Magnetic forward modelling and inversion for high susceptibility

Abstract

SUMMARY We develop an algorithm to invert geophysical magnetic data to recover 3-D distributions of subsurface magnetic susceptibility when the bodies have complicated geometry and possibly high magnetic susceptibility. For the associated forward modelling problem, a full solution to Maxwell's equations for source-free magnetostatics is developed in the differential equation domain using a finite volume discretization. The earth region of interest is discretized into many prismatic cells, each with constant susceptibility. The resulting system of discrete equations is solved using an ILU-preconditioned Bi-Conjugate Gradient Stabilized (BiCGStab) algorithm. Formulations for total and secondary field computations are developed and tested against analytic solutions and against a solution in the integral equation domain. The finite volume forward modelling method forms the foundation for a subsequent inversion algorithm. The underdetermined inverse problem is solved as an unconstrained optimization problem and an objective function composed of data misfit and a regularization term is minimized using a Gauss–Newton search. At each iteration, the CGLS algorithm is used to solve for the search direction. The inversion code is tested on synthetic data from both geometrically simple and complicated bodies and on field survey data collected over a planted ferrous shipping container.