Bigsolver

The regression (18) includes a weighting function, so we need yet another solver module very much like the regularized and preconditioned solvers that we used earlier. The idea is essentially the same. Instead of preparing such a solver here, I refer you to the end of the book for solver_mod , a big solver that incorporates everything that we need in the book. Hopefully we will not need to look at solvers again for a while. Module vrms2int was written by Bob Clapp to get the results in Figures 1 to 3. Notice that he is using solver_mod .

 

module vrms2int_mod {                # Transform from RMS to interval velocity
  use causint
  use cgstep_mod
  use solver_mod
contains
  subroutine vrms2int( niter, eps, weight, vrms, vint) {
    integer,            intent( in)     :: niter     # iterations
    real,               intent( in)     :: eps       # scaling parameter
    real, dimension(:), intent( in out) :: vrms      # RMS velocity    
    real, dimension(:), intent( out)    :: vint      # interval velocity
    real, dimension(:), intent( in)     :: weight    # data weighting
    integer                             :: st,it,nt  
    logical, dimension( size( vint))    :: mask
    real,    dimension( size( vrms))    :: dat ,wt
    nt = size( vrms)
    do it= 1, nt {
       dat( it) = vrms( it) * vrms( it) * it
       wt( it) = weight( it)*(1./it)           # decrease weight with time 
       }
    mask = .false.;   mask( 1) = .true.            # constrain first point
    vint = 0.     ;   vint( 1) = dat( 1)
    call solver_prec( causint_lop, cgstep, x= vint, dat= dat, niter= niter, 
                      known= mask, x0= vint, wt= wt, 
                      prec=causint_lop, eps= eps, nprec= nt)
    call cgstep_close()
    st = causint_lop( .false., .false., vint, dat)
    do it= 1, nt
       vrms( it) = sqrt( dat( it)/it)
    vint = sqrt( vint)
    }
}