Recovery of 5° Mean Gravity Anomalies in Local Areas From ATS-6/GEOS-3 Satellite to Satellite Range-Rate Observations
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Date
1977-09
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Ohio State University. Division of Geodetic Science
Abstract
The recovery of 5° equal area mean anomalies is investigated from ATS-6/GEOS-3 SST real range-rate data using the least squares collocation method. The observational errors can be very satisfactorily filtered out by using piecewise continuous cubic splines (with continuous first and second derivatives) to fit the range-rate data in the least squares sense. The accelerations are obtained by analytical differentiation of the fitted spline. The accelerations are obtained optimally, matching the smoothness characteristics expected at GEOS-3 altitudes, if the nodes of the spline, where adjacent cubic polynomials meet, are kept every 60 seconds to fit range-rate observations at 10 seconds interval. It is found that the initial state vectors of ATS-6 and GEOS-3 are best determined by using observations over a 4 to 6 day period to avoid biased values due to occasional faulty observations. The initial state vectors for any other epoch during this period, but not before or after this period, may be obtained by integration. The recovery of anomalies can be examined using observations in one GEOS-3 revolution at a time. Two revolutions having faulty observations could be identified in this manner. The residual errors in the initial state vector of GEOS-3 of 10 to 20 meters in position, and 1 to 2 cm/sec in velocity were found to cause small linear errors in the radial derivative ( ∂T / ∂r) of the anomalous potential. These systematic errors may be adjusted for minimum variance of the discordance between ∂T / ∂r values in ascending and descending revolutions at cross-over points. The number of ascending and descending revolutions should be more than four each to obtain an over-determined solution. The recovery of eight 5° anomalies was attempted using three descending and two ascending revolutions without applying cross-over constraints. The RMS anomaly discrepancy was about 8 mgals with standard deviation of predicted anomalies as about 12 mgals. Tests indicate that these values could be much reduced by using observations from additional revolutions, and applying cross-over constraints.