A simple objective method for minimizing crossover errors in marine gravity data

Abstract

A method is presented which does not require a model for the source of crossover errors in marine gravity data in order to minimize them. The cruises are divided up into straight line segments and the assumption is made that whatever the sources of error, their net effect will be constant over the length of the track segment. A least‐squares approach is used where the crossover differences in the original data are the observations which it is desired to match. The desired set of constant corrections, one for each segment, is that which will minimize the sum of the squares of the residual crossover errors. This method has the advantage of reducing the crossover errors while simultaneously preserving the relative gravity anomalies along individual ship’s profiles. A data set consisting of gravity measurements made on nine cruises in the region of the Vema fracture zone in the equatorial Atlantic is used as a case study. The resulting least squares solution reduces the root mean square (rms) of 298 crossover errors from 10.3 mGals in the original data to 2.9 mGals after the calculated segment corrections are made. An F‐test shows that the reduced rms deviation from the mean is statistically significant at the 99 percent confidence level. A least‐squares fit was also done to find the best single cruise corrections for each of the 9 cruises for the 204 crossings between cruises. The original rms error is reduced from 11.4 to 7.8 mGals and the improvement is again significant at the 99 percent confidence level. An analysis of the variances shows that 37.5 percent of the total variance can he explained by constant corrections to each of the 9 cruises, while an additional 49.5 percent of the total variance can be explained by individual segment corrections. A linear regression analysis of the segment corrections as a function of elapsed time in the cruise suggests that for two of the cruises, drift of the gravity meter was not properly corrected for in the original data. Analysis of the segment corrections as a function of ship’s heading suggests that for two other cruises, cross‐coupling effects were not properly corrected. Eötvös corrections caused by navigational errors are the most likely explanation for many of the remaining individual segment corrections. After the calculated corrections were made, a free‐air anomaly map of the region was drawn. A comparison with an earlier published, free‐air anomaly map of the right half of this region shows that the contours are similar, but that the new map is shifted by a few mGals relative to the older map. This discrepancy between the old and new maps is a consequence of matching the data between the left and right sides of the new map and does not arise if the right side is considered alone with the least‐squares technique.