Distance-regularized level set inversion of magnetic data

Abstract

Inversion is one of the key and difficult issues in potential field data processing and interpretation, and high-precision inversion has long been a popular research topic. We develop the distance-regularized level set inversion of the magnetic data (DRLSI-M) method. A double-well function is introduced into the objective function of the level set inversion, and we take advantage of its mathematical properties to minimize the gradient of the level set function so that it reaches a minimum value at points 0 and 1. As a result, the distance-regularized term not only replaces the costly reinitialization process so that the level set function maintains a signed distance property but also stabilizes the evolution of the level set function. When solving for the minimum value of the objective function, we transform the optimization problem into an initial-boundary value problem and solve it with the finite-difference method. The distance-regularized level set inversion method and the reinitialization level set inversion method are tested using three models: a single-level-set double-inclined plate model, a double-level-set double-inclined plate model, and a multiple-level-set three-cuboid model. Through model tests, the soundness of our method is verified and compared with the reinitialization level set inversion method. Our method avoids the limitations such as low efficiency and instability caused by the reinitialization of the level set inversion method. Furthermore, we apply our method for the inversion of aeromagnetic data from the Jinchuan copper-nickel mine. The results are consistent with the known geologic information, thus validating the practicality and effectiveness of DRLSI-M. The distance-regularized level set inversion method provides a theoretical basis for deep mine exploration.