起伏地形下各向异性的2D大地电磁无网格法数值模拟

作为一种基于节点的计算方法,无网格法具有构造高阶导数方便,自适应分析便利的优点,特别适合复杂地质构造的数值模拟.本文针对实际地球物理勘探中存在的起伏地形和各向异性的地电结构,提出用无网格法来模拟大地电磁响应,采用复合二次径向基函数构造了形函数,推导了大地电磁无网格法等价线性方程组,研究了系数矩阵的压缩存储方法以及大型稀疏复线性方程组快速求解算法,实现了起伏地形下各向异性的2D大地电磁高精度数值模拟.基于层状模型验证了算法的正确性,计算结果表明:无论是TM模式还是TE模式,计算相对误差均小于1%;通过对地垒和地堑模型的模拟,得出了起伏地形对视电阻率和相位的影响规律;对起伏地形下含有不同各向异性系数异常体的模型进行了数值模拟,为开展复杂地质结构的电磁场特征研究以及地形校正奠定了理论基础.随着计算科学的快速发展,无网格法必将成为新的高精度电磁场数值模拟方法.

2D anisotropic magnetotelluric numerical simulation using meshfree method under undulating terrain

As a kind of calculation method based on nodes, meshfree method is easy to construct the higher derivative and convenient to do adaptive analysis, it is especially suitable for the numerical simulation of complex models and complex medium structures. In view of the widespread existing problem that undulating terrain and anisotropic in the actual geophysical prospecting, we propose meshfree method to simulate the magnetotelluric response. The shape function is constructed by MQ-RBF function, the equivalent linear equations based on meshfree method is derived. We also study the compression and storage method of coefficient matrix and large sparse complex fast algorithm for solving linear equations, the 2D anisotropic magnetotelluric numerical simulation under undulating terrain is realized. The correctness of the algorithm is verified based on the layered model. The calculation results show that the relative error is less than 1% in both TM and TE mode; Through the simulation of horst and graben model, the influence rule of topography on the apparent resistivity and phase is obtained.We also study the numerical simulation of different anisotropic coefficients of horst and graben model, it establishes the theoretical basis for the study of electromagnetic field and the topographic correction of complex geological structure. With the rapid development of computational science, the meshfree method will surely become a new robust and high precision numerical method for electromagnetic field simulation.