三维电阻率空间结构约束反演成像方法
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摘要
反演的多解性是三维电阻率探测的固有问题,极易造成地质解释的误差甚至错误。针对该问题,提出利用其他勘探地球物理方法(如地震反射方法、地质雷达方法等)获得的异常体的空间结构和形态信息作为电阻率反演先验约束的学术思路。首先,提出空间结构约束这一新约束的构制方法,将已知异常区域(由其他勘探地球物理方法得到)映射到三维反演模型中,使得对应区域的各网格之间的电阻率差异极小,建立一种表达简单、易于实现的空间结构约束矩阵,可表征常见典型构造,特别是形态或结构较复杂的地质构造。在此基础上,构造携带空间结构约束的三维电阻率探测反演目标函数及其反演成像方程,形成三维电阻率探测空间约束反演成像方法。然后,基于上述反演方法,开展数值试验和工程应用,将地质雷达和地质分析获得的空间结构约束施加到三维电阻率反演中,发现利用三维电阻率空间结构约束反演方法大大增加了异常区域的先验信息,可有效去除反演成像中的假异常和多余构造,对异常体的定位精度和界面分辨效果较传统的电阻率反演方法有了很大的提高,使得反演结果与地质原型较为一致,显著压制了电阻率探测反演的多解性问题,证明三维电阻率探测空间结构约束反演成像方法是抑制多解性、改善定位精度和界面分辨效果的可行途径。
Multiplicity of solutions to inversion is a inherent problem of 3D electrical resistivity detection,which always causes errors and even mistakes in the geological interpretation.A research thought is presented to solve the problem,in which the structural and morphology information of anomalous body gained by other geophysical methods,e.g.seismic prospecting,ground penetrating radar,is used as prior constraints in resistivity inversion.First,construction method of a novel constraint named spatial structural constraint is proposed.The known anomalous regions obtained with other geophysical methods are mapped into 3D inversion model;and the difference between grids in corresponding regions is restricted to minimum.Thus,spatial structural constraint matrix is established to characterize typical geological structures,especially the more complicated structures;and it is relatively easy to be expressed mathematically and constructed.Based on above research,the objective function and inversion tomography equation of 3D resistivity inversion with spatial structural constraint are constructed.Then,numerical tests and engineering application are implemented;and the spatial structural constraint gained by ground penetrating radar(GPR) is applied to 3D resistivity inversion.It is found that the prior information increases greatly and false anomaly in inversion tomography is eliminated effectively.And the location precision and interface identification-effect are improved significantly compared with traditional method,making the inversion result be consistent with geological model or actual situation and the multiplicity of solutions be pressed obviously.And it is proved that the 3D resistivity inversion tomography with spatial structural constraint is a feasible way to reduce multiplicity of solutions and improve location precision and interface identification-effect.
Multiplicity of solutions to inversion is a inherent problem of 3D electrical resistivity detection,which always causes errors and even mistakes in the geological interpretation.A research thought is presented to solve the problem,in which the structural and morphology information of anomalous body gained by other geophysical methods,e.g.seismic prospecting,ground penetrating radar,is used as prior constraints in resistivity inversion.First,construction method of a novel constraint named spatial structural constraint is proposed.The known anomalous regions obtained with other geophysical methods are mapped into 3D inversion model;and the difference between grids in corresponding regions is restricted to minimum.Thus,spatial structural constraint matrix is established to characterize typical geological structures,especially the more complicated structures;and it is relatively easy to be expressed mathematically and constructed.Based on above research,the objective function and inversion tomography equation of 3D resistivity inversion with spatial structural constraint are constructed.Then,numerical tests and engineering application are implemented;and the spatial structural constraint gained by ground penetrating radar(GPR) is applied to 3D resistivity inversion.It is found that the prior information increases greatly and false anomaly in inversion tomography is eliminated effectively.And the location precision and interface identification-effect are improved significantly compared with traditional method,making the inversion result be consistent with geological model or actual situation and the multiplicity of solutions be pressed obviously.And it is proved that the 3D resistivity inversion tomography with spatial structural constraint is a feasible way to reduce multiplicity of solutions and improve location precision and interface identification-effect.
引文
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[10]PIDLISECKY A,HABER E,KNIGHT R.RESINVM3D:a 3Dresistivity inversion package[J].Geophysics,2007,72(2):H1–H10.
[11]KIM H J,SONG Y,LEE K H.Inequality constraint in least-squaresinversion of geophysical data[J].Earth Planets Space,1999,51:255–259.
[12]MUSIL M,MAURER H R,GREEN A G.Discrete tomography andjoint inversion for loosely connected or unconnected physicalproperties:application to crosshole seismic and georadar data sets[J].Geophysical Journal International,2003,153(2):389–402.
[13]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[J].地球物理学报,2012,55(1):260–268.(LIU Bin,LI Shucai,LI Shuchen,et al.3D electrical resistivityinversion with least-squares method based on inequality constraint andits computation efficiency optimization[J].Chinese Journal ofGeophysics,2012,55(1):260–268.(in Chinese))
[14]KAIPIO J P,KOLEHMAINEN V,VAUHKONEN M,et al.Inverseproblems with structural prior information[J].Inverse Problems,1999,15(3):713–729.
[15]LI Y G,OLDENBURG D W.Incorporating geological dip informationinto geophysical inversions[J].Geophysics,2000,65(1):148–157.
[16]SAUNDERS J H,HERWANGER J V,PAIN C C,et al.Constrainedresistivity inversion using seismic data[J].Geophysical Journal International,2005,160(3):785–796.
[17]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[J].岩土工程学报,2012,34(9):1646–1 653.(LIU Bin,LI Shucai,NIE Lichao,et al.Study on inversion methodof 3D resistivity detection using adaptive-weighted smooth constraint andPCG algorithm[J].Chinese Journal of Geotechnical Engineering,2012,34(9):1 646–1 653.(in Chinese))
[2]王家映.地球物理反演理论[M].北京:高等教育出版社,2002:20–21.(WANG Jiaying.Inverse theory in geophysics[M].Beijing:Higher Education Press,2002:20–21.(in Chinese))
[3]SASAKI Y.3D resistivity inversion using the finite elementmethod[J].Geophysics,1994,59(11):1 839–1 848.
[4]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 Baiyao,MURAKAMI Y,XU Shizhe.2D inversion program of inducedpolarization data[J].Computing Techniques for Geophysical andGeochemical Exploration,1999,21(2):116–125.(in Chinese))
[5]黄俊革.三维电阻率/极化率有限元正演模拟与反演成像[博士学位论文][D].长沙:中南大学,2003.(HUANG Junge.3D resistivity/IPmodeling and inversion based on FEM[Ph.D.Thesis][D].Changsha:Central South University,2003.(in Chinese))
[6]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 Qingyun,WANG Miaoyue.3D resistivitytomography by integral method[J].Chinese Journal of Geophysics,2001,44(6):843–852.(in Chinese))
[7]JIE Z,MACKIE R L,.MADDEN T R.3D resistivity forwardmodeling and inversion using conjugate gradients[J].Geophysics,60(5):1 313–1 325.
[8]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 Xiaoping,XU Guoming.Studyon 3D resistivity inversion using conjugate gradient method[J].Chinese Journal of Geophysics,2000,43(3):420–426.(in Chinese))
[9]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 Xinlin,XI Daoying,GAO Ergen,et al.3-D resistivityinversion by the least-squares QR factorization method underimproved smoothness constraint condition[J].Chinese Journal ofGeophysics,2005,48(1):439–444.(in Chinese))
[10]PIDLISECKY A,HABER E,KNIGHT R.RESINVM3D:a 3Dresistivity inversion package[J].Geophysics,2007,72(2):H1–H10.
[11]KIM H J,SONG Y,LEE K H.Inequality constraint in least-squaresinversion of geophysical data[J].Earth Planets Space,1999,51:255–259.
[12]MUSIL M,MAURER H R,GREEN A G.Discrete tomography andjoint inversion for loosely connected or unconnected physicalproperties:application to crosshole seismic and georadar data sets[J].Geophysical Journal International,2003,153(2):389–402.
[13]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[J].地球物理学报,2012,55(1):260–268.(LIU Bin,LI Shucai,LI Shuchen,et al.3D electrical resistivityinversion with least-squares method based on inequality constraint andits computation efficiency optimization[J].Chinese Journal ofGeophysics,2012,55(1):260–268.(in Chinese))
[14]KAIPIO J P,KOLEHMAINEN V,VAUHKONEN M,et al.Inverseproblems with structural prior information[J].Inverse Problems,1999,15(3):713–729.
[15]LI Y G,OLDENBURG D W.Incorporating geological dip informationinto geophysical inversions[J].Geophysics,2000,65(1):148–157.
[16]SAUNDERS J H,HERWANGER J V,PAIN C C,et al.Constrainedresistivity inversion using seismic data[J].Geophysical Journal International,2005,160(3):785–796.
[17]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[J].岩土工程学报,2012,34(9):1646–1 653.(LIU Bin,LI Shucai,NIE Lichao,et al.Study on inversion methodof 3D resistivity detection using adaptive-weighted smooth constraint andPCG algorithm[J].Chinese Journal of Geotechnical Engineering,2012,34(9):1 646–1 653.(in Chinese))
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