三维地电断面电阻率测深有限元数值模拟  

FINITE ELEMENT METHOD FOR MODELING RESISTIVITY SOUNDING ON 3-D GEOELECTRIC SECTION

作　　者：阮百尧[1] 熊彬[1] 徐世浙[2] 

机构地区：[1]桂林工学院资源与环境工程系,桂林541004 [2]浙江大学地球科学系,杭州310027

出　　处：《地球科学（中国地质大学学报）》2001年第1期73-77,共5页Earth Science-Journal of China University of Geosciences

基　　金：高等学校骨干教师资助计划资助项目;国家自然科学基金! (No .40 0 6 40 0 1) ;广西自然科学基金! (桂科自 0 0 0 70 2 4)资助项目

摘　　要：用有限单元法进行了电导率分块均匀的三维点源电场电阻率测深的数值模拟 .首先给出了三维构造中点源电场的边值问题、变分问题 ;然后 ,用有限单元法求解变分问题 ,将区域剖分成六面体单元 ,在单元中进行三线性函数插值 ,将变分方程化为线性代数方程组 ;最后解方程组 ,得各节点的电位值 ,进而计算出地表的视电阻率 .对几例较典型的地电模型进行试算 。The finite element method is used for the numerical modeling of the resistivity sounding in a 3-D point-source electric field whose conductivities are homogeneous for each block. In this paper, the 3-D boundary value and variational equation concerning the point-source electrical field in the 3-D structure are both presented. Then the finite element method is used to solve the variational equation. The entire region is divided into many hexahedral units in each of which a trilinear function is interpolated. The variational equation is converted into a linear equation system. Finally the equation system is solved to obtain the potential value on each of the nodes, resulting in the calculation of the apparent resistivity on the ground surface. The test of several relatively typical geoelectric models shows that this finite element method is effective.

关 键 词：电阻率测探 三维地电断面 有限单元法 数值模拟 

分 类 号：P631.322[天文地球—地质矿产勘探]