Estimating the Net Magnetic Moment of Geological Samples From Planar Field Maps Using Multipoles

Recent advances in magnetic microscopy have enabled studies of geological samples whose weak and spatially nonuniform magnetizations were previously inaccessible to standard magnetometry techniques. A quantity of central importance is the net magnetic moment, which reflects the mean direction and the intensity of the magnetization states of numerous ferromagnetic crystals within a certain volume. The planar arrangement of typical magnetic microscopy measurements, which originates from measuring the field immediately above the polished surface of a sample to maximize sensitivity and spatial resolution, makes estimating net moments considerably more challenging than with spherically distributed data. In particular, spatially extended and nonuniform magnetization distributions often cannot be adequately approximated by a single magnetic dipole. To address this limitation, we developed a multipole fitting technique that can accurately estimate net moment using spherical harmonic multipole expansions computed from planar data. Given that the optimal location for the origin of such expansions is unknown beforehand and generally unconstrained, regularization of this inverse problem is critical for obtaining accurate moment estimates from noisy experimental magnetic data. We characterized the performance of the technique using synthetic sources under different conditions (noiseless data, data corrupted with simulated white noise, and data corrupted with measured instrument noise). We then validated and demonstrated the technique using superconducting quantum interference device microscopy measurements of impact melt spherules from Lonar crater, India and dusty olivine chondrules from the CO chondrite meteorite Dominion Range 08006.