Spaceborne gravitational field determination by means of locally supported wavelets |
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| Authors: | W Freeden M Schreiner |
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| Institution: | (1) Geomathematics Group, University of Kaiserslautern, 67653 Kaiserslautern, P.O. Box 3049, Germany;(2) Laboratory for Industrial Mathematics, University of Buchs, Werdenbergstrasse 4, CH, 9471 Buchs, Switzerland |
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| Abstract: | In space-borne gravitational field determination, two challenges are inherent. First, the continuation of the data down to
the surface of the Earth is an ill-posed problem, requiring therefore regularization techniques. Second huge data sets result
requiring efficient numerical methods. In this paper, we show how locally supported wavelets on the sphere can be developed
by means of a spherical version of the so-called up function. By construction, the corresponding scaling functions and wavelets
are infinitely smooth, so that they can be used for regularization purposes. In particular, we show how the ill-posed pseudo-differential
equations coming from satellite missions can be regularized by efficient numerical schemes using locally supported wavelets.
These methods seem in particular to be interesting for regional gravity field modelling. |
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| Keywords: | Locally supported spherical wavelets Ill-posed problems Tree-algorithms Rregularization Satellite gravity gradiometry Satellite-to-satellite tracking |
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