NAME

     lsqr - perform conjugate  gradient  least  square  inversion
     using iterative call to forward and adjoint forward modeling
     programs.

SYNOPSIS

     lsqr [ -Nfile_data ] [  -Pfile_prior  ]  [  -iterniter  ]  [
     -decreasedecrease  ] [ -weightweight ] [ -subsub-directory ]
     [  -prevsuboldsub-directory  ]  [  -FORWARDcmdforward  ]   [
     -BACKWARDcmdbackward ] [ -V ] [ -? ]

DESCRIPTION

     lsqr minimizes the folowing quadratic objective function  by
     means of conjugate gradient algorithm:
        J(m)  = J1(m) + J2(m)
        J1(m) = || Fm- d ||**2
        J2(m) = || m - m0 ||**2
        F  : the forward modeling operator
        d  : the data to be inverted
        m0 : an a priori model

     The inversion is performed using the forward  modeling  pro-
     gram (F) and its adjoint backward modeling program; the com-
     mand line  arguments  for  both  this  program  is  entered,
     between  quote,  on  the  command line arguments. The result
     called solution is written in the subdirectory specified  on
     the  command  line.  In  this  subdirectory we find also the
     objective function value  at  each  iteration  in  the  file
     MINIMIZER.process_id, the forward modeled calculated data of
     the solution called data.calc, as well as the  solution  and
     corresponding  forward modeled calculated data of the previ-
     ous iteration, called solution.old and  data.calc.old.  This
     allows  lsqr  to  restart  from  a  previous minimization by
     specifying on the command line the subdirectory name of  the
     previous minimization from which we wish to restart.

  Command line arguments
     -N file_data
          Enter the usp input file name that contains the data to
          be inverted (no default).

     -P file_prior
          Enter the usp file that contains the  a  priori  model.
          Default is nothing.

     -iter niter
          Enter the number of iterations  of  conjugate  gradient
          algorithm. The default value is 4.

     -weight weight
          Enter the normalized weighting parameter of the  second
          term  of  the  objective function. The default value is
          0.05 which means that the influence of second  term  of
          the  objective  function  is 5% of the influence of the
          first term during the minimization.

     -decrease decrease
          Enter the stop test value for the algorithm. The  algo-
          rithm will stop before the given iteration number niter
          if the objective function is less than the norm of  the
          data  multipled  by  decrease or if the decrease of the
          objective function between two  consecutive  iterations
          is  less  than  the  norm  of  the  data  multipled  by
          decrease. The default value is 0.01  which  means  that
          the  minimization  stop if the objective function falls
          under 1% of the data norm or if  the  decrease  of  the
          objective  function  between two consecutive iterations
          is less than 1% of the data norm.

     -sub sub-directory
          Enter the name of the subdirectory were the result will
          be     written.    The    default    subdirectory    is
          result.process_id.  Note  that   sub-direc   tory   and
          oldsub-directory can be the same (see below).

     -prevsub oldsub-directory
          Enter the name of the directory from which the  minimi-
          zation  will  restart. In this case niter correspond to
          the additional iteration number to perform. The default
          value is nothing.

     -FORWARD cmdforward
          Enter between quote, the command line argument  (execpt
          for  the  -O  and  -N options) for the forward modeling
          program (no default).

     -BACKWARD cmdbackward
          Enter between quote, the command line argument  (execpt
          for  the  -O  and  -N  options) for the adjoint forward
          modeling program (no default).

     -V   Enter the command line argument '-V' to obtain  verbose
          output.

     -?   Enter the command line  argument  '-?'  to  get  online
          help.   The program terminates after the help screen is
          printed.

     NOTE1 : The program does system calls to  the  folowing  usp
     programs: vstak, vmult, linear, linear2, lnorm and putzero.

     NOTE2 : The program assumes that the input and output  files
     of both forward and adjoint program are real values.

BUGS

     No bugs known at present.

REFERENCES

     Duquet, B., 1996, Improvement of seismic imaging of  complex
     geologic structures: Ph.D. Thesis, Univ. of Paris XIII.

CONTRACT AGREEMENT

     This product is brought to you as a 4th quarter  deliverable
     (filtering  of  coherent  noise  in  the  depth  domain)  by
     Research Agreement D96-2518 (Seismic Signal Analysis). Thank
     you for your support.

AUTHORS

     Bertrand Duquet, Amoco EPTG, 1996.

COPYRIGHT

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