x_system - A Cross-Over Error Analysis Tool

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.

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.

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.

gmt(1gmt),

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 Measurements, J. Geophys. Res., 93, 393-413, 1988.