## 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.

Author: Carsten Mayer urn:nbn:de:hbz:386-kluedo-12815 Schriften zur Funktionalanalysis und Geomathematik (5) Report English 2004 2004 Technische Universität Kaiserslautern 2004/01/22 Biot-Savart Operator; Vektorkugelfunktionen ; Vektorwavelets Biot-Savart operator; vector spherical harmonics ; vectorial wavelets Inverses Problem ; Regularisierung; Wavelet Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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