Ubuntu Manpage: x_system - A Cross-Over Error Analysis Tool

NAME

       x_system - A Cross-Over Error Analysis Tool

INTRODUCTION

The x_system was developed to aid in the task of gridding geophysical 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.

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 program archives the COE information, and
       the remaining programs do various 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 solution 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 information 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
initially 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 create 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-consuming 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 rearranges 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.

AUTHOR

       Paul  Wessel,  Dept.  of  Geology  and  Geophysics,  SOEST, University of Hawaii at Manoa.
       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 Measurements, J. Geophys.
       Res., 93, 393-413, 1988.

NAME

INTRODUCTION

x_system PHILOSOPHY

HOW TO DO IT

SEE ALSO

AUTHOR