Abstract
This paper deals with multiscale modeling of poloidal and toroidal fields such as geomagnetic field and currents. The wavelets are developed from scale-dependent regularizations of the Green function with respect to the Beltrami operator. They are constructed as to be locally compact, thus, allowing a locally reflected (zooming-in) reconstruction of the geomagnetic quantities. Finally, a reconstruction algorithm is indicated in form of a tree algorithm.
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Freeden, W., Gerhards, C. Poloidal and Toroidal Field Modeling in Terms of Locally Supported Vector Wavelets. Math Geosci 42, 817–838 (2010). https://doi.org/10.1007/s11004-009-9262-0
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DOI: https://doi.org/10.1007/s11004-009-9262-0