3D sparse inversion of magnetic amplitude data when strong remanence exists

Abstract

Three-dimensional inversion for susceptibility distributions is a common approach for quantitative interpretation of magnetic data. However, this approach will fail when strong remanence exists because the total magnetization direction is unknown. Magnetic amplitude inversion can reduce remanence effects and thus improve reconstructed results. In this paper, we propose a sparse magnetic amplitude inversion method which minimizes an L0-like-norm of model parameters subject to bound constraints. By using the iteratively reweighed least squares technique, the bound-constrained L0-like-norm sparse inversion is transformed to a sequence of bound-constrained nonlinear least squares subproblems. To deal with the bound constraints, we use a logarithm barrier algorithm to solve each subproblem. Compared with the classical L2-norm inversion method, the proposed sparse method utilizes the known physical property information to produce binary results characterized by sharp boundaries. This method is tested on synthetic data produced by a dipping dyke model and a field data set acquired in Australia.