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We provide a space domain oriented separation of magnetic fields into partsgenerated by sources in the exterior and sources in the interior of a givensphere. The separation itself is well-known in geomagnetic modeling, usually interms of a spherical harmonic analysis or a wavelet analysis that is sphericalharmonic based. In contrast to these frequency oriented methods, we use a morespatially oriented approach in this paper. We derive integral representationswith explicitly known convolution kernels. Regularizing these singular kernelsallows a multiscale representation of the internal and external contributionsto the magnetic field with locally supported wavelets. This representation isapplied to a set of CHAMP data for crustal field modeling

LOCALLY SUPPORTED WAVELETS FOR THE SEPARATION OF SPHERICAL VECTOR FIELDS WITH RESPECT TO THEIR SOURCES