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The development of appropriate modeling and adjustment procedures for the estimation of harmonic coefficients of the geopotential, from surface gravity data was studied, in order to provide an optimum way of utilizing the terrestrial gravity information in combination solutions currently developed at NASA/Goddard Space Flight Center, for use in the TOPEX/POSEIDON mission. The mathematical modeling was based on the fundamental boundary condition of the linearized Molodensky boundary value problem. Atmospheric and ellipsoidal corrections were applied to the surface anomalies. Terrestrial gravity solutions were found to be in good agreement with the satellite ones over areas which are well surveyed (gravimetrically), such as North America or Australia. However, systematic differences between the terrestrial only models and GEMT1, over extended regions in Africa, the Soviet Union, and China were found. In Africa, gravity anomaly differences on the order of 20 mgals and undulation differences on the order of 15 meters, over regions extending 2000 km in diameter, occur. Comparisons of the GEMT1 implied undulations with 32 well distributed Doppler derived undulations gave an RMS difference of 2.6 m, while corresponding comparison with undulations implied by the terrestrial solution gave RMS difference on the order of 15 m, which implies that the terrestrial data in that region are substantially in error. Pavlis, Nikolaos K. Unspecified Center BOUNDARY VALUE PROBLEMS; GEOPOTENTIAL; GRAVITY ANOMALIES; MATHEMATICAL MODELS; PREDICTION ANALYSIS TECHNIQUES; SPHERICAL HARMONICS; ATMOSPHERIC EFFECTS; BOUNDARY CONDITIONS; LEAST SQUARES METHOD; NUMERICAL ANALYSIS; TERRAIN; WEIGHTING FUNCTIONS...
This paper examines the application of the statistical prediction concept to the prediction of useful mean gravity anomalies from actual existing gravity data. The primary method of estimation is the least squares prediction procedure of Moritz. Mathematical derivation of the prediction equations and explanation of the notation system are given and prediction equations are applied to the prediction of mean gravity anomalies of 1 degrees and 5 degrees near equal-area blocks.
We previously described (14,14) spherical-harmonic global adjustments of satellite altimetry using the AFGL short-arc technique supplemented with point masses to allow incorporation of short-wavelength geoidal detail. Recently, we have also investigated another technique to enhance short-wavelength detail: least squares collocation with noise. Both methods provide a means to determine a high resolution gravity field on a local, regional or global scale. Statistical comparisons of these two methods have been made in selected areas and the results tabulated.