The Formation and Evaluation of Detailed Geopotential Models Based on Point Masses

摘要

Detailed models of the geopotential defined in a geocentric coordinate system must currently be based on a combination of satellite derived data and terrestrial gravity observations. This investigation concerns the use of such data to develop a geopotential model consisting of a spherical harmonic series supplemented by point masses of defined magnitude and position. An undulating reference equipotential surface described by a 14th degree and order set of spherical harmonic potential coefficients is established and conventional terrestrial gravity anomalies are redefined to refer to this surface. These anomalies are used to determine mass magnitudes for point mass arrays positioned to approximate Green's equivalent layers. The technique is demonstrated by developing a geopotential model for the central third of the United States that is approximately equivalent to a model expressed in spherical harmonic coefficients to 180th degree and order. A much more detailed model is also developed for a more limited area. Extensive comparisons are made between geopotential functions computed from these models and comparison standards derived through classical geodetic procedures. The results of this study show that a complex and accurate model of the geopotential can be developed using the described techniques. The method would be most useful in situations requiring repetitive computations of geopotential functions in limited areas. (Author)