Topographic-Isostatic Reductions in Satellite Gravity Gradiometry Based on a Generalized Condensation Model

Abstract

In satellite gravity gradiometry, the gravitational signals from the Earth’s topography and its isostatic compensation still exist in the gravity gradients observed along the satellite orbit. Due to the high-frequency behaviour of the combined topographic-isostatic effect, downward continuation of the gravitational signal from satellite height to sea level is rather difficult, requiring some mathematical method of regularization. On the other hand, the complete calculation of topographic-isostatic effects according to, say, the Airy-Heiskanen isostatic model is too laborious for the practical evaluation of gravity gradiometry data. In this paper, another approach is proposed, which is based on a generalized condensation model corresponding to Helmert’s first condensation model; here the condensed masses are assumed to be situated on a surface at a constant depth D below the geoid. The respective formulae representing the effects of the topographic and condensation masses on the vertical gravity gradient (V_rr) at satellite level are derived. A simulation based on the JGP95E rock-equivalent terrain model proves that the order of magnitude of both topographic and condensation effects is about 10 E.U. The magnitude of the combined topographic-condensation effect is much smaller, amounting to 0.6 E.U. and 0.06 E.U. for Helmert’s first and second condensation model, respectively.