Locally Supported Wavelets for the Separation of Spherical Vector Fields with Respect to their Sources
For geomagnetic modelers, this provides a spatially localized alternative to frequency-based separation methods, though it is an incremental improvement over existing wavelet approaches.
The authors present a space-domain method to separate spherical vector fields into internal and external source contributions using locally supported wavelets, applied to CHAMP satellite data for crustal field modeling.
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.