NAME

       x_system - A Cross-Over Error Analysis Tool


INTRODUCTION

            The x_system was developed to aid in the task of gridding geophys-
       ical track data, e.g.  gravity, magnetics, or bathymetry. It  has  long
       been recognized that although the data quality along track may be quite
       good, one usually finds discrepancies at the points  where  two  tracks
       intersect.  These  cross-over errors (COE) can be large enough to cause
       artificial features in the final gridded dataset,  which  would  render
       geological  interpretations  of such a map questionable.  Also, notori-
       ously bad cruises will generate  high  COEs  along  their  tracks,  and
       should  ideally  be  removed  from  the  data  base  before gridding is
       attempted. The reasons why COEs arise are many and will  not  be  dealt
       with  here.  Although originally intended to be used for marine gravity
       data only, x_system has been designed to handle magnetics and  bathyme-
       try  as  well.  (For  an overview of gravity COEs, see Wessel and Watts
       [1988]). In most cases, marine gravity COEs can be explained by a  sim-
       ple model having only 2 parameters. These are a d.c.-shift and a drift-
       rate that apply for the duration of the cruise. The  goal  of  the  COE
       analysis  is  thus  to determine the dc-shifts and drift-rates for each
       leg that will minimize the COEs in a least squares sense,  and  at  the
       same  time flag cruises that exhibit unreasonably high COEs (even after
       correction for d.c.-shift/drift). Furthermore, we  can  also  assign  a
       'quality index' for each cruise by looking at the standard deviation of
       the COEs. The d.c.-shift/drift rate model may not be as meaningful  for
       magnetics  and  bathymetry  as  it is for gravity. However, looking for
       high COEs is still one of  the  best  ways  of  identifying  systematic
       errors in the magnetic/bathymetric data sets.


x_system PHILOSOPHY

            Since  the  d.c.-shift/drift corrections for a given cruise depend
       entirely on the  values of the COEs  generated  at  intersections  with
       other  cruises,  there is no such thing as a 'final correction' as long
       as we keep on adding data to the data base. This means that the  system
       must  be  able  to  incorporate  new  data  and  compute  a  new set of
       d.c.-shifts/drift-rates that takes the new COEs into account.  x_system
       is  made modular so that one program computes the actual COEs, one pro-
       gram archives the COE information, and the remaining programs do  vari-
       ous tasks like reporting statistics (to flag bad cruises), extracting a
       subset  of  the  COE  database,  and  solving  for  the  best   fitting
       d.c.-shift/drift corrections. This way only the new COEs generated need
       to be computed and added to the database before a new correction  solu-
       tion is sought.
            All  the  8  programs  that make up the x_system package have been
       written in the C programming language and are intended to be run  on  a
       UNIX  machine.  Thus,  it  is  assumed that the user has access to UNIX
       tools like awk, grep, and sort, and that the operating system  provides
       a  means for redirecting input/output. Likewise, it is assumed that all
       the geophysical data are stored in the GMT-format as  outlined  in  the
       GMT  MGG supplements man pages, and that the 1 by 1 degree bin informa-
       tion files (gmtindex.b and gmtlegs.b) have been created and  are  being
       maintained by the database librarian.


HOW TO DO IT

            To  illustrate how one would set things up, we will go through the
       necessary steps and point out usage, useful tricks,  and  pitfalls.  (A
       more  complete  description  of  what  exactly each program does can be
       found in the man pages for each program).  We will assume that we  ini-
       tially  have  N  cruises  in  our  GMT data bank, and that we just have
       received the x_system package. The first thing to do is to  run  x_init
       which will create an empty data base system. This will normally be done
       only once.  With N cruises on our hands we will in the worst case  have
       to compare the N*(N+1)/2 possible pairs. This is where x_setup comes in
       handy. It will read the 1 by 1 degree bin information files  and  print
       out  a list of pairs that need to be checked. The two cruises that make
       up a pair will at least once occupy the same 1 by 1 degree bin, and may
       thus intersect. Those combinations which do not have any bins in common
       obviously don't have to be checked.  Let's  call  this  list  of  pairs
       xpairs.lis.
            x_over is the main program in the package as it is responsible for
       locating and computing the COEs  For details on algorithm,  see  Wessel
       [1989].  It  takes two cruise names as arguments and writes out all the
       COEs generated between them (if  any).  Since  xpairs.lis  may  contain
       quite  a few pairs, the most efficient way of running x_over is to cre-
       ate an executable command (batch) file  that  starts  x_over  for  each
       pair.  Using awk to do this, we would say:

            pratt%  awk  '{  printf  "x_over  -<options>  %s  %s\n",  $1, $2}'
       xpairs.lis > xjob
            pratt% chmod +x xjob     (make it executable)
            pratt% xjob > xjob.d &

       and relax while xjob is crunching the numbers. This is the time-consum-
       ing  part  of  the  COE analysis, and on a SUN-3 computer with Floating
       Point  Accelerator  installed  we  average  about   10,000   pairs   of
       cruises/day.  It  may  pay  off  to split a huge xjob file into smaller
       parts, and call the output files xjob.d1, xjob.d2 etc. Most of the run-
       time  is  taken  up by reading the GMT files; when in memory the actual
       computations are remarkably fast. The output file xjob.d will now  have
       all the COE information in ASCII form. For each pair of legs there will
       be a header record stating the names of the cruises and their  starting
       years.  The  following records up to the next header record (or End-Of-
       File) will contain lat, lon, time, value, etc. for each COE found. This
       is a temporary file, but it is wise to back it up to tape just in case.
            When the x_over part is done, time has come to  archive  the  data
       more efficiently than ASCII files. This is done by x_update which rear-
       ranges the data and updates the binary data  base  system.  After  this
       step  the  xjob.d files can be deleted (presuming they have been backed
       up to tape).  At this stage we have several options available.  We  can
       list  some  of the COEs by running x_list, which will extract COEs that
       match the options we pass, e.g. we might ask for all the internal  COEs
       for  cruise c2104, and only print out time and gravity COE. See the man
       pages for more details. x_report can be run, and will output statistics
       for  separate cruises, i.e. mean and standard deviation of the COEs for
       different data sets (gravity/magnetics/bathymetry). To  solve  for  the
       best  fitting  corrections  we would run x_solve_dc_drift. This program
       will solve for the d.c.-shift/drift-rates for all cruises, update  that
       information  in  the  data  base  system,  and create correction tables
       (ASCII and/or binary). We have now completed the COE analysis  for  our
       initial GMT data bank.
            At  some  later time, however, we will get a new batch of cruises.
       We will then follow the the same recipe and go back and runx_setup, but
       this  time  we  will use the -L option so that only the pairs involving
       new cruises are returned. Then we  would  run  the  remaining  programs
       exactly as described above.


SEE ALSO

       gmt(GMTMANSECTION),


AUTHOR

       Paul  Wessel,  Lamont-Doherty  Geological  Observatory,  Palisades,  NY
       10964.  Wessel, P. XOVER: A Cross-over Error Detector for  Track  Data,
       Computers & Geosciences, 15, 333-346.

       Wessel,  P. and A. B. Watts, On the Accuracy of Marine Gravity Measure-
       ments, J. Geophys. Res., 93, 393-413, 1988.



VERSION                              DATE              x_system(GMTMANSECTION)

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