nonlinear computation of the gravity field of an aspherical planetMrs Virginie Belleguic^{(1)}and Dr Philippe Lognonné^{(1)} ^{(1)}
Institut de physique du globe de Paris,
4, Av. de Neptune,
94107 Saint Maur,
France
Abstract GOCE will provide global gravity models of the Earth with an improvement of an order of magnitude, with a resolution in wavelength greater than 100 km. To take full advantage of these highquality data in the determining the distribution of mass density, we need an accurate way to calculate the predicted gravity field caused by topography or internal structures and lateral variations in density. In addition, incorrect estimation of their contributions to the global field lead to misinterpretations of the gravity signal. The method presented here allows the computation of the global gravity field and its derivatives inside and outside a planet for models with lateral density variations as well as lateral variations of interfaces. So far, the global methods already developped are either based on the masssheet approximation, or allow only the evaluation of the gravity field at a single given altitude. In addition, these methods use ClebschGordan coefficients for the computation of lateral variations effects and are thus computer intensive, allowing only the study of large scale structures. Our method is based on the propagation (and not a downard continuation) of a solution of Newton's equation from a given height, for example the observation point, toward the center of the planet. In order to reduce the computation time, all the lateral variational effects and the angular derivations are performed using Legendre tranforms between the physical and spectral domains. Such an approach reduces by l^2 the amount of computation in angular order, thereby allowing nonlinear modeling to be performed for models with high angular degrees. The computation is adapted to the modeling of gravity fields for models with lateral variations larger than 200 in angular orders and might therefore be used for a rapid modeling of the gravity fields of Mars, the Moon and the Earth at tectonic scales.
Keywords: ESA European Space Agency  Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry
