NAME

     rhwvint  - obtain F(f,r) from F(f,k) output from hspec8  and
     hspect

SYNOPSIS

     rhwvint [ -C ] [ [ -Nnames ] [ -Onames ] [ -cxcmax ] [ -c1c1
     ] [ -c2c2 ] [ -cmcmin ] [ -nrnr ] [ -x0xmin ] [ -gidx ] ]

DESCRIPTION

     This program takes the F(f,k) spectra generated by the  pro-
     grams  hspec8  or  hspect and integrates along wavenumber to
     obtain the F(f,r) spectra.  The program rhfoc will use  this
     output  to  form  the  F(t,r) time histories.  Note that the
     input is either from an input  file  or  from  commend  line
     parameters.

     The Hankel transform of the various sources of hspec8 or the
     explosion  source  of  hspect  is computed.  The appropriate
     near-field terms for the dislocation  sources  (hspec8)  are
     also included.

     There  are  two  aspects  for  the  program  which  must  be
     described,  the  method  of handling shallow sources and the
     method of integration.

     For all sources, the low frequency, large wavenumber  varia-
     tion  of  the  F(f,k) function is of the form (A + Bk + Ckk)
     exp (-kh), where h is the source depth and k is  wavenumber.
     Since  the  Hankel transform requires integration from k = 0
     to k = infinity, an excessive number of function evaluations
     would  be  required  when h is small, since there is no easy
     place to truncate the integration without significant error.
     On  the  other  hand,  if  the large wavenumber variation is
     known, the integrand may be modified from

             INT F(f,k) Jn(kr) dk


     to

             INT [F(f,k) - (A+Bk+Ckk)exp(-kh)] Jn(kr) dk +
                    INT [A+Bk+Ckk)exp(-kh)] Jn(kr) dk


     The second  integral  can  be  analytically  evaluated.  The
     choice  of when to use the second form depends upon the fre-
     quency.  When the largest frequency dependent wavenumber  of
     hspec8  (or hspect) is greater than 6.0/h, the first form is
     used. The choice of 6.0/h was made after determining a point
     at  which  the  original integrand is relatively small. When
     the  asymptotic  form,  second  integral  form,   is   used,
     functional evaluations at 2.5/h and 6.0/h are used to deter-
     mine two of A, B, and C. Only two are needed because of  the
     expansion  of  a halfspace solution for the various sources.
     The inclusion of this asymptotic option is  the  reason  for
     appending the "a" to the program name.

     The other feature of the program is the technique of numeri-
     cal  integration.  A number of techniques have been proposed
     in  the  literature.  Implementation  of  other   techniques
     requires  a  rewrite  of  the sampling subroutine "excit" in
     hspec8 and a rewrite of the wavenumber integration  program.
     A  Bouchon  integration  technique is used. This uses a tra-
     pezoidal rule for integration and is quite acceptable.

  Command line arguments
     -C   Enter the command line argument '-C'  to  bring  global
          parameters  from the command line (default is card file
          for everything).

     -N names
          Enter name of input file containing hspecX output

     -O names
          Enter name of file to be created to run the other  pro-
          grams in the stream

     -cx cmax
          Enter inverse of  the  maximum  phase  velocity  to  be
          passed (default=-1.0)

     -c1, -c2 c1, c2
          Enter two corners of the passband (default= -1,100)

     -cm cmin
          Enter inverse of  the  minimum  phase  velocity  to  be
          passed (default=100)

     -x0 xmin
          Enter near offset (no default)

     -gi dx
          Enter group interval (no default)

     -nr nr
          Enter number of groups (no defaults)

INPUT (from card file)

     See the back of this  series  of  manual  pages  for  sample
     script files.

     The control input is on UNIT LIN:

     *****LINE 1:
               read(LIN,60)names
            60 format(a)

     names
          Name of the binary file generated by the program hspec8
          or hspect

     *****LINE 2:
               read(LIN,60)names
            60 format(a)

     names
          Name of the output file to be generated by this program

     *****LINE 3:
               read(LIN,1)cmax,c1,c2,cmin
             1 format(4f10.5)

     Definition of the wavenumber corners for  a  phase  velocity
     window.

     cmax cmax is the inverse of the maximum phase velocity to be
          passed

     c1,c2
          c1 and c2 mark the pass band

     cmin cmin is the inverse of the minimum phase velocity to be
          passed

          A cosine taper is  applied  between  cmax  and  c1  and
          between  c2  and  cmin. If no windowing is desired, set
          cmax < 0.0 This windowing is introduced  following  the
          use  of  such  a window in Fuch's original reflectivity
          programs.

     *****LINE 4:
              read(LIN,1)r,tshift,vred
            1 format(4f10.5)

     r    Distance at which Hankel transform is to  be  computed.
          This  must  be  in  the  same units that have been used
          throughout the previous steps.
          A value of r <= 0 causes termination  of  the  program.
          Note  r=0  is not computed since the method of integra-
          tion requires a term of the form (1/r) which would blow
          up.

     tshift
          Time of first point in time series

     vred Reduction velocity for computing first time point.

          If vred = 0, then the first time point is t0 =  tshift,
          else t0 = tshift + r/vred

OUTPUT

     The output consist of the data written on UNIT 04,  as  well
     as some diagnostic output in standard printout file.

SEE ALSO

     dspec8, hspect, hspec8, rhfoc, mrhwvint

AUTHOR

     R. B. Herrmann, Saint Louis University, 1983

COPYRIGHT

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