The ES-GNF Method of Unstructured Tetrahedral Mesh for Fast Inversion of Gravity and Magnetic Data With Undulating Terrain

The inversion of gravity and magnetic data with unstructured tetrahedral mesh is the main means to obtain subsurface information for exploring regions with undulating terrain. However, carrying out these inversions with unstructured tetrahedral meshes is time-consuming. In this work, we propose a novel method for fast inversion with an unstructured tetrahedral mesh, which we call the equivalent surface and Gaussian quadrature with a nonuniform fast Fourier transform (ES-GNF) method. The ES-GNF method can improve the kernel matrix computing efficiency in the inversion process. We use the equivalent surface element characteristics of the common facets of adjacent tetrahedral cells to reduce the kernel matrix calculation process and apply Gaussian quadrature with a nonuniform fast Fourier transform (NUFFT) method to efficiently calculate the function of a triangular facet in the kernel matrix. Calculation analysis and synthetic model tests verify that the computing efficiency of the ES-GNF method is nearly $10 \times $ that of the traditional method, with almost no reduction in precision and no additional memory requirements. Finally, we apply the ES-GNF method to obtain physical property distributions in order to analyze deep magma and the source of ore-forming material in the southern Greater Khingan Mountains and the northern margin of the North China Craton. The inversion results indicate that mineral resources are under the proximal control of volcanic activity. Furthermore, magma has migrated through large faults to the shallow crust and formed metallic ores.