Analysis of geomagnetic data using wavelet frames

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The aim of this proposal is to establish frames of spherical wavelets as a versatile modelling tool in geomagnetism. We plan to develop a global and regional magnetic field modelling method which can take into account the very inhomogeneous distribution of ground-based geomagnetic measurements together with the more homogeneously distributed data provided by satelite measurements. The emphasis of this project is on the geophysical implementation of the by now well established mathematical technique called wavelet frames. The improvement compared to the commonly used method of spherical harmonic analysis is the essentially regional support of basis functions. It will allow high resolution in areas covered well by data while avoiding spurious structure in sparsely covered regions. By now improvements of this method could be shown for scalar data and first results for vector data could be obtained. The tasks projected in this proposal are optimizing (grid, degree, scales) the frames obtained so far to improve specific field representation, studying the feasability of regional modelling using local wavelet frames, incorporating magnetospheric sources in field models and incorporating time dependency and non-linear data (e.g. intensity measurements).