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

摘要

We provide a space domain-oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of a spherical harmonic analysis or a wavelet analysis that is spherical harmonic-based. In contrast to these frequency-oriented methods, we use a more spatially-oriented approach in this paper. We derive integral representations with explicitly known convolution kernels. Regularizing these singular kernels allows a multiscale representation of the internal and external contributions to the magnetic field with locally supported wavelets. This representation is applied to a set of CHAMP data for crustal field modeling.