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Wavelet-Mie-Representations for Solenoidal Vector Fields with Applications to Ionospheric Geomagnetic Data

  • A wavelet technique, the wavelet-Mie-representation, is introduced for the analysis and modelling of the Earth's magnetic field and corresponding electric current distributions from geomagnetic data obtained within the ionosphere. The considerations are essentially based on two well-known geomathematical keystones, (i) the Helmholtz-decomposition of spherical vector fields and (ii) the Mie-representation of solenoidal vector fields in terms of poloidal and toroidal parts. The wavelet-Mie-representation is shown to provide an adequate tool for geomagnetic modelling in the case of ionospheric magnetic contributions and currents which exhibit spatially localized features. An important example are ionospheric currents flowing radially onto or away from the Earth. To demonstrate the functionality of the approach, such radial currents are calculated from vectorial data of the MAGSAT and CHAMP satellite missions.

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Author:Thorsten Maier
URN (permanent link):urn:nbn:de:hbz:386-kluedo-13029
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (7)
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):2004/02/05
Tag:Geomagnetismus; Helmholtz-Zerlegung; Mie-Darstellung; Vektor-Wavelets
Geomagnetic Field Modelling; Helmholtz-Decomposition; Mie-Representation; Vectorial Wavelets
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 / 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