Approximating the Earth's Magnetic Field with Locally Supported Kernel Functions

Abstract:

The Earth's magnetic field consists of various source regions, mainly the core, the lithosphere, the ionosphere, and the magnetosphere. The separation of magnetic field measurements into the different sources as well as their modeling is a difficult task (mathematically as well as from a physical point of view). In this talk we show  how locally supported (vectorial and tensorial) kernel functions can be constructed to suit the problem of separating vector fields into contributions of interior and exterior origin, as well as the reconstruction of ionospheric current systems. Furthermore, we present some considerations for solving boundary value problems on subdomains of the sphere.