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Wavelet Modelling of the Spherical Inverse Source Problem with Application to Geomagnetism

  • The article is concerned with the modelling of ionospheric current systems from induced magnetic fields measured by satellites in a multiscale framework. Scaling functions and wavelets are used to realize a multiscale analysis of the function spaces under consideration and to establish a multiscale regularization procedure for the inversion of the considered vectorial operator equation. Based on the knowledge of the singular system a regularization technique in terms of certain product kernels and corresponding convolutions can be formed. In order to reconstruct ionospheric current systems from satellite magnetic field data, an inversion of the Biot-Savart's law in terms of multiscale regularization is derived. The corresponding operator is formulated and the singular values are calculated. The method is tested on real magnetic field data of the satellite CHAMP and the proposed satellite mission SWARM.

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Author:Carsten Mayer
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (5)
Document Type:Report
Language of publication:English
Year of Completion:2004
Year of Publication:2004
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2004/01/22
Tag:Biot-Savart Operator; Vektorkugelfunktionen; Vektorwavelets
Biot-Savart operator; vector spherical harmonics; vectorial wavelets
GND-Keyword:Wavelet; Inverses Problem; Regularisierung
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
65-XX NUMERICAL ANALYSIS / 65Rxx Integral equations, integral transforms / 65R32 Inverse problems
65-XX NUMERICAL ANALYSIS / 65Zxx Applications to physics / 65Z05 Applications to physics
86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A25 Geo-electricity and geomagnetism [See also 76W05, 78A25]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011