任意各向异性介质中三维可控源音频大地电磁正演模拟

在一些地层层理发育的地区，地下介质存在显著的电各向异性，此时基于各向同性模型解释含各向异性效应的可控源音频大地电磁（CSAMT）测深观测数据会导致错误的结果.本文通过引入3×3的对称正定张量表征电导率各向异性，采用非结构四面体网格和矢量有限元方法离散电场满足的矢量Helmholtz方程，并将电磁场源等效为系列电偶极子，实现任意各向异性介质中CSAMT高效数值模拟.本文首先通过层状各向异性模型检验三维有限元算法的精度和有效性，进一步建立三维地电模型研究异常体各向异性和围岩各向异性对CSAMT响应的影响，最后使用视电阻率极性图来识别各向异性电导率主轴方向.数值模拟结果表明，各向异性电导率对CSAMT视电阻率幅值及分布规律都有很大影响，视电阻率极性图能够很好地识别各向异性主轴方向.

3D forward modeling of controlled-source audio-frequency magnetotellurics in arbitrarily anisotropic media

Controlled-source audio-frequency magnetotellurics (CSAMT) is playing an important role in shallow subsurface exploration. Most current three-dimensional (3D) forward modeling for CSAMT are based on an isotropic earth model which neglects the electrical anisotropy in the earth. Here we implement a 3D vector finite-element modeling algorithm to solve the frequency-domain Helmholtz equation for the total electrical field and analyze the effect of earth anisotropy on tensor CSAMT apparent resistivity responses. First we introduce a 3×3 positive-definite conductivity tensor to represent the arbitrarily electrical anisotropy. Then we discretize the weak-form of vector Helmholtz equation with an unstructured tetrahedral grid and lowest order of Nédélec vector basis functions. Besides, we approximate the horizontal transmitting sources for CSAMT by a series of electrical dipoles and solve the final system of equations with the direct solver MUMPS that can speed up the forward modeling while guaranteeing the numerical precision. We compare our 3D numerical results with one-dimensional solutions for a layered anisotropic earth to verify the accuracy and reliability of the proposed 3D anisotropic finite element algorithm. To further explore the anisotropic effect of a 3D anomalous body and host rock, we design a conductive brick model embedded in a homogeneous half-space. Then, we rotate the principal conductivity tensor of the anomalous body and host rock around x-axis and z-axis separately, and simulate the apparent resistivity for tensor CSAMT. Numerical results show that both the amplitude and distribution pattern of the CSAMT apparent resistivity vary with the anisotropic conductivity tensors. To recognize the electrical anisotropy of the earth, we show the CSAMT apparent resistivity in polar plots, thus one can clearly identify the principal axis of the anisotropic conductivity.