三维主轴各向异性介质中张量CSAMT正反演研究（英文）
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摘要
相较于常用的标量CSAMT而言,由于使用多发射源,张量可控源音频大地电磁(CSAMT)可以接收到更加丰富的电场与磁场信息。然而,目前大多数关于张量CSAMT的理论、数值模拟算法以及反演研究都是基于远区的测量和地下介质为电阻率各向同性的假设。本文采用三维交错网格有限差分数值模拟算法,研究电阻率主轴各向异性介质与各向同性介质的响应差异,并在此基础上采用有限内存拟牛顿法(LBFGS)实现了三维张量CSAMT主轴各向异性反演。为加速和稳定LBFGS反演算法,本文采用了模型参数转换策略并修改了LBFGS第一次迭代的初始步长与线搜索停止条件。反演试算结果表明,当地质体存在主轴各向异性特征时,三维主轴各向异性的反演能在一定程度上较好的反演出地下构造,而不考虑各向异性效应,直接使用各向同性的三维张量CSAMT反演程序,会使最终的反演结果出现严重的假异常。
Tensor controlled-source audio-frequency magnetotellurics(CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional(3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory BroydenFletcher-Goldfarb-Shanno(LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic,the isotropic inversion will introduce errors to the interpretation.
Tensor controlled-source audio-frequency magnetotellurics(CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional(3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory BroydenFletcher-Goldfarb-Shanno(LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic,the isotropic inversion will introduce errors to the interpretation.
引文
Boerner,D.E.,Wright,J.A.,Thurlow,J.G.,and Reed,L.E.,1993,Tensor CSAMT studies at the Buchans Mine in central New found land:Geophysics,58(1),12-19.
Caldwell,T.G.,Bibby,H.M.,and Colin,B.,2002,Controlled source apparent resistivity tensors and their relationship to the Magnetotelluric impedance tensor:Geophysical Journal International,151,755-770.
Commer,M.,and Newman,G.A.,2008,New advances in three-dimensional controlled-source electromagnetic inversion:Geophysical Journal International,172,513-535.
Constable,S.,2010,Ten years of marine CSEM for hydrocarbon exploration:Geophysics,75(5),75A67-75A81.
Egbert,G.D.,and Kelbert,A.,2012,Computational recipes for electromagnetic inverse problems:Geophysical Journal International,189,251-267.
Freund,R.W.and Nachtigal,N.M.,1991,QMR:a quasiminimal residual method for non-Hermitian linear systems:Numerische Mathematik,60(1),315-339.
Garcia,X.,Boerner,D.,and Pedersen,L.B.,2003,Electric and magnetic galvanic distortion decomposition of tensor CSAMT data.Application to data from the Buchans Mine(Newfoundland,Canada):Geophysical Journal International,154,957-969.
Garcia,X.,and Jones,A.G.,2008,Robust processing of magnetotelluric data in the AMT dead band using the continuous wavelet transform:Geophysics,73(6),F223-F234.
Hagiwara,T.,2012,Determination of dip and anisotropy from transient triaxial induction measurements:Geophysics,77(4),D105-D112.
Hu,Y.C.,Li,T.L.,Fan,C.S.,et al.,2005,Threedimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method:Applied Geophysics,12(1),35-46.
Key,K.,2009,1D inversion of multicomponent,multifrequency marine CSEM data:Methodology and synthetic studies for resolving thin resistive layers:Geophysics,74(2),F9-F20.
Key,K.,2016,MARE2DEM:a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data:Geophys J.Int,207,571-588.
Korvin,G.,2012,Bounds for the Resistivity Anisotropy in Thinly-Laminated Sand-Shale:Petrophysics,53(1),14-21.
Lei,D.,Zhang,G.,Huang,G.,et al.,2014,The Application of Tensor CSAMT Method:Chinese Journal of Engineering Geophysics(in Chinese),11(3),1672-7940.
Li,X.,Oskooi,B.,and Pedersen,B.L.,2000,Inversion of controlled-source tensor magnetotelluric data for a layered earth with azimuthal anisotropy:Geophysics,65(2),452-464.
Li,X.,and Pedersen,L.B.,1991,Controlled source tensor magnetotellurics:Geophysics,56(9),1456-1461.
Li,X.,and Pedersen,L.B.,1992,Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy:Geophysical Journal International,111,91-103.
Li,Y.,and Pek,J.,2008,Adaptive finite element modelling of two-dimensional Magnetotelluric fields in general anisotropic media:Geophysical Journal International,175,942-954.
Li,Y.,and Key,K.,2007,2D marine controlled-source electromagnetic modeling:Part I-an adaptive finiteelement algorithm:Geophysics,72(2),WA51-WA62.
Liu,Y.,and Yin,C.,2013,Electromagnetic divergence correction for 3D anisotropic EM modeling:Journal of Applied Geophysics,96,19-27.
Lin,C.,Tan,H.,Shu,Q.,et al.,2012,Three-dimensional conjugate gradient inversion of CSAMT data:Chinese J.Geophys.(in Chinese),55(11),3829-3838.
Lu,X.,Martyn,U.,and John,B.,1999,Rapid relaxation inversion of CSAMT data:Geophysical Journal International,138,381-392.
Newman,G.A.,and Alumbaugh,D.L.,2000,Threedimensional Magnetotelluric inversion using non-linear conjugate gradients:Geophysical Journal International,140,410-424.
Newman,G.A.,Commer,M.,and Carazzone,J.J.,2010,Imaging CSEM data in the presence of electrical anisotropy:Geophysics,75(2),F51-F61.
Nichols,E.A.,Morrison,H.F.,and Clarke,J.,1988,Signals and noise in measurements of low-frequency geomagnetic fields:Journal of Geophysical ResearchSolid Earth and Planets,93(B11),13743-13754.
North,L.J.,and Best,A.I.,2014,Anomalous electrical resistivity anisotropy in clean reservoir sandstones:Geophysical Prospecting,62(6),1315-1326.
Nocedal,J.and Wright,S.J.,2006,Numerical Optimization(2nd ed):Springer Verlag,New York,135-160.
Routh,P.S.,and Oldenburg,D.W.,1999,Inversion of controlled source audio-frequency Magnetotelluric data for a horizontally layered Earth:Geophysics,64(6),1689-1697.
Troiano,A.,Giuseppe,M.G.D.,Petrillo,Z.,and Patella,D.,2009,Imaging 2D structures by the CSAMT method:application to the Pantano di S.Gregorio Magno faulted basin(Southern Italy):Journal of Geophysics&Engineering,6(2),120-130.
Wang,Y.,Di,Q.,and Wang,R.,2017a,Three-dimensional modeling of controlled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid:Chinese J.Geophys.(in Chinese),60(3),1158-1167.
Wang,K.,Tan,H.,and Wang,T.,2017b,2D joint inversion of CSAMT and magnetic data based on cross-gradient theory:Applied Geophysics,14(2),279-290.
Wang,K.,and Tan,H.,2017c,Research on the forward modeling of controlled-source audio-frequency magnetotellurics in three-dimensional axial anisotropic media:Journal of Applied Geophysics,146,27-36.
Wannamaker,P.E.,1997,Tensor CSAMT survey over the Sulphur Springs thermal area,Valles Caldera,New Mexico,United States of America,PartⅡ:Implications for CSAMT methodology:Geophysics,62(2),466-476.
Weng,A.H.,Liu,Y.H.,Jia,D.Y.,et al.,2012,Threedimensional controlled source electromagnetic inversion using non-linear conjugate gradients:Chinese J.Geophys.(in Chinese),55(10),3506-3515.
Yang,B.,Xu,Y.X.,He,Z.X.,et al.,2012,3D frequencydomain modeling of marine controlled-source electromagnetic responses with topography using finite volume method:Chinese J.Geophys.(in Chinese),55(4),1390-1399.
Younis,A.,El-Qady,G.,Alla,M.A.,et al.,2015,AMT and CSAMT methods for hydrocarbon exploration at Nile Delta,Egypt:Arabian Journal of Geosciences,8(4),1965-1975.
Zhou,J.,Wang,J.,Shang,Q.,Wang,H.,and Yin,C.,2014,Regularized inversion of controlled source audiofrequency Magnetotelluric data in horizontally layered transversely isotropic media:Journal of Geophysics&Engineering,11(2),25003-25014.
Zonge,K.L.,and Hughes,L.J.,1991,Controlled source audio-frequency magnetotellurics,in Nabighian M.N.Eds.,Electromagnetic methods in applied geophysics:Society of Exploration Geophysicists Press,USA,713-810.
Caldwell,T.G.,Bibby,H.M.,and Colin,B.,2002,Controlled source apparent resistivity tensors and their relationship to the Magnetotelluric impedance tensor:Geophysical Journal International,151,755-770.
Commer,M.,and Newman,G.A.,2008,New advances in three-dimensional controlled-source electromagnetic inversion:Geophysical Journal International,172,513-535.
Constable,S.,2010,Ten years of marine CSEM for hydrocarbon exploration:Geophysics,75(5),75A67-75A81.
Egbert,G.D.,and Kelbert,A.,2012,Computational recipes for electromagnetic inverse problems:Geophysical Journal International,189,251-267.
Freund,R.W.and Nachtigal,N.M.,1991,QMR:a quasiminimal residual method for non-Hermitian linear systems:Numerische Mathematik,60(1),315-339.
Garcia,X.,Boerner,D.,and Pedersen,L.B.,2003,Electric and magnetic galvanic distortion decomposition of tensor CSAMT data.Application to data from the Buchans Mine(Newfoundland,Canada):Geophysical Journal International,154,957-969.
Garcia,X.,and Jones,A.G.,2008,Robust processing of magnetotelluric data in the AMT dead band using the continuous wavelet transform:Geophysics,73(6),F223-F234.
Hagiwara,T.,2012,Determination of dip and anisotropy from transient triaxial induction measurements:Geophysics,77(4),D105-D112.
Hu,Y.C.,Li,T.L.,Fan,C.S.,et al.,2005,Threedimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method:Applied Geophysics,12(1),35-46.
Key,K.,2009,1D inversion of multicomponent,multifrequency marine CSEM data:Methodology and synthetic studies for resolving thin resistive layers:Geophysics,74(2),F9-F20.
Key,K.,2016,MARE2DEM:a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data:Geophys J.Int,207,571-588.
Korvin,G.,2012,Bounds for the Resistivity Anisotropy in Thinly-Laminated Sand-Shale:Petrophysics,53(1),14-21.
Lei,D.,Zhang,G.,Huang,G.,et al.,2014,The Application of Tensor CSAMT Method:Chinese Journal of Engineering Geophysics(in Chinese),11(3),1672-7940.
Li,X.,Oskooi,B.,and Pedersen,B.L.,2000,Inversion of controlled-source tensor magnetotelluric data for a layered earth with azimuthal anisotropy:Geophysics,65(2),452-464.
Li,X.,and Pedersen,L.B.,1991,Controlled source tensor magnetotellurics:Geophysics,56(9),1456-1461.
Li,X.,and Pedersen,L.B.,1992,Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy:Geophysical Journal International,111,91-103.
Li,Y.,and Pek,J.,2008,Adaptive finite element modelling of two-dimensional Magnetotelluric fields in general anisotropic media:Geophysical Journal International,175,942-954.
Li,Y.,and Key,K.,2007,2D marine controlled-source electromagnetic modeling:Part I-an adaptive finiteelement algorithm:Geophysics,72(2),WA51-WA62.
Liu,Y.,and Yin,C.,2013,Electromagnetic divergence correction for 3D anisotropic EM modeling:Journal of Applied Geophysics,96,19-27.
Lin,C.,Tan,H.,Shu,Q.,et al.,2012,Three-dimensional conjugate gradient inversion of CSAMT data:Chinese J.Geophys.(in Chinese),55(11),3829-3838.
Lu,X.,Martyn,U.,and John,B.,1999,Rapid relaxation inversion of CSAMT data:Geophysical Journal International,138,381-392.
Newman,G.A.,and Alumbaugh,D.L.,2000,Threedimensional Magnetotelluric inversion using non-linear conjugate gradients:Geophysical Journal International,140,410-424.
Newman,G.A.,Commer,M.,and Carazzone,J.J.,2010,Imaging CSEM data in the presence of electrical anisotropy:Geophysics,75(2),F51-F61.
Nichols,E.A.,Morrison,H.F.,and Clarke,J.,1988,Signals and noise in measurements of low-frequency geomagnetic fields:Journal of Geophysical ResearchSolid Earth and Planets,93(B11),13743-13754.
North,L.J.,and Best,A.I.,2014,Anomalous electrical resistivity anisotropy in clean reservoir sandstones:Geophysical Prospecting,62(6),1315-1326.
Nocedal,J.and Wright,S.J.,2006,Numerical Optimization(2nd ed):Springer Verlag,New York,135-160.
Routh,P.S.,and Oldenburg,D.W.,1999,Inversion of controlled source audio-frequency Magnetotelluric data for a horizontally layered Earth:Geophysics,64(6),1689-1697.
Troiano,A.,Giuseppe,M.G.D.,Petrillo,Z.,and Patella,D.,2009,Imaging 2D structures by the CSAMT method:application to the Pantano di S.Gregorio Magno faulted basin(Southern Italy):Journal of Geophysics&Engineering,6(2),120-130.
Wang,Y.,Di,Q.,and Wang,R.,2017a,Three-dimensional modeling of controlled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid:Chinese J.Geophys.(in Chinese),60(3),1158-1167.
Wang,K.,Tan,H.,and Wang,T.,2017b,2D joint inversion of CSAMT and magnetic data based on cross-gradient theory:Applied Geophysics,14(2),279-290.
Wang,K.,and Tan,H.,2017c,Research on the forward modeling of controlled-source audio-frequency magnetotellurics in three-dimensional axial anisotropic media:Journal of Applied Geophysics,146,27-36.
Wannamaker,P.E.,1997,Tensor CSAMT survey over the Sulphur Springs thermal area,Valles Caldera,New Mexico,United States of America,PartⅡ:Implications for CSAMT methodology:Geophysics,62(2),466-476.
Weng,A.H.,Liu,Y.H.,Jia,D.Y.,et al.,2012,Threedimensional controlled source electromagnetic inversion using non-linear conjugate gradients:Chinese J.Geophys.(in Chinese),55(10),3506-3515.
Yang,B.,Xu,Y.X.,He,Z.X.,et al.,2012,3D frequencydomain modeling of marine controlled-source electromagnetic responses with topography using finite volume method:Chinese J.Geophys.(in Chinese),55(4),1390-1399.
Younis,A.,El-Qady,G.,Alla,M.A.,et al.,2015,AMT and CSAMT methods for hydrocarbon exploration at Nile Delta,Egypt:Arabian Journal of Geosciences,8(4),1965-1975.
Zhou,J.,Wang,J.,Shang,Q.,Wang,H.,and Yin,C.,2014,Regularized inversion of controlled source audiofrequency Magnetotelluric data in horizontally layered transversely isotropic media:Journal of Geophysics&Engineering,11(2),25003-25014.
Zonge,K.L.,and Hughes,L.J.,1991,Controlled source audio-frequency magnetotellurics,in Nabighian M.N.Eds.,Electromagnetic methods in applied geophysics:Society of Exploration Geophysicists Press,USA,713-810.