Stable Extrapolation of Field Produced by Volumetric Magnetizations

Overview & Synopsis

In the particular setup of the planar scanning Superconducting Quantum Interference Device (SQUID), the vertical component of the magnetic field produced by a magnetized sample is measured. Recovering the sample’s internal magnetization from this measured data, an inverse problem that is central in the field of paleomagnetism, is a severely ill-posed process. Moreover, standard recovery methods are further hindered by limited measurements and the noise therein. To address these issues, we develop a method to simultaneously extrapolate and denoise the field data, thereby solving a preliminary inverse problem for an auxiliary function of the magnetization. The proposed approach is based on a regularization framework that exploits an explicit field-magnetization relation. To encode the harmonic structure of the problem, we construct a set of basis functions derived from spherical harmonics via the Kelvin transform. The method is applicable to both volumetric and planar magnetization distributions.