基于非结构化三角网格的大地电磁二维h-型自适应有限元正演模拟

Two-dimensional H-type adaptive finite element forward modeling of magnetotelluric based on unstructured triangular mesh

采用规则化网格剖分的传统有限元求解大地电磁二维正演问题时,由于其节点拓扑结构不够灵活,对复杂模型会产生较大的几何离散误差。为解决该问题,在前人研究的基础上,将非结构化三角网格与h-型自适应有限元结合使用,以此来提高网格剖分灵活性。将Gmsh划分的粗网格作为初始网格,以单元网格的局部后验误差估算值作为局部网格细化的标准,直至计算结果的精度满足设定的精度要求为止,该过程只针对局部网格进行细化,从而最大限度地优化了网格数目和网格质量,使在同样精度下的计算速度得到提升。利用该算法对层状模型与COMMEMI-2D1模型进行了数值模拟,表明了该方法的准确性;对起伏地电模型进行了模拟计算,对比分析了不同频率下复杂构造的二维大地电磁响应特征。

The node topology is not flexible enough when the traditional finite element method with regular meshing is used to solve the magnetotelluric forward modeling problem.This woulld produce large geometric discretization errors for complex models.In order to solve this problem,based on previous studies,we combine unstructured triangular mesh with h-shaped adaptive finite element to improve meshing flexibility.The coarse grid divided by Gmsh is used as the initial grid,and the local posterior error estimate of the unit grid is used as the local grid refinement standard until the accuracy of the calculation result meets the set accuracy requirements.Refine the local grids,thereby optimizing the number of grids and grid quality to the greatest extent,so that the calculation speed under the same accuracy is improved.Numerical simulation of the layered model and COMMEMI-2D1 model using the algorithm in this paper shows the accuracy of the method.The undulating geoelectric model is simulated,and the two-dimensional magnetotelluric response characteristics of complex structures under different frequencies are compared and analyzed.