22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

An Inverse Magnetization Problem on the Sphere with Localization Constraints

22 Sep 2021, 12:00
20m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

Speaker

Xinpeng Huang (TU Bergakademie Freiberg, Institute of Geophysics and Geoinformatics)

Description

We study an inverse magnetization problem arising in geo- and planetary magnetism. This problem is non-unique and the null space can be characterized by the Hardy-Hodge decomposition. The additional assumption that the underlying magnetization is spatially localized in a subdomain of the sphere (which can be justified when interested, e.g., in regional magnetic anomalies) ameliorates the non-uniqueness issue so that only the tangential divergence-free contribution remains undetermined. In a previous reconstruction approach, we addressed the localization by including an additional penalty term in the minimizing functional. This, however, requires the coestimation of the undetermined divergence-free contribution. Here, we present a first attempt at more directly including the localization constraint without requiring such a coestimation. In addition, we show that the localization constraint is closely connected to the problem of extrapolation in Hardy spaces.

Primary authors

Alexander Kegeles (TU Bergakademie Freiberg, Institute of Geophysics and Geoinformatics) Christian Gerhards (TU Bergakademie Freiberg, Institute of Geophysics and Geoinformatics) Xinpeng Huang (TU Bergakademie Freiberg, Institute of Geophysics and Geoinformatics)

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