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Spherical decompositions in a global and local framework: theory and an application to geomagnetic modeling

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Abstract

This paper gives an overview on decompositions of vector fields on the sphere that are of importance in geoscientific modeling. Various versions of the Mie and Helmholtz decomposition are presented. A special emphasis is set to integral representations for the different contributions, which is of interest, e.g., in numerical applications. Furthermore, the decompositions are treated in a global framework on the entire sphere and in a local framework on regular subsurfaces. In the end, an application to the modeling of ionospheric currents is indicated.

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  1. TU Kaiserslautern, Geomathematics Group, PO Box 3049, 67663, Kaiserslautern, Germany

    C. Gerhards

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  1. C. Gerhards
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Gerhards, C. Spherical decompositions in a global and local framework: theory and an application to geomagnetic modeling. Int J Geomath 1, 205–256 (2011). https://doi.org/10.1007/s13137-010-0011-9

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