NAME

     hspec9  - evaluate elastic F(f,r) based on  data  output  of
     dspec8

SYNOPSIS

     hspec9 [ -msmdpths ] [ -dsdsinc ] [ -mrmdpthr ] [ -drdrinc ]
     [ -nrindists ] [ -x0x0 ] [ -gidx ] < [ parameter_file ]

DESCRIPTION

     The purpose of  this  program  is  to  evaluate  the  medium
     response  for  16  basic  Green's functions as a function of
     wavenumber and frequency.

     The sequence of steps for computing seismograms is  as  fol-
     lows:

     dspec8
                - model specification and diagnostics
     hspec9
                - evaluate (f,r) response
     rhfoc
                - compute (x,t) from (f,r) responses


     The model assumed is a plane  stratified  medium  with  each
     layer  characterized  by thickness,  compressional and shear
     speeds, density, and compressional and shear  Q.  A  surface
     fluid  layer  with shear speed zero is supported.  These and
     other necessary parameters are written into an input file by
     running  dspec8 with the appropriate parameters.  Any source
     or receiver depths are permitted, e.g. a VSP  may  be  simu-
     lated in either receiver or source mode.

     Each group has seismograms in the order of Green's  function
     response  (see man page for dspec8 for an explanation of the
     response functions),  followed  by  source/receiver  depths,
     followed by trace distance.


     Plane layered homogeneous  media  are  assumed.  A  Haskell-
     Thompson  propagator  technique is used. For each frequency,
     selected wavenumbers are sampled.  The sampling in the  sub-
     routine  "excit" is designed to provide adequate sampling of
     the functions so that later  numerical  integration  by  the
     "wvint"  programs will be as noise free as possible. To pro-
     vide stable evaluation of the integrands,  the  surface-wave
     poles  on  the  real  wavenumber  axis are removed using the
     artifice of complex frequency (alpha parameter) and  anelas-
     tic medium attenuation.

     The computations are stable for high frequencies because  of
     the  use  of  compound  matrices and because of the extended
     floating point notation. When the eigenfunction response  in
     a  layer  becomes  exponential,  the propagator matrices are
     normalized and the logarithm of the normalization  parameter
     is  carried in the variables exel, exll, exe and exl.  Since
     the medium response is of the  form  NUM/DENOM,  the  medium
     response   with   the   extended   floating  point  is  just
     (NUM/DENOM) * exp (exl - exe).  Thus  none  of  the  numbers
     become  larger  than  is  permitted by the machine hardware.
     This factorization is taken into account by  the  subroutine
     "var".

     The sampling in the wavenumber domain is essentially equally
     spaced, but differs from the suggestion of Bouchon (1981) in
     that a trapezoidal integration rule is not  used,  rather  a
     shifted  rectangular  rule  in  the  programs  rhwvinta  and
     mrhwvinta.

  Command line arguments
     -ms mdpths
          Enter initial source depth (in model units).  Default =
          0

     -ds dsinc
          Enter source depth increment (in model units).  Default
          = 0

     -mr mdpthr
          Enter initial receiver depth (in model units).  Default
          = 0

     -dr drinc
          Enter  receiver  depth  increment  (in  model   units).
          Default = 0

     -nr ndist
          Enter number of groups (no default)

     -x0 x0
          Enter near offset (ft,m) (no default)

     -gi dx
          Enter group interval (ft,m) (no default)

INPUT FILE

     The input parameter file is fed to hspec9 by the  input  re-
     direction  arrow.   This file is created by dspec8 which can
     be conveniently run under IKP

AUTHOR

     R. B. Herrmann, Saint Louis University, 1982

SEE ALSO

     dspec8, rhfoc

COPYRIGHT

     copyright 2001, Amoco Production Company
               All Rights Reserved
          an affiliate of BP America Inc.