Three-dimensional magnetotelluric modelling in anisotropic media using the A-phi method
Three-dimensional magnetotelluric modelling in anisotropic media using the A-phi method
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DOI：
10.1080/08123985.2018.1564274
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发表时间：
2019-01
影响因子：
0.9
通讯作者：
Tiaojie Xiao;Xiangyu Huang;Yun Wang
中科院分区：
文献类型：
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作者：
Tiaojie Xiao;Xiangyu Huang;Yun Wang
摘要研究大地电磁法在各向异性介质中的响应具有重要意义。然而，MT各向异性研究主要集中在一维（1D）和二维（2D）解决方案上。因此，我们开发了一种三维（3D）有限元（FE）算法，用于各向异性介质中的大地电磁学建模。这种方法是基于使用库仑测量电位的麦克斯韦方程组的弱公式。本文采用基于节点的有限元方法，采用六面体网格获取系数矩阵值。为了验证该方法的正确性和准确性，将其结果分别与二维各向异性模型和三维任意各向异性模型的解进行了比较。对不同预条件下的求解方法进行了测试，结果表明，不完全LU预条件下的拟最小残差法比其他方案更稳定，求解速度更快。然后，我们研究了三种不同条件下的三维各向异性模型，并对结果进行了详细分析。最后，得到了三个主要结论：当主电导率在x方向时，xy型和y型视电阻率几乎不变；如果主电导率在y方向，则x型和x型视电阻率几乎保持不变；z方向上的主电导率对视电阻率几乎没有影响。
ABSTRACT It is important to study the responses of the magnetotelluric (MT) method in anisotropic media. However, MT anisotropy research has focused mainly on one-dimensional (1D) and two-dimensional (2D) solutions. Therefore, we developed a three-dimensional (3D) finite element (FE) algorithm for MT modelling in anisotropic media. This approach is based on the weak formulation of the governing Maxwell equations using Coulomb-gauged potentials. The node-based FE method is adopted here, and the values of the coefficient matrixes are obtained with hexahedral meshes. To validate the correctness and accuracy of this method, its results are compared with previous solutions for a 2D anisotropic model and a 3D arbitrary anisotropic model, respectively. Different solvers with different preconditioners are tested, and the results show that the quasi-minimum residual method with the incomplete LU preconditioner is more stable and faster compared with the other schemes. We then studied a 3D anisotropic model in three different conditions, and analysed the results in detail. Finally, three main conclusions are obtained: the xy- and yy-mode apparent resistivities remain almost unchanged if a principal conductivity is in the x-direction; the yx- and xx-mode apparent resistivities remain almost the same if a principal conductivity is in the y-direction; a principal conductivity in the z-direction has almost no influence on apparent resistivities.