A differential equation-based framework for magnetic inversion

Abstract

Although magnetic data are widely inverted to estimate subsurface susceptibility or remanent magnetization, most current methods do not explicitly account for the complicating factors of both remanent magnetization and self-demagnetization. This limits their applicability to recover accurate physical property distributions when highly susceptible and remanently magnetized materials are present. Here, we introduce a general finite-volume framework for forward modeling and inversion of magnetic data using the differential form of Maxwell's equations for magnetics. The aims of this framework are twofold. First, the approach models directly in terms of intrinsic physical properties, specifically magnetic susceptibility and remanent magnetization, which is advantageous for incorporating a priori information. Second, the differential approach enables magnetic vector inversion (MVI) to be performed on large scales with lower memory requirements than standard integral approaches. We validate the formulation against analytic and integral solutions and show that it accurately models induced magnetization in highly susceptible materials while accounting for remanent magnetization. Using a synthetic inversion example, we show that jointly inverting for susceptibility and remanent magnetization increases the non-uniqueness of the problem, but that incorporating appropriate a priori information through a parametric formulation leads to improved recovery of both geometry and physical properties, as compared to a parametric MVI inversion. We then apply the differential approach to magnetic vector inversion and show that it scales favorably to very large-scale problems. We invert data from the Mt. Isa Inlier in Australia for a model with 47.3 million model parameters in under two hours.