The construction of sparse models of Mars's crustal magnetic field

Previous work has shown that Mars's crustal magnetic field is highly nonuniform, with large regions of either very weak or very strong magnetic field. Commonly used techniques of magnetic field analysis (such as truncation or L2 regularization of a spherical harmonic expansion) have a smoothing effect and are not well suited to representing magnetic fields which may have regions of zero magnetization or sharp contrasts in magnetization. Indeed, there is no a priori reason to expect that the crustal field should be smooth. In this study, we use L1 and elastic net regularizations of Mars Global Surveyor magnetometer data to create sparse representations of the magnetic field of Mars, and examine what percentage of the surface field is actually required to have nonzero magnetization in order to fit the data. We find that solutions with up to 98% or higher sparsity yield an adequate fit to the data, although solutions with 85% sparsity are more realistic. These sparse solutions are substantially different from other smoothed solutions. The choice of inversion method used to analyze the data significantly impacts the resulting field morphology, which may affect the resulting physical interpretation. Plain Language Summary We reanalyze magnetic field data from the Mars Global Surveyor mission (1997-2006) using new math techniques. Previous studies used techniques that generate smooth solutions, but there is no reason to assume the crustal field should be smooth. Our paper uses math designed to generate sparse solutions (where most of the solution is zero) to make new models of Mars's magnetic field. These models look very different from past models and show that only about 15% of Mars's surface needs to be magnetized in order to explain Mars Global Surveyor data. Our models do, however, agree with previous estimates for when the Martian dynamo shut off. Overall, this study provides a caution for future studies, suggesting the choice of analysis method can significantly affect the interpretation of local features of Mars's field.