Time-Space Dependent Multiscale Modelling of the Magnetic Field Using Satellite Data (i.e. CHAMP-data)

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The purpose of the project MAMF is to introduce a multiscale method using trial fields for the time-space dependent computation of the Earth`s magnetic field from satellite data within source regions of ionospheric and magnetospheric currents.On the one hand, space-dependent modelling will be essentially based on two geomagnetic keystones, namely the Mie-representa- tion of a solenoidal vector field (such as the Earth`s magnetic field) in terms of toroidal and poloidal parts and the Helmholtz decomposition of tangential fields on a spherical orbit. Vector wavelets will be shown to provide adequate tools for multiscale geomagnetic modelling in form of a multiresolu- tion analysis, thereby completely circumventing the numerical obstacles caused by vector harmonics.On the other hand, time-dependent modelling will be proposed as a multiscale technique by means of (one-dimensional) Legendre- wavelets.Altogether, an integrated wavelet concept of time-space depen- dent (MAMF) resolution (in quasi-static formulation) is proposed as a twofold multiscale procedure (in tensor-product form) using satellite data, (for example, CHAMP-data).