3-D Magnetic Unstructured Inversion

Magnetic inversion methods based on structured grids have been used extensively in geomagnetic research. Nevertheless, structured grids limit the modeling capability and accuracy of models with arbitrary geometries. To address these challenges, 3-D magnetic numerical forward modeling and inversion methods using an unstructured tetrahedral grid based on a partial differential equation (PDE) framework are proposed. The methods are derived from Maxwell's partial equations and constructed using the finite element method. Arbitrary undulating topographies, complex geometries, and demagnetization effects can be represented exactly, leading to high-accuracy forward modeling and inversion solutions. The proposed methods are suitable for both local- and global-scale magnetic data interpretation, for example, in mineral exploration and tectonic research. A synthetic example and real airborne magnetic survey data collected from Mount Iliamna, Alaska, USA, are tested. The results demonstrate that the novel methods significantly improve the capability and accuracy of magnetic data interpretation. Plain Language Summary 3-D magnetic data inversion is widely used to map the 3-D subsurface susceptibility of geological structures according to forward modeling of the physical processes associated with the anomalous magnetic field B-s induced by the ambient geomagnetic field B-0. The conventional magnetic inversion methods were built based on structured grids composed of orthogonal cuboids and employ an analytic forward solver. However, complicated geological structures, such as undulating topographies and interfaces, cannot be readily described with a limited number of orthogonal cuboids. The resulting geometrical modeling errors decrease the accuracy of the forward modeling and related inversion solutions and increase the ambiguity of data interpretation. To address these problems, we reformulate the forward modeling and inversion methods based on Maxwell's equations with the finite element method and an unstructured tetrahedral grid. The proposed method can recover an arbitrary complicated geometric model by an unstructured tetrahedral grid. The experimental results demonstrate that the proposed methods significantly improve the capability and accuracy of 3-D magnetic data inversion and interpretation.