A numerical comparison of different ellipsoidal corrections to Stokes’ formula

Abstract

This paper reviews the new method (recently derived by L.E. Sjöberg) of the ellipsoidal correction for Stokes’ formula. Importantly, the correction can also be expressed in a series of spherical harmonics of the disturbing potential, which is a considerable computational advantage. In order to assess the applicability of this approach, it is numerically compared with two other methods. The results reveal that the new method practically coincides with one of the earlier methods, although their derivational approaches and resulting expressions are considerably different. The new method is adapted for the modified Stokes formula, which combines regional terrestrial gravity data with a global geopotential model. The magnitude of the ellipsoidal correction in the modified Stokes formula does not exceed cm level, globally.