## 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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Verfasserangaben: Thorsten Maier urn:nbn:de:hbz:386-kluedo-13029 Schriften zur Funktionalanalysis und Geomathematik (7) Bericht Englisch 2004 2004 Technische Universität Kaiserslautern 05.02.2004 Geomagnetismus; Helmholtz-Zerlegung; Mie-Darstellung; Vektor-WaveletsGeomagnetic Field Modelling; Helmholtz-Decomposition; Mie-Representation; Vectorial Wavelets Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 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] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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