Topographic Effects in Geoid Determinations
Traditionally, geoid determination is applied by Stokes' formula with gravity anomalies after removal of the attraction of the topography by a simple or refined Bouguer correction, and restoration of topography by the primary indirect topographic effect (PITE) after integration. This technique leads to an error of the order of the quasigeoid-to-geoid separation, which is mainly due to an incomplete downward continuation of gravity from the surface to the geoid. Alternatively, one may start from
... one may start from the modern surface gravity anomaly and apply the direct topographic effect on the anomaly, yielding the no-topography gravity anomaly. After downward continuation of this anomaly to sea-level and Stokes integration, a theoretically correct geoid height is obtained after the restoration of the topography by the PITE. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the "secondary indirect topographic effect", which is a necessary correction in removing all topographic signals. In modern applications of an Earth gravitational model (EGM) in geoid determination a topographic correction is also needed in continental regions. Without the correction the error can range to a few metres in the highest mountains. The remove-compute-restore and Royal Institute of Technology (KTH) techniques for geoid determinations usually employ a combination of Stokes' formula and an EGM. Both techniques require direct and indirect topographic corrections, but in the latter method these corrections are merged as a combined topographic effect on the geoid height. Finally, we consider that any uncertainty in the topographic density distribution leads to the same error in gravimetric and geometric geoid estimates, deteriorating GNSS-levelling as a tool for validating the topographic mass distribution correction in a gravimetric geoid model.