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. Plain Language Summary: Rocks may acquire records of the ambient magnetic field that can be preserved over geological timescales. This occurs when ferromagnetic minerals in those rocks cool, crystallize, or experience a pressure pulse. Magnetic microscopes are very sensitive instruments that can measure weak magnetic fields produced by rock samples at close proximity. They enable the analysis of rocks that were previously inaccessible to traditional paleomagnetic instrumentation. However, special data analysis techniques are required for obtaining the magnetic record preserved in a rock from the measurements collected by a magnetic microscope. We developed a novel analytical technique that allows us to use those instruments to successfully study small rock samples with nonuniform magnetization. We validate and demonstrate the technique using magnetic microscopy measurements of impact spherules from Lonar crater, India and mineral grains extracted from the meteorite Dominion Range 08006. Key Points: A spherical harmonic multipole expansion model can be used to estimate net magnetic moment from magnetic microscopy dataPlanar geometry and indeterminacy of the origin location for the multipole expansion require regularization of an ill‐posed inverse problemAccurate moment estimates can be obtained for measurements of compact geological samples even with low signal‐to‐noise ratios [ABSTRACT FROM AUTHOR]