Gravity gradiometry is strongly sensitive to the gravity field induced by the topographic and isostatic masses of the Earth. The downward continuation of the gravitational signals from satellite height to sea level is rather difficult because of the high frequency behaviour of the combined topographic-isostatic effect. Therefore a topographic-isostatic reduction is proposed in order to smooth the signals. Based on different isostatic models (Airy-Heiskanen, Pratt-Hayford, Airy-Heiskanen/Pratt-Hayford), the generalized Helmert model and the crust density model via CRUST2.0 the topographic-isostatic effects are calculated for a GOCE-like satellite orbit. Using tesseroids modelled by Gauss-Legendre cubature (3D) leads to high numerical efficiency. For the Marussi tensor of the gravitational potential the order of magnitude of both topographic and isostatic components is about +/-8 E.U., while the combined topographic-isostatic effect varies from +/-0.08 E.U. (Helmert II). +/-0.8 E.U. (Airy-Heiskanen, Pratt-Hayford, Airy-Heiskanen/Pratt-Hayford, Helmert I) and 4 E.U. (crust density model). In this paper, the focus is put on the gravitational effect of massive bodies in regard to the comparison between the classical isostatic models, the condensation models of Helmert and the crust density model.

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.

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,) 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.

Gravity gradiometry is strongly sensitive to the gravity field induced by the topographic and isostatic masses of the Earth. The downward continuation of the gravitational signals from satellite height to sea level is rather difficult because of the high-frequency behaviour of the combined topographic and isostatic effect. Therefore it is reasonable to smooth the gravitational signals by some topographic-isostatic reduction method. In addition, the application of the conventional remove-restore techniques to gravity gradiometry, using for example the decomposition in prisms (3D- integrals) and the Airy-Heiskanen isostatic model, leads to high numerical efforts. In this paper, the focus is on the comparison of the Airy-Heiskanen model with the Helmert condensation models I and II. The difference in terms of the second radial derivative of the potential between the Airy-Heiskanen model and the first Helmert model (D = 21 km) is much smaller ( = 0.06 E.U.) than the difference between the Airy-Heiskanen model and the second Helmert model ( = 0.15 E.U.). However, by varying the depth of the condensation layer of the first Helmert model, the Airy-Heiskanen model becomes practically equivalent to Helmert model I at a depth of about 32 km.