五极纵轴激电测深三维有限元正演模拟

doi:10.13278/j.cnki.jjuese.201603302

吉林大学学报(地球科学版) ›› 2016, Vol. 46 ›› Issue (3): 884-892.doi: 10.13278/j.cnki.jjuese.201603302

五极纵轴激电测深三维有限元正演模拟

刘海飞^1,2, 柳杰², 高寒², 郭荣文^1,2, 童孝忠^1,2, 麻昌英²

1. 有色资源与地质灾害探查湖南省重点实验室, 长沙 410083;
2. 中南大学地球科学与信息物理学院, 长沙 410083

收稿日期:2015-10-10 出版日期:2016-05-26 发布日期:2016-05-26
作者简介::刘海飞(1975),男,副教授,博士,主要从事电磁法数值模拟与反演成像研究,E-mail:liuhaifei@126.com
基金资助:
国家自然科学基金项目（41174102）

3D Finite Element Forward Modeling of Five-Pole Longitude Induced Polarization Sounding

Liu Haifei^1,2, Liu Jie², Gao Han², Guo Rongwen^1,2, Tong Xiaozhong^1,2, Ma Changying²

1. Hunan Key Laboratory of Nonferrous Resources and Geological Hazard Detection, Changsha 410083, China;
2. School of Geosciences and InfoPhysics, Central South University, Changsha 410083, China

Received:2015-10-10 Online:2016-05-26 Published:2016-05-26
Supported by:
Supported by the National Natural Science Foundation of China (41174102)

摘要/Abstract

摘要：

本文研究了五极纵轴激电测深三维有限元正演模拟方法。首先，从三个点电流源总电位的边值问题出发，导出了异常电位的边值问题，证明了与异常电位的边值问题对应的变分问题。然后，基于三维连续电性介质模型，推导了有限元法求解变分问题的计算过程，编制了五极纵轴激电测深的三维模拟程序。最后，通过模拟水平层状介质模型的五极纵轴激电测深曲线，发现最大相对误差小于0.25%，耗费时间为18 s；从精度和效率的角度验证了算法和程序是正确的，为后续模拟复杂地电模型五极纵轴激电测深曲线、分析曲线异常特征规律以及开展反演工作奠定了基础。

关键词: 五极纵轴激电测深, 三维有限元正演模拟, 边值问题, 变分问题, 异常电位

Abstract:

The authors develop a three-dimensional(3D) finite element forward modeling method for five-pole longitude induced polarization (IP) soundingin this paper. Boundary value problems of the secondary potential field are derived from that of the primary potential field with the three-point current sources, it also proves the corresponding variation equation saccording to the boundary value problem of the secondary potential field. Then we solved the variation equations of the secondary potential field using a finite element method (FEM) based on a 3D continuous model of the electrical conductivity, specifically for five-pole longitude array. Finally, we calculate the induced polarization sounding curve with the five-pole longitude array based on the horizontal layered medium, the results show that the maximum relative error is less than 0.25% and the total computational time is about 18 seconds. Three examples indicate the accuracy and efficiency of the proposed algorithm, which will facilitate the application of the five-pole longitude IP sounding for complex geoelectrical structure, understanding of the IP sounding curve anomaly, and further carrying out the inversion.

Key words: five-pole longitude induced polarization sounding, 3D FEM forward modeling, boundary value problem, variation problem, secondary potential

中图分类号:

P631.3

刘海飞, 柳杰, 高寒, 郭荣文, 童孝忠, 麻昌英. 五极纵轴激电测深三维有限元正演模拟[J]. 吉林大学学报(地球科学版), 2016, 46(3): 884-892.

Liu Haifei, Liu Jie, Gao Han, Guo Rongwen, Tong Xiaozhong, Ma Changying. 3D Finite Element Forward Modeling of Five-Pole Longitude Induced Polarization Sounding[J]. Journal of Jilin University(Earth Science Edition), 2016, 46(3): 884-892.

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五极纵轴激电测深三维有限元正演模拟

3D Finite Element Forward Modeling of Five-Pole Longitude Induced Polarization Sounding

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