GRAVIMETRIC GEODESY FREE OF DENSITY ESTIMATES THROUGH ANALYSIS OF DISCRETE GRAVITY DATA.
ARMY ENGINEER GEODESY INTELLIGENCE AND MAPPING RESEARCH AND DEVELOPMENT AGENCY FORT BELVOIR VA
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For many years, geodesists have been trying to find the method which would make it possible to reduce gravity data from the surface of the earth down to a reference sphere or ellipsoid in such a way that the actual boundary value problem could be properly solved in an explicit way. Early methods failed except for low-order harmonic determination because there is no way of determining the density. Recent studies of Molodensky indicated that there is no general way of making an analytical continuation of the gravity field. Undoubtedly, these studies are correct if we regard the gravity field in the classical way as a uniquely defined continuum. In the present report, however, the gravity field is defined by a finite set of discrete points all in conformity with the actual circumstances. A solution that fits all used points always exists. For this solution, a simple integral equation is solved by the aid of either regression analysis of harmonic analysis. The gravity reduction problem is thereby solved for the first time without making use of any hypotheses. The solution is derived from adjacent gravity data, using a non-iterative method. Author