A discussion on the approximations made in the practical implementation of the remove–compute–restore technique in regional geoid modelling

Abstract.

The remove-compute-restore (RCR) technique is the most well known method for regional gravimetric geoid determination today. Its basic theory is the first-order approximation of either Molodensky’s method for quasi-geoid determination or the classical geoid modelling by Helmert’s second method of condensing the topography onto the geoid. Although the basic approximate formulae do not meet today’s demands for a 1-cm geoid, it is sometimes assumed that the removal of the less precise long-wavelength terrestrial gravity anomaly field from Stokes’s integral by utilising a higher-order reference field represented by a more precise Earth gravity model (EGM) and the restoration of the EGM as a low-degree geoid contribution will produce a geoid model of the desired accuracy. Further improvement is achieved also by removing and restoring a residual topographic effect, which favourably smoothes the gravity anomaly to be integrated in Stokes’s formula. However, it is shown here that the RCR technique fails to tune down the long-wavelength gravity signal from the terrestrial data, and the EGM actually only reduces, in a non-optimised way, the truncation error committed by limiting the Stokes integration to a small region around the computation point. Hence, in order to take full advantage of a precise EGM, especially one from new dedicated satellite gravimetry, Stokes’s kernel must be modified in a suitable way to match the errors of terrestrial gravity, EGM and truncation. In addition, topographic, atmospheric and ellipsoidal effects must be carefully applied.