Use of global geopotential models for comparison of gravimetric geoid estimators by the modification of Stoke's formula

Abstract

Considering today struggles towards the 1-cm geoid, in an attempt to study the efficiency of some geoidal height estimators, Molodensky et al. (1962), Wong and Gore (1969), Vincent and Marsh (1974), Sjöberg's least-squares (1984) and Vanicek and Kleusberg (1987) modification models are numerically evaluated. These estimators combine a Global Geopotential Model (GGM) with the regional gravity data convolved with Stokes's kernel. The geoidal heights are computed in a test area using the above-mentionedgeoidal height estimators. Next, geoidal heights are computed in the test area only using the geopotential coefficients. This geoid model is considered as "reference geoid model" in this study. The geoid heights computed with five estimators have then been compared with this reference model. It is shown that the different procedures to modify the original Stokes's formula result in different geoidal heights. The results of comparisons show that the least-squares and Vanicek and Kleusberg (1987) estimators are in better agreement with the "reference geoid model" than the other estimators in this study. They use the spheroidal-type kernel in the model and, therefore, the truncation error in these two models reduces significantly.

Use of global geopotential models for comparison of gravimetric geoid estimators by the modification of Stoke's formula