Modifying Stokes' function to reduce the error of geoid undulation computations

Abstract

A comparison is made of the errors in determining the geoid undulation according to the conventional Molodenskii truncation theory and its modifications as suggested by Molodenskii (1958) and Meissl (1971). The undulation is assumed to be computed from gravity anomalies in a spherical cap and a finite set of harmonic potential coefficients (e.g., GEM 9 or GEM 10B). Only the effects of errors in the coefficients, as well as the neglect of higher degree coefficients, are considered. It is found that the error estimates (rms values) are significantly lower for any of the modified methods than for the conventional method. For example, errorless and continuous gravity data in a cap with 10° radius and the GEM 9 coefficients together yield undulations with an average error of 109 cm if the unmodified truncation theory is applied and 41 cm and 33 cm with Meissl's method and a Molodenskii type of modification, respectively.