Local Multiscale Modelling of Geoid Undulations from Deflections of the Vertical |
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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, Buchs, 9471, Switzerland
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| Abstract: | This paper deals with the problem of determining a scalar spherical field from its surface gradient, i.e., the modelling of geoid undulations from deflections of the vertical. Essential tools are integral formulae on the sphere based on Green’s function of the Beltrami operator. The determination of geoid undulations from deflections of the vertical is formulated as multiscale procedure involving scale-dependent regularized versions of the surface gradient of Green’s function. An advantage of the presented approach is that the multiscale method is based on locally supported wavelets. In consequence, local modelling of geoid undulations are calculable from locally available deflections of the vertical |
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