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Fg(n)2809 672 y Fo(\))g(cannot)g(b)s(e)f(n)m(umerical-)0 793 y(ly)40 b(computed)h(at)f(this)h(stage,)i(as)e Fh(p)1367 808 y Fg(n)1454 793 y Fo(are)g(not)g(y)m(et)g(kno)m(wn,)j(w)m(e)e(can)f (express)i(them)d(analytically)-8 b(.)0 913 y(\()p Fh(G)115 877 y Fk(\()p Fg(m)p Fk(\))236 913 y Fo(\()p Fh(p)323 928 y Fg(n)370 913 y Fo(\))43 b(are)h(solutions)e(of)h(the)h(cubic)f (equation)g(\(19\).\))75 b(W)-8 b(e)44 b(can)f(also)g(suitably)f (exploit)g(cer-)0 1033 y(tain)36 b(w)m(ell-kno)m(wn)i(prop)s(erties)f (of)g(\000)1357 1048 y Fg(ik)1423 1033 y Fo(\()p Fh(p)1510 1048 y Fg(n)1557 1033 y Fo(\).)57 b(One)38 b(immediately)c(sees)39 b(from)d(\(17\))h(that)g(\000)3374 1048 y Fg(ik)3440 1033 y Fo(\()p Fh(p)3527 1048 y Fg(n)3574 1033 y Fo(\))g(are)0 1154 y(homogeneous)27 b(functions)f(of)h(the)g(second)h(degree)f(in)f Fh(p)2036 1169 y Fg(n)2083 1154 y Fo(.)42 b(Consequen)m(tly)-8 b(,)30 b(also)25 b Fh(G)3037 1118 y Fk(\()p Fg(m)p Fk(\))3159 1154 y Fo(\()p Fh(p)3246 1169 y Fg(n)3293 1154 y 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y(Im[)p Fh(G)1450 2092 y Fk(\()p Fg(m)p Fk(\))1571 2133 y Fo(\()p Fh(N)1687 2148 y Fg(n)1756 2133 y Fo(+)22 b(i)p Fh(\016)t(M)2023 2148 y Fg(n)2070 2133 y Fo(\)])83 b(=)g(0)32 b Fh(:)1121 b Fo(\(23\))0 2324 y(F)-8 b(or)24 b(giv)m(en)h(unit)e(v)m(ectors)k Fm(N)d Fo(and)h Fm(M)p Fo(,)h(Equations)f(\(22\))f(and)h(\(23\))f(represen)m(t)i(the)f (\014nal)f(t)m(w)m(o)h(equations)0 2444 y(for)k Fh(\016)k Fo(and)c Fl(C)466 2408 y Fk(2)506 2444 y Fo(.)43 b(Equation)29 b(\(23\))f(do)s(es)i(not)f(dep)s(end)i(on)e Fl(C)2109 2408 y Fk(2)2178 2444 y Fo(and)g(can)h(b)s(e)g(directly)e(used)j(to)e (determine)0 2565 y Fh(\016)t Fo(.)43 b(Once)34 b Fh(\016)i Fo(is)c(determined)h(from)e(\(23\),)h(w)m(e)i(can)e(insert)h(it)f(in)m (to)f(\(22\))h(and)h(compute)g Fl(C)3256 2529 y Fk(2)3295 2565 y Fo(.)146 2756 y(Th)m(us,)d(the)d(pro)s(cedure)h(of)e (determining)f Fh(\016)31 b Fo(and)c Fl(C)1982 2720 y Fk(2)2048 2756 y Fo(for)f(giv)m(en)h Fm(N)g Fo(and)g Fm(M)p Fo(,)h(in)e(the)h(case)h(of)e(general)0 2876 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b(inhomogeneous)g(plane)f(w)m(a)m(v)m(es)j(do)e (not)g(exist)g(for)f(suc)m(h)j Fm(N)d Fo(and)h Fm(M)p Fo(.)44 b(In)32 b(this)f(case)i(w)m(e)g(sp)s(eak)g(of)0 4895 y(forbidden)28 b(directions)g Fm(N)h Fo(and)f Fm(M)p Fo(.)43 b(See)29 b(Kreb)s(es)h(and)e(Le)h(\(1994\),)g(Carcione)f(and)h (Ca)m(v)-5 b(allini)25 b(\(1995\),)0 5015 y(and)33 b(Carcione)f (\(2001,)g(p.)43 b(146-147\).)146 5206 y(Once)d Fh(\016)449 5170 y Fk(\()p Fg(m)p Fk(\))608 5206 y Fl(\025)e Fo(0)g(and)h Fl(C)1064 5170 y Fk(\()p Fg(m)p Fk(\))1223 5206 y Fl(\025)f Fo(0)h(ha)m(v)m(e)g(b)s(een)h(determined)e(from)f(\(23\))h(and)h (\(22\))f(for)g(sp)s(eci\014ed)0 5327 y Fm(N)p Fh(;)17 b Fm(M)32 b Fo(and)h Fh(m)p Fo(,)g(the)g(relev)-5 b(an)m(t)32 b(complex-v)-5 b(alued)32 b(slo)m(wness)i(v)m(ector)f Fm(p)2573 5291 y Fk(\()p Fg(m)p Fk(\))2728 5327 y Fo(can)f(b)s(e)h (determined,)1280 5556 y Fh(p)1329 5515 y Fk(\()p Fg(m)p Fk(\))1329 5581 y Fg(n)1478 5556 y Fo(=)1657 5489 y(1)p 1592 5533 180 4 v 1592 5625 a Fl(C)1650 5596 y Fk(\()p Fg(m)p Fk(\))1782 5556 y Fo(\()p Fh(N)1898 5571 y Fg(n)1967 5556 y Fo(+)22 b(i)p Fh(\016)2140 5515 y Fk(\()p Fg(m)p Fk(\))2260 5556 y Fh(M)2354 5571 y Fg(n)2402 5556 y Fo(\))32 b Fh(;)1107 b Fo(\(24\))1817 5824 y(177)p eop %%Page: 178 10 178 9 bop 0 100 a Fo(see)34 b(\(11\).)0 499 y Fi(5)161 b(Comp)t(onen)l(tal)52 b(sp)t(eci\014cation)i(of)f(the)g(slo)l(wness)f (v)l(ector)0 789 y Fo(There)35 b(are)f(t)m(w)m(o)g(main)f(disadv)-5 b(an)m(tages)34 b(of)f(the)h(directional)e(sp)s(eci\014cation)h(of)h (the)g(slo)m(wness)h(v)m(ector,)0 910 y(in)27 b(whic)m(h)h(the)h (real-v)-5 b(alued)26 b(unit)h(v)m(ectors)i Fm(N)e Fo(and)h Fm(M)g Fo(are)g(\022)-49 b(a)28 b(priori)d(kno)m(wn.)44 b(The)28 b(\014rst)h(disadv)-5 b(an)m(tage)0 1030 y(is)41 b(that)g(the)h(algorithm)c(to)k(determine)f Fl(C)1608 994 y Fk(2)1689 1030 y Fo(and)h Fh(\016)j Fo(is)c(rather)g (complicated.)69 b(The)42 b(second)h(disad-)0 1150 y(v)-5 b(an)m(tage)35 b(is)g(that)g(the)h(algorithm)c(ma)m(y)k(yield)e(nonph)m (ysical)i(solutions)e(for)h Fl(C)2901 1114 y Fk(2)2976 1150 y Fo(and)g Fh(\016)t Fo(,)h(for)f(example)0 1271 y Fl(C)58 1235 y Fk(2)140 1271 y Fh(<)41 b Fo(0.)69 b(Suc)m(h)42 b(solutions,)g(of)e(course,)45 b(m)m(ust)c(b)s(e)g(excluded.)70 b(In)41 b(this)f(section,)k(w)m(e)e(shall)d(discuss)0 1391 y(the)j(comp)s(onen)m(tal)e(sp)s(eci\014cation)g(\(12\))h(of)f (the)i(slo)m(wness)h(v)m(ector,)h(whic)m(h)e(o)m(v)m(ercomes)g(b)s(oth) f(these)0 1511 y(di\016culties.)j(W)-8 b(e)33 b(shall)e(assume)j(that)e (the)i(complex-v)-5 b(alued)31 b(v)m(ector)j Fm(p)2663 1475 y Fk(\006)2752 1511 y Fo(and)f(the)g(real-v)-5 b(alued)31 b(unit)0 1632 y(v)m(ector)j Fm(n)e Fo(are)h(kno)m(wn,)h(and)f(try)g(to) f(determine)g(the)h(complex-v)-5 b(alued)31 b(quan)m(tit)m(y)j Fh(\033)t Fo(.)146 1823 y(Inserting)f(\(12\))f(in)m(to)g(constrain)m(t) g(relations)f(\(6\))i(yields)752 2016 y([)p Fh(a)830 2031 y Fg(ij)t(k)r(l)951 2016 y Fo(\()p Fh(p)1038 1975 y Fk(\006)1038 2041 y Fg(j)1115 2016 y Fo(+)22 b Fh(\033)t(n)1330 2031 y Fg(j)1367 2016 y Fo(\)\()p Fh(p)1492 1975 y Fk(\006)1492 2041 y Fg(l)1569 2016 y Fo(+)g Fh(\033)t(n)1784 2031 y Fg(l)1810 2016 y Fo(\))g Fl(\000)h Fh(\016)2013 2031 y Fg(ik)2080 2016 y Fo(])p Fh(U)2173 2031 y Fg(k)2244 2016 y Fo(=)k(0)33 b Fh(;)114 b(i)28 b Fo(=)f(1)p Fh(;)17 b Fo(2)p Fh(;)g Fo(3)32 b Fh(:)578 b Fo(\(25\))0 2209 y(This)22 b(represen)m(ts)i(a)e(system)g(of)g(three)g(complex-v)-5 b(alued)20 b(linear)h(homogeneous)g(equations)h(for)g Fh(U)3536 2224 y Fk(1)3575 2209 y Fh(;)17 b(U)3685 2224 y Fk(2)3725 2209 y Fh(;)g(U)3835 2224 y Fk(3)3874 2209 y Fo(.)0 2329 y(The)34 b(condition)d(of)h(solv)-5 b(abilit)m(y)30 b(of)i(\(25\))g(reads)1025 2522 y(det[)p Fh(a)1238 2537 y Fg(ij)t(k)r(l)1359 2522 y Fo(\()p Fh(p)1446 2481 y Fk(\006)1446 2547 y Fg(j)1523 2522 y Fo(+)22 b Fh(\033)t(n)1738 2537 y Fg(j)1775 2522 y Fo(\)\()p Fh(p)1900 2481 y Fk(\006)1900 2547 y Fg(l)1977 2522 y Fo(+)g Fh(\033)t(n)2192 2537 y Fg(l)2219 2522 y Fo(\))g Fl(\000)g Fh(\016)2421 2537 y Fg(ik)2488 2522 y Fo(])28 b(=)g(0)k Fh(:)851 b Fo(\(26\))0 2715 y(Equation)41 b(\(26\))g(is)g(an)h(algebraic)e(equation)h(of)g (the)h(sixth)g(order)g(in)e Fh(\033)t Fo(.)71 b(It)42 b(can)f(b)s(e)h(solv)m(ed)g(for)g Fh(\033)0 2835 y Fo(b)m(y)34 b(v)-5 b(arious)31 b(metho)s(ds.)44 b(Six)32 b(solutions)g(are)h (obtained,)f(corresp)s(onding)g(to)h(qS1,)g(qS2)g(and)f(qP)i(plane)0 2956 y(w)m(a)m(v)m(es,)h(propagating)c(a)m(w)m(a)m(y)j(from)d(plane)h (\006,)h(to)g(b)s(oth)f(sides)h(of)f(it.)146 3147 y(F)-8 b(or)27 b(eac)m(h)h Fh(\033)t Fo(,)h(satisfying)e(\(26\),)h(w)m(e)g (can)g(determine)f(the)h(relev)-5 b(an)m(t)27 b(slo)m(wness)i(v)m (ector)g Fm(p)f Fo(from)e(\(12\).)0 3267 y(The)34 b(pro)s(cedure)g(can) g(b)s(e)f(applied)g(b)s(oth)g(to)g(homogeneous)g(and)g(inhomogeneous)g (plane)g(w)m(a)m(v)m(es,)j(to)0 3388 y(isotropic)31 b(and)i (anisotropic)e(media,)g(to)i(visco)s(elastic)e(and)i(p)s(erfectly)f (elastic)g(media.)0 3743 y Fn(5.1)135 b Fb(6)26 b Fd(\002)h Fb(6)44 b 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5525 y Fm(A)27 b Fo(=)1651 5379 y Fa( )1759 5464 y Fm(A)1844 5479 y Fk(11)2001 5464 y Fm(A)2086 5479 y Fk(12)1759 5584 y Fm(A)1844 5599 y Fk(21)2001 5584 y Fm(A)2086 5599 y Fk(22)2202 5379 y Fa(!)2317 5525 y Fh(:)1262 b Fo(\(28\))1817 5824 y(178)p eop %%Page: 179 11 179 10 bop 0 100 a Fo(The)34 b(3)21 b Fl(\002)i Fo(3)32 b(complex-v)-5 b(alued)32 b(partition)e(matrices)i Fm(A)2023 115 y Fg(I)5 b(J)2140 100 y Fo(are)32 b(giv)m(en)h(b)m(y)g(relations) 638 313 y Fm(A)723 328 y Fk(11)825 313 y Fo(=)27 b Fl(\000)p Fm(C)1086 277 y Fk(\(1\))p Ff(\000)p Fk(1)1271 313 y Fm(C)1352 277 y Fk(\(2\))1474 313 y Fo(=)h Fm(A)1663 277 y Fg(T)1663 338 y Fk(22)1769 313 y Fh(;)478 b Fm(A)2359 328 y Fk(12)2461 313 y Fo(=)27 b Fl(\000)p Fm(C)2722 277 y Fk(\(1\))p Ff(\000)p Fk(1)2940 313 y Fh(;)638 435 y Fm(A)723 450 y Fk(21)825 435 y Fo(=)g Fl(\000)p Fh(\032)p Fm(I)c Fo(+)f Fm(C)1299 399 y Fk(\(4\))1415 435 y Fl(\000)h Fm(C)1596 399 y Fk(\(3\))1690 435 y Fm(C)1771 399 y Fk(\(1\))p Ff(\000)p Fk(1)1956 435 y 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(\(32\),)f(nev)m(er)i(represen)m(t)h(the)e(forbidden)f(directions.)1817 5824 y(179)p eop %%Page: 180 12 180 11 bop 0 100 a Fn(5.2)135 b(Matrix)45 b(A)e(in)h(a)g(suitably)g(c)l (hosen)g(Cartesian)h(co)t(ordinate)g(system)0 355 y Fo(All)29 b(the)i(equations)f(of)g(Section)g(5.1)h(are)f(applicable)e(to)j (arbitrary)e(visco)s(elastic)g(mo)s(duli)f Fh(c)3386 370 y Fg(ij)t(k)r(l)3507 355 y Fo(,)j(sp)s(ec-)0 476 y(i\014ed)45 b(in)g(an)g(arbitrary)f(Cartesian)h(co)s(ordinate)g (system,)k(to)c(an)g(arbitrary)g(plane)g(\006)g(\(with)g(unit)0 596 y(normal)33 b Fm(n)p Fo(\),)k(and)e(to)g(arbitrarily)e(giv)m(en)j (complex-v)-5 b(alued)34 b Fm(p)2294 560 y Fk(\006)2349 596 y Fo(,)i(satisfying)f(orthogonalit)m(y)e(relation)0 716 y Fm(p)62 680 y Fk(\006)144 716 y Fl(\001)26 b Fm(n)38 b Fo(=)g(0.)61 b(Without)38 b(loss)h(of)f(generalit)m(y)-8 b(,)39 b(w)m(e)h(can)f(c)m(ho)s(ose)g(the)g(Cartesian)g(co)s(ordinate)f (system)0 837 y(in)d(some)g(sp)s(ecial)f(w)m(a)m(y)-8 b(.)53 b(Of)35 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Fo(-axis)e(p)s(erp)s(endicular)h(to)g(\006,)j(w)m(e)e (can)g(also)e(c)m(ho)s(ose)i(the)g Fh(x)3325 4513 y Fk(1)3365 4498 y Fo(-axis)e(in)h(a)0 4619 y(suitable)31 b(w)m(a)m(y)-8 b(.)45 b(W)-8 b(e)33 b(can)f(tak)m(e)h(it)f(along)e(the)j(in)m (tersection)f(of)g(plane)g(\006)h(with)f(a)g(plane)g(normal)e(to)i (\006,)0 4739 y(con)m(taining)f(v)m(ector)j(Re\()p Fm(p)982 4703 y Fk(\006)1037 4739 y Fo(\))f(or)f(Im)o(\()p Fm(p)1443 4703 y Fk(\006)1499 4739 y Fo(\).)43 b(In)33 b(the)g(\014rst)g(case,)h (w)m(e)f(obtain)1719 4959 y Fh(P)1782 4974 y Fk(2)1849 4959 y Fo(=)27 b(0)33 b Fh(;)1545 b Fo(\(37\))0 5179 y(and)33 b(in)e(the)i(second)h(case,)1714 5299 y Fh(A)1787 5314 y Fk(2)1854 5299 y Fo(=)27 b(0)33 b Fh(:)1540 b Fo(\(38\))0 5474 y(V)-8 b(ector)24 b Fm(p)362 5438 y Fk(\006)441 5474 y Fo(is)g(then)g(fully)f(sp)s(eci\014ed)i(b)m(y)g(the) f(three)h(real-v)-5 b(alued)22 b(quan)m(tities)i Fh(P)2862 5489 y Fk(1)2901 5474 y Fh(;)17 b(A)3018 5489 y Fk(1)3057 5474 y Fh(;)g(A)3174 5489 y Fk(2)3237 5474 y Fo(or)24 b Fh(P)3411 5489 y Fk(1)3450 5474 y Fh(;)17 b(P)3557 5489 y Fk(2)3596 5474 y Fh(;)g(A)3713 5489 y Fk(1)3752 5474 y Fo(.)1817 5824 y(180)p eop %%Page: 181 13 181 12 bop 0 100 a Fi(6)161 b(Mixed)54 b(sp)t(eci\014cation)g(of)g(the) f(slo)l(wness)e(v)l(ector)0 390 y Fo(The)28 b(comp)s(onen)m(tal)e(sp)s (eci\014cation)h(of)f(the)i(slo)m(wness)g(v)m(ector,)i(describ)s(ed)e (in)e(Section)h(5,)h(yields)f(a)g(con-)0 510 y(v)m(en)m(tional)33 b(eigen)m(v)-5 b(alue)33 b(algorithm)d(to)j(determine)g(the)h(slo)m (wness)h(v)m(ector)f(of)f(plane)g(inhomogeneous)0 630 y(w)m(a)m(v)m(es,)38 b(if)c Fh(p)448 594 y Fk(\006)448 655 y Fg(i)539 630 y Fo(\()p Fh(i)e Fo(=)g(1)p Fh(;)17 b Fo(2)p Fh(;)g Fo(3\))34 b(are)h(giv)m(en,)h(satisfying)f (orthogonalit)m(y)e(relation)g Fh(p)2958 594 y Fk(\006)2958 655 y Fg(i)3013 630 y Fh(n)3071 645 y Fg(i)3132 630 y Fo(=)f(0.)51 b(Indeed,)37 b(it)0 751 y(is)d(su\016cien)m(t)h(to)f(sp)s (ecify)h(only)f Fh(p)1222 715 y Fk(\006)1222 775 y Fg(I)1311 751 y 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b(205/01/0927)e(of)h(the)h(Gran)m(t)f(Agency)i(of)e(the)h(Czec)m(h)h (Republic.)0 4302 y Fm(References)146 4493 y Fo(Aki,)e(K.,)h(and)f(Ric) m(hards,)g(P)-8 b(.,)33 b(1980.)42 b Fe(Quantitative)35 b(seismolo)-5 b(gy.)43 b(The)-5 b(ory)34 b(and)g(metho)-5 b(ds)p Fo(.)43 b(F)-8 b(ree-)0 4613 y(man,)32 b(San)h(F)-8 b(rancisco.)146 4805 y(Auld,)33 b(B.A.,)g(1973.)42 b Fe(A)-5 b(c)g(oustic)35 b(\014elds)f(and)h(waves)f(in)g(solids)p Fo(.)43 b(Wiley)-8 b(,)32 b(New)h(Y)-8 b(ork.)146 4996 y(Borc)m(herdt,)36 b(R.D.,)e(1973.)47 b(Energy)36 b(and)e(plane)g(w)m (a)m(v)m(es)i(in)e(linear)e(visco)s(elastic)h(media.)47 b Fe(J.)37 b(Ge)-5 b(o-)0 5116 y(phys.)45 b(R)-5 b(es.)p Fo(,)32 b Fm(78)p Fo(,)g(2442{2453.)146 5307 y(Brok)m(e)-5 b(\024)-44 b(so)m(v\023)-49 b(a,)57 b(J.)50 b(and)1006 5282 y(\024)995 5307 y(Cerv)m(en)q(\023)-50 b(y,)57 b(V.,)e(1998.)96 b(Inhomogeneous)50 b(plane)g(w)m(a)m(v)m(es)j(in)c(dissipativ)m(e)0 5428 y(isotropic)25 b(and)i(anisotropic)e(media.)40 b (Re\015ection/transmission)25 b(co)s(e\016cien)m(ts.)43 b(In)27 b Fe(Seismic)h(waves)h(in)0 5548 y(c)-5 b(omplex)36 b(3-D)g(structur)-5 b(es,)38 b(R)-5 b(ep)g(ort)37 b(7)p Fo(,)e(pp.)51 b(57{146.)e(Dept.)h(of)34 b(Geoph)m(ysics,)j(Charles)e (Univ)m(ersit)m(y)-8 b(,)1817 5824 y(185)p eop %%Page: 186 18 186 17 bop 0 100 a Fo(Praha.)44 b(\(Av)-5 b(ailable)30 b(online)h(at)h("h)m(ttp://sw3d.m\013.cuni.cz/".\))146 291 y(Buc)m(hen,)43 b(P)-8 b(.W.,)41 b(1971.)63 b(Plane)39 b(w)m(a)m(v)m(es)i(in)e(linear)e(visco)s(elastic)i(media.)62 b Fe(Ge)-5 b(ophys.)63 b(J.R.)40 b(astr.)0 411 y(So)-5 b(c.)p Fo(,)32 b Fm(23)p Fo(,)h(531{542.)146 603 y(Carcione,)43 b(J.M.,)h(2001.)68 b Fe(Wave)43 b(\014elds)e(in)i(r)-5 b(e)g(al)42 b(me)-5 b(dia:)59 b(Wave)43 b(pr)-5 b(op)g(agation)41 b(in)i(anisotr)-5 b(opic,)0 723 y(anelastic)34 b(and)g(p)-5 b(or)g(ous)35 b(me)-5 b(dia)p Fo(.)42 b(P)m(ergamon,)33 b(Amsterdam.)146 914 y(Carcione,)e(J.M.,)h(and)f(Ca)m(v)-5 b(allini,)28 b(F.,)j(1995.)42 b(F)-8 b(orbidden)30 b(directions)g(for)g (inhomogeneous)g(pure)0 1035 y(shear)j(w)m(a)m(v)m(es)i(in)d (dissipativ)m(e)g(anisotropic)f(media.)42 b Fe(Ge)-5 b(ophysics)p Fo(,)32 b Fm(60)p Fo(,)h(522{530.)146 1226 y(Ca)m(viglia,)g(G.,)i(and)f(Morro,)h(A.,)g(1992.)49 b Fe(Inhomo)-5 b(gene)g(ous)34 b(waves)i(in)g(solids)g(and)g(\015uids)p Fo(.)49 b(W)-8 b(orld)0 1346 y(Scien)m(ti\014c,)33 b(Singap)s(ore.)157 1512 y(\024)146 1537 y(Cerv)m(en)q(\023)-50 b(y,)35 b(V.,)e(2001.)43 b Fe(Seismic)34 b(r)-5 b(ay)35 b(the)-5 b(ory)p Fo(.)43 b(Cam)m(bridge)32 b(Univ.)44 b(Press.,)34 b(Cam)m(bridge.)157 1703 y(\024)146 1729 y(Cerv)m(en)q(\023)-50 b(y,)31 b(V.,)e(2003a.)41 b(Homogeneous)27 b(plane)h(w)m(a)m(v)m(es)h(in)e(visco)s(elastic)g (anisotropic)f(media.)40 b(This)0 1849 y(v)m(olume.)157 2015 y(\024)146 2040 y(Cerv)m(en)q(\023)-50 b(y,)48 b(V.,)d(2003b.)72 b(Inhomogeneous)43 b(plane)f(w)m(a)m(v)m(es)j(in)d(visco)s(elastic)f (media.)72 b(Analytical)0 2161 y(solutions.)42 b(This)33 b(v)m(olume.)146 2352 y(Chapman,)d(C.H.,)h(1994.)42 b (Re\015ection/transmission)28 b(co)s(e\016cien)m(ts)i(recipro)s(cities) e(in)h(anisotropic)0 2472 y(media.)42 b Fe(Ge)-5 b(ophys.)45 b(J.)35 b(Int.)p Fo(,)d Fm(116)p Fo(,)h(498{501.)146 2664 y(F)-8 b(edoro)m(v,)33 b(F.I.,)g(1968.)42 b(Theory)34 b(of)e(elastic)g(w)m(a)m(v)m(es)j(in)d(crystals.)44 b(Plen)m(um,)32 b(New)i(Y)-8 b(ork.)146 2855 y(F)g(razer,)49 b(L.N.,)g(and)c(F)-8 b(ry)m(er,)50 b(G.J.,)e(1989.)81 b(Useful)46 b(prop)s(erties)f(of)g (the)h(system)g(matrix)e(for)h(a)0 2975 y(homogeneous)33 b(anisotropic)e(visco)s(elastic)g(solid.)42 b Fe(Ge)-5 b(ophys.)45 b(J.)p Fo(,)33 b Fm(97)p Fo(,)f(173{177.)146 3166 y(Ga)5 b(jewski,)28 b(D.,)e(and)g(P)-5 b(\024)-44 b(sen)m(\024)e(c)-11 b(\023)-38 b(\020k,)28 b(I.,)f(1987.)40 b(Computation)24 b(of)h(high-frequency)i(seismic)d(w)m(a)m(v)m (e\014elds)0 3287 y(in)g(3-D)g(laterally)f(inhomogeneous)i(anisotropic) e(media.)40 b Fe(Ge)-5 b(ophys.)42 b(J.R.)29 b(astr.)42 b(So)-5 b(c.)p Fo(,)26 b Fm(91)p Fo(,)h(383{411.)146 3478 y(Ha)m(y)m(es,)35 b(M.,)e(1984.)42 b(Inhomogeneous)33 b(plane)g(w)m(a)m(v)m(es.)45 b Fe(A)n(r)-5 b(ch.)45 b(R)-5 b(at.)45 b(Me)-5 b(ch.)44 b(A)n(nal.)p Fo(,)32 b Fm(85)p Fo(,)h(41{79.)146 3669 y(Hosten,)h(B.,)e(Desc)m(hamps,)h(M.,)g(and)g (Tittmann,)e(B.R.,)h(1987.)43 b(Inhomogeneous)32 b(w)m(a)m(v)m(e)j (genera-)0 3790 y(tion)g(and)i(propagation)d(in)i(lossy)g(anisotropic)f (solids.)54 b(Applications)34 b(to)i(the)h(c)m(haracterization)e(of)0 3910 y(visco)s(elastic)d(comp)s(osite)f(materials.)41 b Fe(J.)35 b(ac)-5 b(oust.)45 b(So)-5 b(c.)44 b(A)n(m.)p Fo(,)32 b Fm(82)p Fo(,)h(1763{1770.)146 4101 y(Helbig,)50 b(K.,)i(1994.)88 b Fe(F)-7 b(oundations)47 b(of)h(anisotr)-5 b(opy)49 b(for)f(explor)-5 b(ation)48 b(seismics)p Fo(.)88 b(P)m(ergamon,)0 4222 y(Oxford.)146 4413 y(Kreb)s(es,)29 b(E.S.,)g(and)e(Le,)i(L.H.T.,)g(1994.)41 b(Inhomogeneous)27 b(plane)g(w)m(a)m(v)m(es)i(and)e(cylindrical)e(w)m(a)m(v)m(es)0 4533 y(in)32 b(anisotropic)f(anelastic)h(media.)42 b Fe(J.)35 b(Ge)-5 b(ophys.)44 b(R)-5 b(es.)p Fo(,)32 b Fm(99)p Fo(,)h(No.)43 b(B12,)33 b(23899{23919.)146 4725 y(Musgra)m(v)m(e,)i(M.J.P)-8 b(.,)34 b(1970.)42 b Fe(Crystal)35 b(ac)-5 b(oustics)p Fo(.)43 b(Holden)32 b(Da)m(y)-8 b(,)33 b(San)g(F)-8 b(rancisco.)146 4916 y(Romeo,)33 b(M.,)g(1994.)44 b(Inhomogeneous)34 b(w)m(a)m(v)m(es)h(in)e(anisotropic)e(dissipativ)m (e)i(solids.)44 b Fe(Q.J.)35 b(Me)-5 b(ch.)0 5036 y(Appl.)45 b(Math.)p Fo(,)33 b Fm(47)p Fo(,)f(481{491.)149 5202 y(\024)146 5227 y(S)-11 b(\023)-38 b(\020len)q(\023)-50 b(y,)24 b(J.,)g(1981.)39 b(Anomalous)20 b(b)s(eha)m(viour)i(of)f (seismic)g(w)m(a)m(v)m(es)j(at)d(in)m(terfaces)i(b)s(et)m(w)m(een)g (anisotrop-)0 5348 y(ic)32 b(media.)42 b(Studia)32 b(geoph.)44 b(et)33 b(geo)s(d.,)f Fm(25)p Fo(,)h(152{159.)146 5539 y(Thomson,)42 b(C.J.,)f(1998.)63 b(Notes)40 b(on)g(Rmatrix,)f(a)g (program)f(to)h(\014nd)h(the)g(seismic)e(plane-w)m(a)m(v)m(e)1817 5824 y(186)p eop %%Page: 187 19 187 18 bop 0 100 a Fo(resp)s(onse)25 b(of)f(a)g(stac)m(k)h(of)e (anisotropic)g(la)m(y)m(ers.)41 b(Queen's)26 b(Univ)m(ersit)m(y)-8 b(,)26 b(Dept.)41 b(of)23 b(Geol.)40 b(Sci,)25 b(Kingston.)1817 5824 y(187)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF