On the topographic effects by Stokes' formula

Abstract

Traditional gravimetric geoid determination relieson Stokes' formula with removal and restoration of thetopographic effects. It is shown that this solution is in errorof the order of the quasigeoid-to-geoid difference, which ismainly due to incomplete downward continuation (dwc)of gravity from the Earth's surface to the geoid. A slightlyimproved estimator, based on the surface Bouguer gravityanomaly, is also biased due to the imperfect harmonic dwcthe Bouguer anomaly. Only the third estimator,which usesthe (harmonic) surface no-topography gravity anomaly, isconsistent with the boundary condition and Stokes' formula,providing a theoretically correct geoid height.The difference between the Bouguer and no-topographygravity anomalies (on the geoid or in space) is the "secondaryindirect topographic effect", which is a necessarycorrection in removing all topographic signals.