A comparison of different isostatic models applied to satellite gravity gradiometry

Abstract

In satellite gradiometry, the gravitational signals originating from the Earth’s topography and its isostatic compensation can be recognized in the gravity gradients observed along the satellite orbit. One general task should be the reduction of these effects to produce a smooth gravity field suitable for downward continuation. Based on different isostatic models such as the Airy-Heiskanen model, the Pratt-Hayford model, the combination of the Airy-Heiskanen model (land area) and the Pratt-Hayford model (ocean area), and the generalized Helmert model, the topographic-isostatic effects are calculated for a GOCE-like satellite orbit. For the second vertical (radial) derivative of the gravitational potential the order of magnitude of both topographic and isostatic components amounts to about 10 E.U. while the combined topographic-isostatic effect reduces to about 1 E.U.. In this paper, the focus lies on the comparison between the classical isostatic models and the generalized Helmert model, consistently using a rigorous spherical formulation for all models. By variation of the depth of the condensation layer, it is possible to demonstrate that the classical isostatic models become equivalent to the Helmert model related to a specific condensation depth d. E.g., the standard Airy-Heiskanen model related to a normal crustal thickness T = 25 km is best approximated using the compensation depth d = 24 km in the generalized Helmert model. Instead of the conventional remove-restore techniques which lead to high numerical efforts, the use of the generalized Helmert model is recommended.