3D magnetic sparse inversion using an interior-point method

Abstract

Rock susceptibility measurements are sometimes taken on outcrop and borehole rocks, and they provide valuable information for constraining magnetic data inversion. We have developed two approaches for 3D magnetic sparse inversion that effectively take advantage of the rock susceptibility information. Both approaches minimize a total objective function subject to bound constraints using an interior-point method. The first approach directly minimizes an [Formula: see text]-norm of the susceptibility model by keeping the bounds positive, in which case the objective function is differentiable in the feasible region. The second approach minimizes a more generalized [Formula: see text]-like-norm ([Formula: see text]) of the susceptibility model by approximating the [Formula: see text]-like-norm inversion as an iteratively reweighted least-squares problem. Moreover, this approach allows the model values to be either positive or negative. We also revealed the equivalence of our approaches and the binary inversion. The recovered models of both approaches are characterized by sharp boundaries. However, the credibility of recovered boundaries depends on the accuracy and validity of the user-specified upper and lower bounds. Our approaches are tested on the synthetic data and field data acquired over a copper-nickel deposit.