Using Localization Constraints for the Unique Reconstruction of Magnetizations

Abstract:

In general, the reconstruction of (vertically integrated) magnetizations on the Earth's surface from the knowledge of the corresponding magnetic field in the exterior of the Earth is highly non-unique. However, we show that if one assumes that the magnetization vanishes in a certain region (i.e., if it is locally supported), this can improve the non-uniqueness issues of reconstructing the magnetization. In particular, induced magnetizations for which the inducing field (i.e., the Earth's main magnetic field) is known can be recovered uniquely. In the case of general (vertically integrated) magnetizations, one does not get uniqueness but one can at least recover more contributions than without the additional assumption of local support. We illustrate the results by some examples.