Modelling the Earth's gravity field using wavelet frames

摘要

Present and forthcoming satellite gravity missions provide us with new and unique datasets in order to model the Earth's gravity field at 100 km resolution. These new models will bring significant advances in our understanding of the Earth's structure and dynamics. However, it will be necessary to combine satellite data with surface and airborne measurements in order to improve the short wavelength components of the gravity field. The derived regional models with an increased spatial resolution will be used to carry out geodynamic studies at lithospheric or crustal scale. Whereas the classical spherical harmonics decomposition leads to strong numerical difficulties when dealing with local features, wavelet-based representations can handle the local scales as well as the global ones; they should thus be extremely useful to derive local models taking into account data of different origins. Here we describe the construction of wavelet frames on the sphere based on the Poisson multipole wavelet. Those wavelets are of special interest for field modelling since their shape is linked to the potential of multipole sources, and their scaling parameter to the multipole depth (Holschneider et al, 2003). We also compute a local wavelet decomposition of the gravity field at high resolution from evenly and unevenly distributed data using least squares collocation. Our first results show the efficiency of such a representation.