## Wavelet Analysis of the Geomagnetic Field Within Source Regions of Ionospheric and Magnetospheric Currents

• A multiscale method is introduced using spherical (vector) wavelets for the computation of the earth's magnetic field within source regions of ionospheric and magnetospheric currents. The considerations are essentially based on two geomathematical keystones, namely (i) the Mie representation of solenoidal vector fields in terms of toroidal and poloidal parts and (ii) the Helmholtz decomposition of spherical (tangential) vector fields. Vector wavelets are shown to provide adequate tools for multiscale geomagnetic modelling in form of a multiresolution analysis, thereby completely circumventing the numerical obstacles caused by vector spherical harmonics. The applicability and efficiency of the multiresolution technique is tested with real satellite data.

Author: Michael Bayer, Willi Freeden, Thorsten Maier urn:nbn:de:hbz:386-kluedo-8157 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (217) Preprint English 1999 1999 Technische Universität Kaiserslautern 1999/10/06 Helmholtz decomposition ; Mie representation ; geomagnetic field modelling from MAGSAT data; multiresolution analysis ; vector wavelets Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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