3D inversion of magnetic data using Lanczos bidiagonalization and unstructured element

This work presents an algorithm to construct a 3D magnetic susceptibility property from magnetic geophysical data. Physical model discretization has substantial impact on accurate inverse modeling of the sought sources in potential field geophysics, where structural meshing suffers from edge preserving of complex-shaped geological sources. In potential field geophysics, a finite-element (FE) methodology is usually employed to discretize the desired physical model domain through an unstructured mesh. The forward operator is calculated through a Gauss-Legendre quadrature technique rather than an analytic equation. To stabilize mathematical procedure of inverse modeling and cope with the intrinsic non-uniqueness arising from magnetometry data modeling, regularization is often implemented by utilizing a norm-based Tikhonov cost function. A so-called fast technique, “Lanczos Bidiagonalization (LB) algorithm”, can be utilized to solve the central system of equations derived from optimizing the function, where it decreases the execution time of the inverse problem by replacing the forward matrix with a lower dimension one. In addition, to obtain best regularization parameter, a weighted generalized cross-validation (WGCV) curve is plotted, that makes a balance between misfit norm and model norm introduced in the cost function. In order to tackle the normal propensity of physical structures to focus at the shallow depth, an expression of depth weighting is used. This procedure is applied to a synthetic scenario presenting a complex-shaped geometry along with a real set of magnetic data in central part of Iran. So the capability of the proposed algorithm for inversion indicates the accuracy of the inversion algorithm. Additionally, the modeling results pertaining to a field case study are in good agreement with the drilling data.