Fractal model-based 2.5 D finite element modeling of complex resistivity method

Long Xiu-Jie; Chen Han-Bo; Mo Ya-Jun; Ou Xiao-Yi; Lu Sheng-Hui

doi:10.11720/wtyht.2022.1377

2022 Vol. 46, No. 4

Article Contents

Article navigation > Geophysical and Geochemical Exploration > 2022 > 46(4): 887-896

Next Article Previous Article

Long Xiu-Jie, Chen Han-Bo, Mo Ya-Jun, Ou Xiao-Yi, Lu Sheng-Hui. 2022. Fractal model-based 2.5 D finite element modeling of complex resistivity method. Geophysical and Geochemical Exploration, 46(4): 887-896. doi: 10.11720/wtyht.2022.1377

Citation:

Long Xiu-Jie, Chen Han-Bo, Mo Ya-Jun, Ou Xiao-Yi, Lu Sheng-Hui. 2022. Fractal model-based 2.5 D finite element modeling of complex resistivity method. Geophysical and Geochemical Exploration, 46(4): 887-896. doi: 10.11720/wtyht.2022.1377

Fractal model-based 2.5 D finite element modeling of complex resistivity method

1. Guangxi Geophysical Investigation Institute,Liuzhou 545005,China；
2. College of Earth Sciences, Guilin University of Technology,Guilin 541006,China

Received Date: 09 July 2021

Revised Date: 20 August 2022

Publish Date: 17 August 2022

Abstract

Abstract

This study proposed the variational problem of 2.5D finite element forward modeling of the complex resistivity method and detailed the process of solving stiff matrix of finite equations. The Fractal model was introduced as a research model for studying the equivalent induced polarization anomalies of spectra. Furthermore, the complex conductivity and complex potential of a grid unit were linearly interpolated. Then, to obtain anomalous complex potential, finite element linear equations were solved using the biconjugate gradient stabilized method with incomplete LU decomposition. The results of three typical geoelectric models validated the correctness and accuracy of the algorithm proposed in this study. Furthermore, this study analyzed the abnormal response characteristics of 2.5D complex resistivity under different frequencies.
- finite element method /
- complex resistivity /
- Fractal model /
- anomalous complex potential

FullText(HTML)

References

[1]	杨振威, 郑伟, 李晓斌, 等. 频谱激电法的发展与展望[J]. 物探与化探, 2015, 39(1):22-28. Google Scholar
[2]	Yang Z W, Zhen W, Li X B, et al. The development and prospect of the spectral induced polarization method[J]. Geophysical and Geochemical Exploration, 2015, 39(1):22-28. Google Scholar
[3]	罗延钟, 张桂青. 频率域激电法原理[M]. 北京: 地质出版社, 1988. Google Scholar
[4]	Luo Y Z, Zhang G Q. Principle of frequency domain IP method[M]. Beijing: Geological Publishing House, 1988. Google Scholar
[5]	罗延钟, 方胜. 视复电阻率频谱的一种近似反演方法[J]. 地球科学, 1986, 11(1) : 9-102. Google Scholar
[6]	Luo Y Z, Fang S. An approximate invrtsion of the apparent complex resistivity spectrum[J]. Earth Science, 1986, 11(1) : 9-102. Google Scholar
[7]	张桂青, 崔先文, 罗延钟. 一种反演频谱激电法视频谱求取真参数的方法[J]. 地质与勘探, 1987, 23(4) : 48-54. Google Scholar
[8]	Zhang G Q, Cui X W, Luo Y Z. The Determination of intrinsic parameters by inversing IP apparent spectrum[J]. Geology and Exploration, 1987, 23(4) : 48-54. Google Scholar
[9]	刘崧, 官善友, 高鹏飞. 求极化椭球体真 Cole-Cole 参数的联合谱激电反演[J]. 地球物理学报, 1994, 37(S1) : 542-551. Google Scholar
[10]	Liu S, Guan S Y, Gao P F. Joint sip inversion for estimation of intrinsiccole-cole parameters of apolarizable ellipsoid[J]. Chinese Journal of Geophysice, 1994, 37(S1) : 542-551. Google Scholar
[11]	Hohmann G W. Three-dimensional induced polarization and electromagnetic modelling[J]. Geophysics, 1975, 40 (2) :309-324. Google Scholar
[12]	Weller A, Seichter M, Kampke A. Induced-polarization modelling using complex electrical conductivities[J]. Geophys. J. Int., 1996, 127(1):387-398. Google Scholar
[13]	Oldenburg D W, Li Y. Inversion of induced polarization data[J]. Geophysics, 1994, 59 (9) :1327-1341. Google Scholar
[14]	Rocha B R P, Habashy T M. Fractal geometry, porosity and complex resistivity. I: From rough pore interfaces to hand specimens, in: Developments in Petrophysics[M], London: Geological Society Publishing House, London, 1995. Google Scholar
[15]	柳建新, 蒋鹏飞, 童孝忠, 等. 不完全LU分解预处理的BICGSTAB算法在大地电磁二维正演模拟中的应用[J]. 中南大学学报:自然科学版, 2009, 40(2):484 -491. Google Scholar
[16]	Liu J X, Jiang P F, Tong X Z, et al. Application of BICGSTAB algorithm with incomplete LU decomposition preconditioning to two-dimensional magnetotelluric forward modeling[J]. Journal of Central South University: Science and Technology, 2009, 40(2):484 -491. Google Scholar