3D resistivity inversion with multiple priori-information constraint
Guo Laigong1,2, Dai Guanglong2, Yang Bencai2, Xue Junhua3, Chen Benliang3
1. School of Electronics and Information Engineering, Anhui University of Sciences and Technology, Huainan, Anhui 232001, China; 2. School of Mining and Safety Engineering, Anhui University of Sciences and Technology, Huainan, Anhui 232001, China; 3. State Key Laboratory of Deep Coal Mining & Environment Protection, Huainan, Anhui 232001, China
Abstract：The use of prior-information constraint can improve the inversion accuracy of 3D DC electrical resistivity.However,in most cases,single prior-information is used to modify the objective function and the results are inaccurate.In order to solving the problems,the inversion equation of iterative re-weighted least-squares is modified; parameters such as the structural metric,weight mean,and standard deviation are added; and the weight function of the model parameters is replaced by the error function and complementary error function.Then different prior-information can constrain the inversion with modifying parameters of weight function in different zones.The parallel conjugate gradient least-square method is used to effectively improve the inversion calculation.In synthetic data inversions,smoothness constraint,block constraint,and resistivity extreme-constraint are used.The results show that the inversion constrained with multiple priori-information is more accurate than that with single prior-information.In practice,parameters of weight functions can be selected based on geological structures to improve the accuracy of 3D resistivity inversion and the calculation efficiency.
黄俊革,杨庭伟,农观海等.井-地充电法圈定矿体边界异常特征研究.地球物理学进展,2013,28(3):1375-1389.Huang Junge,Yang Tingwei,Nong Guanhaiet al.Study on anomalous of borehole-surface mise-a-la-masse method in delineating the ore body.Progress in Geophysics,2013,28(3):1375-1389.
[2]
刘盛东,刘静,岳建华.中国矿井物探技术发展现状和关键问题.煤炭学报,2014,39(1):19-25.Liu Shengdong,Liu Jing,Yue Jianhua.Development status and key problems of Chinese mining geophysical technology.Journal of China Coal Society,2014,39(1):19-25.
[3]
张亚伟,严加永,张昆等.分布式三维电法研究进展.地球物理学进展,2015,30(4):1959-1970.Zhang Yawei,Yan Jiayong,Zhang Kunet al.Review of distributed 3D DC/IP method.Progress in Geophysics,2015,30(4):1959-1970.
[4]
Karaoulis M,Revil A,Tsourlos Oet al.IP4DI:A software for time-lapse 2D/3D DC-resistivity and induced polarization tomography.Computers & Geosciences,2013,54(4):164-170.
[5]
李术才,王传武,聂利超等.基于松弛变量的不等式约束三维电阻率并行反演方法研究.岩石力学与工程学报,2016,35(6):1122-1132.Li Shucai,Wang Chuanwu,Nie Lichaoet al.Parallel 3D electrical resistivity inversion method with inequality constraint based on slack variables.Chinese Journal of Rock Mechanics and Engineering,2016,35(6):1122-1132.
[6]
刘征宇,李术才,刘斌等.基于距离加权约束算法的围岩三维电阻率CT反演成像研究.岩土工程学报,2017,39(4):652-661.Liu Zhengyu,Li Shucai,Liu Binet al.3D cross-hole resistivity inversion imaging of surrounding rock based on distance weighting constraint algorithm.Chinese Journal of Geotechnical Engineering,2017,39(4):652-661.
[7]
刘斌,李术才,聂利超等.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.岩土工程学报,2012,34(9):1646-1653.Liu Bin,Li Shucai,Nie Lichaoet al.Inversion imaging of 3D resistivity detection using adaptive-weighted smooth constraint and PCG algorithm.Chinese Journal of Geotechnical Engineering,2012,34(9):1646-1653.
[8]
王传武,李术才,刘斌等.基于参考模型的三维电阻率约束反演方法研究.岩土工程学报,2016,38(9):1685-1694.Wang Chuanwu,Li Shucai,Liu Binet al.3D constrained electrical resistivity inversion method based on reference model.Chinese Journal of Geotechnical Engineering,2016,38(9):1685-1694.
[9]
刘鑫明,刘树才,姜志海等.电阻率三维反演中加权光滑因子的影响及注浆检测应用.中国矿业大学学报,2013,42(1):88-92.Liu Xinming,Liu Shucai,Jiang Zhihai et al.Weighted smooth factor impact on 3D DC resistivity inversion and application in grouting effect detection.Journal of China University of Mining & Technology,2013,42(1):88-92.
[10]
吴小平,刘洋,王威.基于非结构网格的电阻率三维带地形反演.地球物理学报,2015,58(8):2706-2717.Wu Xiaoping,Liu Yang,Wang Wei.3D resistivity inversion incorporating topography based on unstructured meshes.Chinese Journal of Geophysics,2015,58(8):2706-2717.
[11]
Johnson T C,Wellman D.Accurate modeling and inversion of electrical resistivity data in the presence of metallic infrastructure with known location and dimension.Geophysical Journal International,2015,202(2):1096-1108
[12]
Johnson T C,Glenn E H,Xing Y C.PFLOTRAN-E4D:A parallel open source PFLOTRAN module for simulating time-lapse electrical resistivity data.Computers & Geosciences,2017,99(1):72-80.
[13]
Farquharson C G.Constructing piecewise-constant models in multidimensional minimum-structure inversions.Geophysics,2008,73(1):K1-K9.
[14]
Thomas G,Carsten R,Klauss S.Three-dimensional modeling and inversion of DC resistivity data incorporating topography-Ⅱ:Inversion.Geophysical Journal International,2006,166(2):506-517.
[15]
刘海飞,阮百尧,柳建新等.混合范数下的最优化反演方法.地球物理学报,2007,50(6):1877-1883.Liu Haifei,Ruan Bairao,Liu Jianxin et al.Optimized inversion method based on mixed norm.Chinese Journal of Geophysics,2007,50(6):1877-1883.
[16]
刘斌,李术才,李树忱等.基于不等式约束的最小二乘法三维电阻率反演及其算法优化.地球物理学报,2012,55(1):260-268.Liu Bin,Li Shucai,Li Shuchen et al.3D electrical resistivity inversion with least-squares method based on inequality constraint and its computation efficiency optimization.Chinese Journal of Geophysics,2012,55(1):260-268.
[17]
尹洪东,杨怀章,薛亚茹等.基于混合正则化的最小二乘三维电阻率反演成像.中国石油大学学报(自然科学版),2015,39(5):72-81.Yin Hongdong,Yang Huaizhang,Xue Yaru et al.Least square method based on hybrid regularization for 3D resistivity inversion imaging.Journal of China University of Petroleum (Edition of Natural Science),2015,39(5):72-81.
[18]
李静和,何展翔.三维井间电磁最小二乘法反演.石油地球物理勘探,2014,49(3):586-595.Li Jinghe,He Zhanxiang.Three-dimensional cross-well electromagnetic inversion using the least-square method.OGP,2014,49(3):586-595.
[19]
Johnson T C,Roelof J V,Ward A et al.Improved hydro geophysical characterization and monitoring through parallel modeling and inversion of time-domain resistivity and induced-polarization data.Geophysics,2010,75(4):WA27-WA41.
[20]
Sven F.Resolution,stability and efficiency of resistivity tomography estimated from a generalized inverse approach.Geophysical Journal International,2003,153(2):305-316.
[21]
EllisRG,Oldenburg D W.Applied geophysical inversion.Geophysical Journal International,1994,116(1):5-11.
[22]
Scales J A,Gersztenkorn A.Robust methods in inverse theory.Inverse Problems,1988,4(4):1071-1091.
[23]
Carsten R,Thomas R,Klaus S.Three-dimensional modeling and inversion of DC resistivity data incorporation topography-I:Modeling.Geophysical Journal International,2006,166(2):495-505.
