电导率连续变化2.5维直流电阻率法有限元数值模拟

2.5-D numerical modeling on DC resistivity by FEM with continuous variation of conductivity

在阮百尧、徐世浙(1998,2001)工作基础上,给出四边形内三角网格单元剖分,电导率连续变化2.5维直流电阻率数值模拟方法.在二维起伏地形情况下,有限单元设计为四边形内剖分四个三角网格单元,单元内的电位值和电导率设计为线性变化,将研究区域远边界的第三类边界条件简化为第二类齐次边界条件,重新给出一组适用性较好的Fourier反变换系数,并采用分离式Cholesky分解法快速求解线性方程组.通过对3个地电模型的计算与对比分析,其结果与解析法的均方根误差小于0.2%,计算速度比较常规方法提高了5倍,能有效模拟起伏地形和复杂形态的地电体模型.

Based on the study of Ruan and Xu（1998,2001）,the triangle division method in the quadrangle and the thinking of continuous variation of conductivity within each element are presented for numerical modeling on 2.5dimensional（2.5-D）direct-current（DC）resistivity.Under the condition of twodimensional topography,the finite element is designed to the method of four triangles division in a quadrangle,then potential and conductivity are also designed to bilinear variation within each triangle element.In the paper,the third class boundary condition is simplified for the second class of homogeneous boundary condition at far boundaries of the study area,a set of suitability better inverse Fourier transform coefficients is given,and the separate Cholesky decomposition method is used for quickly solving linear equations.By calculating and comparative analysis on three geoelectric models lastly,the result of our method show a high accuracy（the mean square error is less than 0.2%）,the calculation speed of the numerical method can be increased at least 5times than general methods,and the method can model arbitrarily complicated terrain and geoelectric bodies preferably.