x_system - A Cross-Over Error Analysis Tool


               The  x_system was developed to aid in the task of gridding geo-
       physical 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,
       notoriously 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
       bathymetry  as  well.  (For an overview of gravity COEs, see Wessel and
       Watts [1988]). In most cases, marine gravity COEs can be explained by a
       simple  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.


               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.


       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
               x_over  is the main program in the package as it is responsible
       for locating and computing the COEs For details on algorithm, see  Wes-
       sel  [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  run
       x_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.




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