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Locally Supported Wavelets for the Separation of Spherical Vector Fields with Respect to their Sources

  • We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of a spherical harmonic analysis or a wavelet analysis that is spherical harmonic based. However, it can also be regarded as a modification of the Helmholtz decomposition for which we derive integral representations with explicitly known convolution kernels. Regularizing these singular kernels allows a multiscale representation of the magnetic field with locally supported wavelets. This representation is applied to a set of CHAMP data for crustal field modeling.

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Author:Christian Gerhards
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16835
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (48)
Document Type:Report
Language of publication:English
Year of Completion:2011
Year of Publication:2011
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2011/02/08
Tag:Green’s function; locally supported wavelets; magnetic field; single layer kernel; spherical decomposition
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A30 Approximation by other special function classes
42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems
86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A99 Miscellaneous topics
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011