Downward Continuation of the Free-Air Gravity Anomalies to the Ellipsoid Using the Gradient Solution, Poisson's Integral and Terrain Correction Numerical Comparison and the Computations
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Date
1988-06
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Ohio State University. Division of Geodetic Science
Abstract
The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere - at least to the ellipsoid. The goal of this work is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g1 term). The terrain correction has also been computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. Because there is no global, dense gravity anomaly data, 5' x 5' mean elevation data has been used for the computations of the g1 term and the terrain correction on a global basis. The fast Fourier transformation has been applied to the computations. The maximum g1 term for the 5' x 5' mean blocks is located in the Himalaya Mountains and has the magnitude of 442 mgals. The standard deviation is ± 2.56 mgals for the 5' x 5' mean block values. The terrain correction has the maximum value of 183 mgals, and standard deviation ± 1.01 mgals for 5' x 5' the mean block values. The root mean square value of the degree variances of the correction terms, the g1 term and the terrain correction, are about 2% of the degree variance of the disturbing potential. The root mean square effect of the geoid undulation due to the correction terms is about 0.7 meter for terms taken to degree 180. For the deflections of the vertical the correction terms contribute 0.1". [Some mathematical expressions are not fully represented in the metadata. Full text of abstract available in document.]