NAME

     hspec8  - evaluate elastic F(f,k) based on  data  output  of
     dspec8

SYNOPSIS

     hspec8

DESCRIPTION

     The purpose of  this  program  is  to  evaluate  the  medium
     response  for  ten  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
     hspec8
                - evaluate (f,k) response
     [m]rhwvinta
                - integrate (f,k) to (f,x) offset response
     [rh,tp]foc
                - compute (x,t) or (p-tau) from (f,k) or (f,p)


     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  provide  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 anelastic 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.

INPUT (UNIT 05)

     All input is on this file unit is generated using dspec8  to
     output a properly formatted parameter file (currently called
     hspec8.dat) to be input on stdin.  The next step may be sim-
     ply invoked by typing

               hspec8 < hspec8.dat

AUTHOR

     R. B. Herrmann, Saint Louis University, 1982

SEE ALSO

     dspec8, rhwvinta, mrhwvinta, rhfoc