电导率线性变化高密度电法有限元正演模拟

Forward modeling for linear variation of conductivity with high density resistivity method by using finite element method

本文从点电流源的边值问题出发,推导了相应的变分问题,采用矩形网格剖分、双线性插值的有限元法,给出了完整的电导率线性变化的高密度电法正演算法,进而编制了相应的正演程序。利用该程序对一个水平层状的地电模型进行计算,将有限元解与解析解对比分析,验证了该算法的正确性和有效性;然后以电导率线性变化的层状模型、对称高阻体、对称低阻体典型模型进行正演计算,得到了相应的视电阻率断面图,结果表明其模拟效果良好。

Through the boundary value problem of borehole-ground electrical method, the variational problem is derived and a complete high density electrical forward algorithm with linearly variation of conductivity is given, in which the rectangular mesh and the bilinear interpolation of the finite element method are used. According to the algorithm a program is developed. Using the program, the forward results of a horizontally layered ground model is calculated which are compared with the results from the analytical solution to verify the correctness and effectiveness of the algorithm. The results of forward modeling from three typical models including the layer model whose resistive is linear, the high resistance model and the low resistive model are obtained, which show that this modeling method can meet the needs.