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二维大地电磁测深曲线的正演和反演问题,Rodi 曾提出用矩形有限元求解的方法。但是,应用矩形网格剖分一个区域时,在很多地方会出现网格过密现象,因而增加了未知节点的个数,亦即增加了计算机的存储量和运算量。特别是在地质构造复杂,出现斜界面的情况下,矩形单元就难以发挥其作用。为此,本文提出了适应于求解具有斜界面或各种不规则二维地质构造的大地电磁问题的三角形二次插值有限元法。用此法对 Rodi 计算过的两个地质模型进行了试算,取得了与 Rodi 一致的结果,而且在使用的节点总数和计算量上都有明显地减少。
Rodi has proposed a method of solving rectangular mesoscale finite element method. However, when a rectangular grid is used to divide a region, grid over-dense phenomena occur in many places, thus increasing the number of unknown nodes, that is, increasing the amount of storage and computation of the computer. Especially in the complex geological structure, the emergence of oblique interface case, the rectangular unit is difficult to play its role. To this end, this paper presents a triangular quadratic interpolation finite element method that is suitable for solving the electromagnetic problems of the earth with a slanting interface or various irregular two-dimensional geological structures. By using this method, two geological models calculated by Rodi were tested and the results consistent with Rodi were obtained, and the total number of nodes used and the computational cost were significantly reduced.