任政勇^1,2,3,,
邱乐稳^1,2,3,
汤井田^1,2,3,,,
周峰^1,2,3,
陈超健^1,2,3,
陈煌^1,2,3,
胡双贵^1,2,3
1. 中南大学地球科学与信息物理学院, 长沙 410083
2. 中南大学有色金属成矿预测与地质环境监测教育部重点实验室, 长沙 410083
3. 有色资源与地质灾害探查湖南省重点实验室, 长沙 410083

基金项目: 青年973（2015CB060200），国家自然科学基金（41574120），国家自然科学基金（41474103），国家高技术研究发展计划（2014AA06A602），湖南省自然科学基金（2016JJ2139），中南大学创新驱动计划（2016CX005），中南大学研究生自主探索创新项目（2017zzts559）联合资助


详细信息

作者简介: 任政勇, 男, 1983年生, 副教授, 从事地球物理电磁法及重磁正反演研究.E-mail:renzhengyong@csu.edu.cn

通讯作者: 汤井田, 男, 1965年生, 教授, 从事地球物理电磁法方法理论及正反演研究.E-mail:jttang@csu.edu.cn

中图分类号: P631

收稿日期:2016-12-08
修回日期:2017-11-15
上线日期:2018-01-05

3D modeling of direct-current anisotropic resistivity using the adaptive finite-element method based on continuity of current density

REN ZhengYong^1,2,3,,
QIU LeWen^1,2,3,
TANG JingTian^1,2,3,,,
ZHOU Feng^1,2,3,
CHEN ChaoJian^1,2,3,
CHEN Huang^1,2,3,
HU ShuangGui^1,2,3
1. School of Geosciences and Info-physics of Central South University, Changsha 410083, China
2. The Key Laboratory of Metallogenic Prediction of Nonferrous Metals of Ministry of Education, Central South University, Changsha 410083, China
3. The Key Laboratory of Non-ferrous Resources and Geological Hazard Detection, Changsha 410083, China


More Information

Corresponding author: TANG JingTian,E-mail:jttang@csu.edu.cn

MSC: P631

--> Received Date: 08 December 2016
Revised Date: 15 November 2017
Available Online: 05 January 2018


摘要
摘要:直流电阻率法被广泛应用在工程和环境及水文地球物理、野外采矿、地热探测等领域.地下岩石常具有层理面和裂缝等具有方向依赖性的结构，岩石电导率常常呈现各向异性特征，因此研究复杂直流电阻率各向异性问题的高精度正演算法具有迫切的理论和学术需求.本文利用面向目标的自适应有限元算法和非结构化网格相结合的方式，解决了带地形任意复杂直流电阻率各向异性问题的高精度正演这一难题.有别于前人的研究成果，本文提出了一种特别的二次虚拟场算法实现带源的任意起伏地形问题模拟；另外，本文第一次基于电流密度连续性条件构建适合直流电阻率各向异性问题的后验误差估计算法，有效地驱动面向目标有限元网格自适应加密过程.最后，通过三组电阻率各向异性模型验证本文提出算法的正确性和适应性，测试结果表明：对于任意复杂直流电阻率各向异性问题，本文提出的算法具有精度高、适应性强等特点；另外，我们还发现电流密度连续性条件可用于设计直流电阻率问题的有效后验误差估计算法.
关键词: 数值模拟/
电磁理论/
电各向异性/
自适应有限元

Abstract:The direct current (DC) resistivity method has been widely applied in engineering, environmental, and hydrological geophysics as well as field mining, geothermal exploration and so forth. Because of existence of bedding surfaces or fissures with directional dependence, underground rocks often exhibit resistivity anisotropy. Therefore it provides an urgent impetus to develop a high-accuracy algorithm to deal with such a complex problem. This work has conducted a high-precision forward modeling for the complex DC anisotropic resistivity problem with arbitrary topography by combining the goal-oriented adaptive finite-element method with an unstructured grid. Different from previous work, we applied an extraordinary secondary virtual potential strategy to simulate the DC problem with arbitrary topography and sources. Furthermore, we built an a-posteriori error estimating algorithm based on the continuity of the normal component of current density adjusting to the DC anisotropic resistivity problem to effectively drive the goal-oriented adaptive grid refinement. Finally, three synthetic anisotropic resistivity models were designed to verify the accuracy and effectiveness of the developed algorithm. The results show that this new algorithm has high accuracy and robust effectiveness. In addition, we found the continuity condition of normal component of electric current density can be adopted to design effective a-posteriori error estimating algorithms for the DC resistivity problem.
Key words:Numerical modeling/
Electromagnetic theory/
Electrical anisotropy/
Adaptive finite element



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