基于异常复电位2.5维CR有限元数值模拟

J4 ›› 2011, Vol. 41 ›› Issue (5): 1596-1604.

基于异常复电位2.5维CR有限元数值模拟

李勇¹|林品荣¹|李桐林²|王有学³|尚晓¹

1.中国地质科学院地球物理地球化学勘查研究所|河北廊坊065000;
2.吉林大学地球探测科学与技术学院|长春130026;
3.桂林理工大学资源与环境工程系|广西桂林541004

收稿日期:2010-11-22 出版日期:2011-09-26 发布日期:2011-09-26
作者简介:李勇(1980-)|男|云南宾川人|硕士|主要从事地球物理数值模拟与反演成像研究|E-mail:liyong@igge.cn
基金资助:
国家“863”计划重点项目（2007AA060601）；中国地质调查局项目（1212011120193）；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（AS2010J01，AS2007J14）

Finite Element Method for Solving Anomalous Complex Potential of 2.5-D Complex Resistivity

LI Yong¹, LIN Pin-rong¹, LI Tong-lin², WANG You-xue³, SHANG Xiao¹

1.Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Science, Langfang065000,Hebei,China;
2.College of GeoExploration Science and Technology, Jilin University, Changchun130026, China;
3.Department of Resources and Environment Engineering, Guilin University of Technology, Guilin541004|Guangxi,China

Received:2010-11-22 Online:2011-09-26 Published:2011-09-26

摘要/Abstract

摘要：

论述了基于异常复电位2.5维复电阻率法的正演计算技术。首先给出了二维地电断面、三维交流双点电源复电阻法的变分问题；然后利用有限单元法求解变分问题，在矩形网格中增加2条对角线形成三角网格对研究区域进行剖分，在单元中对复电位和岩、矿石复电导率进行线性插值，将变分方程化为线性代数方程组；最后，求解线性方程组，得到各节点的异常复电位值，并根据选定的测量装置计算出地表的视复电阻率，进而计算出复电阻率的振幅、相位或复电阻率的实、虚分量。通过理论模型的计算检验算法的有效性后构建模型算例，给出了其不同测量装置下的计算结果。

关键词: 有限单元法, 复电阻率法, Cole-Cole模型, 异常复电位

Abstract:

The computation technique of the finite-element forward modeling for 2.5-dimensional complex resistivity based on anomalous complex potential is described. The variational equations are established for 2D structure with 3D alternating two-point sources. The finite element method is used to solve the equations. The computing area is divided into rectangular elements, each of which is subdivided into four triangles by two diagonal lines. The complex potential and the complex conductivity of rocks within each triangular lattice are described by a linear interpolation to create a linear equation system from the variational equations. For a specific array, the linear equations are solved to calculate the anomalous complex potential at each node and the apparent complex resistivity on the surface. The feasibility of the algorithm is verified through the theoretical model calculation, and the computation results of different survey configurations are demonstrated.

Key words: finite element method, complex resistivity, Cole-Cole model, anomalous complex potential

中图分类号:

P631.3

李勇| 林品荣, 李桐林, 王有学, 尚晓. 基于异常复电位2.5维CR有限元数值模拟[J]. J4, 2011, 41(5): 1596-1604.

LI Yong, LIN Pin-rong, LI Tong-lin, WANG You-xue, SHANG Xiao. Finite Element Method for Solving Anomalous Complex Potential of 2.5-D Complex Resistivity[J]. J4, 2011, 41(5): 1596-1604.

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