The terrain correction in gravimetric geoid computation—is it needed?

SUMMARY It is well known among geodesists that the gravitational effect of the topography must be removed (direct topographic effect) prior to geoid computation, for example, by Stokes' formula, and restored afterward (indirect topographic effect). The direct effect is usually decomposed into the effects of the Bouguer shell (− V B ) and the terrain. While the computation of V B is a simple matter, the detailed consideration of the terrain effect is more difficult. This study emphasizes, that, in principle, the geoid height can be determined by the remove–restore technique in considering only V B and the effect of an arbitrarily small area of the terrain along the radius vector at the computation point, and that the determination of V B requires only the density distribution be known along this radius. The method is justified by the approximation theorems of Runge–Krarup and Keldysh–Lavrentieff. The answer to the headline question is therefore no. A closely related question is how to find a candidate method for the analytical continuation of the external potential. The paper studies whether a Taylor series can take on this role. It is concluded that this series will converge, if the direct effects of the Bouguer potential and the mass of the terrain in a near‐zone around the computation point (P) are applied prior to downward continuation. The radius of the near‐zone is shown not to exceed that of the height of any mountain around P, which, in the worst case (with P located near the top of Mt Everest) yields a radius of convergence within 9 km. In most cases the radius is much smaller. Hence, only a very local part of the terrain potential must be removed to allow the determination of the geoid height by Taylor expansion. Importantly, if the height of P is at least twice that of any point of the near‐zone topography (e.g. for airborne and satellite gravity), the Taylor series always converges without any reduction for terrain.