Three-dimensional numerical modeling of anisotropic magnetic field for high susceptibility in space-wavenumber domain

Anisotropy generally exists inhigh magnetism minerals. To study the magnetic field response characteristics of anisotropic high magnetism minerals, a numerical simulation algorithm of the three-dimensional anisotropic magnetic field in spatial wavenumber mixed domain is proposed in this paper. Firstly, the three-dimensional partial differential equation satisfied by the magnetic potential of anisotropic high magnetism bodies is transformed into a one-dimensional ordinary differential equation independent of different wavenumbers by two-dimensional Fourier-transform in the horizontal direction. Then the accurate upper and lower boundary conditions are loaded. The quadratic interpolation finite element method is used to calculate the one-dimensional ordinary differential equation. The pentadiagonal equation obtained is solved by the pursuit method efficiently. Finally, the iterative method is used to solve the field components, and the compression operator is introduced to ensure the stable convergence of the iteration. This method combines the high efficiency of Fourier transform, the rapidity of solving the one-dimensional equations, and the stability of iterative algorithm, and realizes the three-dimensional high-efficiency and highprecision numerical simulation of anisotropic high magnetism body magnetic field. The anisotropic ellipsoid model is designed to verify the correctness of the algorithm, and the iterative convergence of the compression operator for different anisotropic susceptibility models is analyzed. Compared with COMSOL Multiphysics software, the calculation efficiency shows that the efficiency of this algorithm is better than the conventional three-dimensional finite element method under the same nodes. The more the total number of computing nodes, the more obvious the computing advantage will be. The effects of anisotropic parameters on the abnormal field responses of VTI, HTI, and TTI high magnetism media are studied. Finally, the DEM elevation data of magnetite is used to simulate the influence of undulating topography on the amplitude and shape of magnetic anomaly field of anisotropic high magnetism media, which reflects the adaptability of this algorithm to large-scale undulating topography and complex anisotropic high magnetism bodies.