Fast inversion of magnetic field maps of unidirectional planar geological magnetization

Scanning magnetic microscopes are being increasingly utilized in paleomagnetic studies of geological samples. These instruments typically map a single component of the sample's magnetic field at close proximity with submillimeter horizontal spatial resolution. However, in most applications, an image of the magnetization distribution within the sample is desired rather than its external magnetic field. This requires carefully solving an ill‐posed inverse problem to obtain solutions that are nearly free of artifacts and consistent with both natural and laboratory magnetization processes. We present a new, fast inversion technique based on classic methods developed for the Fourier domain that retrieves planar unidirectional magnetization distributions from magnetic field maps. Whereas our approach considers the subtle peculiarities of scanning magnetic microscopy which otherwise can complicate this technique, much of the formalism and algorithms described in this work can also be directly applied to province‐scale magnetic field data from aeromagnetic surveys and may be used as an initial step in the modeling of magnetic sources with complex three‐dimensional geometries. We discuss sources of inaccuracy observed in practical implementations of the technique and present strategies to improve the quality of inversions. Numerous examples of inversion of both synthetic and experimental data demonstrate the performance of the technique under different conditions. In particular, we retrieve magnetization distributions of a Hawaiian basalt and compare it to inversions calculated in a previous work. We conclude by showing a reconstructed magnetization for the eucrite meteorite ALHA81001 that displays in high resolution the spatial distribution of high‐coercivity grains within the sample. Key Points Superior inversions of scanning magnetic microscopy data can be quickly obtained The inversion of unidirectional magnetizations with finite extension is unique Enhanced regularization tames artifacts that may appear in the solution