An efficient three-dimensional (3D) inversion algorithm for recovering magnetic targets when remanence exists

In mineral exploration, the ores with different magnetic susceptibility can be well delineated by physical property inversion of magnetic data. However, further wide applications of the magnetic inversion method have been seriously restricted by the existence of strong remanence and the computation of large-scale datasets. To solve these two problems, this study innovatively presents an efficient magnetic inversion algorithm in the presence of strong remanence. The weighted data misfit term and regularization term were used to establish the objective function. The detailed related formulas were derived and presented. For numerical computation, the Taylor series approximation was introduced in the objective function to linearize the relationship between the transformed magnetic data and magnetic susceptibility. The objective function was converted to a general Tikhonov form by several matrix transformations. To realize computational efficiency, a fast randomized algorithm was utilized to efficiently solve the Tikhonov problem and to efficiently determine the suitable regularization parameter along with the generalized cross-validation (GCV) method. Comparative tests on synthetic example show the effectiveness and efficiency of the proposed algorithm. The proposed efficient algorithm is successfully applied to two sets of real magnetic data, and the inversion results are verified.