The effect on the geoid of lateral topographic density variations

Abstract

Gravimetric geoid determination by Stokes’ formula requires that the effects of topographic masses be removed prior to Stokes integration. This step includes the direct topographic and the downward continuation (DWC) effects on gravity anomaly, and the computations yield the co-geoid height. By adding the effect of restoration of the topography, the indirect effect on the geoid, the geoid height is obtained. Unfortunately, the computations of all these topographic effects are hampered by the uncertainty of the density distribution of the topography. Usually the computations are limited to a constant topographic density, but recently the effects of lateral density variations have been studied for their direct and indirect effects on the geoid. It is emphasised that the DWC effect might also be significantly affected by a lateral density variation. However, instead of computing separate effects of lateral density variation for direct, DWC and indirect effects, it is shown in two independent ways that the total geoid effect due to the lateral density anomaly can be represented as a simple correction proportional to the lateral density anomaly and the elevation squared of the computation point. This simple formula stems from the fact that the significant long-wavelength contributions to the various topographic effects cancel in their sum. Assuming that the lateral density anomaly is within 20% of the standard topographic density, the derived formula implies that the total effect on the geoid is significant at the centimetre level for topographic elevations above 0.66 km. For elevations of 1000, 2000 and 5000 m the effect is within ± 2.2, ± 8.8 and ± 56.8 cm, respectively. For the elevation of Mt. Everest the effect is within ± 1.78 m.