三维CSAMT法非结构化网格有限元数值模拟

Three-dimensional modeling of controlled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid

考虑到可控源音频大地电磁法(CSAMT)电偶极发射源与地下介质的三维结构特点,本文采用非结构化网格剖分技术,开展了三维CSAMT方法有限元数值模拟研究,将三维电磁场的背景场和异常场分别求解,避免了电偶极发射源的奇异性问题,并减小了计算区域.推导了三维异常电场遵循的有限元方程,加入散度条件进行约束以消除电场伪解;对非结构化网格单元采用高斯加权平均算法,得到了精度较高的异常磁场.针对层状介质模型,与积分方程法对比,验证了有限元算法的正确性;计算分析了典型三维地质模型的电磁响应,异常体反映明显.结果表明本文算法正确、可靠,适用于三维地质模型的CSAMT方法正反演研究.

Considering both the transmitter subsurface media in the controlled-source configuration and the complicated characteristics of audio-frequency magnetotellurics survey, a threedimensional finite element modeling method based on an unstructured grid is developed. We solve the secondary field problem to avoid singularity near the source and reduce the computation domain. The governing equations for the secondary electric field are deduced firstly. By incorporating the divergence-free condition, our solution for the electric field is guaranteed to be numerically accurate and physically reasonable. The secondary magnetic field value of high precision is then obtained by Gaussian weighted technique from the electric field. The liability of our algorithm is verified by a comparative study with the IE （Integral Equation） method. Thereafter the electromagnetic responses of some canonical models are simulated and analyzed. The results show that the algorithm is correct and reliable, and suitable for the numerical simulation of 3D geological models.