Problems Encountered in the Stokes' Numerical Integration of Terrestrial Gravity Anomalies

摘要

Various sets of gravimetric geoid undulations were completed at 600 globally distributed Doppler station sites using geopotential coefficients and different cap sizes of terrestrial gravity data. The means and standard deviations of the residuals between these gravimetric undulations and corresponding Doppler-derived geometric undulations were then computed for each set and compared. The gravimetric undulations were determined using either the OSU 81 or WGS 84 set of geopotential coefficients, each complete to degree and order 180, or a combination of the OSU 81 model truncated to degree and order 36 and terrestrial gravity data consisting of a global set of 1 deg X 1 deg mean free air anomalies. The radii of the caps containing the terrestrial data were, by design, varied from 0 deg to 65 deg. The Doppler undulations were derived by subtracting the mean sea level elevations at the stations from the Doppler-determined ellipsoid heights. The smallest standard deviations of the geoid undulation residuals were obtained when using a cap size of 6 deg. Unexpectedly, as the cap size was increased from 6 deg, increasingly larger standard deviations were produced. This basic trend remained after the global set was divided into eastern and western hemispheres. Studies of the change in gravimetric geoid undulation accuracies with increasing cap size for fifteen regional areas were also made with varying results. It was found that 1) propagation error in the Stokes' numerical integration of erroneous mean terrestrial gravity anomalies increases rapidly with increasing cap size and 2) significant errors can result from using terrestrial gravity data which have been referenced to inconsistent vertical datums. (jhd)