ALBERT

Description: Abstract : The report develops working equations for carrying out the combination of gravimetric and satellite data starting from the equations of Moritz, and using the principles of the usual least squares adjustment and the least squares collocation. Of the two methods of combining data considered, one could not be carried out because of the need to invert a 1654 x 1654 full matrix. Numerical tests were conducted through the estimation of ten sets of potential coefficients complete to degree 20 plus certain resonance coefficients which have been derived starting from the GEM 3 potential coefficients and a 5 degree equal area block anomaly field. The solutions differ in two ways: first, the weighting applied to the a priori known potential coefficients, and second whether the usual least squares or collocation adjustment scheme is used for the estimation of the potential coefficients. To determine a best overall set of potential coefficients, comparisons have been made with astro-geodetic undulations (4196 values in Australia and the United States); with 5 degree anomalies; with anomaly degree variances, and by use of the coefficient sets in orbit fitting and prediction. Such comparisons indicate that collocation derived potential coefficients yield better values than those found using the usual least squares approach. A recommended set of potential coefficients and a consistent 5 degree equal area block anomaly field are given. (Author)

Description: The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.