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Multiscale Solution for the Molodensky Problem on Regular Telluroidal Surfaces

  • Based on the well-known results of classical potential theory, viz. the limit and jump relations for layer integrals, a numerically viable and e±cient multiscale method of approximating the disturbing potential from gravity anomalies is established on regular surfaces, i.e., on telluroids of ellipsoidal or even more structured geometric shape. The essential idea is to use scale dependent regularizations of the layer potentials occurring in the integral formulation of the linearized Molodensky problem to introduce scaling functions and wavelets on the telluroid. As an application of our multiscale approach some numerical examples are presented on an ellipsoidal telluroid.

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Author:Willi Freeden, Carsten Mayer
URN (permanent link):urn:nbn:de:hbz:386-kluedo-13568
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (14)
Document Type:Preprint
Language of publication:English
Year of Completion:2004
Year of Publication:2004
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2004/12/02
Tag:Molodensky Problem; Wavelet Analysis auf regulären Flächen
Molodensky problem; harmonic scaling functions and wavelets; multiscale approximation on regular telluroidal surfaces
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems
45-XX INTEGRAL EQUATIONS / 45Bxx Fredholm integral equations / 45B05 Fredholm integral equations
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011