空间波数混合域三维各向异性强磁性介质磁场数值模拟

各向异性普遍存在于强磁性体矿物中，为研究各向异性强磁性体磁场响应特征，本文提出一种空间波数混合域三维各向异性磁场数值模拟方法.该方法首先将各向异性强磁性体磁位满足的三维偏微分方程进行水平方向二维傅里叶变换，将其降为不同波数之间相互独立的一维常微分方程；然后加载准确的上下边界条件，采用二次插值有限单元法计算一维常微分方程，得到五对角方程，采用追赶法进行高效求解；最后采用迭代法求解场分量，引入紧算子保证迭代稳定收敛；综合傅里叶变换的高效性、一维方程求解的快速性和迭代算法的稳定性，实现各向异性强磁性体磁场的三维高效、高精度数值模拟.设计各向异性椭球模型验证算法的正确性，并分析紧算子对不同各向异性磁化率模型的迭代收敛性；与COMSOL Multiphysics软件对比计算效率，表明相同节点下本文算法效率优于常规三维有限元方法，且计算节点总数越多优势越明显.重点研究各向异性参数改变对VTI、HTI、TTI强磁介质异常场响应的影响.最后采用某磁铁矿DEM高程数据模拟起伏地形对各向异性强磁性体磁异常场幅值和形态的影响，体现出本文算法对各向异性强磁性体大规模复杂地形的适应性.

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 high-precision 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.