On the Topographic Effects of Helmert’s Method of Condensation

Abstract

Assuming a constant or laterally variable topographic density the direct and indirect topographic effects on the geoidal and quasigeoidal heights are presented as strict surface integrals with respect to topographic elevation (H) on a spherical approximation of sea level. By Taylor expanding the integrals with respect to H we derive the power series of the effects to arbitrary orders. The study is primarily limited to terms of second order of H, and we demonstrate that current planar approximations of the formulas lead to significant biases, which may range to several decimetres. Adding the direct and indirect geoid effects yields a simple combined effect, while the corresponding combined effect of the quasi-geoid vanishes. Thus we conclude that only the effect of downward continuation of gravity anomaly to sea level under Stokes integral remains as a major computational burden among the topographic effects.