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 gravitational potential of the earth has been presented in a spherical harmonic series that is complete to degree and order 250. This solution has been obtained by first carrying out a combination of satellite derived potential coefficients (GEML2') with a set of 1 deg by 1 deg mean free air anomalies. These anomalies were formed from a merger of a June 1986 terrestrial set and a set derived from Geos-3/Sesat altimeter data. The combination solution was carried out after making downward continuation corrections to the surface anomalies and ellipsoidal corrections to the a priori potential coefficients. The adjustment yielded 582 potential coefficients and 64800 1 deg by 1 deg anomalies. Two combination solutions were made, one (OSU86C) that excluded geophysically predicted anomalies and one (OSU86D) that included 5547 such anomalies. The potential coefficients are determined through an optimal estimation procedure where, primarily, sampling error was minimized. Tests of the new solution were made by comparing undulation residuals at Doppler stations, and by using the field, up to degree 36, in orbit calculations. In North American the root mean square undulation difference was + or - 1.55 m. The undulation residuals are found to correlated with elevation although it is not clear why.

Description: Beschreibung: Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360.