基于自适应加权光滑约束与PCG算法的三维电阻率探测反演成像

刘斌; 李术才; 聂利超; 李利平; 刘征宇; 宋杰; 隋斌; 周宗青

基于自适应加权光滑约束与PCG算法的三维电阻率探测反演成像 English Version

山东大学岩土与结构工程研究中心，山东济南 250061

详细信息

作者简介:
刘斌(1983– )，男，山东高唐人，讲师，从事地下工程地质灾害预报与防治研究。

中图分类号: P631.322
计量
- 文章访问数: 01121
- HTML全文浏览量: 0
- PDF下载量: 0463
出版历程
- 收稿日期: 2011-05-22
- 发布日期: 2012-10-09

Inversion imaging of 3D resistivity detection using adaptive-weighted smooth constraint and PCG algorithm

Research Center of Geotechnical & Structural Engineering, Shandong University, Jinan 250061, China

摘要

摘要: 三维电阻率探测在实际工程中日益受到重视，但存在着深部分辨率低、反演效率低等关键问题，严重制约了三维电阻率探测技术的应用和推广。针对深部分辨率低的问题，提出了一种随三维模型网格尺寸自适应调整的加权光滑约束，改善了深部网格的电阻率差异容许程度，实现了对不同深度网格约束的差异化加权处理，有效的提高了深部反演的分辨率和成像效果。针对反演计算耗时长、效率低的问题，基于预条件共轭梯度法求解快速稳定的优势，提出了三维电阻率快速稳定反演成像算法。在该算法中，将雅可比迭代中的对角阵作为预条件矩阵，其具有求逆方便、无需内存空间的特点，显著加快了收敛速度。最后，利用合成算例和隧道导水裂隙探测的工程实例验证了上述反演方法的可行性与有效性，表明借助于自适应调整加权光滑约束和预条件共轭梯度算法，有效的提高了深部分辨率和计算效率，显著改善了反演效果。
- 三维电阻率反演 /
- 自适应加权光滑约束 /
- 深部分辨率 /
- 预条件共轭梯度算法 /
- 导水裂隙探测
Abstract: Three-dimensional resistivity detection is increasingly concerned in actual projects. However, its application and extension is excessively restricted because of some key problems such as low deep resolution and low inversion efficiency. For the problem of low deep resolution, an adaptive-weighted smooth constraint is proposed, which is adjusted adaptively to the mesh size in a three-dimensional model. It improves resistivity difference tolerance of deep grids and achieves difference weighted processing of grid constraints at different depths. With the adaptive-weighted smooth constraint, the deep resolution and inversion imaging quality are improved effectively. For the problem of time-consuming and low inversion efficiency in inversion, a rapid and stable method of 3D resistivity inversion and imaging based on preconditioned conjugate gradient (PCG) algorithm is proposed. The diagonal matrix in Jacobi iteration is used as the preconditioned matrix for speeding up the convergence speed significantly. The inversion of the preconditioned matrix is convenient to be solved and doesn’t occupy memory spacing. At last, the inversion method is applied in a synthetic example and water flowing fracture detection in tunnel engineering for checking its feasibility and effectiveness. The results show that the deep resolution, calculation efficiency and inversion quality of 3D resistivity detection are improved effectively by using the adaptive-weighted smooth constraint and the PCG algorithm.
- 3D resistivity inversion /
- adaptive-weighted smooth constraint /
- deep resolution /
- PCG algorithm /
- water flowing fracture detection

HTML全文

参考文献(25)

[1]	PETRICK W R Jr, SILL W R, WARD S H. Three dimensional resistivity inversion using alpha centers[J]. Geophysics, 1981, 46(8): 1148–1163.
[2]	LI Y, OLDENBURG D W. Approximate inverse mappings in DC resistivity problems[J]. Geophys J Int, 1992, 109: 343–362.
[3]	ZOHDY A A R. A new method for the automatic interpretation of schlumberger and wenner sounding curves[J]. Geophysics, 1989, 54(2): 245–253.
[4]	毛先进, 冯锐, 鲍光淑. 边界积分方程用于电阻率Zohdy反演的初步研究[J]. 地球物理学报, 2000, 43(4): 574–579. (MAO Xian-jin, FENG Rui, BAO Guang-shu. Primary research on Zohdy inversion of resistivity using boundary integral equation[J]. Chinese Journal of Geophysics, 2000, 43(4): 574–579. (in Chinese))
[5]	SASAKI Yutaka. 3D resisitivity inversion using the finite-element method[J]. Geophysics, 1994, 59(11): 1839–1848.
[6]	阮百尧, 村上峪, 徐世浙. 电阻率/激发极化率数据的二维反演程序[J]. 物探化探计算技术, 1999, 21(2): 116–125. (RUAN Bai-yao, Murakami Y, XU Shi-zhe. 2D inversion program of induced polarization data[J]. Computing Techniques For Geophysical and Geochemical Exploration, 1999, 21(2): 116–125. (in Chinese))
[7]	黄俊革, 阮百尧, 鲍光淑. 基于有限单元法的三维地电断面电阻率反演[J]. 中南大学学报(自然科学版), 2004, 35(2): 295–299. (HUANG Jun-ge, RUAN Bai-yao, BAO Guang-shu. Resistivity inversion on 3D section based on FEM[J]. Journal of Central South University (Natural Science), 2004, 35(2): 295–299. (in Chinese))
[8]	底青云, 王妙月. 积分法三维电阻率成像[J]. 地球物理学报, 2001, 44(6): 843–852. (DI Qing-yun, WANG Miao-yue. 3-D resistivity tomography by integral method[J]. Chinese Journal of Geophysics, 2001, 44(6): 843–852. (in Chinese))
[9]	ZHANG Jie, MACKIE Randall L, MADDEN Theodore R. 3-D resistivity forward modeling and inversion using conjugate gradients[J]. Geophysics, 1994, 60(5): 1313–1325.
[10]	吴小平, 徐果明. 利用共轭度法的电阻率三维反演研究[J].地球物理学报, 2000, 43(3): 420–426. (WU Xiao-ping, XU Guo-ming. Study on 3D resistivity inversion using conjugate gradient method[J]. Chinese Journal of Geophysics, 2000, 43(3): 420–426. (in Chinese))
[11]	宛新林, 席道瑛, 高尔根, 等. 用改进的光滑约束最小二乘正交分解法实现电阻率三维反演[J]. 地球物理学报, 2005, 48(1): 439–444. (WAN Xin-lin, XI Dao-ying, GAO Er-gen, et al. 3-D resistivity inversion by the least-squares QR factorization method under improved smoothness constraint condition[J]. Chinese Journal of Geophysics, 2005, 48(1): 439–444. (in Chinese))
[12]	PIDLISECKY Adam, HABER Eldad, KNIGHT Rosemary. RESINVM3D: A 3D resistivity inversion package[J]. Geophysics, 2007, 72(2): H1–H10.
[13]	孙跃. 直流电阻率法的三维有限元无限元数值分析[J].岩土工程学报, 2005, 27(7): 733–737. (SUN Yue. Numerical analysis for three-dimensional resistivity model by using finite element/infinite element methods[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(7): 733–737. (in Chinese))
[14]	STEPHEN Jimmy, MANOJ C, SINGH S B. A direct inversion scheme for deep resistivity sounding data using artificial neural networks[J]. Journal of Earth System Science, 2004, 113(1): 49–66.
[15]	SINGH U K, TIWARI R K, SINGH S B. One-dimensional inversion of geo-electrical resistivity sounding data using artificial neural networks—a case study[J]. Computers & Geosciences, 2005, 31(1): 99–108.
[16]	徐海浪, 吴小平. 电阻率二维神经网络反演[J]. 地球物理学报, 2006, 49(2): 584–589. (XU Hai-lang, WU Xiao-ping. 2D resistivity inversion using the neural network method[J]. Chinese Journal of Geophysics, 2006, 49(2): 584–589. (in Chinese))
[17]	DITTMER J K, SZYMANSKI J E. The stochastic inversion of magnetic and resistivity data using the simulated annealing algorithm[J]. Geophysical Prospecting, 1995, 43: 397–416.
[18]	卢元林, 王兴泰, 王若, 等. 电阻率成像反演中的模拟退火方法[J]. 地球物理学报, 1999, 42(增刊1): 225–233. (LU Yuan-lin, WANG Xing-tai, WANG Ruo, et al. The simulated annealing method of electrical resistivity tomography[J]. Chinese Journal of Geophysics, 1999, 42(S1): 225–233. (in Chinese))
[19]	李帝铨, 王光杰, 底青云, 等. 基于遗传算法的CSAMT最小构造反演[J]. 地球物理学报, 2008, 51(4): 1234–1245. (LI Di-quan, WANG Guang-jie, DI Qing-yun, et al. The application of genetic algorithm to CSAMT inversion for minimum structure[J]. Chinese Journal of Geophysics, 2008, 51(4): 1234–1245. (in Chinese))
[20]	闫永利, 陈本池, 赵永贵, 等. 电阻率层析成像非线性反演[J]. 地球物理学报, 2009, 52(3): 758–764. (YAN Yong-li, CHEN Ben-chi, ZHAO Yong-gui, et al. Nonlinear inversion for electrical resistivity tomography[J]. Chinese Journal of Geophysics, 2009, 52(3): 758–764. (in Chinese))
[21]	王家映. 地球物理反演理论[M]. 北京: 高等教育出版社, 2002. (WANG Jia-ying. Inverse theory in geophysics[M]. Beijing: Higher Education Press, 2002. (in Chinese))
[22]	雷光耀. 预处理技术与PCG 算法[J]. 数学进展, 1992, 21(2): 129–139. (LEI Guang-yao. Preconditioned technique and PCG algorithm[J]. Advances in Mathematics, 1992, 21(2): 129–139. (in Chinese))
[23]	王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2003. (WANG Xu-cheng. Finite element method[M]. Beijing: Tsinghua University Press, 2003. (in Chinese))
[24]	刘斌, 李术才, 李树忱, 等. 电阻率层析成像法监测系统在矿井突水模型试验中的应用研究[J]. 岩石力学与工程学报, 2010, 29(2): 297–307. (LIU Bin, LI Shu-cai, LI Shu-chen, et al. Application and study of ERT monitoring system to mine water inrush model test[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(2): 297–307. (in Chinese))
[25]	刘斌, 李术才, 李树忱, 等. 隧道含水构造直流电阻率法超前探测研究[J]. 岩土力学, 2009, 30(10): 3093–3100. (LIU Bin, LI Shu-cai, LI Shu-chen, et al. Study of advanced detection of water-bearing geological structures with DC resistivity method[J]. Rock and Soil Mechanics, 2009, 30(10): 3093–3100. (in Chinese))