The analysis of gradiometric data with Slepian functions

In the last two years the representation of harmonic functions defined only through data on spheres with polar caps, has been studied by the authors, using a set of functions orthonormal both on the sphere and on the data set, which is a generalization of planar Slepian functions to the spherical case. This idea can be applied for instance to derive the anomalous potential T both at satellite's altitude and at ground level, from a set of satellite radial gradiometric observations, T-rr. The method has been compared with a simple harmonic analysis showing a superior capability of retrieving the unknown potential, particularly close to the polar caps. (C) 2000 Elsevier Science Ltd. All rights reserved.