en)q(\023)-26 b(y,)0 2025 y(Klime)m(\024)k(s)15 b(&)i(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)16 b(2007,)g(eq.)h(166\).)22 b(Considering)15 b(de\014nition)g(\(140\),)i (equation)g(\(149\))g(ma)o(y)f(b)q(e)0 2085 y(expressed)f(in)i(the)f (form)p 0 2131 1890 2 v 0 2234 2 103 v 733 2203 a Fu(M)787 2210 y Fm(4)823 2203 y Fs(=)e Fu(Q)919 2182 y Fl(\000)p Fm(1)972 2172 y(T)1003 2203 y Fu(M)1057 2182 y Fp(\013)1057 2215 y Fm(4)1136 2203 y Fq(;)617 b Fs(\(150\))p 1888 2234 V 0 2236 1890 2 v 0 2306 a(with)16 b(initial)g(conditions)g Fu(M)550 2313 y Fm(4)586 2306 y Fs(=)e Fu(M)693 2288 y Fp(\013)693 2318 y Fm(4)722 2306 y Fs(.)100 2367 y(Quan)o(tit)o(y)487 2430 y Fq(M)535 2437 y Fm(44)591 2430 y Fs(=)g Fo(\000)p Fs(\()p Fq(!)735 2409 y Fm(0)757 2430 y Fs(\))776 2409 y Fl(\000)p Fm(2)830 2430 y Fq(k)858 2409 y Fp(\013)856 2442 y(i)886 2430 y Fs(\()p Fq(\022)929 2409 y Fm(0)p Fl(00)986 2430 y Fs(+)d(i)p Fq(!)1083 2409 y Fl(\000)p Fm(1)1136 2430 y Fq(K)1182 2409 y Fp(\013)1211 2430 y Fs(\))1230 2408 y Fl(\000)p Fm(1)1230 2443 y Fp(ij)1283 2430 y Fq(k)1311 2409 y Fp(\013)1309 2442 y(j)1389 2430 y Fq(;)374 b Fs(\(151\))0 2507 y(app)q(earing)11 b(in)h(equation)g (\(96\))h(can)f(b)q(e)g(obtained)f(from)h(equations)g(\(131\),)h (\(145\),)g(\(146\))g(and)f(\(147\).)0 2567 y(It)17 b(reads)p 0 2604 V 0 2706 2 103 v 450 2675 a Fq(M)498 2682 y Fm(44)554 2675 y Fs(=)d Fq(M)660 2655 y Fp(\013)655 2687 y Fm(44)708 2675 y Fo(\000)d Fu(M)812 2655 y Fp(\013)812 2687 y Fm(4)841 2652 y(T)872 2675 y Fs([)p Fu(Q)929 2682 y Ff(2)954 2653 y Fl(\000)p Fm(1)1007 2675 y Fu(Q)1050 2682 y Ff(1)1086 2675 y Fs(+)g Fu(M)1190 2655 y Fp(\013)1219 2675 y Fs(])1233 2655 y Fl(\000)p Fm(1)1286 2675 y Fu(M)1340 2655 y Fp(\013)1340 2687 y Fm(4)1419 2675 y Fq(;)334 b Fs(\(152\))p 1888 2706 V 0 2708 1890 2 v 920 2806 a(41)p eop %%Page: 42 16 42 15 bop 0 -54 a Fs(where)p 0 -17 1890 2 v 0 139 2 156 v 661 85 a Fq(M)714 65 y Fp(\013)709 98 y Fm(44)765 85 y Fs(=)14 b Fo(\000)p Fs(\()p Fq(!)909 65 y Fm(0)931 85 y Fs(\))950 65 y Fl(\000)p Fm(2)1010 52 y Fs(\()p Fq(k)1057 26 y Fm(\()p Fp(q)q Fm(\))1055 65 y(3)1110 52 y Fs(\))1129 34 y Fm(2)p 1010 74 142 2 v 1059 120 a Fq(m)1207 85 y(:)546 b Fs(\(153\))p 1888 139 2 156 v 0 141 1890 2 v 0 211 a(It)14 b(is)f(in)o(teresting)f(that)i(equation) g(\(152\))g(for)f(the)h(frequency)f(dep)q(endence)g(of)h(the)g (scattered)f(Gaus-)0 270 y(sian)19 b(b)q(eam)g(has)g(the)h(same)f(form) g(as)g(the)h(equation)g(for)f(the)h(time)g(dep)q(endence)f(of)h(a)g (Gaussian)0 330 y(pac)o(k)o(et)e(\(Klime)m(\024)-22 b(s,)17 b(2004,)h(eq.)g(80;)659 318 y(\024)653 330 y(Cerv)o(en)q(\023)-26 b(y,)18 b(Klime)m(\024)-22 b(s)17 b(&)g(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)18 b(2007,)g(eq.)g(167\).)26 b(Considering)0 390 y(de\014nition)15 b(\(140\),)i(equation)g(\(152\))g (ma)o(y)f(b)q(e)h(expressed)e(in)h(the)h(form)578 483 y Fq(M)626 490 y Fm(44)683 483 y Fs(=)c Fq(M)788 462 y Fp(\013)783 495 y Fm(44)837 483 y Fo(\000)e Fu(M)941 462 y Fp(\013)941 495 y Fm(4)970 459 y(T)1001 483 y Fu(Q)1044 462 y Fl(\000)p Fm(1)1097 483 y Fu(Q)1140 490 y Ff(2)1165 483 y Fu(M)1219 462 y Fp(\013)1219 495 y Fm(4)1298 483 y Fq(:)465 b Fs(\(154\))0 575 y(The)21 b(appro)o(ximate)f(frequency)i (dep)q(endence)f(\(96\))h(of)g(the)g(scattered)f(Gaussian)f(b)q(eam)h (can)h(b)q(e)0 635 y(expressed)15 b(in)i(lo)q(cal)f(Cartesian)g(co)q (ordinates)f(as)p 0 682 V 0 790 2 108 v 386 753 a Fq(T)422 733 y Fp(\013)415 766 y(!)450 753 y Fs(\()p Fu(x)p Fs(\))g(=)f Fq(T)622 733 y Fp(\013)615 767 y(!)641 757 y Fg(0)663 753 y Fs(\()p Fu(x)p Fs(\))e(+)f(\001)p Fq(x)863 728 y Fm(\()p Fp(q)q Fm(\))863 768 y Fp(K)916 753 y Fq(M)964 760 y Fp(K)r Fm(4)1029 734 y(\001)p Fp(!)p 1029 742 60 2 v 1045 771 a(!)1105 753 y Fs(+)1161 734 y Fm(1)p 1161 742 20 2 v 1161 771 a(2)1186 753 y Fq(M)1234 760 y Fm(44)1285 713 y Fn(\000)1314 734 y Fm(\001)p Fp(!)p 1314 742 60 2 v 1330 771 a(!)1379 713 y Fn(\001)1402 722 y Fm(2)1482 753 y Fq(;)271 b Fs(\(155\))p 1888 790 2 108 v 0 792 1890 2 v 0 862 a(or)16 b(in)g(ra)o(y{cen)o(tred)f(co)q(ordinates)h(as) 436 963 y Fq(T)472 942 y Fp(\013)465 975 y(!)500 963 y Fs(\()p Fu(x)p Fs(\))f(=)f Fq(T)672 942 y Fp(\013)665 976 y(!)691 966 y Fg(0)713 963 y Fs(\()p Fu(x)p Fs(\))e(+)f Fu(q)873 942 y Fm(T)904 963 y Fu(M)958 970 y Fm(4)987 943 y(\001)p Fp(!)p 987 951 60 2 v 1003 980 a(!)1063 963 y Fs(+)1119 943 y Fm(1)p 1119 951 20 2 v 1119 980 a(2)1144 963 y Fq(M)1192 970 y Fm(44)1243 922 y Fn(\000)1272 943 y Fm(\001)p Fp(!)p 1272 951 60 2 v 1288 980 a(!)1337 922 y Fn(\001)1360 932 y Fm(2)1440 963 y Fq(:)323 b Fs(\(156\))0 1122 y Fu(4.4.3.)24 b(Amplitude)18 b(of)g(the)i(Gaussian)e(b)r(eam)0 1199 y Fs(W)l(e)24 b(express)e(the)i(complex{v)m(alued)e(relativ)o(e)h (geometrical)g(spreading)e(in)i(terms)g(of)g(the)h(2)7 b Fo(\002)g Fs(2)0 1259 y(submatrix)j Fu(Q)275 1266 y Fm(2)297 1259 y Fs(\()p Fu(x)p Fq(;)e Fu(x)398 1241 y Fl(0)413 1259 y Fs(\))k(of)g(paraxial{ra)o(y)e(propagator)g(matrix)h (\(113\))h(in)f(ra)o(y{cen)o(tred)f(co)q(ordinates,)326 1395 y Fq(L)p Fs(\()p Fu(x)p Fq(;)e Fu(x)461 1374 y Fp(\013)491 1395 y Fs(\))14 b(=)576 1313 y Fn(s)p 626 1313 874 2 v 784 1361 a Fq(h)p Fs(\()p Fu(x)p Fs(\))h Fq(h)p Fs(\()p Fu(x)974 1347 y Fp(\013)1002 1361 y Fs(\))p 632 1383 542 2 v 632 1433 a Fq(v)r Fs(\()p Fu(x)p Fs(\))741 1413 y Fm(d)p Fp(\034)p 733 1422 60 2 v 733 1450 a Fm(d)p Fp(q)773 1455 y Fg(3)799 1433 y Fs(\()p Fu(x)p Fs(\))g Fq(v)r Fs(\()p Fu(x)957 1419 y Fp(\013)985 1433 y Fs(\))1018 1413 y Fm(d)p Fp(\034)p 1011 1422 V 1011 1450 a Fm(d)p Fp(q)1051 1455 y Fg(3)1076 1433 y Fs(\()p Fu(x)1125 1419 y Fp(\013)1154 1433 y Fs(\))1188 1395 y(det[)p Fu(Q)1314 1402 y Fm(2)1336 1395 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1437 1380 y Fp(\013)1467 1395 y Fs(\)])50 b Fq(:)213 b Fs(\(157\))0 1535 y(Jacobian)11 b Fq(h)i Fs(is)f(de\014ned)g(b)o(y)g(\(103\),)i(and) e Fq(v)i Fs(is)e(the)h(phase)f(v)o(elo)q(cit)o(y)l(,)h(see)g(\(21\).)21 b(Relativ)o(e)13 b(geometrical)0 1595 y(spreading)i(\(157\))i(should)e (correctly)h(include)g(p)q(ossible)f(phase)h(shifts)g(due)g(to)h (caustics.)100 1656 y(W)l(e)11 b(insert)f(expression)g(\(157\))h(in)o (to)g(equation)g(\(79\).)20 b(Then)11 b(the)g(pro)q(duct)f(of)i(the)f (determinan)o(ts)0 1716 y(in)16 b(\(79\))h(can)g(b)q(e)f(expressed)g (using)f(\(126\))i(as)0 1839 y(det\()p Fu(Q)131 1846 y Fm(2)154 1839 y Fs(\))g(det\()p Fq(K)324 1818 y Fp(\013)320 1851 y(ij)362 1839 y Fo(\000)6 b Fs(i)p Fq(!)r(\022)478 1818 y Fm(0)p Fl(00)477 1851 y Fp(;k)q(l)527 1839 y Fs(\))14 b(=)f([)p Fq(h)p Fs(\()p Fu(x)704 1818 y Fp(\013)733 1839 y Fs(\)])766 1818 y Fl(\000)p Fm(2)828 1839 y Fs(det)889 1768 y Fn(\024)915 1839 y Fo(\000)p Fs(i)p Fq(!)1001 1768 y Fn(\022)1045 1809 y Fu(Q)1088 1816 y Ff(1)1125 1809 y Fs(+)d Fu(Q)1217 1816 y Ff(2)1243 1809 y Fs(\()p Fu(T)1302 1791 y Fm(\()p Fp(q)q Fm(\))1366 1809 y Fs(+)h(i)p Fq(!)1463 1791 y Fl(\000)p Fm(1)1516 1809 y Fu(K)1561 1791 y Fm(\()p Fp(q)q Fm(\))1614 1809 y Fs(\))50 b Fu(Q)1726 1816 y Ff(2)1751 1809 y Fu(m)1300 1868 y(m)1351 1850 y Fm(T)1719 1868 y Fq(m)1807 1768 y Fn(\023)-8 b(\025)1876 1839 y Fq(:)1777 1928 y Fs(\(158\))0 1997 y(W)l(e)15 b(ma)o(y)g(m)o(ultiply)e(the)j(third)e(column)g(of)h(the)g(matrix)g(at) g(the)h(righ)o(t{hand)c(side)j(of)g(\(158\))h(b)o(y)1820 1978 y Ff(m)1857 1963 y Fg(T)p 1820 1986 64 2 v 1834 2014 a Fp(m)0 2057 y Fs(and)g(subtract)g(the)h(pro)q(duct)e(from)h(the) h(\014rst)f(t)o(w)o(o)g(columns,)41 2150 y(det\()p Fu(Q)172 2157 y Fm(2)195 2150 y Fs(\))h(det\()p Fq(K)365 2129 y Fp(\013)361 2162 y(ij)408 2150 y Fo(\000)11 b Fs(i)p Fq(!)r(\022)529 2129 y Fm(0)p Fl(00)528 2162 y Fp(;k)q(l)577 2150 y Fs(\))236 2261 y(=)j([)p Fq(h)p Fs(\()p Fu(x)381 2240 y Fp(\013)409 2261 y Fs(\)])442 2240 y Fl(\000)p Fm(2)504 2261 y Fs(det)565 2191 y Fn(\024)592 2261 y Fo(\000)p Fs(i)p Fq(!)678 2191 y Fn(\022)722 2236 y Fu(Q)765 2243 y Ff(1)801 2236 y Fs(+)d Fu(Q)894 2243 y Ff(2)919 2236 y Fs(\()p Fu(T)978 2218 y Fm(\()p Fp(q)q Fm(\))1042 2236 y Fs(+)g(i)p Fq(!)1139 2218 y Fl(\000)p Fm(1)1192 2236 y Fu(K)1237 2218 y Fm(\()p Fp(q)q Fm(\))1301 2236 y Fo(\000)1357 2216 y Ff(m)c(m)1438 2201 y Fg(T)p 1357 2224 109 2 v 1394 2253 a Fp(m)1471 2236 y Fs(\))50 b Fu(Q)1583 2243 y Ff(2)1608 2236 y Fu(m)1076 2295 y(0)1105 2277 y Fm(T)1576 2295 y Fq(m)1664 2191 y Fn(\023)-8 b(\025)1736 2261 y Fq(:)27 b Fs(\(159\))0 2383 y(Considering)14 b(\(130\))j(and)f (\(140\),)242 2505 y(det\()p Fu(Q)373 2512 y Fm(2)396 2505 y Fs(\))h(det\()p Fq(K)566 2485 y Fp(\013)562 2518 y(ij)609 2505 y Fo(\000)10 b Fs(i)p Fq(!)r(\022)729 2485 y Fm(0)p Fl(00)728 2518 y Fp(;k)q(l)778 2505 y Fs(\))k(=)f([)p Fq(h)p Fs(\()p Fu(x)955 2485 y Fp(\013)984 2505 y Fs(\)])1017 2485 y Fl(\000)p Fm(2)1079 2505 y Fs(det)1140 2435 y Fn(\024)1166 2505 y Fo(\000)p Fs(i)p Fq(!)1252 2435 y Fn(\022)1305 2475 y Fu(Q)58 b(Q)1449 2482 y Ff(2)1474 2475 y Fu(m)1296 2535 y(0)1325 2517 y Fm(T)1442 2535 y Fq(m)1530 2435 y Fn(\023)-9 b(\025)1634 2505 y Fq(;)129 b Fs(\(160\))0 2623 y(i.e.,)288 2686 y(det)q(\()p Fu(Q)420 2693 y Fm(2)442 2686 y Fs(\))17 b(det\()p Fq(K)612 2665 y Fp(\013)608 2698 y(ij)655 2686 y Fo(\000)11 b Fs(i)p Fq(!)r(\022)776 2665 y Fm(0)p Fl(00)775 2698 y Fp(;k)q(l)824 2686 y Fs(\))j(=)g([)p Fq(h)p Fs(\()p Fu(x)1002 2665 y Fp(\013)1031 2686 y Fs(\)])1064 2665 y Fl(\000)p Fm(2)1117 2686 y Fs(\()p Fo(\000)p Fs(i)p Fq(!)r(m)p Fs(\))j(det\()p Fo(\000)p Fs(i)p Fq(!)r Fu(Q)p Fs(\))50 b Fq(:)175 b Fs(\(161\))920 2806 y(42)p eop %%Page: 43 17 43 16 bop 0 -54 a Fs(W)l(e)17 b(insert)f(\(161\))h(in)o(to)f(\(79\))h (with)f(\(157\),)66 96 y Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)22 b Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)431 76 y Fp(\013)461 96 y Fs(\))480 -1 y Fn(s)p 530 -1 563 2 v 528 53 a Fq(\045)p Fs(\()p Fu(x)603 38 y Fp(\013)631 53 y Fs(\))664 33 y Fm(d)p Fp(\034)p 657 41 60 2 v 657 70 a Fm(d)p Fp(q)697 75 y Fg(3)722 53 y Fs(\()p Fu(x)p Fs(\))805 33 y Fm(d)p Fp(\034)p 797 41 V 797 70 a Fm(d)p Fp(q)837 75 y Fg(3)863 53 y Fs(\()p Fu(x)912 38 y Fp(\013)941 53 y Fs(\))p Fq(h)p Fs(\()p Fu(x)1038 38 y Fp(\013)1067 53 y Fs(\))p 528 85 559 2 v 711 130 a Fq(\045)p Fs(\()p Fu(x)p Fs(\))p Fq(h)p Fs(\()p Fu(x)p Fs(\))1118 63 y Fq(!)1163 50 y Fn(b)1151 63 y Fq(A)q Fs(\()p Fu(x)1238 44 y Fp(\013)1267 63 y Fq(;)g(!)r Fs(\))g Fq(r)1372 44 y Fp(\013)1401 63 y Fs(\()p Fu(x)p Fs(\))p 1098 85 393 2 v 1098 95 a Fn(p)p 1148 95 343 2 v 42 x Fs(det[)p Fo(\000)p Fs(i)p Fu(Q)p Fs(\()p Fu(x)p Fq(;)g Fu(x)1428 123 y Fp(\013)1457 137 y Fs(\)])1539 21 y Fo(p)p 1581 21 56 2 v 42 x Fs(2)p Fq(\031)p 1502 85 171 2 v 1502 95 a Fo(p)p 1544 95 130 2 v 39 x(\000)p Fs(i)p Fq(!)r(m)1696 96 y(:)67 b Fs(\(162\))0 223 y(The)16 b(initial)g(v)m(alue)h(of)g(the)g(amplitude)e(of)h(the)h(Gaussian)e(b)q (eam)h(at)h(p)q(oin)o(t)f Fu(x)1464 205 y Fp(\013)1510 223 y Fs(reads)p 0 269 1890 2 v 0 430 2 161 v 418 364 a Fn(b)-28 b Fq(a)q Fs(\()p Fu(x)494 344 y Fp(\013)523 364 y Fq(;)8 b(!)r Fs(\))14 b(=)f(i)p Fq(!)722 352 y Fn(b)710 364 y Fq(A)p Fs(\()p Fu(x)796 344 y Fp(\013)825 364 y Fq(;)8 b(!)r Fs(\))15 b Fq(r)937 344 y Fp(\013)966 364 y Fs(\()p Fu(x)p Fs(\))1062 345 y Fm(d)p Fp(\034)p 1055 353 60 2 v 1055 382 a Fm(d)p Fp(q)1095 387 y Fg(3)1120 364 y Fs(\()p Fu(x)1169 346 y Fp(\013)1198 364 y Fs(\))1261 289 y Fo(p)p 1302 289 56 2 v 1302 331 a Fs(2)p Fq(\031)p 1224 353 171 2 v 1224 363 a Fo(p)p 1265 363 130 2 v 1265 403 a(\000)p Fs(i)p Fq(!)r(m)1450 364 y(:)303 b Fs(\(163\))p 1888 430 2 161 v 0 432 1890 2 v 0 500 a(When)15 b(determining)e(the)i (sign)g(of)660 458 y Fn(p)p 710 458 343 2 v 42 x Fs(det[)p Fo(\000)p Fs(i)p Fu(Q)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)990 486 y Fp(\013)1019 500 y Fs(\)])15 b(at)g(p)q(oin)o(t)g Fu(x)f Fs(=)f Fu(x)1381 482 y Fp(\013)1410 500 y Fs(,)i(w)o(e)g(to)q (ok)h(in)o(to)f(accoun)o(t)0 560 y(that)f(matrix)f Fu(Q)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)408 542 y Fp(\013)437 560 y Fs(\))14 b(is)f(unit)h(at)f Fu(x)i Fs(=)e Fu(x)804 542 y Fp(\013)833 560 y Fs(,)h(but)f(has)g(a)g(small)g(p)q(ositiv)o (e{de\014nite)g(imaginary)f(part)0 620 y(along)k(the)h(ra)o(y)f(in)g (the)g(vicinit)o(y)h(of)g Fu(x)714 602 y Fp(\013)742 620 y Fs(.)100 680 y(W)l(e)i(no)o(w)f(express)h(the)g(amplitude)f(of)h (the)h(Gaussian)d(b)q(eam)i(in)g(terms)f(of)h(its)g(initial)g(v)m(alue) 0 740 y(\(163\),)p 0 788 1890 2 v 0 1005 2 218 v 153 914 a Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))15 b(=)22 b Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)518 893 y Fp(\013)547 914 y Fs(\))566 809 y Fn(v)566 837 y(u)566 867 y(u)566 897 y(t)p 619 809 394 2 v 617 871 a Fq(\045)p Fs(\()p Fu(x)692 856 y Fp(\013)721 871 y Fs(\))754 851 y Fm(d)p Fp(\034)p 746 859 60 2 v 746 888 a Fm(d)p Fp(q)786 893 y Fg(3)812 871 y Fs(\()p Fu(x)p Fs(\))p Fq(h)p Fs(\()p Fu(x)958 856 y Fp(\013)987 871 y Fs(\))p 617 903 390 2 v 631 952 a Fq(\045)p Fs(\()p Fu(x)p Fs(\))740 933 y Fm(d)p Fp(\034)p 732 941 60 2 v 732 970 a Fm(d)p Fp(q)772 975 y Fg(3)798 952 y Fs(\()p Fu(x)847 938 y Fp(\013)876 952 y Fs(\))p Fq(h)p Fs(\()p Fu(x)p Fs(\))1176 880 y(1)p 1019 903 340 2 v 1019 913 a Fn(p)p 1069 913 290 2 v 42 x Fs(det[)p Fu(Q)p Fs(\()p Fu(x)p Fq(;)g Fu(x)1296 941 y Fp(\013)1325 955 y Fs(\)])1372 914 y Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)1448 893 y Fp(\013)1477 914 y Fq(;)8 b(!)r Fs(\))50 b Fq(:)152 b Fs(\(164\))p 1888 1005 2 218 v 0 1007 1890 2 v 0 1076 a(Here)22 b Fq(v)r Fs(\()p Fu(x)p Fs(\))h(is)f(the)g(phase)g(v)o(elo)q(cit)o(y)l(,)h Fq(\045)p Fs(\()p Fu(x)p Fs(\))g(is)f(the)g(densit)o(y)l(,)h Fu(Q)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1329 1058 y Fp(\013)1358 1076 y Fs(\))23 b(is)e(the)i(complex{v)m(alued)0 1136 y(matrix)14 b(of)i(geometrical)e(spreading)f(of)i(the)g(Gaussian)e(b)q (eam,)i(and)f Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)1435 1118 y Fl(0)1450 1136 y Fs(\))16 b(is)e(the)h(accum)o(ulated)0 1196 y(recipro)q(cal)h(transmission)e(co)q(e\016cien)o(t)j(describing)e (amplitude)g(losses)h(b)q(et)o(w)o(een)h(p)q(oin)o(ts)f Fu(x)1732 1178 y Fl(0)1763 1196 y Fs(and)g Fu(x)0 1256 y Fs(due)g(to)h(atten)o(uation)f(and)f(due)h(to)h(re\015ections)f(and)f (scattering)h(in)o(to)g(directions)f(leading)h(outside)0 1315 y(the)d(vicinit)o(y)g(of)g(p)q(oin)o(t)f Fu(x)p Fs(.)21 b(Re\015ectivit)o(y)13 b(function)g Fq(r)977 1297 y Fp(\013)1019 1315 y Fs(in)f(\(163\))h(is)g(giv)o(en)f(b)o(y)h (\(68\))g(and)f Fq(m)h Fs(is)f(de\014ned)0 1375 y(b)o(y)18 b(\(128\).)27 b(T)l(erm)358 1333 y Fn(p)p 408 1333 290 2 v 42 x Fs(det[)p Fu(Q)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)635 1361 y Fp(\013)664 1375 y Fs(\)])19 b(is)f(equal)g(to)g(1)g(at)h Fu(x)d Fs(=)h Fu(x)1201 1357 y Fp(\013)1229 1375 y Fs(,)i(and)e(then)h (v)m(aries)g(con)o(tin)o(uously)0 1435 y(along)e(the)h(ra)o(y)l(.)0 1558 y Fu(4.4.4.)24 b(Note)19 b(on)g(\\e\013ectiv)n(e)j(relativ)n(e)g (slo)n(wness)d(p)r(erturbation")0 1634 y Fs(W)l(e)e(de\014ne)f(the)g (\\e\013ectiv)o(e)i(second)e(deriv)m(ativ)o(es)g(of)g(tra)o(v)o(el)g (time")h(b)o(y)f(equation)723 1725 y Fq(T)759 1705 y Fm(e\013)752 1738 y Fp(;ij)820 1725 y Fs(=)d Fq(T)908 1705 y Fp(\013)901 1738 y(;ij)959 1725 y Fo(\000)e Fq(T)1045 1701 y Fm(ra)o(y)1038 1739 y Fp(;ij)1153 1725 y Fq(:)610 b Fs(\(165\))0 1816 y(The)17 b(second)g(deriv)m(ativ)o(es)g Fq(T)550 1798 y Fp(\013)543 1829 y(;ij)607 1816 y Fs(of)h(tra)o(v)o(el) e(time)i(of)f(the)h(inciden)o(t)e(w)o(a)o(v)o(e)h(are)g(de\014ned)f(b)o (y)h(equation)0 1876 y(\(38\).)30 b(They)19 b(include)f(b)q(oth)h(the)g (second)f(deriv)m(ativ)o(es)h(of)g(tra)o(v)o(el)f(time)h(due)g(to)g (the)g(curv)m(ature)g(of)0 1936 y(the)e(w)o(a)o(v)o(efron)o(t)e(and)h (due)g(to)h(the)f(curv)m(ature)h(of)f(the)h(ra)o(y)l(.)k(Matrix)507 2027 y Fq(T)543 2003 y Fm(ra)o(y)536 2041 y Fp(;ij)615 2027 y Fs(=)13 b Fo(\000)p Fq(H)747 2034 y Fp(;i)776 2027 y Fq(p)801 2034 y Fp(j)833 2027 y Fo(\000)e Fq(p)908 2034 y Fp(i)925 2027 y Fq(H)966 2034 y Fp(;j)1010 2027 y Fs(+)g Fq(p)1085 2034 y Fp(i)1101 2027 y Fq(p)1126 2034 y Fp(j)1147 2027 y Fq(H)1192 2007 y Fp(;m)1242 2027 y Fq(H)1283 2034 y Fp(;m)1777 2027 y Fs(\(166\))0 2118 y(corresp)q(onds)20 b(to)j(the)f(scattered)g(w)o(a)o(v)o(e)g(and)f(con) o(tains)g(only)h(the)h(second)e(deriv)m(ativ)o(es)h(\(109\))h(of)0 2178 y(tra)o(v)o(el)14 b(time)g(due)f(to)i(the)f(curv)m(ature)g(of)g (the)h(ra)o(y)l(.)20 b(Deriv)m(ativ)o(es)14 b Fq(H)1242 2160 y Fp(;i)1286 2178 y Fs(and)f Fq(H)1421 2185 y Fp(;i)1464 2178 y Fs(of)h(the)h(homogeneous)0 2238 y(Hamiltonian,)23 b(de\014ned)f(b)o(y)h(\(102\),)i(corresp)q(ond)c(to)i(the)g(cen)o(tral) f(ra)o(y)h(of)g(the)g(Gaussian)e(b)q(eam)0 2298 y(scattered)i(at)g(p)q (oin)o(t)f Fu(x)453 2280 y Fp(\013)482 2298 y Fs(.)41 b(In)22 b(ra)o(y{cen)o(tred)g(co)q(ordinates,)h(matrix)f Fq(T)1372 2280 y Fp(\013)1365 2311 y(;ij)1435 2298 y Fs(is)g(giv)o(en)h(b)o(y)f(equation)0 2358 y(\(122\),)16 b(and)e(matrix)g Fq(T)434 2334 y Fm(ra)o(y)427 2371 y Fp(;ij)507 2358 y Fs(can)h(b)q(e)g(describ)q(ed)e(b)o(y)i(equation)f (\(133\))i(with)f Fu(M)f Fs(=)f Fu(0)p Fs(,)i Fu(M)1623 2365 y Fm(3)1660 2358 y Fs(=)e Fu(M)1766 2340 y Fp(\013)1766 2370 y Fm(3)1810 2358 y Fs(and)0 2417 y Fq(M)48 2424 y Fm(33)104 2417 y Fs(=)h Fq(M)210 2399 y Fp(\013)205 2430 y Fm(33)247 2417 y Fs(.)100 2478 y(Matrix)22 b Fq(T)308 2460 y Fm(e\013)301 2491 y Fp(;ij)370 2478 y Fs(+)16 b(i)p Fq(!)472 2460 y Fl(\000)p Fm(1)525 2478 y Fq(K)571 2460 y Fp(\013)567 2491 y(ij)625 2478 y Fs(can)23 b(b)q(e)g(expressed)f (in)h(ra)o(y{cen)o(tred)f(co)q(ordinates)g(in)h(terms)f(of)0 2538 y(quan)o(tities)16 b(\(127\),)h(\(128\))g(and)f(\(130\))h(as)687 2588 y Fn(\022)732 2633 y Fu(M)786 2615 y Fp(\013)826 2633 y Fs(+)881 2614 y Ff(mm)955 2599 y Fg(T)p 881 2622 102 2 v 914 2651 a Fp(m)1038 2633 y Fu(m)821 2693 y(m)872 2675 y Fm(T)1040 2693 y Fq(m)1095 2588 y Fn(\023)1189 2659 y Fq(;)574 b Fs(\(167\))920 2806 y(43)p eop %%Page: 44 18 44 17 bop 0 -54 a Fs(where)14 b Fq(m)h Fs(is)f(related)h(to)g(the)g (e\013ectiv)o(e)g(second)f(deriv)m(ativ)o(es)h(\(165\))g(of)g(tra)o(v)o (el)f(time)h(through)e(equa-)0 6 y(tion)532 75 y Fq(m)g Fs(=)h Fq(H)687 54 y Fp(;i)716 75 y Fs(\()p Fq(T)771 54 y Fm(e\013)764 87 y Fp(;ij)829 75 y Fs(+)d(i)p Fq(!)926 54 y Fl(\000)p Fm(1)979 75 y Fq(K)1025 54 y Fp(\013)1021 87 y(ij)1056 75 y Fs(\))p Fq(H)1120 54 y Fp(;j)1162 75 y Fs(\()1195 55 y Fm(d)p Fp(\034)p 1187 63 60 2 v 1187 92 a Fm(d)p Fp(q)1227 97 y Fg(3)1253 75 y Fs(\))1272 54 y Fm(2)1345 75 y Fq(;)418 b Fs(\(168\))0 164 y(see)17 b(\(99\).)22 b(Then)103 272 y(\()p Fq(T)158 251 y Fm(e\013)151 284 y Fp(;ij)216 272 y Fs(+)11 b(i)p Fq(!)313 251 y Fl(\000)p Fm(1)366 272 y Fq(K)412 251 y Fp(\013)408 284 y(ij)444 272 y Fs(\)\()p Fq(x)510 279 y Fp(i)538 272 y Fo(\000)g Fq(x)616 251 y Fp(\013)616 284 y(i)645 272 y Fs(\)\()p Fq(x)711 279 y Fp(j)744 272 y Fo(\000)g Fq(x)822 251 y Fp(\013)822 284 y(j)851 272 y Fs(\))j(=)g Fu(q)967 251 y Fm(T)998 272 y Fu(M)1052 251 y Fp(\013)1081 272 y Fu(q)d Fs(+)g Fq(m)d Fs(\()p Fq(q)1265 279 y Fm(3)1299 272 y Fo(\000)j Fq(q)1373 251 y Fp(\013)1371 284 y Fm(3)1412 272 y Fs(+)1468 252 y Ff(m)1505 237 y Fg(T)p 1468 260 64 2 v 1482 289 a Fp(m)1538 272 y Fu(q)p Fs(\))1587 251 y Fm(2)1660 272 y Fq(;)103 b Fs(\(169\))0 383 y(where)16 b Fq(x)172 365 y Fm(R)172 396 y Fp(i)204 383 y Fs(\()p Fq(q)247 365 y Fp(\013)245 395 y Fm(3)276 383 y Fs(\))f(=)f Fq(x)391 365 y Fp(\013)391 396 y(i)420 383 y Fs(.)24 b(W)l(e)17 b(ma)o(y)f(consider)g(plane)g(w)o(a)o(v)o(e)g(with)h (amplitude)1464 370 y Fn(b)1452 383 y Fq(A)p Fs(\()p Fu(x)1538 365 y Fp(\013)1567 383 y Fq(;)8 b(!)r Fs(\))17 b(inciden)o(t)f(in)0 443 y(direction)g Fq(p)233 425 y Fm(0)233 456 y Fp(i)272 443 y Fs(on)o(to)g(relativ)o(e)g(slo)o(wness)f (p)q(erturbation)287 542 y Fo(\000)332 522 y Fp(\016)q(v)p 332 530 41 2 v 341 559 a(v)378 542 y Fs(\()p Fu(x)p Fs(\))g(=)f Fq(r)537 521 y Fp(\013)566 542 y Fs(\()p Fu(x)p Fs(\))j(exp[)747 522 y Fm(1)p 747 530 20 2 v 747 559 a(2)773 542 y Fs(\()p Fq(x)820 549 y Fp(i)849 542 y Fo(\000)10 b Fq(x)926 521 y Fp(\013)926 554 y(i)955 542 y Fs(\)\()p Fo(\000)p Fq(K)1078 521 y Fp(\013)1074 554 y(ij)1121 542 y Fs(+)h(i)p Fq(!)r(T)1254 521 y Fm(e\013)1247 554 y Fp(;ij)1300 542 y Fs(\)\()p Fq(x)1366 549 y Fp(j)1400 542 y Fo(\000)f Fq(x)1477 521 y Fp(\013)1477 554 y(j)1506 542 y Fs(\)])50 b Fq(:)174 b Fs(\(170\))0 640 y(The)16 b(corresp)q(onding)f(tra)o(v)o(el{time)g(p) q(erturbation)549 761 y Fq(\016)r(\034)20 b Fs(=)660 694 y Fn(Z)698 761 y Fs(d)p Fq(\034)13 b Fs(\()p Fo(\000)825 742 y Fp(\016)q(v)p 825 750 41 2 v 835 779 a(v)872 761 y Fs(\))h(=)950 694 y Fn(Z)988 761 y Fs(d)p Fq(q)1038 768 y Fm(3)1083 728 y Fs(d)p Fq(\034)p 1074 750 73 2 v 1074 796 a Fs(d)p Fq(q)1124 803 y Fm(3)1161 761 y Fs(\()p Fo(\000)1225 742 y Fp(\016)q(v)p 1225 750 41 2 v 1235 779 a(v)1272 761 y Fs(\))486 b(\(171\))0 883 y(calculated)16 b(in)g(ra)o(y{cen)o(tred)f(co)q(ordinates)h(then)h(reads)434 1015 y Fq(\016)r(\034)6 b Fs(\()p Fu(q)p Fs(\))14 b(=)g Fq(r)644 995 y Fp(\013)673 1015 y Fs(\()p Fu(q)p Fs(\))765 981 y(d)p Fq(\034)p 756 1004 73 2 v 756 1049 a Fs(d)p Fq(q)806 1056 y Fm(3)877 940 y Fo(p)p 919 940 56 2 v 41 x Fs(2)p Fq(\031)p 840 1004 171 2 v 840 1014 a Fo(p)p 882 1014 130 2 v 39 x(\000)p Fs(i)p Fq(!)r(m)1025 1015 y Fs(exp\(i)p Fq(!)1173 996 y Fm(1)p 1173 1004 20 2 v 1173 1032 a(2)1199 1015 y Fu(q)1229 995 y Fm(T)1260 1015 y Fu(M)1314 995 y Fp(\013)1343 1015 y Fu(q)p Fs(\))50 b Fq(:)321 b Fs(\(172\))0 1139 y(The)17 b(corresp)q(onding)e (\014rst{order)g(p)q(erturbation)h(of)h(the)h(inciden)o(t)e(plane)g(w)o (a)o(v)o(e)h(is)g(then)g(equal)g(to)0 1200 y(the)i(scattered)f (Gaussian)f(b)q(eam)h(with)g(initial)g(amplitude)f(\(163\).)29 b(F)l(actor)1480 1180 y Fm(d)p Fp(\034)p 1472 1188 60 2 v 1472 1217 a Fm(d)p Fp(q)1512 1222 y Fg(3)1538 1158 y Fo(p)p 1579 1158 56 2 v 1579 1200 a Fs(2)p Fq(\031)r(=)1659 1160 y Fo(p)p 1701 1160 130 2 v 40 x(\000)p Fs(i)p Fq(!)r(m)17 b Fs(in)0 1266 y(\(163\))g(th)o(us)f(represen)o(ts)e(the)j(in)o(tegral) f(of)g(function)476 1365 y(exp[)p Fo(\000)611 1345 y Fm(1)p 611 1353 20 2 v 611 1382 a(2)637 1365 y Fs(\()p Fq(x)684 1372 y Fp(i)712 1365 y Fo(\000)11 b Fq(x)790 1344 y Fp(\013)790 1377 y(i)819 1365 y Fs(\)\()p Fq(K)903 1344 y Fp(\013)899 1377 y(ij)946 1365 y Fo(\000)g Fs(i)p Fq(!)r(T)1079 1344 y Fm(e\013)1072 1377 y Fp(;ij)1125 1365 y Fs(\)\()p Fq(x)1191 1372 y Fp(j)1224 1365 y Fo(\000)g Fq(x)1302 1344 y Fp(\013)1302 1377 y(j)1331 1365 y Fs(\)])413 b(\(173\))0 1463 y(with)16 b(resp)q(ect)h(to)g(tra)o(v)o(el)f(time)g (along)g(the)h(cen)o(tral)f(ra)o(y)g(of)g(the)h(scattered)g(Gaussian)e (b)q(eam.)100 1528 y(In)o(v)o(erse)g(matrix)h(\()p Fq(T)486 1509 y Fm(e\013)544 1528 y Fs(+)11 b(i)p Fq(!)641 1509 y Fl(\000)p Fm(1)694 1528 y Fq(K)740 1509 y Fp(\013)768 1528 y Fs(\))787 1506 y Fl(\000)p Fm(1)787 1541 y Fp(;ij)858 1528 y Fs(in)16 b(ra)o(y{cen)o(tred)f(co)q(ordinates)h(reads)546 1595 y Fn(\022)648 1629 y Fu(M)702 1611 y Fp(\013)731 1607 y Fl(\000)p Fm(1)947 1629 y Fo(\000)p Fu(M)1040 1611 y Fp(\013)1069 1607 y Fl(\000)p Fm(1)1128 1609 y Ff(m)p 1128 1617 38 2 v 1129 1646 a Fp(m)591 1703 y Fo(\000)636 1683 y Ff(m)673 1668 y Fg(T)p 636 1691 64 2 v 650 1720 a Fp(m)706 1703 y Fu(M)760 1685 y Fp(\013)788 1681 y Fl(\000)p Fm(1)905 1683 y(1)p 898 1691 36 2 v 898 1720 a Fp(m)950 1703 y Fs(+)1006 1683 y Ff(m)1043 1668 y Fg(T)1070 1683 y Ff(M)1112 1668 y Fc(\013)r Fd(\000)p Fg(1)1184 1683 y Ff(m)p 1006 1691 216 2 v 1086 1720 a Fp(m)1121 1710 y Fg(2)1235 1595 y Fn(\023)1330 1666 y Fq(:)433 b Fs(\(174\))0 1803 y(W)l(e)15 b(th)o(us)g(see)g(that)h(in)o(v)o(erse)d (matrix)i Fu(M)757 1785 y Fp(\013)786 1781 y Fl(\000)p Fm(1)855 1803 y Fs(to)g(matrix)g Fu(M)1129 1785 y Fp(\013)1158 1803 y Fs(,)g(whic)o(h)f(describ)q(es)g(the)i(initial)f(shap)q(e)0 1863 y(of)g(the)g(Gaussian)e(b)q(eam,)i(represen)o(ts)e(the)i(pro)s (jection)f(of)g(matrix)h(\()p Fq(T)1320 1845 y Fm(e\013)1374 1863 y Fs(+)7 b(i)p Fq(!)1467 1845 y Fl(\000)p Fm(1)1521 1863 y Fq(K)1567 1845 y Fp(\013)1595 1863 y Fs(\))1614 1842 y Fl(\000)p Fm(1)1614 1877 y Fp(;ij)1682 1863 y Fs(in)o(v)o(erse)14 b(to)0 1931 y(matrix)i Fq(T)198 1913 y Fm(e\013)191 1944 y Fp(;ij)256 1931 y Fs(+)11 b(i)p Fq(!)353 1913 y Fl(\000)p Fm(1)406 1931 y Fq(K)452 1913 y Fp(\013)448 1944 y(ij)500 1931 y Fs(on)o(to)16 b(the)h(w)o(a)o(v)o (efron)o(t)e(tangen)o(t)h(plane,)524 2043 y Fq(M)577 2023 y Fp(\013)606 2020 y Fl(\000)p Fm(1)606 2056 y Fp(K)r(L)686 2043 y Fs(=)738 2030 y Fn(b)739 2043 y Fq(h)768 2023 y Fp(K)768 2055 y(i)820 2043 y Fs(\()p Fq(T)875 2023 y Fm(e\013)933 2043 y Fs(+)10 b(i)p Fq(!)1029 2023 y Fl(\000)p Fm(1)1083 2043 y Fq(K)1129 2023 y Fp(\013)1157 2043 y Fs(\))1176 2022 y Fl(\000)p Fm(1)1176 2057 y Fp(;ij)1243 2030 y Fn(b)1244 2043 y Fq(h)1273 2023 y Fp(L)1273 2055 y(j)1352 2043 y Fq(:)411 b Fs(\(175\))0 2142 y(This)18 b(pro)s(jection)h(on)o(to)g(the)g(w)o(a)o(v)o(efron)o(t)f(tangen)o(t)h (plane)f(is)h(p)q(erformed)f(in)h(the)g(direction)f(of)i(the)0 2202 y(ra)o(y)l(.)920 2806 y(44)p eop %%Page: 45 19 45 18 bop 0 -54 a Fu(4.5.)25 b(Cen)n(tral)20 b(ra)n(ys)f(of)f(the)i (Gaussian)e(b)r(eam)o(s)0 29 y Fs(The)c(cen)o(tral)g(ra)o(y)f(of)i(the) f(Gaussian)f(b)q(eam)h(scattered)g(at)g(frequency)h Fq(!)1354 11 y Fm(0)1390 29 y Fs(is)f(determined)f(b)o(y)h(initial)0 90 y(p)q(oin)o(t)g Fu(x)158 72 y Fp(\013)201 90 y Fs(and)g(initial)g (slo)o(wness)e(v)o(ector)j Fq(p)807 72 y Fm(0)807 103 y Fp(i)829 90 y Fs(.)21 b(The)14 b(cen)o(tral)g(ra)o(y)g(of)h(the)f (Gaussian)f(b)q(eam)h(scattered)0 150 y(at)20 b(sligh)o(tly)f (di\013eren)o(t)f(frequency)i Fq(!)h Fs(is)f(close)f(to)h(this)f(ra)o (y)l(,)g(but)h(is)f(di\013eren)o(t.)30 b(It)20 b(do)q(es)g(not)f(pass)0 210 y(exactly)f(through)d(p)q(oin)o(t)h Fu(x)520 192 y Fp(\013)565 210 y Fs(and)g(its)h(initial)e(slo)o(wness)g(v)o(ector)i (is)f(sligh)o(tly)f(di\013eren)o(t)h(from)g Fq(p)1788 192 y Fm(0)1788 223 y Fp(i)1810 210 y Fs(.)0 351 y Fu(4.5.1.)24 b(F)-5 b(requency)20 b(dep)r(endence)f(of)g(the)g(cen)n(tral)i(ra)n(ys) e(of)f(the)h(Gaussian)g(b)r(eam)o(s)0 435 y Fs(A)o(t)c(frequency)f Fq(!)326 417 y Fm(0)363 435 y Fs(giv)o(en)f(b)o(y)h(equations)g(\(90\)) h(and)f(\(91\),)h(the)f(cen)o(tral)g(ra)o(y)g(of)g(the)h(Gaussian)d(b)q (eam)0 495 y(is)19 b(determined)e(b)o(y)i(initial)g(p)q(oin)o(t)f Fu(x)696 477 y Fp(\013)744 495 y Fs(and)g(initial)h(slo)o(wness)e(v)o (ector)i Fq(p)1368 477 y Fm(0)1368 508 y Fp(i)1390 495 y Fs(,)h(see)f(equation)g(\(143\))h(or)0 555 y(\(144\).)i(A)o(t)16 b(frequencies)e Fq(!)j Fs(from)e(the)g(vicinit)o(y)g(of)g Fq(!)987 537 y Fm(0)1010 555 y Fs(,)g(the)g(cen)o(tral)g(ra)o(y)f(of)i (the)f(Gaussian)f(b)q(eam)h(is)0 615 y(deviated.)22 b(In)15 b(the)h(ra)o(y{cen)o(tred)f(co)q(ordinates)g Fq(q)922 622 y Fp(i)938 615 y Fs(,)h(attac)o(hed)g(to)g(the)g(axial)g(ra)o(y)f (with)g(initial)h(p)q(oin)o(t)0 676 y Fu(x)30 657 y Fp(\013)75 676 y Fs(and)g(initial)g(slo)o(wness)f(v)o(ector)h Fq(p)689 657 y Fm(0)689 689 y Fp(i)712 676 y Fs(,)g(the)h(cen)o(tral)f(ra)o(y)g (of)g(the)h(Gaussian)e(b)q(eam)h(is)p 639 746 31 2 v 639 774 a Fu(q)e Fs(=)f Fo(\000)p Fs(\(Im)p Fu(M)p Fs(\))926 754 y Fl(\000)p Fm(1)980 774 y Fs(Im)p Fu(M)1094 781 y Fm(4)1123 754 y(\001)p Fp(!)p 1123 763 60 2 v 1139 791 a(!)1237 774 y Fq(:)526 b Fs(\(176\))0 873 y(see)22 b(equations)g(\(143\))g(and)g(\(155\).)39 b(Inserting)21 b(equation)h(\(150\))g(and)g(iden)o(tit)o(y)f(\(Klime)m(\024)-22 b(s,)23 b(2004,)0 933 y(eq.)17 b(75\))635 1013 y(Im)p Fu(M)d Fs(=)g Fu(Q)859 993 y Fl(\000)p Fm(1)912 983 y(T)943 1013 y Fs(Im)p Fu(M)1057 993 y Fp(\013)1085 1013 y Fu(Q)1128 993 y Fl(\000)p Fm(1)1182 983 y Fl(\003)1777 1013 y Fs(\(177\))0 1097 y(in)o(to)i(equation)g(\(176\),)h(w)o(e)g(arriv)o(e)e(at)p 575 1167 31 2 v 575 1195 a Fu(q)f Fs(=)f Fo(\000)p Fs(Im[)p Fu(Q)827 1175 y Fl(\003)849 1195 y Fs(\(Im)p Fu(M)982 1175 y Fp(\013)1011 1195 y Fs(\))1030 1175 y Fl(\000)p Fm(1)1084 1195 y Fu(M)1138 1175 y Fp(\013)1138 1208 y Fm(4)1167 1195 y Fs(])1187 1176 y Fm(\001)p Fp(!)p 1187 1184 60 2 v 1203 1213 a(!)1301 1195 y Fq(:)462 b Fs(\(178\))0 1294 y(Considering)14 b(de\014nition)i(\(140\),)h(equation)f(\(178\))h (ma)o(y)f(b)q(e)h(expressed)e(as)p 0 1364 31 2 v 0 1392 a Fu(q)6 b Fs(=)g Fo(f\000)p Fu(Q)188 1399 y Fm(1)209 1392 y Fs(\(Im)p Fu(M)342 1372 y Fp(\013)364 1392 y Fs(\))383 1372 y Fl(\000)p Fm(1)437 1392 y Fs(Im)o Fu(M)550 1372 y Fp(\013)550 1405 y Fm(4)574 1392 y Fs(+)s Fu(Q)659 1399 y Fm(2)681 1392 y Fs([Im)o Fu(M)808 1372 y Fp(\013)837 1392 y Fs(\(Im)p Fu(M)970 1372 y Fp(\013)992 1392 y Fs(\))1011 1372 y Fl(\000)p Fm(1)1064 1392 y Fs(Re)p Fu(M)1177 1372 y Fp(\013)1177 1405 y Fm(4)1201 1392 y Fo(\000)s Fs(Re)o Fu(M)1355 1372 y Fp(\013)1384 1392 y Fs(\(Im)p Fu(M)1517 1372 y Fp(\013)1539 1392 y Fs(\))1558 1372 y Fl(\000)p Fm(1)1612 1392 y Fs(Im)o Fu(M)1725 1372 y Fp(\013)1725 1405 y Fm(4)1754 1392 y Fs(])p Fo(g)1799 1373 y Fm(\001)p Fp(!)p 1799 1381 60 2 v 1815 1410 a(!)1876 1392 y Fq(:)1777 1453 y Fs(\(179\))0 1513 y(Equation)16 b(\(179\))h(describ)q(es)f(the)g (paraxial)g(ra)o(y)p 691 1583 31 2 v 691 1611 a Fu(q)e Fs(=)g Fu(Q)831 1618 y Fm(1)p 853 1583 V 853 1611 a Fu(q)883 1591 y Fp(\013)923 1611 y Fs(+)d Fu(Q)1016 1618 y Fm(2)p 1038 1583 32 2 v 1038 1611 a Fu(p)1070 1591 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)1777 1611 y Fs(\(180\))0 1710 y(with)16 b(initial)g(conditions)p 614 1750 31 2 v 614 1779 a Fu(q)645 1758 y Fp(\013)687 1779 y Fs(=)d Fo(\000)p Fs(\(Im)p Fu(M)911 1758 y Fp(\013)940 1779 y Fs(\))959 1758 y Fl(\000)p Fm(1)1013 1779 y Fs(Im)o Fu(M)1126 1758 y Fp(\013)1126 1791 y Fm(4)1161 1759 y(\001)p Fp(!)p 1161 1767 60 2 v 1177 1796 a(!)1777 1779 y Fs(\(181\))0 1862 y(and)p 88 1933 32 2 v 88 1961 a Fu(p)120 1940 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)213 1961 y Fs(=)g([Re)p Fu(M)392 1940 y Fp(\013)392 1973 y Fm(4)432 1961 y Fo(\000)e Fs(Re)o Fu(M)594 1940 y Fp(\013)623 1961 y Fs(\(Im)p Fu(M)756 1940 y Fp(\013)785 1961 y Fs(\))804 1940 y Fl(\000)p Fm(1)858 1961 y Fs(Im)o Fu(M)971 1940 y Fp(\013)971 1973 y Fm(4)1000 1961 y Fs(])1020 1941 y Fm(\001)p Fp(!)p 1020 1949 60 2 v 1036 1978 a(!)1099 1961 y Fs(=)i(Re)p Fu(M)1264 1940 y Fp(\013)1264 1973 y Fm(4)1299 1941 y(\001)p Fp(!)p 1299 1949 V 1315 1978 a(!)1375 1961 y Fs(+)e(Re)o Fu(M)1537 1940 y Fp(\013)p 1566 1933 31 2 v 1566 1961 a Fu(q)1596 1940 y Fp(\013)1675 1961 y Fq(:)88 b Fs(\(182\))0 2059 y(Equation)15 b(\(180\))g(determines)f(the)h(cen)o(tral)f(ra)o(y)h (of)g(the)g(Gaussian)f(b)q(eam)h(scattered)g(at)g(frequency)0 2119 y Fq(!)j Fs(in)e(the)h(ra)o(y)e(cen)o(tred)h(co)q(ordinates)f (corresp)q(onding)f(to)j(frequency)g Fq(!)1358 2101 y Fm(0)1380 2119 y Fs(.)22 b(The)16 b(paraxial)f(appro)o(xi-)0 2180 y(mation)h(of)h(the)f(slo)o(wness{v)o(ector)f(corresp)q(onding)f (to)j(paraxial)e(ra)o(y)h(\(180\))h(is)p 661 2250 32 2 v 661 2278 a Fu(p)693 2258 y Fm(\()p Fp(q)q Fm(\))760 2278 y Fs(=)c Fu(P)851 2285 y Fm(1)p 874 2250 31 2 v 874 2278 a Fu(q)904 2258 y Fp(\013)943 2278 y Fs(+)e Fu(P)1032 2285 y Fm(2)p 1055 2250 32 2 v 1055 2278 a Fu(p)1087 2258 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)1215 2278 y Fq(:)548 b Fs(\(183\))0 2377 y(The)24 b(cen)o(tral)g(ra)o(y)f (of)i(the)g(Gaussian)d(b)q(eam)i(is)g(giv)o(en)g(b)o(y)g(initial)g(p)q (osition)f(\(181\))i(and)f(initial)0 2437 y(slo)o(wness)15 b(v)o(ector)h(\(182\).)920 2806 y(45)p eop %%Page: 46 20 46 19 bop 0 -54 a Fu(4.5.2.)24 b(Shap)r(e)18 b(of)h(the)g(Gaussian)g(b) r(eam)o(s)0 20 y Fs(W)l(e)e(denote)g(b)o(y)317 19 y Fn(e)316 20 y Fu(q)g Fs(the)g(ra)o(y{cen)o(tered)e(co)q(ordinates)h(measured)f (from)h(the)h(frequency{dep)q(enden)o(t)0 80 y(cen)o(tral)f(ra)o(y)g (\(180\))h(of)g(the)f(Gaussian)f(b)q(eam,)804 169 y Fu(q)f Fs(=)p 901 141 31 2 v 14 w Fu(q)d Fs(+)993 168 y Fn(e)992 169 y Fu(q)50 b Fq(:)691 b Fs(\(184\))0 258 y(Note)20 b(that)g(the)f(co)q(ordinate)g(planes)f(of)786 257 y Fn(e)785 258 y Fu(q)h Fs(are)g(still)g(tangen)o(t)g(to)h(w)o(a)o(v)o (efron)o(ts)d(along)i(ra)o(y)g Fu(q)f Fs(=)h Fu(0)p Fs(,)0 318 y(not)e(along)e(ra)o(y)309 317 y Fn(e)307 318 y Fu(q)f Fs(=)g Fu(0)p Fs(.)100 378 y(P)o(araxial)d(expansion)g(\(156\))i(with)f (\(144\))h(of)f(the)h(complex{v)m(alued)f(tra)o(v)o(el{time)f(of)h(the) h(Gaus-)0 438 y(sian)j(b)q(eam)g(in)g(ra)o(y{cen)o(tered)f(co)q (ordinates)h Fu(q)h Fs(reads)162 527 y Fq(T)198 506 y Fp(\013)191 539 y(!)227 527 y Fs(\()p Fu(x)p Fs(\))e(=)e Fq(T)398 506 y Fp(\013)438 527 y Fs(+)d Fq(\034)515 506 y Fp(\013)543 527 y Fs(\()p Fu(x)592 506 y Fm(R)624 527 y Fs(\()p Fq(q)665 534 y Fm(3)688 527 y Fs(\)\))i(+)794 507 y Fm(1)p 794 515 20 2 v 794 544 a(2)820 527 y Fu(q)850 506 y Fm(T)881 527 y Fu(Mq)f Fs(+)g Fu(q)1056 506 y Fm(T)1087 527 y Fu(M)1141 534 y Fm(4)1170 507 y(\001)p Fp(!)p 1170 515 60 2 v 1187 544 a(!)1246 527 y Fs(+)1302 507 y Fm(1)p 1302 515 20 2 v 1302 544 a(2)1328 527 y Fq(M)1376 534 y Fm(44)1418 527 y Fs(\()1443 507 y Fm(\001)p Fp(!)p 1444 515 60 2 v 1460 544 a(!)1509 527 y Fs(\))1528 506 y Fm(2)1600 527 y Fq(:)163 b Fs(\(185\))0 616 y(In)21 b(co)q(ordinates)338 615 y Fn(e)337 616 y Fu(q)h Fs(measured)d(from)i (the)h(cen)o(tral)e(ra)o(y)h(of)h(the)g(scattered)f(Gaussian)f(b)q (eam,)i(w)o(e)0 676 y(shall)16 b(analogously)f(write)162 770 y Fq(T)198 749 y Fp(\013)191 782 y(!)227 770 y Fs(\()p Fu(x)p Fs(\))g(=)e Fq(T)398 749 y Fp(\013)438 770 y Fs(+)f Fn(e)-30 b Fq(\034)515 749 y Fp(\013)543 770 y Fs(\()563 769 y Fn(e)562 770 y Fu(x)592 749 y Fm(R)624 770 y Fs(\()p Fq(q)665 777 y Fm(3)688 770 y Fs(\)\))12 b(+)794 750 y Fm(1)p 794 758 20 2 v 794 787 a(2)821 769 y Fn(e)820 770 y Fu(q)850 749 y Fm(T)881 770 y Fu(M)936 769 y Fn(e)935 770 y Fu(q)f Fs(+)1028 769 y Fn(e)1026 770 y Fu(q)1056 749 y Fm(T)1090 757 y Fn(f)1087 770 y Fu(M)1141 777 y Fm(4)1170 750 y(\001)p Fp(!)p 1170 758 60 2 v 1187 787 a(!)1246 770 y Fs(+)1302 750 y Fm(1)p 1302 758 20 2 v 1302 787 a(2)1334 757 y Fn(f)1328 770 y Fq(M)1376 777 y Fm(44)1418 770 y Fs(\()1443 750 y Fm(\001)p Fp(!)p 1444 758 60 2 v 1460 787 a(!)1509 770 y Fs(\))1528 749 y Fm(2)1600 770 y Fq(;)163 b Fs(\(186\))0 859 y(where)426 919 y Fn(e)-30 b Fq(\034)452 898 y Fp(\013)480 919 y Fs(\()500 918 y Fn(e)499 919 y Fu(x)529 898 y Fm(R)561 919 y Fs(\()p Fq(q)602 926 y Fm(3)625 919 y Fs(\)\))15 b(=)e Fq(\034)758 898 y Fp(\013)786 919 y Fs(\()p Fu(x)835 898 y Fm(R)867 919 y Fs(\()p Fq(q)908 926 y Fm(3)931 919 y Fs(\)\))f(+)1037 899 y Fm(1)p 1037 907 20 2 v 1037 936 a(2)p 1063 890 32 2 v 1063 919 a Fu(p)1094 898 y Fm(\()p Fp(q)q Fm(\))1148 884 y(T)p 1178 890 31 2 v 1178 919 a Fu(q)g Fs(+)p 1270 890 32 2 v 11 w Fu(p)1301 898 y Fm(\()p Fp(q)q Fm(\))1355 884 y(T)1387 918 y Fn(e)1385 919 y Fu(q)362 b Fs(\(187\))0 993 y(is)14 b(the)h(linear)f(T)l(a)o (ylor)f(expansion)h(of)h(tra)o(v)o(el)f(time)g(in)g(co)q(ordinates)1277 992 y Fn(e)1276 993 y Fu(q)p Fs(.)22 b(Inserting)13 b(\(184\))i(in)o (to)g(\(185\))0 1053 y(and)h(comparing)f(the)h(result)g(with)h (equations)f(\(186\))h(and)f(\(187\),)g(w)o(e)h(obtain)596 1137 y Fn(f)593 1150 y Fu(M)647 1157 y Fm(4)684 1150 y Fs(=)d Fu(M)791 1157 y Fm(4)824 1150 y Fs(+)d Fu(M)p 928 1122 31 2 v(q)981 1130 y Fp(!)p 965 1138 60 2 v 965 1167 a Fm(\001)p Fp(!)1041 1150 y Fo(\000)p 1091 1122 32 2 v 11 w Fu(p)1123 1129 y Fm(\()p Fp(q)q Fm(\))1198 1130 y Fp(!)p 1182 1138 60 2 v 1182 1167 a Fm(\001)p Fp(!)1777 1150 y Fs(\(188\))0 1239 y(and)309 1286 y Fn(f)303 1299 y Fq(M)351 1306 y Fm(44)408 1299 y Fs(=)i Fq(M)508 1306 y Fm(44)562 1299 y Fs(+)e(2)p Fu(M)691 1306 y Fm(4)713 1277 y(T)p 744 1270 31 2 v 744 1299 a Fu(q)797 1279 y Fp(!)p 780 1287 60 2 v 780 1316 a Fm(\001)p Fp(!)856 1299 y Fs(+)p 906 1270 31 2 v 11 w Fu(q)936 1278 y Fm(T)967 1299 y Fu(M)p 1021 1270 V(q)q Fs(\()1094 1279 y Fp(!)p 1077 1287 60 2 v 1077 1316 a Fm(\001)p Fp(!)1142 1299 y Fs(\))1161 1278 y Fm(2)1195 1299 y Fo(\000)p 1245 1270 32 2 v 11 w Fu(p)1277 1278 y Fm(\()p Fp(q)q Fm(\))1330 1264 y(T)p 1361 1270 31 2 v 1361 1299 a Fu(q)p Fs(\()1433 1279 y Fp(!)p 1416 1287 60 2 v 1416 1316 a Fm(\001)p Fp(!)1481 1299 y Fs(\))1500 1278 y Fm(2)1573 1299 y Fq(:)190 b Fs(\(189\))0 1373 y(Considering)14 b(\(188\),)j(equation)g(\(189\))g (reads)537 1457 y Fn(f)531 1470 y Fq(M)579 1477 y Fm(44)635 1470 y Fs(=)d Fq(M)736 1477 y Fm(44)789 1470 y Fs(+)d Fu(M)893 1477 y Fm(4)916 1448 y(T)p 947 1442 31 2 v 947 1470 a Fu(q)999 1450 y Fp(!)p 983 1458 60 2 v 983 1487 a Fm(\001)p Fp(!)1059 1470 y Fs(+)1111 1457 y Fn(f)1109 1470 y Fu(M)1163 1449 y Fm(T)1163 1482 y(4)p 1194 1442 31 2 v 1194 1470 a Fu(q)1247 1450 y Fp(!)p 1230 1458 60 2 v 1230 1487 a Fm(\001)p Fp(!)1345 1470 y Fq(:)418 b Fs(\(190\))0 1559 y(Inserting)15 b(\(138\),)i(\(140\),)g(\(150\),)g (and)f(\(180\))h(in)o(to)f(\(188\),)h(w)o(e)f(obtain)89 1651 y Fn(f)87 1664 y Fu(M)141 1671 y Fm(4)178 1664 y Fs(=)d Fu(Q)273 1643 y Fl(\000)p Fm(1)327 1633 y(T)358 1664 y Fs([)p Fu(M)426 1643 y Fp(\013)426 1676 y Fm(4)465 1664 y Fs(+)e(\()p Fu(P)573 1671 y Ff(1)599 1642 y Fm(T)641 1664 y Fs(+)g Fu(M)745 1643 y Fp(\013)773 1664 y Fu(P)812 1671 y Ff(2)838 1642 y Fm(T)868 1664 y Fs(\)\()p Fu(Q)949 1671 y Ff(1)p 975 1636 31 2 v 975 1664 a Fu(q)1006 1643 y Fp(\013)1045 1664 y Fs(+)g Fu(Q)1138 1671 y Ff(2)p 1163 1636 32 2 v 1163 1664 a Fu(p)1195 1643 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)1274 1664 y Fs(\))1315 1644 y Fp(!)p 1299 1653 60 2 v 1299 1681 a Fm(\001)p Fp(!)1364 1664 y Fs(])g Fo(\000)p 1439 1636 32 2 v 11 w Fu(p)1471 1643 y Fm(\()p Fp(q)q Fm(\))1524 1630 y(T)1577 1644 y Fp(!)p 1561 1653 60 2 v 1561 1681 a Fm(\001)p Fp(!)1676 1664 y Fq(:)87 b Fs(\(191\))0 1753 y(Using)20 b(the)h(symplectic)f (prop)q(ert)o(y)g(of)h(the)g(paraxial)f(ra)o(y)g(propagator)f(matrix,)i (equation)g(\(191\))0 1813 y(ma)o(y)16 b(b)q(e)h(expressed)e(as)2 1902 y Fn(f)0 1915 y Fu(M)54 1922 y Fm(4)91 1915 y Fs(=)e Fu(Q)186 1895 y Fl(\000)p Fm(1)240 1884 y(T)271 1915 y Fo(f)p Fu(M)350 1895 y Fp(\013)350 1927 y Fm(4)381 1915 y Fs(+)s([\()p Fu(Q)499 1922 y Ff(1)524 1893 y Fm(T)558 1915 y Fs(+)s Fu(M)654 1895 y Fp(\013)682 1915 y Fu(Q)725 1922 y Ff(2)750 1893 y Fm(T)781 1915 y Fs(\)\()p Fu(P)858 1922 y Ff(1)p 884 1887 31 2 v 884 1915 a Fu(q)914 1895 y Fp(\013)946 1915 y Fs(+)s Fu(P)1027 1922 y Ff(2)p 1051 1887 32 2 v 1051 1915 a Fu(p)1083 1895 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)1162 1915 y Fs(\))s(+)s Fu(M)1280 1895 y Fp(\013)p 1309 1887 31 2 v 1309 1915 a Fu(q)1339 1895 y Fp(\013)1370 1915 y Fo(\000)p 1412 1887 32 2 v 3 w Fu(p)1444 1895 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)1523 1915 y Fs(])1559 1895 y Fp(!)p 1542 1904 60 2 v 1542 1932 a Fm(\001)p Fp(!)1607 1915 y Fo(g)s(\000)p 1677 1887 32 2 v 3 w Fu(p)1709 1895 y Fm(\()p Fp(q)q Fm(\))1762 1881 y(T)1815 1895 y Fp(!)p 1799 1904 60 2 v 1799 1932 a Fm(\001)p Fp(!)1876 1915 y Fq(:)1777 1975 y Fs(\(192\))0 2035 y(Inserting)f(\(181\))i(and)f(\(182\))g(in)o(to)g(\(192\),)h Fu(M)846 2017 y Fp(\013)846 2047 y Fm(4)889 2035 y Fs(cancels)e(with)i (\()p Fu(M)1238 2017 y Fp(\013)p 1267 2007 31 2 v 1267 2035 a Fu(q)1297 2015 y Fp(\013)1330 2035 y Fo(\000)p 1374 2007 32 2 v 5 w Fu(p)1405 2015 y Fm(\()p Fp(q)q Fm(\))p Fp(\013)1484 2035 y Fs(\))1526 2015 y Fp(!)p 1510 2023 60 2 v 1510 2052 a Fm(\001)p Fp(!)1588 2035 y Fs(and)f(w)o(e)g(obtain)830 2123 y Fn(f)827 2136 y Fu(M)881 2143 y Fm(4)918 2136 y Fs(=)g Fu(0)50 b Fq(:)714 b Fs(\(193\))0 2225 y(Considering)14 b(\(149\),)j(equation)g(\(152\))g (can)f(b)q(e)h(expressed)e(as)610 2314 y Fq(M)658 2321 y Fm(44)715 2314 y Fs(=)e Fo(\000)p Fu(M)860 2321 y Fm(4)883 2293 y(T)914 2314 y Fu(Q)957 2321 y Ff(2)982 2314 y Fu(M)1036 2294 y Fp(\013)1036 2327 y Fm(4)1076 2314 y Fs(+)d Fq(M)1178 2294 y Fp(\013)1173 2327 y Fm(44)1266 2314 y Fq(:)497 b Fs(\(194\))0 2404 y(Equation)16 b(\(190\))h(with)g(\(194\))g(and)f (\(193\))h(reads)541 2488 y Fn(f)535 2500 y Fq(M)583 2507 y Fm(44)639 2500 y Fs(=)d Fu(M)746 2507 y Fm(4)769 2478 y(T)799 2500 y Fs([)p 813 2472 31 2 v Fu(q)866 2481 y Fp(!)p 849 2489 60 2 v 849 2517 a Fm(\001)p Fp(!)926 2500 y Fo(\000)c Fu(Q)1018 2507 y Ff(2)1044 2500 y Fu(M)1098 2480 y Fp(\013)1098 2513 y Fm(4)1126 2500 y Fs(])h(+)g Fq(M)1254 2480 y Fp(\013)1249 2513 y Fm(44)1341 2500 y Fq(:)422 b Fs(\(195\))0 2589 y(Inserting)15 b(\(180\))i(with)g (\(181\))g(and)f(\(182\),)350 2673 y Fn(f)344 2686 y Fq(M)392 2693 y Fm(44)448 2686 y Fs(=)e Fo(\000)p Fu(M)594 2693 y Fm(4)616 2664 y(T)647 2686 y Fs([)p Fu(Q)704 2693 y Ff(1)740 2686 y Fs(+)d Fu(Q)833 2693 y Ff(2)858 2686 y Fu(M)912 2665 y Fp(\013)941 2686 y Fs(]\(Im)o Fu(M)1087 2665 y Fp(\013)1116 2686 y Fs(\))1135 2665 y Fl(\000)p Fm(1)1189 2686 y Fs(Im)p Fu(M)1303 2665 y Fp(\013)1303 2698 y Fm(4)1342 2686 y Fs(+)g Fq(M)1445 2665 y Fp(\013)1440 2698 y Fm(44)1532 2686 y Fq(:)231 b Fs(\(196\))920 2806 y(46)p eop %%Page: 47 21 47 20 bop 0 -54 a Fs(Inserting)15 b(\(150\),)i(w)o(e)g(arriv)o(e)e(at) 501 27 y Fn(f)494 39 y Fq(M)542 46 y Fm(44)599 39 y Fs(=)e Fo(\000)p Fu(M)744 19 y Fp(\013)744 52 y Fm(4)773 16 y(T)804 39 y Fs(\(Im)p Fu(M)937 19 y Fp(\013)965 39 y Fs(\))984 19 y Fl(\000)p Fm(1)1038 39 y Fs(Im)p Fu(M)1152 19 y Fp(\013)1152 52 y Fm(4)1192 39 y Fs(+)d Fq(M)1294 19 y Fp(\013)1289 52 y Fm(44)1382 39 y Fq(;)381 b Fs(\(197\))0 133 y(and)13 b(see)g(that)282 120 y Fn(f)275 133 y Fq(M)323 140 y Fm(44)379 133 y Fs(is)g(constan)o(t)g(along)f(the)i(cen)o(tral)e (ra)o(y)h(of)g(the)h(Gaussian)d(b)q(eam)i(as)g(w)o(e)g(exp)q(ected.)0 193 y(Considering)h(\(181\),)j(w)o(e)g(see)f(that)511 274 y Fn(f)505 286 y Fq(M)553 293 y Fm(44)596 286 y Fs(\()621 267 y Fm(\001)p Fp(!)p 621 275 60 2 v 637 303 a(!)686 286 y Fs(\))705 266 y Fm(2)742 286 y Fs(=)d Fu(M)848 266 y Fp(\013)848 298 y Fm(4)877 263 y(T)p 908 258 31 2 v 908 286 a Fu(q)938 266 y Fp(\013)973 267 y Fm(\001)p Fp(!)p 973 275 60 2 v 989 303 a(!)1049 286 y Fs(+)d Fq(M)1151 266 y Fp(\013)1146 298 y Fm(44)1189 286 y Fs(\()1214 267 y Fm(\001)p Fp(!)p 1214 275 V 1231 303 a(!)1279 286 y Fs(\))1298 266 y Fm(2)1371 286 y Fq(:)392 b Fs(\(198\))0 372 y(Note)25 b(that)f(equation)f(\(198\))i(is)e(also)g(a)h(direct)f (consequence)h(of)g(equation)f(\(156\))i(and)e(of)h(the)0 432 y(de\014nition)15 b(of)p 278 403 31 2 v 17 w Fu(q)p Fs(.)0 546 y Fu(4.5.3.)24 b(F)-5 b(requency)20 b(dep)r(endence)f(of)g (the)g(amplitude)f(of)g(the)h(Gaussian)g(b)r(eam)o(s)0 619 y Fs(F)l(requency)11 b(dep)q(endence)g(of)i(the)f(amplitude)e(of)i (the)g(Gaussian)f(b)q(eams)g(is)g(giv)o(en)g(b)o(y)h(m)o(ultiplication) 0 679 y(factor)711 739 y(exp[i)p Fq(!)854 719 y Fm(1)p 853 727 20 2 v 853 756 a(2)885 726 y Fn(f)879 739 y Fq(M)927 746 y Fm(44)970 739 y Fs(\()995 719 y Fm(\001)p Fp(!)p 995 727 60 2 v 1011 756 a(!)1060 739 y Fs(\))1079 718 y Fm(2)1102 739 y Fs(])49 b Fq(;)598 b Fs(\(199\))0 812 y(see)17 b(equation)f(\(186\))h(with)f(\(193\).)100 872 y(F)l(or)g(giv)o(en)g(frequency)i Fq(!)r Fs(,)f(w)o(e)g(ma)o(y)f(also)h (consider)f(the)h(dep)q(endence)g(of)h(the)f(m)o(ultiplication)0 931 y(factor)i(\(199\))h(on)e(structural)g(w)o(a)o(v)o(en)o(um)o(b)q (ers.)26 b(In)19 b(the)h(w)o(a)o(v)o(en)o(um)o(ber)d(domain,)h(the)h(p) q(oin)o(t)g(of)g(in-)0 991 y(tersection)i(of)h(the)g(w)o(a)o(v)o(en)o (um)o(b)q(er)d(surface)i(\(81\))h(with)f(the)h(half{line)f(leading)g (from)f(the)i(origin)0 1059 y(in)e(the)g(direction)g(of)g Fq(k)451 1041 y Fp(\013)449 1072 y(i)500 1059 y Fs(is)560 1039 y Fp(!)586 1024 y Fg(0)p 560 1048 46 2 v 569 1076 a Fp(!)611 1059 y Fq(k)639 1041 y Fp(\013)637 1072 y(i)667 1059 y Fs(.)34 b(The)20 b(v)o(ectorial)g(di\013erence)f(b)q(et)o(w)o (een)i Fq(k)1478 1041 y Fp(\013)1476 1072 y(i)1526 1059 y Fs(and)e(the)i(p)q(oin)o(t)f(of)0 1119 y(in)o(tersection)15 b(is)768 1178 y(\001)p Fq(k)838 1158 y Fp(\013)836 1191 y(i)879 1178 y Fs(=)938 1159 y Fm(\001)p Fp(!)p 938 1167 60 2 v 954 1196 a(!)1003 1178 y Fq(k)1031 1158 y Fp(\013)1029 1191 y(i)1108 1178 y Fq(:)655 b Fs(\(200\))0 1252 y(In)16 b(ra)o(y{cen)o(tred)f(co)q(ordinates,)743 1318 y(\001)p Fq(k)813 1293 y Fm(\()p Fp(q)q Fm(\))811 1332 y Fp(i)879 1318 y Fs(=)938 1299 y Fm(\001)p Fp(!)p 938 1307 V 954 1336 a(!)1003 1318 y Fq(k)1031 1293 y Fm(\()p Fp(q)q Fm(\))1029 1332 y Fp(i)1133 1318 y Fq(:)630 b Fs(\(201\))0 1392 y(The)16 b(unit)h(v)o(ector)f(p)q(erp)q(endicular)f(to)i(the)g(w)o (a)o(v)o(en)o(um)o(ber)d(surface)i(\(81\))h(is)795 1478 y Fq(n)825 1485 y Fp(i)856 1478 y Fs(=)c Fq(h)937 1457 y Fp(i)937 1490 y Fm(3)965 1455 y(d)p Fp(q)1005 1460 y Fg(3)p 965 1466 V 975 1495 a Fm(d)p Fp(s)1081 1478 y Fq(;)682 b Fs(\(202\))0 1563 y(where)20 b Fq(s)h Fs(is)f(the)g (arclength)g(along)g(the)g(ra)o(y)l(.)33 b(Then)20 b(the)g(p)q(erp)q (endicular)f(distance)h(b)q(et)o(w)o(een)g Fq(k)1862 1545 y Fp(\013)1860 1576 y(i)0 1623 y Fs(and)c(the)h(w)o(a)o(v)o(en)o (um)o(b)q(er)c(surface)j(\(81\))h(is)494 1719 y(\001)p Fq(k)e Fs(=)f Fq(n)660 1726 y Fp(i)685 1719 y Fs(\001)p Fq(k)755 1698 y Fp(\013)753 1731 y(i)796 1719 y Fs(=)854 1696 y Fm(d)p Fp(q)894 1701 y Fg(3)p 854 1707 V 864 1736 a Fm(d)p Fp(s)926 1699 y Fm(\001)p Fp(!)p 926 1707 V 942 1736 a(!)991 1719 y Fq(k)1019 1693 y Fm(\()p Fp(q)q Fm(\))1017 1732 y(3)1086 1719 y Fs(=)1144 1696 y Fm(d)p Fp(q)1184 1701 y Fg(3)p 1144 1707 V 1154 1736 a Fm(d)p Fp(s)1210 1719 y Fs(\001)p Fq(k)1280 1693 y Fm(\()p Fp(q)q Fm(\))1278 1732 y(3)1382 1719 y Fq(:)381 b Fs(\(203\))0 1804 y(Inserting)15 b(\(146\))i(and)f(\(153\))h(in)o(to)f(\(197\),)h(w) o(e)g(obtain)73 1887 y Fn(f)66 1900 y Fq(M)114 1907 y Fm(44)171 1900 y Fs(=)c(\()p Fq(!)275 1879 y Fm(0)298 1900 y Fs(\))317 1879 y Fl(\000)p Fm(1)371 1900 y Fs(\(Im)456 1880 y Ff(m)p 456 1889 38 2 v 457 1917 a Fp(m)499 1900 y Fs(\))518 1879 y Fm(T)549 1900 y Fs(\()p Fq(!)601 1879 y Fm(0)624 1900 y Fs(Im)o Fu(M)737 1879 y Fp(\013)766 1900 y Fs(\))785 1879 y Fl(\000)p Fm(1)839 1900 y Fs(\()p Fu(k)888 1879 y Fm(\()p Fp(q)q Fm(\))953 1900 y Fo(\000)1009 1880 y Ff(m)p 1009 1889 V 1010 1917 a Fp(m)1052 1900 y Fq(k)1080 1874 y Fm(\()p Fp(q)q Fm(\))1078 1913 y(3)1133 1900 y Fs(\))8 b Fq(k)1188 1874 y Fm(\()p Fp(q)q Fm(\))1186 1913 y(3)1252 1900 y Fo(\000)j Fs(\()p Fq(!)1354 1879 y Fm(0)1376 1900 y Fs(\))1395 1879 y Fl(\000)p Fm(2)1463 1880 y(1)p 1455 1889 36 2 v 1455 1917 a Fp(m)1505 1900 y Fs(\()p Fq(k)1552 1874 y Fm(\()p Fp(q)q Fm(\))1550 1913 y(3)1605 1900 y Fs(\))1624 1879 y Fm(2)1696 1900 y Fq(:)67 b Fs(\(204\))0 1986 y(Considering)14 b(\(201\),)j(w)o(e)g(ma) o(y)f(express)f(m)o(ultiplication)g(factor)i(\(199\))g(with)f(\(204\))h (in)f(form)55 2081 y(exp)p Fo(f)162 2062 y Fm(1)p 162 2070 20 2 v 162 2099 a(2)188 2081 y Fs(i)217 2062 y Fp(!)p 208 2070 46 2 v 208 2099 a(!)234 2089 y Fg(0)259 2081 y Fs([\(Im)358 2062 y Ff(m)p 358 2070 38 2 v 359 2099 a Fp(m)402 2081 y Fs(\))421 2061 y Fm(T)452 2081 y Fs(\()p Fq(!)504 2061 y Fm(0)526 2081 y Fs(Im)p Fu(M)640 2061 y Fp(\013)669 2081 y Fs(\))688 2061 y Fl(\000)p Fm(1)742 2081 y Fs(\(\001)p Fu(k)833 2061 y Fm(\()p Fp(q)q Fm(\))897 2081 y Fo(\000)953 2062 y Ff(m)p 953 2070 V 954 2099 a Fp(m)996 2081 y Fs(\001)p Fq(k)1066 2056 y Fm(\()p Fp(q)q Fm(\))1064 2095 y(3)1118 2081 y Fs(\))e(\001)p Fq(k)1221 2056 y Fm(\()p Fp(q)q Fm(\))1219 2095 y(3)1285 2081 y Fo(\000)1371 2062 y Fm(1)p 1340 2070 82 2 v 1340 2099 a Fp(!)1366 2089 y Fg(0)1386 2099 y Fp(m)1436 2081 y Fs(\(\001)p Fq(k)1525 2056 y Fm(\()p Fp(q)q Fm(\))1523 2095 y(3)1577 2081 y Fs(\))1596 2061 y Fm(2)1619 2081 y Fs(])p Fo(g)50 b Fq(;)55 b Fs(\(205\))0 2167 y(and)16 b(after)h(appro)o(ximation)563 2148 y Fp(!)p 553 2156 46 2 v 553 2184 a(!)579 2174 y Fg(0)618 2167 y Fo(\031)d Fs(1)j(as)84 2268 y(exp)p Fo(f)191 2248 y Fm(1)p 191 2256 20 2 v 191 2285 a(2)217 2268 y Fs(i[\(Im)329 2248 y Ff(m)p 329 2256 38 2 v 330 2285 a Fp(m)373 2268 y Fs(\))392 2247 y Fm(T)423 2268 y Fs(\()p Fq(!)475 2247 y Fm(0)498 2268 y Fs(Im)o Fu(M)611 2247 y Fp(\013)640 2268 y Fs(\))659 2247 y Fl(\000)p Fm(1)713 2268 y Fs(\(\001)p Fu(k)804 2247 y Fm(\()p Fp(q)q Fm(\))868 2268 y Fo(\000)924 2248 y Ff(m)p 924 2256 V 925 2285 a Fp(m)967 2268 y Fs(\001)p Fq(k)1037 2242 y Fm(\()p Fp(q)q Fm(\))1035 2281 y(3)1089 2268 y Fs(\))e(\001)p Fq(k)1193 2242 y Fm(\()p Fp(q)q Fm(\))1191 2281 y(3)1256 2268 y Fo(\000)1342 2248 y Fm(1)p 1312 2256 82 2 v 1312 2285 a Fp(!)1338 2275 y Fg(0)1357 2285 y Fp(m)1407 2268 y Fs(\(\001)p Fq(k)1496 2242 y Fm(\()p Fp(q)q Fm(\))1494 2281 y(3)1548 2268 y Fs(\))1567 2247 y Fm(2)1590 2268 y Fs(])p Fo(g)50 b Fq(:)84 b Fs(\(206\))0 2368 y(The)16 b(absolute)g(v)m(alue)h(of)g(factor)f(\(206\))h(dep)q (ends)f(on)g(\001)p Fq(k)1089 2342 y Fm(\()p Fp(q)q Fm(\))1087 2381 y(3)1158 2368 y Fs(only)l(,)325 2464 y(exp)p Fo(f)432 2445 y Fm(1)p 432 2453 20 2 v 432 2482 a(2)458 2464 y Fs([Im)568 2445 y Fm(1)p 537 2453 82 2 v 537 2482 a Fp(!)563 2472 y Fg(0)583 2482 y Fp(m)636 2464 y Fs(+)10 b(\(Im)770 2445 y Ff(m)p 770 2453 38 2 v 771 2482 a Fp(m)814 2464 y Fs(\))833 2444 y Fm(T)864 2464 y Fs(\()p Fq(!)916 2444 y Fm(0)938 2464 y Fs(Im)p Fu(M)1052 2444 y Fp(\013)1081 2464 y Fs(\))1100 2444 y Fl(\000)p Fm(1)1162 2464 y Fs(Im)1227 2445 y Ff(m)p 1227 2453 V 1228 2482 a Fp(m)1271 2464 y Fs(])e(\(\001)p Fq(k)1382 2438 y Fm(\()p Fp(q)q Fm(\))1380 2478 y(3)1434 2464 y Fs(\))1453 2444 y Fm(2)1476 2464 y Fo(g)50 b Fq(:)212 b Fs(\(207\))0 2550 y(In)16 b(terms)g(of)h(the)g (p)q(erp)q(endicular)d(distance)i(b)q(et)o(w)o(een)h Fq(k)1074 2532 y Fp(\013)1072 2563 y(i)1118 2550 y Fs(and)f(the)h(w)o (a)o(v)o(en)o(um)o(b)q(er)c(surface,)285 2636 y(exp)q Fo(f)393 2616 y Fm(1)p 392 2625 20 2 v 392 2653 a(2)418 2636 y Fs([Im)528 2616 y Fm(1)p 498 2625 82 2 v 498 2653 a Fp(!)524 2643 y Fg(0)543 2653 y Fp(m)596 2636 y Fs(+)e(\(Im)730 2616 y Ff(m)p 730 2625 38 2 v 731 2653 a Fp(m)774 2636 y Fs(\))793 2615 y Fm(T)824 2636 y Fs(\()p Fq(!)876 2615 y Fm(0)899 2636 y Fs(Im)o Fu(M)1012 2615 y Fp(\013)1041 2636 y Fs(\))1060 2615 y Fl(\000)p Fm(1)1122 2636 y Fs(Im)1188 2616 y Ff(m)p 1188 2625 V 1189 2653 a Fp(m)1231 2636 y Fs(])d(\()1288 2616 y Fm(d)p Fp(s)p 1278 2625 60 2 v 1278 2653 a Fm(d)p Fp(q)1318 2658 y Fg(3)1344 2636 y Fs(\))1363 2615 y Fm(2)1386 2636 y Fs(\(\001)p Fq(k)r Fs(\))1494 2615 y Fm(2)1516 2636 y Fo(g)50 b Fq(:)172 b Fs(\(208\))920 2806 y(47)p eop %%Page: 48 22 48 21 bop 0 -54 a Fu(4.6.)25 b(Review)c(of)d(scattered)h(Gaussian)g(b)r (eam)o(s)0 23 y Fs(F)l(or)c(eac)o(h)h(frequency)g Fq(!)r Fs(,)g(the)g(scattered)g(w)o(a)o(v)o(e\014eld)f(consists)g(of)h(at)h (most)f(one)f(P{w)o(a)o(v)o(e)h(Gaussian)0 83 y(b)q(eam)22 b(or)g(of)g(at)h(most)e(t)o(w)o(o)h(S{w)o(a)o(v)o(e)f(Gaussian)g(b)q (eams.)38 b(A)23 b(Gaussian)d(b)q(eam)i(is)g(generated)g(if)0 142 y(structural)c(w)o(a)o(v)o(en)o(um)o(b)q(er)f(v)o(ector)i Fq(k)703 124 y Fp(\013)751 142 y Fs(is)g(close)g(to)h(the)g(corresp)q (onding)d Ft(\\wavenumb)m(er)j(surfac)m(e")0 202 y Fo(S)30 209 y Ff(P)p Fp(!)90 202 y Fs(,)c(de\014ned)g(b)o(y)g(transformation) 573 294 y Fu(p)e Fo(2)g(S)k(\000)-9 b(!)14 b Fu(k)g Fs(=)g(\()p Fu(p)d Fo(\000)g Fu(P)p Fs(\))d Fq(!)16 b Fo(2)e(S)1207 301 y Ff(P)p Fp(!)1777 294 y Fs(\(209\))0 386 y(of)20 b(the)f(slo)o(wness)f(surface)h Fo(S)t Fs(,)h(see)f(\(81\).)31 b(F)l(or)18 b(eac)o(h)h(frequency)h Fq(!)r Fs(,)g(the)f(w)o(a)o(v)o(en) o(um)o(b)q(er)e(surface)i(is)0 446 y(parametrized)f(b)o(y)h(initial)f (slo)o(wness)g(v)o(ectors)g Fu(p)928 428 y Fm(0)970 446 y Fs(of)h(generated)g(Gaussian)f(b)q(eams.)29 b(The)19 b(trans-)0 506 y(formation)c(for)i(an)f(inciden)o(t)f(P)i(w)o(a)o(v)o (e)f(is)g(illustrated)f(in)h(Figures)f(4,)i(5)f(and)g(6.)p 0 586 626 2 v 0 1157 2 571 v 16 1145 a /Figure 1 def 16 1145 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 624 1157 2 571 v 0 1159 626 2 v 0 1196 a Fk(Figure)h(4.)h Fj(Slo)o(wness)12 b(surface)h Fb(S)s Fj(.)p 1264 586 V 1264 1157 2 571 v 1280 1145 a /Figure 2 def 1280 1145 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 1157 2 571 v 1264 1159 626 2 v 1264 1196 a Fk(Figure)22 b(5.)34 b Fj(Shifted)17 b(slo)o(wness)g(sur-)1264 1244 y(face)d Fb(S)1376 1251 y Fa(P)1406 1244 y Fj(.)p 0 1288 1890 2 v 0 1858 2 571 v 18 1846 a /Figure 31 def 18 1846 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 1846 a /Figure 33 def 648 1846 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 1846 a /Figure 35 def 1278 1846 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 1858 2 571 v 0 1860 1890 2 v 0 1898 a Fk(Figure)j(6.)h Fj(W)l(a)o(v)o(en)o(um)o(b)q(er)12 b(surfaces)h Fb(S)651 1905 y Fa(P)p Fh(!)719 1898 y Fj(at)i(v)n(arious) e(p)q(ositiv)o(e)h(frequencies)d Fi(!)q Fj(.)100 2023 y Fs(The)22 b(initial)f(amplitude)g(of)i(the)f(Gaussian)f(b)q(eam)h (scattered)g(b)o(y)g(Gab)q(or)g(function)g Fq(g)1793 2004 y Fp(\013)1821 2023 y Fs(\()p Fu(x)p Fs(\))0 2082 y(with)d Fu(k)146 2064 y Fp(\013)194 2082 y Fs(situated)g(at)g(the)g(w) o(a)o(v)o(en)o(um)o(b)q(er)e(surface)h Fo(S)1029 2089 y Ff(P)p Fp(!)1108 2082 y Fs(corresp)q(onding)f(to)i(p)q(ositiv)o(e)g (frequency)0 2142 y Fq(!)f Fs(is)d(giv)o(en)g(b)o(y)g(equation)h (\(163\),)g(in)g(whic)o(h)e(re\015ectivit)o(y)i(function)g Fq(r)1305 2124 y Fp(\013)1350 2142 y Fs(is)f(giv)o(en)g(b)o(y)h(\(68\)) g(and)f Fq(m)h Fs(is)0 2202 y(de\014ned)i(b)o(y)g(\(128\).)28 b(F)l(or)18 b Fu(k)522 2184 y Fp(\013)568 2202 y Fo(2)f(S)648 2209 y Ff(P)p Fp(!)708 2202 y Fs(,)i(the)g(cen)o(tral)f(ra)o(y)g(of)g (the)h(scattered)g(Gaussian)e(b)q(eam)h(pass)0 2262 y(through)d(p)q (oin)o(t)h Fu(x)348 2244 y Fp(\013)377 2262 y Fs(,)g(and)g(its)h (initial)f(slo)o(wness)e(v)o(ector)j(is)730 2354 y Fu(p)762 2333 y Fm(0)798 2354 y Fs(=)d Fu(P)d Fs(+)g Fq(!)984 2333 y Fl(\000)p Fm(1)1037 2354 y Fu(k)1067 2333 y Fp(\013)1146 2354 y Fq(;)617 b Fs(\(210\))0 2446 y(see)18 b(\(91\).)26 b(The)18 b(initial)f(shap)q(e)g(of)h(the)g(Gaussian)e(b)q(eam)i(is)f (determined)f(in)i(ra)o(y{cen)o(tred)e(co)q(ordi-)0 2505 y(nates)g(b)o(y)h(matrix)f Fu(M)416 2487 y Fp(\013)461 2505 y Fs(de\014ned)g(b)o(y)g(equation)g(\(130\).)100 2566 y(F)l(or)h Fu(k)221 2548 y Fp(\013)269 2566 y Fs(from)g(the)i (vicinit)o(y)g(of)g(w)o(a)o(v)o(en)o(um)o(b)q(er)d(surface)i Fo(S)1205 2573 y Ff(P)p Fp(!)1264 2566 y Fs(,)h(the)g(initial)f(p)q (oin)o(t)h(and)f(initial)0 2626 y(slo)o(wness)12 b(v)o(ector)j(of)f (the)h(cen)o(tral)e(ra)o(y)h(of)h(the)f(scattered)h(Gaussian)d(b)q(eam) i(sligh)o(tly)g(dep)q(end)f(on)h Fu(k)1861 2608 y Fp(\013)0 2686 y Fs(through)e(equations)g(\(146\),)i(\(181\))f(\(182\))h(and)e (\(201\).)21 b(F)l(or)12 b Fu(k)1155 2668 y Fp(\013)1196 2686 y Fs(from)g(the)h(vicinit)o(y)g(of)g(w)o(a)o(v)o(en)o(um)o(b)q(er) 920 2806 y(48)p eop %%Page: 49 23 49 22 bop 0 -54 a Fs(surface)12 b Fo(S)194 -47 y Ff(P)p Fp(!)254 -54 y Fs(,)i(the)f(initial)g(amplitude)e(of)j(the)f(Gaussian)f (b)q(eam)h(exp)q(onen)o(tially)f(decrease)h(with)g(the)0 6 y(square)k(of)h(distance)g(\001)p Fq(k)h Fs(from)e(the)h(w)o(a)o(v)o (en)o(um)o(b)q(er)d(surface)i Fo(S)1192 13 y Ff(P)p Fp(!)1270 6 y Fs(according)g(to)h(equation)g(\(208\).)0 66 y(Gaussian)g(w)o(eigh) o(ting)g(factor)i(\(208\))g(of)g(the)g(initial)f(amplitude)f(of)i(the)f (Gaussian)f(b)q(eam)i(in)f(the)0 126 y(vicinit)o(y)d(of)h(w)o(a)o(v)o (en)o(um)o(b)q(er)d(surface)i Fo(S)720 133 y Ff(P)p Fp(!)796 126 y Fs(is)g(illustrated)f(in)h(Figures)f(7)i(and)f(8.)p 0 215 1890 2 v 0 786 2 571 v 18 774 a /Figure 41 def 18 774 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 774 a /Figure 43 def 648 774 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 774 a /Figure 45 def 1278 774 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 786 2 571 v 0 788 1890 2 v 0 825 a Fk(Figure)23 b(7.)36 b Fj(Sensitivit)o(y)19 b(of)h(scattered)f (Gaussian)g(b)q(eams)g(to)h(structural)e(w)o(a)o(v)o(en)o(um)o(b)q(ers) e(at)21 b(v)n(arious)d(p)q(ositiv)o(e)0 873 y(frequencies)12 b Fi(!)k Fj(for)d(an)h(inciden)o(t)e(P)i(w)o(a)o(v)o(e.)k(The)13 b(sensitivit)o(y)h(is)f(giv)o(en)h(b)o(y)g(Gaussian)f(w)o(eigh)o(ting)f (factor)i(\(208\).)p 0 950 V 0 1521 2 571 v 18 1509 a /Figure 141 def 18 1509 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 1509 a /Figure 143 def 648 1509 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 1509 a /Figure 145 def 1278 1509 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 1521 2 571 v 0 1523 1890 2 v 0 1560 a Fk(Figure)23 b(8.)36 b Fj(Sensitivit)o(y)19 b(of)h(scattered)f (Gaussian)g(b)q(eams)g(to)h(structural)e(w)o(a)o(v)o(en)o(um)o(b)q(ers) e(at)21 b(v)n(arious)d(p)q(ositiv)o(e)0 1608 y(frequencies)e Fi(!)21 b Fj(for)e(an)f(inciden)o(t)f(slo)o(w)o(er)g(S)i(w)o(a)o(v)o (e.)32 b(The)18 b(sensitivit)o(y)h(is)f(giv)o(en)g(b)o(y)h(Gaussian)f (w)o(eigh)o(ting)f(factor)0 1656 y(\(208\).)100 1792 y Fs(A)e(scattered)f(Gaussian)f(b)q(eam)i(has)e(a)i(maxim)o(um)e (amplitude)g(if)i(\001)p Fq(k)f Fs(=)g(0,)h(i.e.,)f(if)h Fu(k)1697 1773 y Fp(\013)1739 1792 y Fo(2)g(S)1817 1799 y Ff(P)p Fp(!)1876 1792 y Fs(.)0 1852 y(F)l(or)e(eac)o(h)h Fu(k)227 1834 y Fp(\013)255 1852 y Fs(,)h(there)f(are)g(at)g(most)g(5)g (\014nite)g(p)q(ositiv)o(e)g(frequencies)g Fq(!)h Fs(=)f Fq(!)1397 1859 y Fm(0)1433 1852 y Fs(suc)o(h)f(that)i Fu(k)1679 1834 y Fp(\013)1721 1852 y Fo(2)f(S)1798 1859 y Ff(P)p Fp(!)1854 1864 y Fg(0)1876 1852 y Fs(.)0 1912 y(The)20 b(frequencies)g Fq(!)396 1919 y Fm(0)439 1912 y Fs(are)g(solutions)f(of)i(sixth{order)e(equation)h(\(90\).)35 b(The)20 b(equation)g(has)g(one)0 1972 y(in\014nite)c(trivial)g (solution)f Fq(!)536 1979 y Fm(0)573 1972 y Fs(=)e(+)p Fo(1)p Fs(.)920 2806 y(49)p eop %%Page: 50 24 50 23 bop 0 -54 a Fu(5.)25 b(Scattering)20 b(in)g(the)f(time)f(dom)o (ain)e(|)k(Gaussian)e(pac)n(k)n(ets)0 22 y Fs(Scattered)h(w)o(a)o(v)o (es)f(in)h(the)h(time)f(domain)f(are)h(comp)q(osed)f(of)i(the)f (scattered)h(frequency{domain)0 82 y(Gaussian)g(b)q(eams.)35 b(The)21 b(Gaussian)e(frequency)j(dep)q(endence)e(\(199\))i(of)f(the)h (amplitude)d(of)j(the)0 142 y(scattered)17 b(Gaussian)d(b)q(eam)j (generates)f(a)g(Gaussian)f(pac)o(k)o(et)i(in)f(the)h(time)f(domain.) 100 203 y(F)l(or)h(\014xed)g Fu(k)342 184 y Fp(\013)371 203 y Fs(,)h(the)h(initial)e(p)q(oin)o(t)h(and)f(initial)h(slo)o(wness) e(v)o(ector)i(of)g(the)h(cen)o(tral)e(ra)o(y)h(of)g(the)0 262 y(scattered)23 b(Gaussian)e(b)q(eam)i(sligh)o(tly)f(dep)q(end)g(on) h(frequency)g(through)f(equations)g(\(181\))i(and)0 322 y(\(182\),)18 b(scattering)g(di\013eren)o(t)f(frequencies)g(to)h (di\013eren)o(t)f(directions.)24 b(This)17 b(phenomenon)f(results)0 382 y(in)d(asymmetric)f(Gaussian)g(pac)o(k)o(ets)h(\(Klime)m(\024)-22 b(s,)13 b(2004,)h(\014g.)f(1;)1166 369 y(\024)1161 382 y(Cerv)o(en)q(\023)-26 b(y,)14 b(Klime)m(\024)-22 b(s)12 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)14 b(2007,)0 442 y(\014g.)i(23\).)0 565 y Fu(5.1.)25 b(Narro)n(w{band)17 b(scattering)0 642 y Fs(There)i(are)g(at)g(most)g(5)g(\014nite)g(p)q (ositiv)o(e)g(frequencies)g Fq(!)h Fs(=)e Fq(!)1179 649 y Fm(0)1220 642 y Fs(suc)o(h)g(that)i Fu(k)1476 624 y Fp(\013)1523 642 y Fo(2)e(S)1604 649 y Ff(P)p Fp(!)1660 654 y Fg(0)1682 642 y Fs(.)30 b(If)20 b Fu(k)1809 624 y Fp(\013)1857 642 y Fs(is)0 702 y(su\016cien)o(tly)c(deviated)h(from)g (the)g(tangen)o(t)g(plane)g(to)g Fo(S)1063 709 y Ff(P)p Fp(!)1119 714 y Fg(0)1158 702 y Fs(at)h Fu(k)1250 683 y Fp(\013)1278 702 y Fs(,)g(the)f(b)q(eams)g(are)f(scattered)h(in)0 761 y(a)f(narro)o(w)f(Gaussian)f(frequency)j(band)e(cen)o(tred)g(at)i Fq(!)1039 768 y Fm(0)1061 761 y Fs(,)g(forming)d(a)j(space{time)e (Gaussian)g(w)o(a)o(v)o(e)0 821 y(pac)o(k)o(et)21 b(of)g(prev)m(ailing) e(frequency)i Fq(!)715 828 y Fm(0)738 821 y Fs(.)35 b(Since)20 b(v)o(ector)h Fq(h)1104 803 y Fp(i)1104 834 y Fm(3)1126 821 y Fs(\()p Fu(x)1175 803 y Fp(\013)1204 821 y Fs(\),)h(de\014ned)e (b)o(y)h(\(99\))g(at)g(p)q(oin)o(t)g Fu(x)1848 803 y Fp(\013)1876 821 y Fs(,)0 881 y(is)f(p)q(erp)q(endicular)e(to)j(w)o(a)o (v)o(en)o(um)o(b)q(er)d(surface)h Fo(S)930 888 y Ff(P)p Fp(!)986 893 y Fg(0)1028 881 y Fs(at)i Fu(k)1123 863 y Fp(\013)1152 881 y Fs(,)g(the)g(men)o(tioned)e(deviation)h(can)g(b)q (e)0 951 y(measured)12 b(b)o(y)h Fq(k)313 925 y Fm(\()p Fp(q)q Fm(\))311 964 y(3)366 951 y Fs(,)h(see)g(\(203\).)21 b(A)14 b(su\016cien)o(t)f(deviation)g(of)h Fu(k)1176 932 y Fp(\013)1218 951 y Fs(from)f(the)h(tangen)o(t)f(plane)g(to)h Fo(S)1812 958 y Ff(P)p Fp(!)1868 963 y Fg(0)0 1021 y Fs(at)j Fu(k)91 1003 y Fp(\013)136 1021 y Fs(then)g(means)e(su\016cien) o(tly)g(large)h Fq(k)801 995 y Fm(\()p Fp(q)q Fm(\))799 1034 y(3)871 1021 y Fs(in)g(equation)g(\(153\).)100 1081 y(W)l(e)22 b(shall)f(refer)g(to)i(the)f(set)g(of)g(w)o(a)o(v)o(en)o(um) o(b)q(er)d(v)o(ectors)j Fu(k)1233 1063 y Fp(\013)1261 1081 y Fs(,)i(causing)c(narro)o(w{band)f(scat-)0 1141 y(tering,)h(as)f(the)g(\\high{w)o(a)o(v)o(en)o(um)o(ber)e(domain",)h (see)i(Figures)d(9)j(and)f(10.)30 b(F)l(or)19 b(eac)o(h)g(particular)0 1201 y(broad{band)e(inciden)o(t)i(w)o(a)o(v)o(e,)g(the)h(w)o(a)o(v)o (e\014eld,)f(scattered)g(b)o(y)g(a)h(Gab)q(or)f(function)g(b)q (elonging)g(to)0 1261 y(this)k(domain,)g(consists)f(of)h(at)g(most)g(5) g(narro)o(w{band)d(space{time)i(Gaussian)g(w)o(a)o(v)o(e)g(pac)o(k)o (ets.)0 1321 y(Eac)o(h)h(recorded)g(Gaussian)g(pac)o(k)o(et)h(is)f(lo)q (calized)h(in)g(the)g(time)g(section)g(\(set)h(of)f(seismograms)0 1381 y(corresp)q(onding)14 b(to)j(the)g(source\).)100 1441 y(This)f(is)g(t)o(ypical)h(wide{angle)e(scattering,)i(but)f(o)q (ccurs)h(also)f(for)g(P)h(to)g(S)g(or)f(S)h(to)g(P)g(forw)o(ard)0 1501 y(and)e(narro)o(w{angle)f(scattering.)21 b(The)15 b(high{w)o(a)o(v)o(en)o(um)o(ber)e(domain)i(is)g(usually)g(b)q(eing)g (reco)o(v)o(ered)0 1561 y(b)o(y)h(seismic)g(migration)f(or)h(b)o(y)g (di\013raction)f(tomograph)o(y)l(.)p 0 1641 1890 2 v 0 2211 2 571 v 18 2199 a /Figure 61 def 18 2199 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 2199 a /Figure 62 def 648 2199 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 2199 a /Figure 81 def 1278 2199 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 2211 2 571 v 0 2213 1890 2 v 0 2251 a Fk(Figure)20 b(9.)27 b Fj(High{w)o(a)o(v)o(en)o(um)o(ber)13 b(domain,)j(consisting)g(of)h(the)f(structural)g(w)o(a)o(v)o(en)o(um)o (b)q(er)o(s)e(generating)i(narro)o(w{)0 2299 y(band)d(Gaussian)g(pac)o (k)o(ets)h(for)g(an)h(inciden)o(t)d(P)i(w)o(a)o(v)o(e.)19 b(Three)13 b(colours)g(corresp)q(ond)f(to)j(three)f(p)q(olarizations)f (of)h(the)0 2346 y(scattered)e(w)o(a)o(v)o(e.)18 b(Note)13 b(that)h(di\013eren)o(t)d(p)q(olarizations)h(and)g(di\013eren)o(t)f (directions)g(of)i(the)g(structural)f(w)o(a)o(v)o(en)o(um)o(b)q(e)o(r)0 2394 y(v)o(ector)19 b Fk(k)158 2380 y Fh(\013)204 2394 y Fj(are)f(sensitiv)o(e)g(to)i(di\013eren)o(t)d(linear)h(com)o (binations)f(\(68\))j(of)f(p)q(erturbations)e(of)j(elastic)e(mo)q(duli) g(and)0 2442 y(densit)o(y)l(.)g(When)12 b(c)o(hanging)f(the)h(source,)g (the)g(w)o(a)o(v)o(en)o(um)o(b)q(er)d(domain)j(of)g(sensitivit)o(y)h (\\rotates")g(with)f(the)h(direction)0 2490 y(of)k(the)h(inciden)o(t)d (w)o(a)o(v)o(e\014eld,)h(and)h(the)g(re\015ectivit)o(y)g(function)f (\(68\))i(c)o(hanges,)f(allo)o(wing)f(to)i(resolv)o(e)e(more)g(elastic) 0 2538 y(mo)q(duli.)920 2806 y Fs(50)p eop %%Page: 51 25 51 24 bop 0 -102 1890 2 v 0 469 2 571 v 18 457 a /Figure 181 def 18 457 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 457 a /Figure 162 def 648 457 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 457 a /Figure 163 def 1278 457 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 469 2 571 v 0 471 1890 2 v 0 508 a Fk(Figure)17 b(10.)22 b Fj(High{w)o(a)o(v)o(en)o(um)o(ber)12 b(domain,)h(consisting)h(of)h(the)f(structural)g(w)o(a)o(v)o(en)o(um)o (b)q(er)o(s)e(generating)i(narro)o(w{)0 556 y(band)f(Gaussian)g(pac)o (k)o(ets)h(for)g(an)g(inciden)o(t)f(slo)o(w)o(er)f(S)i(w)o(a)o(v)o(e.) 19 b(Three)13 b(colours)g(corresp)q(ond)f(to)j(three)e(p)q (olarizations)0 604 y(of)h(the)g(scattered)g(w)o(a)o(v)o(e.)k (Analogous)13 b(to)h(Figure)f(9)h(whic)o(h)e(corresp)q(onds)g(to)i(an)g (inciden)o(t)e(P)i(w)o(a)o(v)o(e.)k(Note)c(that)h(the)0 652 y(scattered)g(w)o(a)o(v)o(es)f(are)h(sensitiv)o(e)g(to)h(other)f (linear)f(com)o(binations)f(\(68\))k(of)e(p)q(erturbations)f(of)h (elastic)g(mo)q(duli)f(and)0 700 y(densit)o(y)f(than)h(the)g(scattered) f(w)o(a)o(v)o(es)g(corresp)q(onding)e(to)k(an)f(inciden)o(t)e(P)i(w)o (a)o(v)o(e.)0 817 y Fu(5.2.)25 b(Broad{band)16 b(scattering)0 892 y Fs(If)h(the)h(deviation)f(of)g Fu(k)442 874 y Fp(\013)488 892 y Fs(from)f(the)i(tangen)o(t)f(plane)f(to)i Fo(S)1100 899 y Ff(P)p Fp(!)1156 904 y Fg(0)1195 892 y Fs(at)f Fu(k)1286 874 y Fp(\013)1332 892 y Fs(is)g(small,)f(or)h(if)g Fu(k)1666 874 y Fp(\013)1712 892 y Fs(is)f(small,)0 951 y(the)g(b)q(eams)g(are)f(scattered)h(in)g(a)g(broad)e(frequency)i (band.)21 b(In)16 b(this)f(case,)h(the)h(inciden)o(t)e(w)o(a)o(v)o (e\014eld)0 1011 y(can)k(b)q(e)g(decomp)q(osed)f(in)o(to)g(narro)o (w{band)e(Gab)q(or)j(signals)e(using)h(the)h(Gab)q(or)g(transform.)27 b(The)0 1071 y(scattered)16 b(b)q(eams)g(of)g(eac)o(h)g(narro)o(w{band) d(comp)q(onen)o(t)i(of)h(the)h(broad{band)c(inciden)o(t)j(w)o(a)o(v)o (e\014eld)0 1131 y(form)23 b(a)i(single)e(space{time)h(Gaussian)e(pac)o (k)o(et.)45 b(Gaussian)23 b(pac)o(k)o(ets)g(of)i(di\013eren)o(t)e(prev) m(ailing)0 1191 y(frequencies)14 b(propagate)g(in)g(di\013eren)o(t)g (directions,)g(forming)f(a)h(broad{band)f(fan)h(of)h(narro)o(w{band)0 1250 y(Gaussian)g(pac)o(k)o(ets.)21 b(The)16 b(existence)g(and)g (scattering)g(angle)f(of)i(a)f(Gaussian)e(pac)o(k)o(et)i(dep)q(ends)f (on)0 1310 y(the)i(structural)e(w)o(a)o(v)o(en)o(um)o(b)q(er)f(v)o (ector)i Fu(k)782 1292 y Fp(\013)811 1310 y Fs(.)100 1370 y(This)f(is)h(t)o(ypical)g(forw)o(ard)f(and)h(narro)o(w{angle)e (scattering)i(at)h(lo)o(w)f(w)o(a)o(v)o(en)o(um)o(bers)e Fo(j)p Fu(k)1743 1352 y Fp(\013)1771 1370 y Fo(j)p Fs(,)i(but)0 1430 y(o)q(ccurs)23 b(also)f(for)h(S)g(to)h(P)f(w)o(a)o(v)o(e)g (scattering)g(at)g(high)g(w)o(a)o(v)o(en)o(um)o(b)q(ers)d Fo(j)p Fu(k)1434 1412 y Fp(\013)1462 1430 y Fo(j)p Fs(.)42 b(F)l(or)22 b(a)i(particular)0 1489 y(inciden)o(t)16 b(w)o(a)o(v)o(e,)h(there)g(ma)o(y)g(b)q(e)h(2)f(di\013eren)o(t)f(kinds) h(of)g(broad{band)e(fans)i(of)h(scattered)f(narro)o(w{)0 1549 y(band)12 b(Gaussian)f(pac)o(k)o(ets:)19 b(one)12 b(b)q(elonging)g(to)h(lo)o(w)f(w)o(a)o(v)o(en)o(um)o(b)q(ers)d Fo(j)p Fu(k)1322 1531 y Fp(\013)1351 1549 y Fo(j)j Fs(\()p Fq(!)1429 1531 y Fm(0)1465 1549 y Fs(=)i(+)p Fo(1)p Fs(\),)f(see)g (Figures)0 1609 y(11)19 b(and)f(13,)i(the)f(other)g(b)q(elonging)f(to)i Fu(k)795 1591 y Fp(\013)843 1609 y Fs(from)e(the)h(conical)g(surface)f (tangen)o(t)h(to)h(the)f(P{w)o(a)o(v)o(e)0 1669 y(sheets)g(of)g(the)h (w)o(a)o(v)o(en)o(um)o(b)q(er)c(surfaces)i Fo(S)807 1676 y Ff(P)p Fp(!)886 1669 y Fs(during)g(S)h(to)h(P)f(w)o(a)o(v)o(e)f (scattering)h(\(\014nite)h Fq(!)1751 1651 y Fm(0)1773 1669 y Fs(\),)g(see)0 1729 y(Figure)g(16.)35 b(In)21 b(a)g(strongly)f(anisotropic)f(bac)o(kground,)h(there)h(ma)o(y)g(also)f (o)q(ccur)h(a)g(wide{angle)0 1788 y(broad{band)13 b(S)j(to)g(S)g (scattering)f(with)h(con)o(v)o(ersion)e(from)h(slo)o(w)g(to)h(fast)g(S) g(w)o(a)o(v)o(e)f(\(see)h(Figure)f(15\),)0 1848 y(analogous)g(to)i (wide{angle)e(broad{band)g(S)h(to)h(P)f(scattering.)100 1908 y(W)l(e)d(shall)g(refer)g(to)h(the)g(set)g(of)g(lo)o(w)f(w)o(a)o (v)o(en)o(um)o(b)q(er)d(v)o(ectors)k Fu(k)1245 1890 y Fp(\013)1273 1908 y Fs(,)g(causing)f(forw)o(ard)f(or)h(narro)o(w{)0 1968 y(angle)23 b(broad{band)f(scattering)h(without)g(w)o(a)o(v)o(e)g (con)o(v)o(ersion,)h(as)f(the)h(\\lo)o(w{w)o(a)o(v)o(en)o(um)n(b)q(er)d (do-)0 2027 y(main",)c(see)h(Figures)e(11)i(and)f(13.)26 b(The)17 b(scattering)h(angle)f(of)h(the)g(Gaussian)f(pac)o(k)o(et,)h (generated)0 2087 y(b)o(y)12 b(a)h(Gab)q(or)f(function)g(b)q(elonging)f (to)i(the)g(lo)o(w{w)o(a)o(v)o(en)o(um)o(ber)d(domain,)i(is)g(in)o(v)o (ersely)f(prop)q(ortional)0 2147 y(to)18 b(the)g(prev)m(ailing)f (frequency)h(of)g(the)g(pac)o(k)o(et.)26 b(The)17 b(lo)o(w{w)o(a)o(v)o (en)o(um)o(b)q(er)e(domain)h(is)h(usually)g(b)q(e-)0 2207 y(ing)j(reco)o(v)o(ered)e(b)o(y)i(tra)o(v)o(el{time)f(tomograph)o (y)g(\(see)h(Figures)f(12)h(and)f(14\))i(and)e(w)o(a)o(v)o(e{equation)0 2266 y(tomograph)o(y)l(.)100 2326 y(Note)h(that)f(the)h(union)e(of)i (lo)o(w{w)o(a)o(v)o(en)o(um)n(b)q(er)c(domains)i(corresp)q(onding)f(to) j(di\013eren)o(t)e(inci-)0 2386 y(den)o(t)e(w)o(a)o(v)o(es)e(ma)o(y)i (o)o(v)o(erlap)e(with)i(the)h(union)e(of)h(high{w)o(a)o(v)o(en)o(um)n (b)q(er)d(domains)h(corresp)q(onding)g(to)0 2446 y(di\013eren)o(t)i (inciden)o(t)f(w)o(a)o(v)o(es.)100 2506 y(F)l(ollo)o(wing)20 b(Sections)j(5.3)f(to)h(5.6)g(are)f(dev)o(oted)h(to)g(narro)o(w{band)d (scattering)i(only)l(.)40 b(The)0 2565 y(equations)16 b(should)f(b)q(e)i(generalized)e(to)i(broad{band)d(scattering)i(in)h (future.)920 2806 y(51)p eop %%Page: 52 26 52 25 bop 0 -102 626 2 v 0 469 2 571 v 16 457 a /Figure 82 def 16 457 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 624 469 2 571 v 0 471 626 2 v 0 508 a Fk(Figure)12 b(11.)18 b Fj(Lo)o(w{w)o(a)o(v)o(en)o(um)o(b)q(er)6 b(do-)0 556 y(main,)16 b(consisting)f(of)h(the)h(structural)0 604 y(w)o(a)o(v)o(en)o(um)o(b)q(er)o(s)10 b(generating)i(a)h(broad{)0 652 y(band)21 b(scattered)h(w)o(a)o(v)o(e\014eld,)h(for)f(an)0 700 y(inciden)o(t)12 b(P)i(w)o(a)o(v)o(e.)p 1264 -102 V 1264 469 2 571 v 1280 457 a /Figure 83 def 1280 457 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 469 2 571 v 1264 471 626 2 v 1264 508 a Fk(Figure)23 b(12.)37 b Fj(Ultralo)o(w{w)o(a)o(v)o(en)o(um-)1264 556 y(b)q(er)d(domain,)j(consisting)d(of)g(the)1264 604 y(structural)23 b(w)o(a)o(v)o(en)o(um)o(b)q(ers)f(resolv)o(ed)1264 652 y(b)o(y)12 b(tra)o(v)o(el{time)f(tomograph)o(y)l(,)h(for)f(an)1264 700 y(inciden)o(t)h(P)i(w)o(a)o(v)o(e.)p 0 761 V 0 1332 2 571 v 16 1320 a /Figure 182 def 16 1320 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 624 1332 2 571 v 0 1334 626 2 v 0 1372 a Fk(Figure)e(13.)18 b Fj(Lo)o(w{w)o(a)o(v)o(en)o(um)o(b)q(er)6 b(do-)0 1419 y(main,)16 b(consisting)f(of)h(the)h(structural)0 1467 y(w)o(a)o(v)o(en)o(um)o(b)q(er)o(s)10 b(generating)i(a)h(broad{)0 1515 y(band)21 b(scattered)h(w)o(a)o(v)o(e\014eld,)h(for)f(an)0 1563 y(inciden)o(t)12 b(slo)o(w)o(er)g(S)i(w)o(a)o(v)o(e.)p 1264 761 V 1264 1332 2 571 v 1280 1320 a /Figure 183 def 1280 1320 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 1332 2 571 v 1264 1334 626 2 v 1264 1372 a Fk(Figure)23 b(14.)37 b Fj(Ultralo)o(w{w)o(a)o(v)o(en)o(um-)1264 1419 y(b)q(er)d(domain,)j(consisting)d(of)g(the)1264 1467 y(structural)23 b(w)o(a)o(v)o(en)o(um)o(b)q(ers)f(resolv)o(ed)1264 1515 y(b)o(y)12 b(tra)o(v)o(el{time)f(tomograph)o(y)l(,)h(for)f(an)1264 1563 y(inciden)o(t)h(slo)o(w)o(er)g(S)i(w)o(a)o(v)o(e.)p 0 1625 V 0 2195 2 571 v 16 2183 a /Figure 192 def 16 2183 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 624 2195 2 571 v 0 2197 626 2 v 0 2235 a Fk(Figure)31 b(15.)56 b Fj(High{w)o(a)o(v)o(en)o(um)o(ber)0 2283 y(domain,)24 b(consisting)f(of)g(the)h(struc-)0 2331 y(tural)h(w)o(a)o(v)o(en)o(um)o(b)q(er)o(s)d(generating)j(a)0 2378 y(broad{band)j(scattered)i(w)o(a)o(v)o(e\014eld,)0 2426 y(for)15 b(an)f(inciden)o(t)f(slo)o(w)o(er)g(S)h(w)o(a)o(v)o(e)h (and)0 2474 y(scattered)e(faster)h(S)g(w)o(a)o(v)o(e.)p 1264 1625 V 1264 2195 2 571 v 1280 2183 a /Figure 193 def 1280 2183 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 2195 2 571 v 1264 2197 626 2 v 1264 2235 a Fk(Figure)31 b(16.)56 b Fj(High{w)o(a)o(v)o(en)o(um)o(b)q(e)o(r) 1264 2283 y(domain,)24 b(consisting)f(of)g(the)h(struc-)1264 2331 y(tural)h(w)o(a)o(v)o(en)o(um)o(b)q(er)o(s)d(generating)j(a)1264 2378 y(broad{band)j(scattered)i(w)o(a)o(v)o(e\014eld,)1264 2426 y(for)15 b(an)f(inciden)o(t)f(slo)o(w)o(er)g(S)i(w)o(a)o(v)o(e)f (and)1264 2474 y(scattered)f(P)h(w)o(a)o(v)o(e.)920 2806 y Fs(52)p eop %%Page: 53 27 53 26 bop 0 -54 a Fu(5.3.)25 b(F)-5 b(ourier)19 b(transform)0 25 y Fs(Analytical)g(signal)e Fq(u)415 -1 y Fp(\013)p Fm(\()-7 b(A)g(\))415 39 y Fp(i)490 25 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))20 b(corresp)q(onding)c(to)j(the)g(Gaussian)e(pac)o (k)o(et)i(scattered)f(b)o(y)h(Gab)q(or)0 85 y(function)j Fq(g)227 67 y Fp(\013)255 85 y Fs(\()p Fu(x)p Fs(\))i(can)e(b)q(e)h (obtained)f(b)o(y)h(in)o(v)o(erse)e(F)l(ourier)g(transform)g(\(14\))i (of)g(the)g(frequency{)0 145 y(dep)q(enden)o(t)16 b(Gaussian)f(b)q(eam) j Fn(b)-30 b Fq(u)618 127 y Fp(\013)618 158 y(i)646 145 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\),)488 302 y Fq(u)517 276 y Fp(\013)p Fm(\()-7 b(A)g(\))517 316 y Fp(i)591 302 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)776 268 y(1)p 773 290 31 2 v 773 336 a Fq(\031)820 224 y Fm(+)p Fl(1)819 234 y Fn(Z)823 376 y Fm(0)863 302 y Fs(d)p Fq(!)9 b Fs(exp)q(\()p Fo(\000)p Fs(i)p Fq(!)r(t)p Fs(\))h Fn(b)-30 b Fq(u)1187 281 y Fp(\013)1187 314 y(i)1215 302 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))51 b Fq(:)374 b Fs(\(211\))0 457 y(W)l(e)17 b(insert)f(\(78\))h(in)o(to)f(\(211\),)300 613 y Fq(u)329 587 y Fp(\013)p Fm(\()-7 b(A)g(\))329 627 y Fp(i)404 613 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)588 580 y(1)p 585 602 V 585 647 a Fq(\031)630 613 y(e)653 620 y Fp(i)669 613 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)770 593 y Fp(\013)800 613 y Fs(\))830 535 y Fm(+)p Fl(1)829 545 y Fn(Z)833 687 y Fm(0)873 613 y Fs(d)p Fq(!)14 b Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))18 b(exp)p Fo(f)p Fs(i)p Fq(!)r Fs([)p Fq(T)1312 593 y Fp(\013)1305 626 y(!)1340 613 y Fs(\()p Fu(x)p Fs(\))12 b Fo(\000)f Fq(t)p Fs(])p Fo(g)49 b Fq(:)187 b Fs(\(212\))0 769 y(W)l(e)21 b(assume)e(a)i(smo)q(oth)f(frequency)h(sp)q(ectrum)f(and)g(appro)o (ximate)f(amplitude)g Fn(b)-28 b Fq(a)1602 776 y Fp(i)1619 769 y Fs(\()p Fu(x)p Fq(;)8 b(!)r Fs(\))22 b(b)o(y)e(its)0 829 y(v)m(alue)d(at)g(prev)m(ailing)e(frequency)i Fq(!)677 810 y Fm(0)699 829 y Fs(,)296 982 y Fq(u)325 956 y Fp(\013)p Fm(\()-7 b(A)g(\))325 996 y Fp(i)399 982 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)584 948 y(1)p 581 970 V 581 1016 a Fq(\031)625 982 y(e)648 989 y Fp(i)665 982 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)766 961 y Fp(\013)796 982 y Fs(\))g Fn(b)-28 b Fq(a)q Fs(\()p Fu(x)p Fq(;)8 b(!)954 961 y Fm(0)976 982 y Fs(\))1007 904 y Fm(+)p Fl(1)1006 914 y Fn(Z)1010 1056 y Fm(0)1049 982 y Fs(d)p Fq(!)i Fs(exp)p Fo(f)p Fs(i)p Fq(!)r Fs([)p Fq(T)1316 961 y Fp(\013)1309 994 y(!)1344 982 y Fs(\()p Fu(x)p Fs(\))i Fo(\000)f Fq(t)p Fs(])p Fo(g)50 b Fq(:)182 b Fs(\(213\))0 1148 y(W)l(e)13 b(ha)o(v)o(e)f(th)o(us)f(neglected)i(the)g(frequency)g(dep)q(endence)f (of)g(terms)g Fq(!)1300 1130 y Fm(2)1322 1148 y Fs(,)1361 1136 y Fn(b)1350 1148 y Fq(A)p Fs(\()p Fu(x)1436 1130 y Fp(\013)1465 1148 y Fq(;)c(!)r Fs(\))13 b(and)f Fq(K)1691 1130 y Fp(\013)1687 1161 y(ij)1725 1148 y Fo(\000)s Fs(i)p Fq(!)r(\022)1838 1130 y Fp(\013)p Fl(00)1837 1161 y Fp(;ij)0 1208 y Fs(in)k(\(79\).)100 1271 y(W)l(e)f(insert)g(relation)g(\(155\))h (for)f Fq(T)744 1253 y Fp(\013)737 1283 y(!)773 1271 y Fs(\()p Fu(x)p Fs(\),)h(and)f(express)g(the)h(frequency)f(dep)q (endence)g(of)h(exp)q(o-)0 1331 y(nen)o(tial)g(term)g(i)p Fq(!)r Fs([)p Fq(T)381 1312 y Fp(\013)374 1343 y(!)409 1331 y Fs(\()p Fu(x)p Fs(\))c Fo(\000)f Fq(t)p Fs(])16 b(in)g(\(213\))h(as)0 1434 y(i)p Fq(!)r Fs([)p Fq(T)97 1414 y Fp(\013)90 1447 y(!)125 1434 y Fs(\()p Fu(x)p Fs(\))7 b Fo(\000)g Fq(t)p Fs(])14 b(=)f(i)p Fq(!)391 1414 y Fm(0)413 1434 y Fs([)p Fq(T)463 1414 y Fp(\013)456 1448 y(!)482 1438 y Fg(0)505 1434 y Fs(\()p Fu(x)p Fs(\))7 b Fo(\000)g Fq(t)p Fs(])g(+)g(i\001)p Fq(!)r Fs([)p Fq(T)850 1414 y Fp(\013)843 1448 y(!)869 1438 y Fg(0)889 1434 y Fs(\()p Fu(x)p Fs(\))g Fo(\000)g Fq(t)p Fs(])g(+)g(i\001)p Fq(x)1179 1408 y Fm(\()p Fp(q)q Fm(\))1179 1449 y Fp(K)1232 1434 y Fq(M)1280 1441 y Fp(K)r Fm(4)1338 1434 y Fs(\001)p Fq(!)i Fs(+)1471 1415 y Fm(1)p 1471 1423 20 2 v 1471 1452 a(2)1497 1434 y Fs(i\()p Fq(!)r Fs(\))1582 1414 y Fl(\000)p Fm(1)1636 1434 y Fq(M)1684 1441 y Fm(44)1726 1434 y Fs(\(\001)p Fq(!)r Fs(\))1839 1414 y Fm(2)1876 1434 y Fq(;)1777 1494 y Fs(\(214\))0 1554 y(where)k Fq(T)177 1536 y Fp(\013)170 1570 y(!)196 1560 y Fg(0)218 1554 y Fs(\()p Fu(x)p Fs(\))h(is)f(de\014ned)g(b)o(y)g(equation)g(\(143\).) 21 b(Within)13 b(a)g(su\016cien)o(tly)f(narro)o(w)g(frequency)h(band,)0 1614 y(the)j(frequency{dep)q(enden)o(t)f(matrix)h(\()p Fq(\022)764 1596 y Fm(0)p Fl(00)820 1614 y Fs(+)10 b(i)p Fq(!)916 1596 y Fl(\000)p Fm(1)969 1614 y Fq(K)1015 1596 y Fp(\013)1043 1614 y Fs(\))1062 1593 y Fl(\000)p Fm(1)1062 1628 y Fp(ij)1116 1614 y Fs(,)16 b(used)f(to)i(de\014ne)e Fq(M)1511 1621 y Fp(ij)1562 1614 y Fs(in)h(\(143\))g(and)g(to)0 1681 y(de\014ne)h Fu(M)199 1688 y Fm(4)240 1681 y Fs(and)h Fq(M)387 1688 y Fm(44)448 1681 y Fs(in)f(\(214\))i(ma)o(y)e(b)q(e)i (appro)o(ximated)d(b)o(y)i(their)f(v)m(alue)i(at)f Fq(!)g Fs(=)f Fq(!)1657 1662 y Fm(0)1679 1681 y Fs(.)26 b(W)l(e)19 b(also)0 1741 y(appro)o(ximate)i Fq(!)327 1722 y Fl(\000)p Fm(1)403 1741 y Fs(in)i(the)g(last)g(term)f(of)h(equation)g(\(214\))g (b)o(y)g(\()p Fq(!)1323 1722 y Fm(0)1345 1741 y Fs(\))1364 1722 y Fl(\000)p Fm(1)1418 1741 y Fs(.)41 b(W)l(e)23 b(then)g(rearrange)0 1801 y(equation)16 b(\(214\))h(as)0 1904 y(i)p Fq(!)r Fs([)p Fq(T)97 1884 y Fp(\013)90 1917 y(!)125 1904 y Fs(\()p Fu(x)p Fs(\))7 b Fo(\000)g Fq(t)p Fs(])14 b Fo(\031)g Fs(i)p Fq(!)392 1884 y Fm(0)414 1904 y Fs([)p Fq(T)464 1884 y Fp(\013)457 1918 y(!)483 1908 y Fg(0)505 1904 y Fs(\()p Fu(x)p Fs(\))7 b Fo(\000)g Fq(t)p Fs(])g(+)718 1885 y Fm(1)p 718 1893 V 718 1921 a(2)744 1904 y Fs(i\()p Fq(!)810 1884 y Fm(0)832 1904 y Fs(\))851 1884 y Fl(\000)p Fm(1)905 1904 y Fq(M)953 1911 y Fm(44)995 1904 y Fo(f)p Fs(\001)p Fq(!)i Fs(+)e Fq(!)1181 1884 y Fm(0)1203 1904 y Fs([)p Fq(T)1253 1884 y Fp(\013)1246 1918 y(!)1272 1908 y Fg(0)1294 1904 y Fs(\()p Fu(x)p Fs(\))g Fo(\000)g Fq(t)g Fs(+)g(\001)p Fq(x)1556 1878 y Fm(\()p Fp(q)q Fm(\))1556 1919 y Fp(K)1610 1904 y Fq(M)1658 1911 y Fp(K)r Fm(4)1716 1904 y Fs(])p Fq(=)m(M)1800 1911 y Fm(44)1843 1904 y Fo(g)1868 1884 y Fm(2)504 2017 y Fo(\000)549 1998 y Fm(1)p 549 2006 V 549 2034 a(2)575 2017 y Fs(i)p Fq(!)622 1997 y Fm(0)644 2017 y Fs([)p Fq(T)694 1997 y Fp(\013)687 2031 y(!)713 2021 y Fg(0)735 2017 y Fs(\()p Fu(x)p Fs(\))12 b Fo(\000)f Fq(t)g Fs(+)g(\001)p Fq(x)1014 1991 y Fm(\()p Fp(q)q Fm(\))1014 2032 y Fp(K)1067 2017 y Fq(M)1115 2024 y Fp(K)r Fm(4)1173 2017 y Fs(])1187 1997 y Fm(2)1210 2017 y Fq(=)m(M)1280 2024 y Fm(44)1372 2017 y Fq(;)391 b Fs(\(215\))0 2097 y(where)14 b(all)g(quan)o(tities)g(at)g(the)h(righ)o(t{hand)d(side,)i (except)h(\001)p Fq(!)r Fs(,)f(are)g(appro)o(ximated)f(b)o(y)h(their)g (v)m(alue)0 2157 y(at)j Fq(!)f Fs(=)d Fq(!)193 2139 y Fm(0)215 2157 y Fs(.)100 2219 y(Replacing)21 b(in)o(tegration)h(v)m (ariable)g(d)p Fq(!)i Fs(in)e(\(213\))h(b)o(y)g(d\001)p Fq(!)g Fs(and)f(calculating)g(the)h(in)o(tegral)0 2279 y(analytically)l(,)16 b(w)o(e)g(obtain)g(Gaussian)f(pac)o(k)o(et)p 0 2327 1890 2 v 0 2432 2 105 v 406 2399 a Fq(u)435 2373 y Fp(\013)p Fm(\()-7 b(A)g(\))435 2413 y Fp(i)510 2399 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)f Fq(e)709 2406 y Fp(i)726 2399 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)827 2378 y Fp(\013)856 2399 y Fs(\))g Fq(a)907 2406 y Fe(G)l(P)963 2399 y Fs(\()p Fu(x)p Fs(\))g(exp)q([i)p Fq(!)1177 2378 y Fm(0)1207 2399 y Fq(T)1243 2378 y Fp(\013)1234 2411 y Fe(G)l(P)1289 2399 y Fs(\()p Fu(x)p Fq(;)g(t)p Fs(\)])51 b Fq(;)291 b Fs(\(216\))p 1888 2432 V 0 2434 1890 2 v 0 2506 a(where)16 b(the)h(v)o(ectorial)f(amplitude)f(of)i(the)g (scattered)f(Gaussian)f(pac)o(k)o(et)i(is)622 2650 y Fq(a)646 2657 y Fe(G)l(P)702 2650 y Fs(\()p Fu(x)p Fs(\))d(=)f Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)p Fq(;)8 b(!)967 2630 y Fm(0)990 2650 y Fs(\))1009 2559 y Fn(s)p 1059 2559 145 2 v 1068 2617 a Fs(2)p 1065 2639 31 2 v 1065 2685 a Fq(\031)1118 2617 y Fs(i)p Fq(!)1165 2602 y Fm(0)p 1107 2639 91 2 v 1107 2685 a Fq(M)1155 2692 y Fm(44)1254 2650 y Fq(;)509 b Fs(\(217\))920 2806 y(53)p eop %%Page: 54 28 54 27 bop 0 -54 a Fs(and)16 b(the)h(complex{v)m(alued)e(tra)o(v)o(el)h (time)h(of)f(the)h(scattered)g(Gaussian)e(pac)o(k)o(et)h(is)286 29 y Fq(T)322 8 y Fp(\013)313 41 y Fe(G)l(P)368 29 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)f Fq(T)580 8 y Fp(\013)573 42 y(!)599 32 y Fg(0)621 29 y Fs(\()p Fu(x)p Fs(\))e Fo(\000)f Fq(t)g Fo(\000)836 9 y Fm(1)p 836 17 20 2 v 836 46 a(2)862 29 y Fs([)p Fq(T)912 8 y Fp(\013)905 42 y(!)931 32 y Fg(0)953 29 y Fs(\()p Fu(x)p Fs(\))h Fo(\000)f Fq(t)g Fs(+)g(\001)p Fq(x)1232 3 y Fm(\()p Fp(q)q Fm(\))1232 43 y Fp(K)1285 29 y Fq(M)1333 36 y Fp(K)r Fm(4)1391 29 y Fs(])1405 8 y Fm(2)1427 29 y Fq(=)m(M)1497 36 y Fm(44)1590 29 y Fq(:)173 b Fs(\(218\))0 104 y(W)l(e)20 b(appro)o(ximate)e(the)h(second)g(term)g Fq(T)790 86 y Fp(\013)783 120 y(!)809 110 y Fg(0)831 104 y Fs(\()p Fu(x)p Fs(\))i(in)e(\(218\))h(b)o(y)f(its)g(linear)g(T)l(a)o(ylor)f (expansion)g(with)0 177 y(resp)q(ect)f(to)f(\001)p Fq(x)301 151 y Fm(\()p Fp(q)q Fm(\))301 191 y Fp(i)355 177 y Fs(,)591 248 y Fq(T)627 228 y Fp(\013)620 262 y(!)646 252 y Fg(0)669 248 y Fs(\()p Fu(x)p Fs(\))f Fo(\031)e Fq(T)840 228 y Fp(\013)880 248 y Fs(+)e Fq(\034)958 228 y Fm(0)990 248 y Fs(+)1054 229 y Fm(d)p Fp(\034)p 1046 237 60 2 v 1046 265 a Fm(d)p Fp(q)1086 270 y Fg(3)1112 248 y Fs(\001)p Fq(x)1182 222 y Fm(\()p Fp(q)q Fm(\))1182 262 y(3)1285 248 y Fq(;)478 b Fs(\(219\))0 325 y(see)17 b(\(53\))g(and)f(\(143\).)22 b(Then)33 411 y Fq(T)69 390 y Fp(\013)60 423 y Fe(G)l(P)115 411 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)f Fq(T)327 390 y Fp(\013)320 424 y(!)346 414 y Fg(0)368 411 y Fs(\()p Fu(x)p Fs(\))s Fo(\000)s Fq(t)d Fo(\000)566 391 y Fm(1)p 566 399 20 2 v 566 428 a(2)592 411 y Fs(\()p Fq(M)659 418 y Fm(44)702 411 y Fs(\))721 390 y Fl(\000)p Fm(1)775 411 y Fs(\()p Fq(M)842 418 y Fp(K)r Fm(4)901 411 y Fs(\001)p Fq(x)971 385 y Fm(\()p Fp(q)q Fm(\))971 425 y Fp(K)1024 411 y Fs(\))1043 390 y Fm(2)235 500 y Fs(+)g(\()p Fq(M)352 507 y Fm(44)395 500 y Fs(\))414 479 y Fl(\000)p Fm(1)468 500 y Fq(M)516 507 y Fp(K)r Fm(4)574 500 y Fs(\001)p Fq(x)644 474 y Fm(\()p Fp(q)q Fm(\))644 514 y Fp(K)697 500 y Fs(\()p Fq(t)s Fo(\000)s Fq(T)815 479 y Fp(\013)846 500 y Fo(\000)s Fq(\034)916 479 y Fm(0)949 500 y Fo(\000)1012 480 y Fm(d)p Fp(\034)p 1004 488 60 2 v 1004 517 a Fm(d)p Fp(q)1044 522 y Fg(3)1070 500 y Fs(\001)p Fq(x)1140 474 y Fm(\()p Fp(q)q Fm(\))1140 513 y(3)1193 500 y Fs(\))235 596 y Fo(\000)291 576 y Fm(1)p 291 584 20 2 v 291 613 a(2)317 596 y Fs(\()p Fq(M)384 603 y Fm(44)427 596 y Fs(\))446 575 y Fl(\000)p Fm(1)500 596 y Fs([\()546 576 y Fm(d)p Fp(\034)p 539 584 60 2 v 539 613 a Fm(d)p Fp(q)579 618 y Fg(3)604 596 y Fs(\))623 575 y Fm(2)646 596 y Fs(\(\001)p Fq(x)735 570 y Fm(\()p Fp(q)q Fm(\))735 609 y(3)789 596 y Fs(\))808 575 y Fm(2)841 596 y Fo(\000)g Fs(2)930 576 y Fm(d)p Fp(\034)p 922 584 V 922 613 a Fm(d)p Fp(q)962 618 y Fg(3)988 596 y Fs(\001)p Fq(x)1058 570 y Fm(\()p Fp(q)q Fm(\))1058 609 y(3)1111 596 y Fs(\()p Fq(t)s Fo(\000)s Fq(T)1229 575 y Fp(\013)1260 596 y Fo(\000)s Fq(\034)1330 575 y Fm(0)1351 596 y Fs(\))g(+)g(\()p Fq(t)s Fo(\000)s Fq(T)1549 575 y Fp(\013)1580 596 y Fo(\000)s Fq(\034)1650 575 y Fm(0)1671 596 y Fs(\))1690 575 y Fm(2)1713 596 y Fs(])17 b Fq(:)i Fs(\(220\))0 678 y(W)l(e)f(insert)f(\(143\))h(in)o (to)f(\(220\))h(and)f(obtain)g(the)h(complex{v)m(alued)f(tra)o(v)o(el)f (time)i(of)g(the)g(Gaussian)0 738 y(pac)o(k)o(et)e(in)g(the)h(form)221 821 y Fq(T)257 800 y Fp(\013)248 833 y Fe(G)l(P)303 821 y Fs(\()p Fu(x)p Fq(;)8 b(t)p Fs(\))15 b(=)e Fq(T)514 800 y Fp(\013)545 821 y Fs(+)s Fq(\034)615 800 y Fm(0)640 821 y Fo(\000)s Fq(t)d Fs(+)774 801 y Fm(d)p Fp(\034)p 766 809 V 766 838 a Fm(d)p Fp(q)806 843 y Fg(3)832 821 y Fs(\001)p Fq(x)902 795 y Fm(\()p Fp(q)q Fm(\))902 834 y(3)966 821 y Fs(+)1022 801 y Fm(1)p 1022 809 20 2 v 1022 838 a(2)1047 821 y Fs(\001)p Fq(x)1117 795 y Fm(\()p Fp(q)q Fm(\))1117 834 y Fp(i)1170 821 y Fq(M)1216 828 y Fe(G)l(P)s Fp(ij)1304 821 y Fs(\001)p Fq(x)1374 795 y Fm(\()p Fp(q)q Fm(\))1374 834 y Fp(j)423 917 y Fs(+)h(\001)p Fq(x)543 891 y Fm(\()p Fp(q)q Fm(\))543 930 y Fp(i)596 917 y Fq(M)642 924 y Fe(G)l(P)s Fp(i)p Fm(4)731 917 y Fs(\()p Fq(t)s Fo(\000)s Fq(T)849 896 y Fp(\013)880 917 y Fo(\000)s Fq(\034)950 896 y Fm(0)971 917 y Fs(\))h(+)1057 897 y Fm(1)p 1057 905 V 1057 934 a(2)1083 917 y Fq(M)1129 924 y Fe(G)l(P)s Fm(44)1224 917 y Fs(\()p Fq(t)s Fo(\000)s Fq(T)1342 896 y Fp(\013)1373 917 y Fo(\000)s Fq(\034)1443 896 y Fm(0)1464 917 y Fs(\))1483 896 y Fm(2)1556 917 y Fq(;)207 b Fs(\(221\))0 992 y(where)602 1065 y Fq(M)648 1072 y Fe(G)l(P)s Fp(K)r(L)780 1065 y Fs(=)14 b Fq(M)881 1072 y Fp(K)r(L)958 1065 y Fo(\000)1014 1031 y Fq(M)1062 1038 y Fp(K)r Fm(4)1120 1031 y Fq(M)1168 1038 y Fp(L)p Fm(4)p 1014 1053 205 2 v 1071 1099 a Fq(M)1119 1106 y Fm(44)1274 1065 y Fq(;)489 b Fs(\(222\))742 1190 y Fq(M)788 1197 y Fe(G)l(P)s Fp(K)r Fm(4)913 1190 y Fs(=)972 1156 y Fq(M)1020 1163 y Fp(K)r Fm(4)p 972 1178 107 2 v 980 1224 a Fq(M)1028 1231 y Fm(44)1134 1190 y Fq(;)629 b Fs(\(223\))739 1312 y Fq(M)785 1319 y Fe(G)l(P)s Fm(44)894 1312 y Fs(=)13 b Fo(\000)1024 1279 y Fs(1)p 991 1301 91 2 v 991 1347 a Fq(M)1039 1354 y Fm(44)1137 1312 y Fq(;)626 b Fs(\(224\))691 1413 y Fq(M)737 1420 y Fe(G)l(P)r Fm(34)846 1413 y Fs(=)13 b Fo(\000)p Fq(M)983 1420 y Fe(G)l(P)s Fm(44)1091 1394 y(d)p Fp(\034)p 1084 1402 60 2 v 1084 1430 a Fm(d)p Fp(q)1124 1435 y Fg(3)1777 1413 y Fs(\(225\))0 1497 y(\(Klime)m(\024)-22 b(s,)16 b(2004,)g(eq.)g(68;)494 1484 y(\024)489 1497 y(Cerv)o(en)q(\023)-26 b(y,)16 b(Klime)m(\024)-22 b(s)15 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)17 b(2007,)f(eq.)g(165\),)h (and)624 1572 y Fq(M)670 1579 y Fe(G)l(P)r Fp(i)p Fm(3)773 1572 y Fs(=)c Fo(\000)p Fq(M)910 1579 y Fe(G)l(P)s Fp(i)p Fm(4)1013 1552 y(d)p Fp(\034)p 1005 1561 V 1005 1589 a Fm(d)p Fp(q)1045 1594 y Fg(3)1082 1572 y Fs(+)e Fq(M)1180 1579 y Fp(i)p Fm(3)1777 1572 y Fs(\(226\))0 1661 y(\(Klime)m(\024)-22 b(s,)15 b(2004,)g(eqs.)h(67,)g(69;)591 1649 y(\024)586 1661 y(Cerv)o(en)q(\023)-26 b(y,)15 b(Klime)m(\024)-22 b(s)15 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)15 b(2007,)h(eqs.)f(163,)h(164\).)22 b(Equations)0 1721 y(\(222\))17 b(and)f(\(223\))h(in)f(matrix)g(notation)g(read)689 1830 y Fu(M)741 1837 y Fe(G)l(P)810 1830 y Fs(=)d Fu(M)f Fo(\000)984 1796 y Fu(M)1038 1803 y Fm(4)1060 1796 y Fu(M)1114 1778 y Fm(T)1114 1809 y(4)p 984 1818 163 2 v 1019 1864 a Fq(M)1067 1871 y Fm(44)1777 1830 y Fs(\(227\))0 1927 y(and)765 2000 y Fu(M)817 2007 y Fe(G)l(P)s Fm(4)906 2000 y Fs(=)972 1967 y Fu(M)1026 1974 y Fm(4)p 965 1989 91 2 v 965 2034 a Fq(M)1013 2041 y Fm(44)1111 2000 y Fq(:)652 b Fs(\(228\))0 2095 y(Note)17 b(that)g(the)g(in)o(v)o(erse)e (relations)h(to)g(\(227\),)h(\(228\),)g(\(224\))g(and)f(\(217\))h(read) 636 2204 y Fu(M)d Fs(=)f Fu(M)808 2211 y Fe(G)l(P)875 2204 y Fo(\000)931 2170 y Fu(M)983 2177 y Fe(G)l(P)r Fm(4)1058 2170 y Fu(M)1112 2152 y Fm(T)1110 2183 y Fe(G)l(P)r Fm(4)p 931 2192 255 2 v 987 2238 a Fq(M)1033 2245 y Fe(G)l(P)s Fm(44)1241 2204 y Fq(;)522 b Fs(\(229\))746 2335 y Fu(M)800 2342 y Fm(4)836 2335 y Fs(=)14 b Fo(\000)941 2301 y Fu(M)993 2308 y Fe(G)l(P)r Fm(4)p 934 2323 141 2 v 934 2369 a Fq(M)980 2376 y Fe(G)l(P)r Fm(44)1130 2335 y Fq(;)633 b Fs(\(230\))739 2458 y Fq(M)787 2465 y Fm(44)843 2458 y Fs(=)14 b Fo(\000)999 2424 y Fs(1)p 941 2446 V 941 2492 a Fq(M)987 2499 y Fe(G)l(P)r Fm(44)1137 2458 y Fq(;)626 b Fs(\(231\))0 2549 y(and)543 2633 y Fn(b)-28 b Fq(a)q Fs(\()p Fu(x)p Fq(;)8 b(!)674 2612 y Fm(0)697 2633 y Fs(\))14 b(=)f Fq(a)806 2640 y Fe(G)l(P)862 2633 y Fs(\()p Fu(x)p Fs(\))930 2558 y Fn(r)p 980 2558 303 2 v 986 2599 a Fq(\031)p 986 2621 31 2 v 989 2667 a Fs(2)1140 2599 y(1)p 1028 2621 249 2 v 1028 2667 a Fo(\000)p Fs(i)p Fq(!)1114 2652 y Fm(0)1136 2667 y Fq(M)1182 2674 y Fe(G)l(P)s Fm(44)1333 2633 y Fq(:)430 b Fs(\(232\))920 2806 y(54)p eop %%Page: 55 29 55 28 bop 0 -54 a Fu(5.4.)25 b(Initial)c(v)m(alues)f(of)e(the)h (scattered)h(Gaussian)e(pac)n(k)n(et)0 28 y Fs(The)d(initial)g(v)m (alues)h(of)f(the)h(second{order)e(tra)o(v)o(el{time)g(deriv)m(ativ)o (es)i(\(227\),)g(\(228\),)g(\(224\))g(and)f(of)0 88 y(amplitude)g (\(217\))i(at)g(p)q(oin)o(t)f Fu(x)586 70 y Fp(\013)631 88 y Fs(are)565 185 y Fu(M)619 165 y Fp(\013)617 198 y Fe(G)l(P)686 185 y Fs(=)e Fu(M)793 165 y Fp(\013)832 185 y Fo(\000)d Fs(\()p Fq(M)954 165 y Fp(\013)949 198 y Fm(44)992 185 y Fs(\))1011 165 y Fl(\000)p Fm(1)1065 185 y Fu(M)1119 165 y Fp(\013)1119 198 y Fm(4)1148 185 y Fu(M)1202 165 y Fp(\013)1202 198 y Fm(4)1231 162 y(T)1311 185 y Fq(;)452 b Fs(\(233\))684 290 y Fu(M)738 269 y Fp(\013)736 302 y Fe(G)l(P)r Fm(4)825 290 y Fs(=)13 b(\()p Fq(M)949 269 y Fp(\013)944 302 y Fm(44)987 290 y Fs(\))1006 269 y Fl(\000)p Fm(1)1060 290 y Fu(M)1114 269 y Fp(\013)1114 302 y Fm(4)1193 290 y Fq(;)570 b Fs(\(234\))699 379 y Fq(M)752 359 y Fp(\013)745 392 y Fe(G)l(P)r Fm(44)854 379 y Fs(=)13 b Fo(\000)p Fs(\()p Fq(M)1017 359 y Fp(\013)1012 392 y Fm(44)1055 379 y Fs(\))1074 359 y Fl(\000)p Fm(1)1177 379 y Fq(;)586 b Fs(\(235\))0 462 y(and)594 567 y Fq(a)618 574 y Fe(G)l(P)673 567 y Fs(\()p Fu(x)722 546 y Fp(\013)751 567 y Fs(\))14 b(=)f Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)912 546 y Fp(\013)941 567 y Fq(;)8 b(!)996 546 y Fm(0)1019 567 y Fs(\))1038 478 y Fn(s)p 1088 478 145 2 v 1096 533 a Fs(2)p 1094 555 31 2 v 1094 601 a Fq(\031)1147 533 y Fs(i)p Fq(!)1194 519 y Fm(0)p 1136 555 91 2 v 1136 601 a Fq(M)1189 584 y Fp(\013)1184 614 y Fm(44)1282 567 y Fq(:)481 b Fs(\(236\))0 690 y(Inserting)15 b(\(130\),)i(\(146\))g (and)f(\(153\))h(in)o(to)f(\(233\),)h(w)o(e)g(arriv)o(e)e(at)p 0 744 1890 2 v 0 923 2 180 v 124 844 a Fu(M)178 824 y Fp(\013)176 856 y Fe(G)l(P)245 844 y Fs(=)e Fu(T)337 824 y Fm(\()p Fp(q)q Fm(\))401 844 y Fs(+)e(i)p Fq(!)498 824 y Fl(\000)p Fm(1)551 844 y Fu(K)596 824 y Fm(\()p Fp(q)q Fm(\))660 844 y Fo(\000)716 810 y Fu(k)746 792 y Fm(\()p Fp(q)q Fm(\))p 716 833 84 2 v 717 891 a Fq(k)745 865 y Fm(\()p Fp(q)q Fm(\))743 904 y(3)814 844 y Fu(m)865 824 y Fm(T)904 844 y Fo(\000)f Fu(m)1004 774 y Fn(\022)1044 810 y Fu(k)1074 792 y Fm(\()p Fp(q)q Fm(\))p 1044 833 V 1045 891 a Fq(k)1073 865 y Fm(\()p Fp(q)q Fm(\))1071 904 y(3)1133 774 y Fn(\023)1156 784 y Fm(T)1198 844 y Fs(+)h Fq(m)1306 810 y Fu(k)1336 792 y Fm(\()p Fp(q)q Fm(\))p 1306 833 V 1307 891 a Fq(k)1335 865 y Fm(\()p Fp(q)q Fm(\))1333 904 y(3)1395 774 y Fn(\022)1438 810 y Fu(k)1468 792 y Fm(\()p Fp(q)q Fm(\))p 1438 833 V 1439 891 a Fq(k)1467 865 y Fm(\()p Fp(q)q Fm(\))1465 904 y(3)1527 774 y Fn(\023)1550 784 y Fm(T)1631 844 y Fq(;)122 b Fs(\(237\))p 1888 923 2 180 v 0 925 1890 2 v 0 1000 a(where)17 b Fu(m)d Fs(is)j(de\014ned)f(b)o(y)h(\(127\))g(and)g Fq(m)g Fs(is)g(de\014ned)f (b)o(y)h(\(128\).)24 b(Inserting)17 b(\(146\))g(and)g(\(153\))h(in)o (to)0 1060 y(\(234\),)f(w)o(e)f(arriv)o(e)g(at)p 0 1114 V 0 1287 2 174 v 606 1208 a Fu(M)660 1188 y Fp(\013)658 1221 y Fe(G)l(P)r Fm(4)747 1208 y Fs(=)818 1175 y Fq(!)851 1157 y Fm(0)p 805 1197 81 2 v 805 1255 a Fq(k)833 1229 y Fm(\()p Fp(q)q Fm(\))831 1268 y(3)892 1138 y Fn(\022)928 1208 y Fq(m)978 1175 y Fu(k)1008 1157 y Fm(\()p Fp(q)q Fm(\))p 978 1197 84 2 v 979 1255 a Fq(k)1007 1229 y Fm(\()p Fp(q)q Fm(\))1005 1268 y(3)1079 1208 y Fo(\000)10 b Fu(m)1179 1138 y Fn(\023)1263 1208 y Fq(:)490 b Fs(\(238\))p 1888 1287 2 174 v 0 1289 1890 2 v 0 1364 a(Inserting)15 b(\(153\))i(in)o(to) f(\(235\),)h(w)o(e)g(arriv)o(e)e(at)p 0 1418 V 0 1596 2 178 v 696 1517 a Fq(M)749 1497 y Fp(\013)742 1529 y Fe(G)l(P)s Fm(44)851 1517 y Fs(=)904 1447 y Fn(\022)959 1483 y Fq(!)992 1465 y Fm(0)p 946 1506 81 2 v 946 1564 a Fq(k)974 1538 y Fm(\()p Fp(q)q Fm(\))972 1577 y(3)1025 1447 y Fn(\023)1048 1457 y Fm(2)1078 1517 y Fq(m)50 b(:)581 b Fs(\(239\))p 1888 1596 2 178 v 0 1598 1890 2 v 0 1673 a(Inserting)15 b(\(153\))i(and)f(\(163\))h(in)o(to)f(\(236\),)h(w)o(e)g (arriv)o(e)e(at)450 1801 y Fq(a)474 1808 y Fe(G)l(P)529 1801 y Fs(\()p Fu(x)578 1781 y Fp(\013)607 1801 y Fs(\))g(=)e(i)p Fq(!)740 1781 y Fm(0)774 1789 y Fn(b)762 1801 y Fq(A)q Fs(\()p Fu(x)849 1781 y Fp(\013)878 1801 y Fq(;)8 b(!)r Fs(\))14 b Fq(r)989 1781 y Fp(\013)1018 1801 y Fs(\()p Fu(x)p Fs(\))1114 1782 y Fm(d)p Fp(\034)p 1107 1790 60 2 v 1107 1819 a Fm(d)p Fp(q)1147 1824 y Fg(3)1172 1801 y Fs(\()p Fu(x)1221 1783 y Fp(\013)1250 1801 y Fs(\))1290 1768 y(2)p Fq(!)1348 1750 y Fm(0)p 1290 1790 81 2 v 1290 1848 a Fq(k)1318 1822 y Fm(\()p Fp(q)q Fm(\))1316 1861 y(3)1426 1801 y Fq(:)337 b Fs(\(240\))0 1941 y(Inserting)15 b(\(132\),)i(\(99\))g(and)f(\(81\))h(in)o(to)f(\(240\),)h(w)o(e)g (obtain)p 0 1995 1890 2 v 0 2138 2 144 v 474 2077 a Fq(a)498 2084 y Fe(G)l(P)553 2077 y Fs(\()p Fu(x)602 2057 y Fp(\013)631 2077 y Fs(\))d(=)g(i)p Fq(!)764 2057 y Fm(0)798 2065 y Fn(b)786 2077 y Fq(A)p Fs(\()p Fu(x)872 2057 y Fp(\013)901 2077 y Fq(;)8 b(!)r Fs(\))14 b Fq(r)1012 2057 y Fp(\013)1042 2077 y Fs(\()p Fu(x)p Fs(\))1222 2043 y(2)p 1130 2066 209 2 v 1130 2111 a(1)d Fo(\000)g Fq(P)1248 2118 y Fp(i)1265 2111 y Fq(H)1310 2097 y Fp(;i)1394 2077 y Fq(;)359 b Fs(\(241\))p 1888 2138 2 144 v 0 2140 1890 2 v 0 2214 a(where)17 b Fq(P)177 2221 y Fp(i)210 2214 y Fs(is)g(the)g(slo)o(wness) f(v)o(ector)h(of)g(the)g(inciden)o(t)f(w)o(a)o(v)o(e)h(and)f Fq(H)1295 2196 y Fp(;i)1341 2214 y Fs(is)h(the)g(ra)o(y{v)o(elo)q(cit)o (y)g(v)o(ector)0 2275 y(of)g(the)g(scattered)f(Gaussian)f(pac)o(k)o(et) h(at)h(p)q(oin)o(t)f Fu(x)947 2257 y Fp(\013)976 2275 y Fs(.)920 2806 y(55)p eop %%Page: 56 30 56 29 bop 0 -54 a Fu(5.5.)25 b(Ev)n(olution)20 b(equations)f(of)g(the)g (scattered)h(Gaussian)e(pac)n(k)n(et)0 27 y Fs(W)l(e)f(de\014ne)f (matrices)689 93 y Fu(Q)730 100 y Fe(G)l(P)799 93 y Fs(=)e Fu(Q)895 100 y Fm(1)928 93 y Fs(+)d Fu(Q)1021 100 y Fm(2)1043 93 y Fu(M)1097 73 y Fp(\013)1095 106 y Fe(G)l(P)1777 93 y Fs(\(242\))0 175 y(and)688 241 y Fu(P)725 248 y Fe(G)l(P)794 241 y Fs(=)j Fu(P)886 248 y Fm(1)919 241 y Fs(+)d Fu(P)1008 248 y Fm(2)1031 241 y Fu(M)1085 220 y Fp(\013)1083 253 y Fe(G)l(P)1188 241 y Fq(;)575 b Fs(\(243\))0 322 y(where)22 b Fu(Q)193 329 y Fm(1)216 322 y Fs(,)i Fu(P)293 329 y Fm(1)316 322 y Fs(,)g Fu(Q)397 329 y Fm(2)443 322 y Fs(and)e Fu(P)585 329 y Fm(2)630 322 y Fs(form)g(paraxial)g(ra)o (y)h(propagator)e(matrix)h(\(113\).)42 b(P)o(arameters)0 382 y(describing)15 b(a)h(Gaussian)f(pac)o(k)o(et)i(should)e(ob)q(ey)i (relations)p 0 432 1890 2 v 0 535 2 103 v 735 504 a Fu(M)787 511 y Fe(G)l(P)856 504 y Fs(=)d Fu(P)946 511 y Fe(G)l(P)1001 504 y Fu(Q)1044 483 y Fl(\000)p Fm(1)1042 516 y Fe(G)l(P)1767 504 y Fs(\(244\))p 1888 535 V 0 537 1890 2 v 0 611 a(\(Klime)m(\024)-22 b(s,)16 b(2004,)g(eq.)g(50;)494 598 y(\024)489 611 y(Cerv)o(en)q(\023) -26 b(y,)16 b(Klime)m(\024)-22 b(s)15 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)17 b(2007,)f(eq.)g(135\),)p 0 664 V 0 767 2 103 v 692 736 a Fu(M)744 743 y Fe(G)l(P)s Fm(4)833 736 y Fs(=)e Fu(Q)929 715 y Fl(\000)p Fm(1)927 748 y Fe(G)l(P)982 705 y Fm(T)1013 736 y Fu(M)1067 715 y Fp(\013)1065 748 y Fe(G)l(P)s Fm(4)1767 736 y Fs(\(245\))p 1888 767 V 0 769 1890 2 v 0 843 a(\(Klime)m(\024)-22 b(s,)16 b(2004,)g(eq.)g(74;)494 830 y(\024)489 843 y(Cerv)o(en)q(\023) -26 b(y,)16 b(Klime)m(\024)-22 b(s)15 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)17 b(2007,)f(eq.)g(166\),)p 0 896 V 0 1010 2 115 v 632 967 a Fu(M)684 974 y Fe(G)l(P)s Fm(3)773 967 y Fs(=)d Fo(\000)878 948 y Fm(d)p Fp(\034)p 870 956 60 2 v 870 985 a Fm(d)p Fp(q)910 990 y Fg(3)936 967 y Fu(M)988 974 y Fe(G)l(P)s Fm(4)1074 967 y Fs(+)e Fu(M)1178 974 y Fm(3)1767 967 y Fs(\(246\))p 1888 1010 2 115 v 0 1012 1890 2 v 0 1086 a(\(Klime)m(\024)-22 b(s,)15 b(2004,)h(eq.)h(67;)494 1073 y(\024)488 1086 y(Cerv)o(en)q(\023)-26 b(y,)16 b(Klime)m(\024)-22 b(s)16 b(&)g(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)16 b(2007,)g(eq.)g(163\),)h (where)f Fu(M)1646 1093 y Fm(3)1685 1086 y Fs(is)g(de\014ned)0 1146 y(b)o(y)g(\(110\))h(and)f(\(112\),)p 0 1199 V 0 1302 2 103 v 535 1271 a Fq(M)581 1278 y Fe(G)l(P)s Fm(44)690 1271 y Fs(=)d Fq(M)795 1250 y Fp(\013)788 1283 y Fe(G)l(P)s Fm(44)894 1271 y Fo(\000)e Fu(M)996 1278 y Fe(G)l(P)s Fm(4)1071 1249 y(T)1102 1271 y Fu(Q)1145 1278 y Ff(2)1170 1271 y Fu(M)1224 1250 y Fp(\013)1222 1283 y Fe(G)l(P)s Fm(4)1767 1271 y Fs(\(247\))p 1888 1302 V 0 1304 1890 2 v 0 1378 a(\(Klime)m(\024)-22 b(s,)16 b(2004,)g(eq.)g(79\),)p 0 1431 V 0 1545 2 115 v 687 1502 a Fq(M)733 1509 y Fe(G)l(P)s Fm(34)842 1502 y Fs(=)d Fo(\000)947 1483 y Fm(d)p Fp(\034)p 939 1491 60 2 v 939 1519 a Fm(d)p Fp(q)979 1524 y Fg(3)1005 1502 y Fq(M)1051 1509 y Fe(G)l(P)r Fm(44)1767 1502 y Fs(\(248\))p 1888 1545 2 115 v 0 1547 1890 2 v 0 1621 a(\(Klime)m(\024)-22 b(s,)16 b(2004,)g(eq.)g(68;)494 1608 y(\024)489 1621 y(Cerv)o(en)q(\023)-26 b(y,)16 b(Klime)m(\024)-22 b(s)15 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)17 b(2007,)f(eq.)g(165\),)p 0 1674 V 0 1788 2 115 v 600 1745 a Fq(M)646 1752 y Fe(G)l(P)s Fm(33)755 1745 y Fs(=)d(\()840 1726 y Fm(d)p Fp(\034)p 833 1734 60 2 v 833 1763 a Fm(d)p Fp(q)873 1768 y Fg(3)898 1745 y Fs(\))917 1725 y Fm(2)940 1745 y Fq(M)986 1752 y Fe(G)l(P)s Fm(44)1092 1745 y Fs(+)e Fq(M)1190 1752 y Fm(33)1767 1745 y Fs(\(249\))p 1888 1788 2 115 v 0 1790 1890 2 v 0 1864 a(\(Klime)m(\024)-22 b(s,)15 b(2004,)g(eq.)g(69;)490 1851 y(\024)485 1864 y(Cerv)o(en)q(\023)-26 b(y,)15 b(Klime)m(\024)-22 b(s)14 b(&)h(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)15 b(2007,)g(eq.)h(164\),)f(where)g Fq(M)1628 1871 y Fm(33)1686 1864 y Fs(is)g(de\014ned)0 1924 y(b)o(y)h(\(110\))h (and)f(\(112\),)h(and)p 0 1977 V 0 2194 2 218 v 127 2103 a Fq(a)151 2110 y Fe(G)l(P)206 2103 y Fs(\()p Fu(x)p Fs(\))e(=)22 b Fq(R)p Fs(\()p Fu(x)p Fq(;)8 b Fu(x)489 2082 y Fp(\013)518 2103 y Fs(\))537 1998 y Fn(v)537 2026 y(u)537 2056 y(u)537 2086 y(t)p 590 1998 394 2 v 588 2059 a Fq(\045)p Fs(\()p Fu(x)663 2045 y Fp(\013)692 2059 y Fs(\))725 2040 y Fm(d)p Fp(\034)p 717 2048 60 2 v 717 2077 a Fm(d)p Fp(q)757 2082 y Fg(3)783 2059 y Fs(\()p Fu(x)p Fs(\))p Fq(h)p Fs(\()p Fu(x)929 2045 y Fp(\013)958 2059 y Fs(\))p 588 2091 390 2 v 602 2141 a Fq(\045)p Fs(\()p Fu(x)p Fs(\))710 2121 y Fm(d)p Fp(\034)p 703 2130 60 2 v 703 2158 a Fm(d)p Fp(q)743 2163 y Fg(3)768 2141 y Fs(\()p Fu(x)817 2127 y Fp(\013)846 2141 y Fs(\))p Fq(h)p Fs(\()p Fu(x)p Fs(\))1173 2069 y(1)p 990 2091 393 2 v 990 2101 a Fn(p)p 1039 2101 343 2 v 1039 2144 a Fs(det)q([)p Fu(Q)1164 2151 y Fe(G)l(P)1218 2144 y Fs(\()p Fu(x)p Fq(;)g Fu(x)1319 2129 y Fp(\013)1349 2144 y Fs(\)])1402 2103 y Fq(a)1426 2110 y Fe(G)l(P)1481 2103 y Fs(\()p Fu(x)1530 2082 y Fp(\013)1559 2103 y Fs(\))50 b Fq(:)125 b Fs(\(250\))p 1888 2194 2 218 v 0 2196 1890 2 v 0 2270 a(T)l(erm)130 2227 y Fn(p)p 180 2227 343 2 v 43 x Fs(det[)p Fu(Q)304 2277 y Fe(G)l(P)359 2270 y Fs(\()p Fu(x)p Fq(;)8 b Fu(x)460 2256 y Fp(\013)489 2270 y Fs(\)])15 b(is)f(equal)h(to)g(1)g(at)g Fu(x)f Fs(=)f Fu(x)999 2252 y Fp(\013)1028 2270 y Fs(,)i(and)f(then)h(v)m(aries)f (con)o(tin)o(uously)f(along)h(the)0 2330 y(ra)o(y)l(.)920 2806 y(56)p eop %%Page: 57 31 57 30 bop 0 -54 a Fu(5.6.)25 b(Pro)r(of)17 b(of)h(the)h(ev)n(olution)j (equations)0 27 y Fs(In)i(Section)g(5.3,)h(w)o(e)f(deriv)o(ed)f(the)h (scattered)g(Gaussian)e(pac)o(k)o(ets)i(under)f(the)h(assumption)e(of)0 87 y(narro)o(w{band)15 b(scattering.)26 b(In)18 b(Section)g(5.4,)g(w)o (e)g(determined)f(the)h(initial)f(conditions)g(for)h(these)0 147 y(Gaussian)i(pac)o(k)o(ets,)j(and)e(in)h(Section)f(5.5,)i(w)o(e)f (summarized)d(the)j(ev)o(olution)g(equations)f(whic)o(h)0 207 y(Gaussian)c(pac)o(k)o(ets)h(should)f(ob)q(ey)l(.)28 b(W)l(e)19 b(shall)e(no)o(w)h(pro)o(v)o(e)f(that)i(the)g(equations)f (deriv)o(ed)f(in)h(Sec-)0 267 y(tion)e(5.3)h(are)f(equiv)m(alen)o(t)g (to)h(the)g(equations)f(expressed)g(Section)g(5.5)100 331 y(Equation)g(\(246\))h(is)f(equiv)m(alen)o(t)h(to)f(\(226\).)23 b(Equation)16 b(\(248\))h(coincides)f(with)g(\(225\).)23 b(Equa-)0 391 y(tion)c(\(249\))g(follo)o(ws)f(from)g(\(226\))h(with)g (\(225\).)29 b(W)l(e)19 b(no)o(w)f(pro)o(v)o(e)g(equations)g(\(244\),)i (\(245\),)g(\(247\))0 451 y(and)c(\(250\).)0 586 y Fu(5.6.1.)24 b(Equiv)m(alence)d(of)e Fs(\(227\))g Fu(and)g Fs(\(244\))0 667 y(W)l(e)c(shall)f(con)o(v)o(ert)g(equation)g(\(244\))i(using)d (previously)h(deriv)o(ed)g(equations)g(in)o(to)g(equation)h(\(227\).)0 727 y(Considering)f(equation)j(\(142\),)g(equation)f(\(244\))h(is)f (equiv)m(alen)o(t)h(to)468 824 y Fu(Q)511 803 y Fm(T)542 824 y Fs(\()p Fu(M)613 831 y Fe(G)l(P)680 824 y Fo(\000)10 b Fu(M)p Fs(\))p Fu(Q)843 831 y Fe(G)l(P)913 824 y Fs(=)k Fu(Q)1009 803 y Fm(T)1039 824 y Fu(P)1076 831 y Fe(G)l(P)1143 824 y Fo(\000)c Fu(P)1231 803 y Fm(T)1262 824 y Fu(Q)1303 831 y Fe(G)l(P)1408 824 y Fq(:)355 b Fs(\(251\))0 920 y(Considering)14 b(symplectic)j(prop)q(ert)o(y)466 1016 y Fu(Q)509 995 y Fm(T)540 1016 y Fu(P)577 1023 y Fe(G)l(P)643 1016 y Fo(\000)11 b Fu(P)732 995 y Fm(T)763 1016 y Fu(Q)804 1023 y Fe(G)l(P)872 1016 y Fs(=)j Fu(Q)968 995 y Fp(\013)996 993 y Fm(T)1027 1016 y Fu(P)1066 995 y Fp(\013)1064 1028 y Fe(G)l(P)1130 1016 y Fo(\000)d Fu(P)1219 995 y Fp(\013)1248 993 y Fm(T)1279 1016 y Fu(Q)1322 995 y Fp(\013)1320 1028 y Fe(G)l(P)1777 1016 y Fs(\(252\))0 1112 y(and)16 b(de\014nitions)f (\(140\),)i(\(141\),)g(\(242\),)g(\(243\),)g(equation)f(\(251\))h(is)f (equiv)m(alen)o(t)h(to)539 1208 y Fu(Q)582 1188 y Fm(T)613 1208 y Fs(\()p Fu(M)684 1215 y Fe(G)l(P)751 1208 y Fo(\000)10 b Fu(M)p Fs(\))p Fu(Q)914 1215 y Fe(G)l(P)984 1208 y Fs(=)j Fu(M)1090 1188 y Fp(\013)1088 1221 y Fe(G)l(P)1155 1208 y Fo(\000)e Fu(M)1259 1188 y Fp(\013)1337 1208 y Fq(:)426 b Fs(\(253\))0 1304 y(Considering)14 b(equation)j(\(233\),)g (equation)f(\(253\))h(is)f(equiv)m(alen)o(t)h(to)467 1412 y Fu(M)519 1419 y Fe(G)l(P)588 1412 y Fs(=)d Fu(M)d Fo(\000)g Fu(Q)799 1392 y Fl(\000)p Fm(1)853 1382 y(T)883 1412 y Fu(M)937 1392 y Fp(\013)937 1425 y Fm(4)966 1412 y Fu(M)1020 1392 y Fp(\013)1020 1425 y Fm(4)1049 1389 y(T)1080 1412 y Fu(Q)1123 1392 y Fl(\000)p Fm(1)1121 1425 y Fe(G)l(P)1176 1412 y Fs(\()p Fq(M)1248 1392 y Fp(\013)1243 1425 y Fm(44)1286 1412 y Fs(\))1305 1392 y Fl(\000)p Fm(1)1409 1412 y Fq(:)354 b Fs(\(254\))0 1509 y(De\014nitions)15 b(\(140\))i(and)f(\(242\))h(with)g(relation)f (\(233\))h(yield)467 1605 y Fu(Q)508 1612 y Fe(G)l(P)563 1605 y Fu(Q)606 1584 y Fl(\000)p Fm(1)673 1605 y Fs(=)d Fu(1)d Fo(\000)f Fs(\()p Fq(M)887 1584 y Fp(\013)882 1617 y Fm(44)925 1605 y Fs(\))944 1584 y Fl(\000)p Fm(1)998 1605 y Fu(Q)1041 1612 y Ff(2)1066 1605 y Fu(M)1120 1584 y Fp(\013)1120 1617 y Fm(4)1149 1605 y Fu(M)1203 1584 y Fp(\013)1203 1617 y Fm(4)1232 1582 y(T)1263 1605 y Fu(Q)1306 1584 y Fl(\000)p Fm(1)1409 1605 y Fq(:)354 b Fs(\(255\))0 1701 y(The)16 b(in)o(v)o(erse)f(matrix)i(is)503 1821 y Fu(QQ)589 1801 y Fl(\000)p Fm(1)587 1834 y Fe(G)l(P)657 1821 y Fs(=)c Fu(1)e Fo(\000)880 1788 y Fu(Q)923 1795 y Ff(2)948 1788 y Fu(M)1002 1770 y Fp(\013)1002 1800 y Fm(4)1031 1788 y Fu(M)1085 1770 y Fp(\013)1085 1800 y Fm(4)1114 1766 y(T)1145 1788 y Fu(Q)1188 1770 y Fl(\000)p Fm(1)p 805 1810 513 2 v 805 1862 a Fu(M)859 1844 y Fp(\013)859 1875 y Fm(4)887 1840 y(T)918 1862 y Fu(Q)961 1847 y Fl(\000)p Fm(1)1015 1862 y Fu(Q)1058 1869 y Ff(2)1083 1862 y Fu(M)1137 1844 y Fp(\013)1137 1875 y Fm(4)1177 1862 y Fo(\000)g Fq(M)1280 1844 y Fp(\013)1275 1875 y Fm(44)1373 1821 y Fq(:)390 b Fs(\(256\))0 1953 y(Considering)14 b(equation)j(\(256\),)g (equation)f(\(254\))h(is)f(equiv)m(alen)o(t)h(to)101 2094 y Fu(M)153 2101 y Fe(G)l(P)222 2094 y Fs(=)d Fu(M)d Fo(\000)g Fu(Q)433 2073 y Fl(\000)p Fm(1)487 2063 y(T)518 2094 y Fu(M)572 2073 y Fp(\013)572 2106 y Fm(4)600 2094 y Fu(M)654 2073 y Fp(\013)654 2106 y Fm(4)683 2071 y(T)714 2094 y Fu(Q)757 2073 y Fl(\000)p Fm(1)810 2094 y Fs(\()p Fq(M)882 2073 y Fp(\013)877 2106 y Fm(44)920 2094 y Fs(\))939 2073 y Fl(\000)p Fm(1)993 2009 y Fn(")1014 2094 y Fs(1)g Fo(\000)1181 2060 y Fu(M)1235 2042 y Fp(\013)1235 2073 y Fm(4)1264 2038 y(T)1295 2060 y Fu(Q)1338 2042 y Fl(\000)p Fm(1)1392 2060 y Fu(Q)1435 2067 y Ff(2)1460 2060 y Fu(M)1514 2042 y Fp(\013)1514 2073 y Fm(4)p 1106 2083 V 1106 2134 a Fu(M)1160 2117 y Fp(\013)1160 2147 y Fm(4)1189 2112 y(T)1219 2134 y Fu(Q)1262 2120 y Fl(\000)p Fm(1)1316 2134 y Fu(Q)1359 2141 y Ff(2)1384 2134 y Fu(M)1438 2117 y Fp(\013)1438 2147 y Fm(4)1478 2134 y Fo(\000)g Fq(M)1581 2117 y Fp(\013)1576 2147 y Fm(44)1616 2009 y Fn(#)1662 2094 y Fq(;)101 b Fs(\(257\))0 2232 y(whic)o(h)16 b(is)g(equiv)m(alen)o (t)g(to)506 2368 y Fu(M)558 2375 y Fe(G)l(P)628 2368 y Fs(=)d Fu(M)f Fs(+)847 2335 y Fu(Q)890 2317 y Fl(\000)p Fm(1)944 2306 y(T)975 2335 y Fu(M)1029 2317 y Fp(\013)1029 2347 y Fm(4)1058 2335 y Fu(M)1112 2317 y Fp(\013)1112 2347 y Fm(4)1140 2313 y(T)1171 2335 y Fu(Q)1214 2317 y Fl(\000)p Fm(1)p 801 2357 V 801 2409 a Fu(M)855 2391 y Fp(\013)855 2422 y Fm(4)884 2387 y(T)915 2409 y Fu(Q)958 2394 y Fl(\000)p Fm(1)1012 2409 y Fu(Q)1055 2416 y Ff(2)1080 2409 y Fu(M)1134 2391 y Fp(\013)1134 2422 y Fm(4)1174 2409 y Fo(\000)e Fq(M)1276 2391 y Fp(\013)1271 2422 y Fm(44)1370 2368 y Fq(:)393 b Fs(\(258\))0 2500 y(Considering)14 b(equations)i(\(150\))i(and)d(\(154\),)i(equation)g(\(258\))g(is)f (equiv)m(alen)o(t)g(to)h(equation)g(\(227\).)920 2806 y(57)p eop %%Page: 58 32 58 31 bop 0 -54 a Fu(5.6.2.)24 b(Equiv)m(alence)d(of)e Fs(\(228\))g Fu(and)g Fs(\(245\))0 17 y(W)l(e)k(shall)f(con)o(v)o(ert)g (equation)h(\(228\))g(in)o(to)f(equation)h(\(245\).)41 b(Inserting)22 b(equations)g(\(150\))i(and)0 77 y(\(154\))17 b(in)o(to)f(equation)g(\(228\),)h(w)o(e)g(obtain)554 202 y Fu(M)606 209 y Fe(G)l(P)s Fm(4)695 202 y Fs(=)905 168 y Fu(Q)948 150 y Fl(\000)p Fm(1)1001 140 y(T)1032 168 y Fu(M)1086 150 y Fp(\013)1086 180 y Fm(4)p 754 190 513 2 v 754 242 a Fq(M)807 225 y Fp(\013)802 255 y Fm(44)855 242 y Fo(\000)11 b Fu(M)959 225 y Fp(\013)959 255 y Fm(4)988 220 y(T)1019 242 y Fu(Q)1062 227 y Fl(\000)p Fm(1)1115 242 y Fu(Q)1158 249 y Ff(2)1183 242 y Fu(M)1237 225 y Fp(\013)1237 255 y Fm(4)1322 202 y Fq(:)441 b Fs(\(259\))0 319 y(W)l(e)17 b(m)o(ultiply)e(equation)h(\(259\))i(b)o(y)e(equation) 525 400 y Fu(Q)568 379 y Fm(T)566 412 y Fe(G)l(P)635 400 y Fs(=)e Fu(Q)731 379 y Fm(T)773 400 y Fo(\000)d Fs(\()p Fq(M)895 379 y Fp(\013)890 412 y Fm(44)933 400 y Fs(\))952 379 y Fl(\000)p Fm(1)1005 400 y Fu(M)1059 379 y Fp(\013)1059 412 y Fm(4)1088 400 y Fu(M)1142 379 y Fp(\013)1142 412 y Fm(4)1171 376 y(T)1202 400 y Fu(Q)1245 407 y Ff(2)1270 378 y Fm(T)1351 400 y Fq(:)412 b Fs(\(260\))0 481 y(follo)o(wing)15 b(from)h(\(255\))h(and)f(obtain)346 605 y Fu(Q)389 585 y Fm(T)387 617 y Fe(G)l(P)442 605 y Fu(M)494 612 y Fe(G)l(P)s Fm(4)583 605 y Fs(=)642 571 y Fu(M)696 553 y Fp(\013)696 584 y Fm(4)736 571 y Fo(\000)10 b Fs(\()p Fq(M)857 553 y Fp(\013)852 584 y Fm(44)895 571 y Fs(\))914 553 y Fl(\000)p Fm(1)968 571 y Fu(M)1022 553 y Fp(\013)1022 584 y Fm(4)1051 571 y Fu(M)1105 553 y Fp(\013)1105 584 y Fm(4)1134 550 y(T)1165 571 y Fu(Q)1208 578 y Ff(2)1233 550 y Fm(T)1264 571 y Fu(Q)1307 553 y Fl(\000)p Fm(1)1360 543 y(T)1391 571 y Fu(M)1445 553 y Fp(\013)1445 584 y Fm(4)p 642 594 833 2 v 802 645 a Fq(M)855 628 y Fp(\013)850 659 y Fm(44)903 645 y Fo(\000)h Fu(M)1007 628 y Fp(\013)1007 659 y Fm(4)1036 624 y(T)1067 645 y Fu(Q)1110 631 y Fl(\000)p Fm(1)1163 645 y Fu(Q)1206 652 y Ff(2)1231 645 y Fu(M)1285 628 y Fp(\013)1285 659 y Fm(4)1530 605 y Fq(:)233 b Fs(\(261\))0 722 y(It)13 b(follo)o(ws)e(from)h(equation)g(\(140\))h(and)f(from)f(the)i (symplecticit)o(y)f(of)h(the)f(paraxial{ra)o(y)f(propagator)0 782 y(matrix)16 b(\(113\))h(that)g(matrix)f Fu(Q)605 764 y Fl(\000)p Fm(1)659 782 y Fu(Q)702 789 y Ff(2)743 782 y Fs(is)g(symmetric.)21 b(Equation)16 b(\(261\))i(then)e(reads)636 863 y Fu(Q)679 842 y Fm(T)677 875 y Fe(G)l(P)732 863 y Fu(M)784 870 y Fe(G)l(P)r Fm(4)873 863 y Fs(=)d(\()p Fq(M)997 842 y Fp(\013)992 875 y Fm(44)1035 863 y Fs(\))1054 842 y Fl(\000)p Fm(1)1108 863 y Fu(M)1162 842 y Fp(\013)1162 875 y Fm(4)1240 863 y Fq(;)523 b Fs(\(262\))0 944 y(whic)o(h)16 b(is)g(equiv)m(alen)o(t)g(to)h(equation)g(\(245\))g(with)f(\(234\).)0 1052 y Fu(5.6.3.)24 b(Equiv)m(alence)d(of)e Fs(\(224\))g Fu(and)g Fs(\(247\))0 1123 y(W)l(e)24 b(shall)f(con)o(v)o(ert)h (equation)g(\(224\))g(in)o(to)g(equation)f(\(247\).)45 b(Inserting)23 b(equation)h(\(154\))h(in)o(to)0 1183 y(equation)16 b(\(224\),)h(w)o(e)g(obtain)547 1287 y Fq(M)593 1294 y Fe(G)l(P)s Fm(44)702 1287 y Fs(=)1004 1254 y(1)p 761 1276 513 2 v 761 1328 a Fu(M)815 1310 y Fp(\013)815 1341 y Fm(4)843 1306 y(T)874 1328 y Fu(Q)917 1313 y Fl(\000)p Fm(1)971 1328 y Fu(Q)1014 1335 y Ff(2)1039 1328 y Fu(M)1093 1310 y Fp(\013)1093 1341 y Fm(4)1133 1328 y Fo(\000)11 b Fq(M)1236 1310 y Fp(\013)1231 1341 y Fm(44)1329 1287 y Fq(:)434 b Fs(\(263\))0 1405 y(Subtracting)15 b(equation)i(\(235\),)g(w)o(e)f(arriv)o(e)f(at)355 1523 y Fq(M)401 1530 y Fe(G)l(P)s Fm(44)507 1523 y Fo(\000)c Fq(M)610 1502 y Fp(\013)603 1535 y Fe(G)l(P)s Fm(44)712 1523 y Fs(=)i(\()p Fq(M)836 1502 y Fp(\013)831 1535 y Fm(44)874 1523 y Fs(\))893 1502 y Fl(\000)p Fm(1)1029 1489 y Fu(M)1083 1471 y Fp(\013)1083 1501 y Fm(4)1111 1467 y(T)1142 1489 y Fu(Q)1185 1471 y Fl(\000)p Fm(1)1239 1489 y Fu(Q)1282 1496 y Ff(2)1307 1489 y Fu(M)1361 1471 y Fp(\013)1361 1501 y Fm(4)p 953 1511 V 953 1563 a Fu(M)1007 1546 y Fp(\013)1007 1576 y Fm(4)1036 1541 y(T)1067 1563 y Fu(Q)1110 1549 y Fl(\000)p Fm(1)1163 1563 y Fu(Q)1206 1570 y Ff(2)1231 1563 y Fu(M)1285 1546 y Fp(\013)1285 1576 y Fm(4)1325 1563 y Fo(\000)e Fq(M)1428 1546 y Fp(\013)1423 1576 y Fm(44)1521 1523 y Fq(:)242 b Fs(\(264\))0 1640 y(Considering)14 b(equations)i(\(234\))i(and)d(\(259\),)i(equation)g (\(264\))g(is)f(equiv)m(alen)o(t)g(to)h(equation)g(\(247\).)0 1748 y Fu(5.6.4.)24 b(Equiv)m(alence)d(of)e Fs(\(217\))g Fu(and)g Fs(\(250\))0 1820 y(W)l(e)e(shall)e(con)o(v)o(ert)h(equation)h (\(217\))g(in)o(to)f(equation)g(\(250\).)22 b(Equation)17 b(\(255\))g(yields)463 1896 y(det\()p Fu(Q)592 1903 y Fe(G)l(P)648 1896 y Fs(\))p 463 1918 204 2 v 490 1964 a(det\()p Fu(Q)p Fs(\))687 1929 y(=)c(1)e Fo(\000)g Fs(\()p Fq(M)897 1909 y Fp(\013)892 1942 y Fm(44)935 1929 y Fs(\))954 1909 y Fl(\000)p Fm(1)1008 1929 y Fu(M)1062 1909 y Fp(\013)1062 1942 y Fm(4)1091 1906 y(T)1122 1929 y Fu(Q)1165 1909 y Fl(\000)p Fm(1)1218 1929 y Fu(Q)1261 1936 y Ff(2)1286 1929 y Fu(M)1340 1909 y Fp(\013)1340 1942 y Fm(4)1419 1929 y Fq(:)344 b Fs(\(265\))0 2040 y(Considering)14 b(\(263\),)597 2095 y(det\()p Fu(Q)726 2102 y Fe(G)l(P)781 2095 y Fs(\))p 597 2117 V 623 2162 a(det\()p Fu(Q)p Fs(\))820 2128 y(=)g Fo(\000)p Fs(\()p Fq(M)984 2108 y Fp(\013)979 2141 y Fm(44)1022 2128 y Fq(M)1068 2135 y Fe(G)l(P)r Fm(44)1163 2128 y Fs(\))1182 2108 y Fl(\000)p Fm(1)1285 2128 y Fq(:)478 b Fs(\(266\))0 2229 y(Inserting)15 b(\(224\),)677 2318 y Fq(M)725 2325 y Fm(44)782 2318 y Fs(=)e Fq(M)887 2297 y Fp(\013)882 2330 y Fm(44)939 2284 y Fs(det\()p Fu(Q)1068 2291 y Fe(G)l(P)1124 2284 y Fs(\))p 939 2306 V 966 2352 a(det\()p Fu(Q)p Fs(\))1199 2318 y Fq(:)564 b Fs(\(267\))0 2419 y(Equation)16 b(\(217\))h(with)g(\(267\))g(reads) 490 2551 y Fq(a)514 2558 y Fe(G)l(P)569 2551 y Fs(\()p Fu(x)p Fs(\))e(=)d Fn(b)-27 b Fq(a)p Fs(\()p Fu(x)p Fq(;)8 b(!)834 2531 y Fm(0)857 2551 y Fs(\))876 2462 y Fn(s)p 927 2462 216 2 v 959 2518 a Fs(det\()p Fu(Q)p Fs(\))p 933 2540 204 2 v 933 2586 a(det\()p Fu(Q)1062 2593 y Fe(G)l(P)1117 2586 y Fs(\))1142 2462 y Fn(s)p 1192 2462 145 2 v 1201 2518 a Fs(2)p 1198 2540 31 2 v 1198 2586 a Fq(\031)1251 2518 y Fs(i)p Fq(!)1298 2503 y Fm(0)p 1240 2540 91 2 v 1240 2586 a Fq(M)1293 2568 y Fp(\013)1288 2599 y Fm(44)1387 2551 y Fq(:)376 b Fs(\(268\))0 2674 y(Considering)14 b(equations)i(\(164\))i(and)d(\(236\),)i(equation)g (\(268\))g(is)f(equiv)m(alen)o(t)g(to)h(equation)g(\(250\).)920 2806 y(58)p eop %%Page: 59 33 59 32 bop 0 -54 a Fu(6.)25 b(Limited)18 b(ap)r(erture)0 28 y Fs(In)f(geoph)o(ysics,)f(the)i(ap)q(erture)e(co)o(v)o(ered)h(b)o (y)g(the)g(receiv)o(ers)g(is)f(usually)h(limited)f(\(e.g.,)i(to)g(an)f (area)0 88 y(on)c(the)g(Earth)f(surface\).)21 b(Then)12 b(only)h(a)g(fraction)f(of)h(scattered)g(time{harmonic)e(Gaussian)h(b)q (eams)0 148 y(is)19 b(registered)f(\(compare)g(Figures)g(7)h(and)g (17\).)30 b(Consequen)o(tly)l(,)19 b(only)g(the)h(time{domain)d(w)o(a)o (v)o(es)0 208 y(scattered)f(b)o(y)g(Gab)q(or)g(functions)f(corresp)q (onding)f(to)i(the)h(w)o(a)o(v)o(en)o(um)o(b)q(er)c(v)o(ectors)j(from)f (the)h(cones)0 268 y(co)o(v)o(ered)c(b)o(y)h(the)g(ap)q(erture)f(are)h (registered)f(\(compare)g(Figures)f(9)i(and)f(18\).)21 b(The)13 b(lost)g(information)0 328 y(on)h(the)h(on)e(the)i(corresp)q (onding)d(linear)h(com)o(bination)g(\(68\))i(of)f(elastic)g(mo)q(duli)g (usually)f(cannot)h(b)q(e)0 388 y(reco)o(v)o(ered)h(without)i (additional)e(a)h(priori)f(assumptions.)p 0 478 1890 2 v 0 1048 2 571 v 18 1037 a /Figure 51 def 18 1037 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 1037 a /Figure 53 def 648 1037 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 1037 a /Figure 55 def 1278 1037 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 1048 2 571 v 0 1050 1890 2 v 0 1088 a Fk(Figure)e(17.)18 b Fj(Scattering)10 b(in)g(the)g(frequency)f (domain)g(|)i(sensitivit)o(y)g(of)f(scattered)g(Gaussian)g(b)q(eams)f (to)j(structural)0 1136 y(w)o(a)o(v)o(en)o(um)o(b)q(er)o(s)f(at)k(v)n (arious)e(p)q(ositiv)o(e)h(frequencies)d Fi(!)16 b Fj(for)e(limited)e (ap)q(erture.)17 b(Compare)c(to)h(Figure)f(7.)p 0 1210 V 0 1781 2 571 v 18 1769 a /Figure 71 def 18 1769 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 648 1769 a /Figure 72 def 648 1769 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1278 1769 a /Figure 73 def 1278 1769 a @beginspecial 40 @llx 40 @lly 540 @urx 500 @ury 1189 @rwi @setspecial %%BeginDocument: r17lk1/sens2.ps %! %%BoundingBox: 40 40 540 500 % 1.0 1.0 13.9 12.3 % List of figures (uncomment a line to see the figure): % /Figure 1 def % /Figure 2 def % /Figure 31 def % /Figure 32 def % /Figure 33 def % /Figure 34 def % /Figure 35 def % /Figure 41 def % /Figure 42 def % /Figure 43 def % /Figure 44 def % /Figure 45 def % /Figure 51 def % /Figure 52 def % /Figure 53 def % /Figure 54 def % /Figure 55 def % /Figure 61 def % /Figure 62 def % /Figure 63 def % /Figure 71 def % /Figure 72 def % /Figure 73 def % /Figure 81 def % /Figure 82 def % /Figure 83 def % /Figure 141 def % /Figure 142 def % /Figure 143 def % /Figure 144 def % /Figure 145 def % /Figure 162 def % /Figure 163 def % /Figure 181 def % /Figure 182 def % /Figure 183 def % /Figure 192 def % /Figure 193 def 40 dup scale 8.30 5.60 translate /Xmin -7.30 def /Xmax 5.20 def /Ymin -4.60 def /Ymax 6.90 def /FontSize 0.67 def /PAngle -30 def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /ModelAngle1 0 def % angle with respect to incident slowness vector /ModelAngle2 -15 def /ModelAngle3 -75 def /ModelScale1 {1.00 1.00} def /ModelScale2 {0.90 0.80} def /ModelScale3 {0.50 0.45} def /ModelColor1 {ModelWhite ModelWhite 1} def /ModelColor2 {ModelWhite 1 ModelWhite} def /ModelColor3 {1 ModelWhite ModelWhite} def /IncidentSlowness {0.45 OmegaScale mul} def /WhereP {-0.5} def /NumRings 30 def /HalfWidth 0.05 def /PlottingAxes{ 0.04 setlinewidth 0 0 0 setrgbcolor Xmin 0 moveto Xmax 0 lineto currentpoint stroke moveto -0.80 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (1) show 0 Ymin moveto 0 Ymax lineto currentpoint stroke moveto 0.16 FontSize mul -0.80 FontSize mul rmoveto /Times-Italic 1.00 FontSize mul selectfont AxisLabel show 0.00 FontSize mul -0.20 FontSize mul rmoveto /Times-Roman 0.70 FontSize mul selectfont (2) show newpath } def /WavenumberSurface { PlottingAxes PAngle rotate SurfaceTranslate 0 translate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave ModelScale1 MetricScale scale ModelAngle1 rotate ModelScale1 scale ModelColor1 setrgbcolor 0 0 1 Aperture1 ModelAngle1 sub Aperture2 ModelAngle1 sub arc stroke grestore gsave ModelScale2 MetricScale scale ModelAngle2 rotate ModelScale2 scale ModelColor2 setrgbcolor 0 0 1 Aperture1 ModelAngle2 sub Aperture2 ModelAngle2 sub arc stroke grestore gsave ModelScale3 MetricScale scale ModelAngle3 rotate ModelScale3 scale ModelColor3 setrgbcolor 0 0 1 Aperture1 ModelAngle3 sub Aperture2 ModelAngle3 sub arc stroke grestore } for } for } def /ARC { arc } def /ARCN { arcn } def /Resolution { PlottingAxes PAngle rotate NumRings neg 1 0.5 { dup -1 2 1.5 { mul /N exch def gsave /OmegaScale 1.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale exch dup /Scale1 exch def exch dup /Scale2 exch def scale ModelAngle0 rotate ModelScale0 scale ModelColor0 setrgbcolor 0 0 1 Aperture2 ModelAngle0 sub Aperture1 ModelAngle0 sub ARCN ModelScale0 1 exch div exch 1 exch div exch scale ModelAngle0 neg rotate 1 Scale1 div 1 Scale2 div scale SurfaceTranslate neg 0 translate /OmegaScale 5.00 def SurfaceTranslate 0 translate ModelScale0 MetricScale scale ModelAngle0 rotate ModelScale0 scale 0 0 1 Aperture3 ModelAngle0 sub Aperture4 ModelAngle0 sub ARC closepath fill grestore } for } for } def /Tomography { PlottingAxes NumRings neg 1 0.5 { neg /N exch def /ModelWhite N abs NumRings div def ModelColor0 setrgbcolor 0 0 HalfWidth NumRings div N mul 0 370 arc closepath fill } for } def /IncidentSlownessVector { 0.05 setlinewidth 0 0 0 setrgbcolor 0 0 0.06 0 300 arc fill 0 0 moveto IncidentSlowness 0 translate 0 0 lineto stroke 0 0 moveto -0.40 -0.10 lineto stroke 0 0 moveto -0.40 0.10 lineto stroke } def /TypeOmegaP { PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.50 FontSize mul 0.35 FontSize mul rmoveto /Symbol 1.00 FontSize mul selectfont /omega glyphshow /Times-Bold 1.00 FontSize mul selectfont (P) show } def % Plotting /SurfaceTranslate 0 def /MetricScale {pop /ModelScale exch def /ModelWhite 0 def 0.05 OmegaScale div ModelScale div setlinewidth OmegaScale dup} def /OmegaScale 4.00 def /AxisLabel (p) def Figure 1 eq {gsave PAngle cos IncidentSlowness mul 0.5 mul PAngle sin IncidentSlowness mul 0.5 mul moveto -0.45 FontSize mul -0.85 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def Figure 2 eq {gsave PAngle cos IncidentSlowness mul WhereP mul PAngle sin IncidentSlowness mul WhereP mul moveto -0.30 FontSize mul 0.30 FontSize mul rmoveto /Times-Bold 1.00 FontSize mul selectfont (P) show WavenumberSurface IncidentSlownessVector showpage grestore} if /AxisLabel (k) def /OmegaScale 1.00 def Figure 31 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 32 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 33 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 34 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 35 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /SurfaceTranslate {IncidentSlowness neg} def /MetricScale {pop /ModelScale exch def /ModelWhite N abs NumRings div def HalfWidth ModelScale div NumRings div N mul OmegaScale add HalfWidth ModelScale div dup mul HalfWidth 0.50 div OmegaScale mul dup mul add sqrt NumRings div dup setlinewidth N mul OmegaScale add} def /OmegaScale 1.00 def Figure 41 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 42 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 43 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 44 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 45 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /OmegaScale 1.00 def Figure 51 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 52 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 53 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 54 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 55 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 61 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 62 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 63 eq {gsave Resolution showpage grestore} if /Aperture1 90 def % angle with respect to incident slowness vector /Aperture2 150 def /Aperture3 Aperture1 def /Aperture4 Aperture2 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 71 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 72 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 73 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 81 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def Figure 82 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor3} def Figure 83 eq {gsave Tomography showpage grestore} if -8.30 -5.60 translate 11.30 4.30 translate /Xmin -10.30 def /Xmax 2.20 def /Ymin -3.30 def /Ymax 8.20 def /IncidentSlowness {1.00 OmegaScale mul} def /WhereP {-0.4} def /Aperture1 0 def % angle with respect to incident slowness vector /Aperture2 370 def /OmegaScale 1.00 def Figure 141 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 2.00 def Figure 142 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 3.00 def Figure 143 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 4.00 def Figure 144 eq {gsave WavenumberSurface IncidentSlownessVector showpage grestore} if /OmegaScale 5.00 def Figure 145 eq {gsave TypeOmegaP WavenumberSurface IncidentSlownessVector showpage grestore} if /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 385 def /Aperture3 -25 def /Aperture4 385 def /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def Figure 162 eq {gsave Resolution showpage grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 65 def /Aperture3 -65 def /Aperture4 425 def /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor1} def Figure 163 eq {gsave Resolution showpage grestore} if /Aperture1 31 def % angle with respect to incident slowness vector /Aperture2 329 def /Aperture3 14 def /Aperture4 346 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 181 eq {gsave Resolution showpage grestore} if /Aperture1 -31 def % angle with respect to incident slowness vector /Aperture2 31 def /Aperture3 -14 def /Aperture4 14 def /ModelAngle0 {ModelAngle1} def /ModelScale0 {ModelScale1} def /ModelColor0 {ModelColor1} def Figure 182 eq {gsave Resolution showpage grestore} if /ModelColor0 {ModelColor1} def Figure 183 eq {gsave Tomography showpage grestore} if /ModelAngle0 {ModelAngle2} def /ModelScale0 {ModelScale2} def /ModelColor0 {ModelColor2} def /Aperture1 -25 def % angle with respect to incident slowness vector /Aperture2 -15 def /Aperture3 -25 def /Aperture4 -35 def /ARC { arcn } def /ARCN { arcn } def Figure 192 eq {gsave Resolution grestore} if /Aperture1 25 def % angle with respect to incident slowness vector /Aperture2 15 def /Aperture3 25 def /Aperture4 35 def /ARC { arc } def /ARCN { arc } def Figure 192 eq {gsave Resolution showpage grestore} if /ModelAngle0 {ModelAngle3} def /ModelScale0 {ModelScale3} def /ModelColor0 {ModelColor3} def /Aperture1 65 def % angle with respect to incident slowness vector /Aperture2 45 def /Aperture3 65 def /Aperture4 70 def /ARC { arc } def /ARCN { arc } def Figure 193 eq {gsave Resolution grestore} if /Aperture1 -65 def % angle with respect to incident slowness vector /Aperture2 -45 def /Aperture3 -65 def /Aperture4 -70 def /ARC { arcn } def /ARCN { arcn } def Figure 193 eq {gsave Resolution showpage grestore} if %%EOF %%EndDocument @endspecial 1888 1781 2 571 v 0 1783 1890 2 v 0 1821 a Fk(Figure)k(18.)k Fj(Scattering)13 b(in)h(the)h(time)e(domain)g(|)i (w)o(a)o(v)o(en)o(um)o(b)q(ers)c(a\013ecting)j(the)g(w)o(a)o(v)o (e\014eld)f(scattered)h(within)f(a)0 1868 y(limited)f(ap)q(erture.)18 b(Compare)12 b(to)i(Figure)f(9.)920 2806 y Fs(59)p eop %%Page: 60 34 60 33 bop 0 -54 a Fu(7.)25 b(T)-5 b(rue{am)o(plitude)18 b(migrations)0 22 y Fs(The)e(deriv)o(ed)f(appro)o(ximate)f(solution)h (of)h(the)g(forw)o(ard)f(scattering)g(problem)f(ma)o(y)i(b)q(e)g (utilized)f(in)0 82 y(designing)k(the)i(migration)f(algorithm)f(based)h (on)h(true)g(linearized)e(in)o(v)o(ersion)g(of)i(the)g(complete)0 142 y(set)g(of)g(seismograms)d(recorded)h(for)h(all)h(shots.)33 b(The)21 b(algorithm)e(should)g(b)q(e)i(comp)q(osed)f(of)h(the)0 202 y(follo)o(wing)15 b(steps:)100 263 y(\(a\))g(The)g(migrated)f (section)h(is)f(assumed)g(to)h(b)q(e)g(decomp)q(osed)f(in)o(to)g(Gab)q (or)h(functions)f Fq(g)1793 245 y Fp(\013)1821 263 y Fs(\()p Fu(x)p Fs(\))0 323 y(in)19 b(form)f(\(3\).)30 b(The)19 b(relation)f(b)q(et)o(w)o(een)h(the)g(shap)q(e)g(\(4\))h(of)f (Gab)q(or)f(functions)h(and)f(the)h(shap)q(e)g(of)0 382 y(scattered)g(Gaussian)f(pac)o(k)o(ets)g(should)g(b)q(e)i(emplo)o(y)o (ed)d(to)j(optimize)e(the)i(shap)q(e)f(of)g(Gab)q(or)g(func-)0 442 y(tions.)i(See)c(the)g(note)f(in)h(Section)f(7.1.)100 503 y(\(b\))d(F)l(or)f(eac)o(h)h(source,)g(the)g(w)o(a)o(v)o(es)f (scattered)h(b)o(y)g(individual)e(Gab)q(or)i(functions)f(and)h (arriving)0 563 y(to)19 b(the)h(receiv)o(er)e(arra)o(y)g(are)g (calculated.)29 b(These)19 b(w)o(a)o(v)o(es)f(ma)o(y)g(appro)o (ximately)g(b)q(e)h(comp)q(osed)f(of)0 623 y(Gaussian)d(pac)o(k)o(ets)h (according)f(to)i(this)f(pap)q(er.)100 683 y(\(c\))i(The)e(appro)o (ximate)g(linearized)f(relation)i(b)q(et)o(w)o(een)f(factors)h Fq(c)1354 665 y Fp(\013)1354 698 y(ij)r(k)q(l)1441 683 y Fs(and)f Fq(\045)1564 665 y Fp(\013)1609 683 y Fs(of)h(the)h(Gab)q (or)0 743 y(functions)e(and)g(the)h(w)o(a)o(v)o(e\014eld)f(obtained)g (in)h(step)f(\(b\))i(ma)o(y)e(b)q(e)h(used)f(to)h(estimate)g(these)g (factors)0 803 y(b)o(y)f(a)h(regularized)e(least{square)g(in)o(v)o (ersion.)0 927 y Fu(7.1.)25 b(Optimization)18 b(of)h(the)g(Gab)r(or)f (represen)n(tation)0 1004 y Fs(A)o(t)f(eac)o(h)f(p)q(oin)o(t)g Fu(x)344 985 y Fp(\013)373 1004 y Fs(,)g(w)o(e)h(consider)e(all)h (source{receiv)o(er)f(pairs)g(and)h(all)g(corresp)q(onding)e(com)o (bina-)0 1063 y(tions)j(of)h(elemen)o(tary)f(w)o(a)o(v)o(es.)25 b(F)l(or)17 b(eac)o(h)g(com)o(bination)f(of)i(elemen)o(tary)f(w)o(a)o (v)o(es)g(from)g(the)h(source)0 1123 y(and)f(from)f(the)i(receiv)o(er,) e(w)o(e)h(obtain)g(a)g(set)h(of)f(structural)f(w)o(a)o(v)o(en)o(um)o(b) q(ers)e Fu(k)1476 1105 y Fp(\013)1522 1123 y Fs(with)j(corresp)q(ond-)0 1183 y(ing)f(frequencies)h Fq(!)h Fs(from)f(equation)f(\(81\).)24 b(F)l(or)15 b(eac)o(h)i Fu(k)1068 1165 y Fp(\013)1113 1183 y Fs(and)g(corresp)q(onding)d(frequency)j Fq(!)r Fs(,)g(the)0 1243 y(shap)q(e)f(of)g(the)h(scattered)f(Gaussian)f(pac)o (k)o(et)i(dep)q(ends)e(on)h(initial)g(parameters)f Fu(M)1583 1225 y Fp(\013)1581 1255 y Fe(G)l(P)1636 1243 y Fs(,)h Fu(M)1720 1225 y Fp(\013)1718 1255 y Fe(G)l(P)s Fm(4)1810 1243 y Fs(and)0 1303 y Fq(M)53 1285 y Fp(\013)46 1315 y Fe(G)l(P)s Fm(44)160 1303 y Fs(through)h(equations)i (\(244\){\(249\).)29 b(Six)19 b(initial)f(parameters)f Fu(M)1417 1285 y Fp(\013)1415 1315 y Fe(G)l(P)1471 1303 y Fs(,)i Fu(M)1558 1285 y Fp(\013)1556 1315 y Fe(G)l(P)s Fm(4)1650 1303 y Fs(and)f Fq(M)1802 1285 y Fp(\013)1795 1315 y Fe(G)l(P)s Fm(44)0 1363 y Fs(linearly)e(dep)q(end)g(on)g(six)h (indep)q(enden)o(t)f(comp)q(onen)o(ts)f(of)i(symmetric)f(3)s Fo(\002)s Fs(3)g(matrix)g Fu(K)1673 1345 y Fp(\013)1718 1363 y Fs(through)0 1423 y(equations)g(\(237\){\(239\))h(with)g (\(127\))g(and)f(\(128\).)100 1483 y(It)f(w)o(ould)e(b)q(e)i(nice)g(to) g(\014nd)f(a)h(w)o(a)o(y)f(ho)o(w)g(to)h(optimize)g(the)g(shap)q(e)f (of)h(the)g(scattered)g(Gaussian)0 1543 y(pac)o(k)o(ets)h(b)o(y)g(a)h (prop)q(er)e(selection)h(of)h Fu(K)750 1525 y Fp(\013)795 1543 y Fs(in)f(dep)q(endence)g(on)g Fu(x)1219 1525 y Fp(\013)1265 1543 y Fs(and)f Fu(k)1391 1525 y Fp(\013)1420 1543 y Fs(.)0 1667 y Fu(8.)25 b(Final)c(rem)o(ark)0 1744 y Fs(The)12 b(deriv)o(ed)f(corresp)q(ondence)f(b)q(et)o(w)o(een)i(the)g (p)q(erturbations)f(of)h(the)g(structure)g(and)f(the)h(recorded)0 1803 y(w)o(a)o(v)o(e\014eld)h(ma)o(y)h(pla)o(y)g(a)h(decisiv)o(e)f (role)g(in)h(understanding)d(the)j(information)e(on)h(geological)g (struc-)0 1863 y(tures)k(carried)g(b)o(y)h(seismic)f(w)o(a)o(v)o (e\014elds,)g(in)g(understanding)f(the)i(ph)o(ysical)f(meaning)f(of)j (v)o(elo)q(cit)o(y)0 1923 y(macro)e(mo)q(dels,)g(and)h(in)f(in)o (terpretation)f(of)i(seismic)f(data)h(from)f(forw)o(ard)f(to)i (wide{angle)f(scat-)0 1983 y(tering.)j(It)c(ma)o(y)f(allo)o(w)f(us)h (to)g(understand)f(the)h(ph)o(ysical)f(meaning)g(and)h(resolution)f(of) h(migrated)0 2043 y(images,)h(and)g(to)h(estimate)g(misp)q(ositioning)e (and)h(fuzziness)g(of)h(structural)e(details)h(due)h(to)g(inac-)0 2103 y(curacies)e(in)g(the)h(v)o(elo)q(cit)o(y)g(macro)e(mo)q(del.)0 2227 y Fu(Ac)n(kno)n(wledgemen)n(ts)0 2303 y Fs(The)21 b(researc)o(h)e(has)h(b)q(een)h(supp)q(orted)e(b)o(y)i(the)g(Gran)o(t)f (Agency)h(of)g(the)g(Czec)o(h)g(Republic)e(under)0 2363 y(Con)o(tracts)13 b(205/01/0927,)g(205/04/1104)g(and)g(205/07/0032,)g (b)o(y)g(the)h(Ministry)e(of)i(Education)f(of)0 2423 y(the)f(Czec)o(h)g(Republic)e(within)i(researc)o(h)e(pro)s(ject)i (MSM0021620860,)f(and)g(b)o(y)g(the)i(mem)o(b)q(ers)d(of)i(the)0 2483 y(consortium)d(\\Seismic)h(W)l(a)o(v)o(es)h(in)g(Complex)f(3{D)h (Structures")f(\(see)i(\\h)o(ttp:/)-14 b(/sw3d.m\013.cuni.cz"\).)920 2806 y(60)p eop %%Page: 61 35 61 34 bop 0 -54 a Fu(References)6 8 y Fs(\024)0 21 y(Cerv)o(en)q(\023) -26 b(y,)16 b(V.)h(\(2001\):)22 b Ft(Seismic)d(R)m(ay)g(The)m(ory.)24 b Fs(Cam)o(bridge)14 b(Univ.)j(Press,)e(Cam)o(bridge.)6 68 y(\024)0 80 y(Cerv)o(en)q(\023)-26 b(y,)17 b(V.,)h(Klime)m(\024)-22 b(s,)17 b(L.)h(&)g(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)17 b(I.)h(\(1984\):)25 b(P)o(araxial)16 b(ra)o(y)i(appro)o (ximation)d(in)j(the)g(com-)100 140 y(putation)d(of)i(seismic)e(w)o(a)o (v)o(e\014elds)g(in)h(inhomogeneous)e(media.)21 b Ft(Ge)m(ophys.)e(J.)f (R.)h(astr.)f(So)m(c.)p Fs(,)100 200 y Fu(79)p Fs(,)d(89{104.)6 247 y(\024)0 260 y(Cerv)o(en)q(\023)-26 b(y,)11 b(V.,)h(Klime)m(\024) -22 b(s,)11 b(L.)h(&)f(P)m(\024)-22 b(sen)o(\024)e(c)-6 b(\023)-19 b(\020k,)11 b(I.)h(\(2007\):)20 b(Seismic)11 b(ra)o(y)g(metho)q(d:)19 b(Recen)o(t)12 b(dev)o(elopmen)o(ts.)100 319 y Ft(A)m(dvanc)m(es)19 b(in)g(Ge)m(ophysics)p Fs(,)f Fu(48)p Fs(,)e(1{126.)0 379 y(Klime)m(\024)-22 b(s,)12 b(L.)i(\(1994\):)21 b(T)l(ransformations)10 b(for)j(dynamic)g(ra)o(y)g (tracing)g(in)g(anisotropic)f(media.)20 b Ft(Wave)100 439 y(Motion)p Fs(,)c Fu(20)p Fs(,)g(261{272.)0 499 y(Klime)m(\024)-22 b(s,)20 b(L.)i(\(2004\):)32 b(Gaussian)20 b(pac)o(k)o(ets)h(in)g(smo)q (oth)g(isotropic)g(media.)36 b(In:)c Ft(Seismic)23 b(Waves)100 559 y(in)c(Complex)h(3{D)g(Structur)m(es,)g(R)m(ep)m(ort)h(14)p Fs(,)f(pp.)d(43{54,)i(Dep.)f(Geoph)o(ys.,)f(Charles)g(Univ.,)100 618 y(Prague,)e(online)h(at)h(\\h)o(ttp://sw3d.m\013.cuni.cz".)920 2806 y(61)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF