Locally Supported Wavelets for the Separation of Spherical Vector Fields with Respect to their Sources

TL;DR

This paper introduces a spatially oriented wavelet method for separating magnetic fields into internal and external sources on a sphere, providing a multiscale, locally supported analysis that improves crustal field modeling.

Contribution

It develops a novel spatially oriented wavelet approach with explicit integral kernels for separating spherical vector fields by source location.

Findings

Effective separation of magnetic field sources demonstrated on CHAMP data.

Multiscale, locally supported wavelet representation enhances crustal field modeling.

Regularized kernels enable stable, spatially localized analysis.

Abstract

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.