Computation of Geopotential Coefficients from Gravity Anomalies on the Ellipsoid

Abstract

One of the most important stages in the computation of a global geopotential model is the computation of the spherical harmonic coefficients from gravity anomalies on the normal ellipsoid. None of the existing methods provides an exact solution, and all show severe shortcomings in the high degrees of the spectrum. In this paper, a new, theoretically exact method is proposed, which is moreover easily applicable up to very high degree and order (2160 and beyond). The solution of the geopotential coefficients is presented as a weighted sum over 'spherically approximated' coefficients of equal order, where the gravity anomalies are presumed to reside on a sphere.The weights depend solely upon the degree and order of the coefficient and the definition of the normal ellipsoid and its gravity field. Numerical comparisons with existing methods show substantial differences, especially in the high degrees, which can be explained by the fact that all previous methods are of limited accuracy.