We have developed a three-dimensional (3-D) algorithm for computing the controlled-source audio-frequency magnetotelluric response which is capable of handling local inhomogeneities in the electrical conductivity and magnetic permeability distribution. It is a difference equation algorithm that is based on the integral forms of Maxwell’s equations. To avoid a spatial singularity being introduced by the source, we used a secondary electric field approach. We adopt a staggered-grid finite difference method to disperse the secondary electric field equation which is simple to realize and can calculate relatively complex models. The final sparse equation system after dispersion is solved using an ILU preconditioning quasi-minimal residual (QMR) method. The code is validated for nonmagnetic and permeable conductive structures by two synthetic models. One of them is a two-dimensional (2-D) nonmagnetic conductive geoelectric model; we validate our 3-D computation result by comparing it to the result of 2-D CSEM finite element forward program. The other one is a 3-D permeable geoelectric model; we validate our 3-D computation result by using the COMSOL Multiphysics software. We also designed two theoretical 3-D geoelectrical models to analyze the effects of magnetic permeability heterogeneity. Numerical simulation results well reveal the influence of magnetic permeability heterogeneity on high-resistance and low-resistance models.

我们已经开发了一种用于计算受控源音频大地电磁响应的三维（3-D）算法，该算法能够处理电导率和磁导率分布中的局部不均匀性。这是一种基于麦克斯韦方程组积分形式的差分方程算法。为了避免源引入空间奇异性，我们使用了次级电场方法。我们采用交错网格有限差分法来分散二次电场方程，该方程易于实现并且可以计算相对复杂的模型。使用ILU预处理准最小残差（QMR）方法求解色散后的最终稀疏方程组。该代码已通过两个合成模型针对非磁性和渗透性导电结构进行了验证。其中之一是二维（2-D）非磁性导电地电模型。我们通过将其与2-D CSEM有限元正向程序的结果进行比较来验证3-D计算结果。另一个是3-D可渗透地电模型。我们使用COMSOL Multiphysics软件验证了我们的3-D计算结果。我们还设计了两个理论上的3-D地电模型来分析磁导率异质性的影响。数值模拟结果很好地揭示了磁导率异质性对高阻模型和低阻模型的影响。我们使用COMSOL Multiphysics软件验证了我们的3-D计算结果。我们还设计了两个理论上的3-D地电模型来分析磁导率异质性的影响。数值模拟结果很好地揭示了磁导率异质性对高阻模型和低阻模型的影响。我们使用COMSOL Multiphysics软件验证了我们的3-D计算结果。我们还设计了两个理论上的3-D地电模型来分析磁导率异质性的影响。数值模拟结果很好地揭示了磁导率异质性对高阻模型和低阻模型的影响。