FILES *.PRE:  B-SPLINE APPROXIMATION OF PREM BY DZIEWONSKI AND
  ANDERSON (1981).
  GUIDE TO THE INPUT DATA FOR THE COMPLETE RAY TRACING PROGRAM.

  BY LUDEK KLIMES

  THE SPHERICALLY SYMMETRIC EARTH MODEL IS A B-SPLINE APPROXIMATION TO
  PREM.  THE MODEL CONSISTS OF 13 COMPLEX BLOCKS (LAYERS) LIMITED BY
  EARTH'S SURFACE (SURFACE 1), AND SEPARATED BY 9 INTERFACES OF THE
  FIRST ORDER AND 3 INTERFACES OF THE SECOND ORDER.  THE VALUES OF
  PARAMETERS AT GRID POINTS ARE TAKEN FROM THE TABLE II OF THE PAPER BY
  DZIEWONSKI AND ANDERSON (1981).  SOME VALUES, SPECIFIED IN THE TABLE
  II OF THE PAPER, WHICH WILL LIKELY BE ACCURATELY FITTED BY CUBIC
  SPLINES ARE LEFT OUT.  BETWEEN THE GIVEN POINTS WITHIN EACH COMPLEX
  BLOCK, THE PARAMETERS ARE INTERPOLATED USING NATURAL CUBIC SPLINES.
  THE MODEL IS SPECIFIED IN GEOGRAPHIC SPHERICAL COORDINATES:
  X1=LONGITUDE (IN RADIANS), X2=LATITUDE (IN RADIANS), X3=RADIUS.  FOUR
  ELEMENTARY WAVES PASSING THROUGH THE CORE ARE COMPUTED FOR THE SOURCE
  IN THE DEPTH OF 200 KM.  TO CHANGE THE SOURCE DEPTH, SEE THE NOTE IN
  INPUT DATA FILE 'CRT.PRE'.  TWO-POINT RAYS, COMING TO THE RECEIVERS AT
  THE EARTH'S SURFACE IN THE EPICENTRAL DISTANCES FROM 110 TO 178
  DEGREES WITH THE STEP OF SOME 2 DEGREES, ARE DETERMINED.

  THE FILES *.PRE LISTED BELOW CONTAIN THE SAMPLE INPUT DATA FOR THE
  COMPLETE RAY TRACING PROGRAM.  THE INPUT DATA CONSIST OF THE 7 DATA
  SETS (1) TO (7) LISTED IN THE PACKAGE 'GUIDE.FOR'.  NOTE THAT SEVERAL
  DATA SETS MAY BE LOCATED IN A SINGLE FILE.
      CRT.PRE... FILE CONTAINING THE DATA SETS:
              (1) CRT
              (4) INIT
      MODEL.PRE... FILE CONTAINING THE DATA SET:
              (2) MODEL
      DCRT.PRE... FILE CONTAINING THE DATA SET:
              (3) DCRT
      CODE.PRE... FILES CONTAINING THE DATA SET:
              (5) CODE
      RPAR.PRE... FILES CONTAINING THE DATA SET:
              (6) RPAR
      WRIT.PRE... FILE CONTAINING THE DATA SET:
              (7) WRIT

  REMARKS WITHIN THE INPUT DATA FILES:
      THE COMMENTS IN BRACKETS SITUATED AT THE ENDS OF LINES, AFTER THE
              INPUT ITEMS, ARE NOT THE PART OF THE INPUT DATA.  THEY ARE
              JUST REMARKS PLACED SO AS TO BE SKIPPED WHEN READING THE
              INPUT DATA.
      THE LAST INPUT LINE OF A DATA FILE IS USUALLY FOLLOWED BY
              (A) EMPTY LINE, LINE '====' AND EMPTY LINE, OR BY
              (B) EMPTY LINE, LINE '----', EMPTY LINE, TEXT DESCRIBING
                  THE INPUT DATA, EMPTY LINE, LINE '====' AND EMPTY
                  LINE.

  REFERENCE:
      DZIEWONSKI A.M., ANDERSON D.L.(1981): PRELIMINARY REFERENCE EARTH
             MODEL.  PHYS. EARTH PLANET. INTER., 25, 297.

  DATE: 1991, JANUARY 24

========================================================================