The effect of the smoothing operator on potential coefficient determinations
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Date
1979-03
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Ohio State University. Division of Geodetic Science
Abstract
The determination of the potential coefficients from mean gravity anomalies can be carried out by using the summation formulas derived from the orthogonality relationships of the spherical harmonics. However, certain assumptions have to be made in evaluating the integral in these equations. With these assumptions we arrived at two different methods which are discussed and compared. The first is the "point" method, and the second is the "integrated" method, where the smoothing operator is used. This operator depends on the size of the block where the anomalies are given, and consequently it is a latitude-dependent quantity for non-equal-area blocks. We arrived at the conclusion that the two methods are equivalent, provided that we make proper use of the smoothing operator in applying the integrated technique. Also, a set of 38406 1° x 1° mean gravity anomalies has been used to make a series of tests, applying both the "point" and the "integrated" techniques. The differences between the resulting coefficients were found to be insignificant. Finally, we examined the analogy between potential coefficient determinations from mean gravity anomalies on a sphere, and the Fourier transform of a function which is defined by its mean values on a circle. Using the theoretical and the numerical results which are presented in this paper, we made conclusions on the proper use of the smoothing operator, and on the maximum degree of truncation in potential coefficient determinations.
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Prepared for National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland: Grant No. NGR 36-008-161, OSURF Project No. 3210