摘要
系统地论述了用有限单元法研究复杂地形条件下三维直流电阻率的正演计算技术.首先给出了三维构造中点源电场的边值问题以及相应的变分问题;然后利用有限单元法求解变分问题,采用四面体单元对研究区域进行剖分,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,考虑到节约计算时间,利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组,得到了各节点的电位值,进而计算出地表的视电阻率.通过理论模型的计算检验了算法的可行性之后,给出了几种常见纯地形异常的数值模拟结果和一个组合模型的计算结果,其研究工作为研究三维直流电阻率反演奠定了基础.
The computation technique of forward modeling for three-dimensional DC resistivity under complicated terrain using the finite element method is systematically described in this paper. Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface. We test the effectiveness of the algorithm through theoretical model calculations, and give a few numerical modeling results of several common terrains and a combined model. This research effort has setup a basis for research of three-dimensional DC resistivity inversion.
出处
《地球物理学进展》
CSCD
北大核心
2009年第3期1039-1046,共8页
Progress in Geophysics
基金
国家863重点项目(2007AA060601)
中国地质调查局项目(1212010660301)
中国地质科学院地球物理地球化学勘查研究所基本科研业务费专项资金(AS2007J14)资助.
关键词
有限单元法
直流电阻率法
复杂地形
三维
finite element method （FEM）,DC resistivity,complicated terrain,three-dimensional,（3-D）
