大地电磁相位超象限现象的各向异性模型研究——以上下结构为例
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摘要
大地电磁观测数据中的相位超象限现象可以由不同的电性结构产生.本文在已实现大地电磁三维任意各向异性有限差分正演的基础上,以具有上下结构关系的三维各向异性模型为例,分析各向异性体的规模以及参数变化对阻抗相位的影响.在下部各向异性体规模明显大于上部各向异性体或表现为层状特征的情况下,上部各向异性体在两个水平方向上的尺度差异较大,可以看作准二维体时容易发生相位超象限;当上部各向异性体在两个水平方向上尺度相近表现为规则三维体时,要产生相位超象限的现象则需要各向异性体具有更高的各向异性比.在同等条件下,增加各向异性体的各向异性比更容易发生相位超象限;而各向异性走向方位角的变化将直接影响到发生相位超象限的范围.对于准二维模型引起相位超象限的条件,沿用二维模型的近似解析分析方法,进一步构建了基于各向异性体的电导率、背景电导率以及各向异性走向角的相位超象限指标函数,从而更加直观地解释在二维或准二维条件下发生相位超象限现象的模型参数特征.
The PROQ(Phase Roll out of Quadrant)phenomenon in magnetotelluric observed data may be caused by different electrical resistivity structure.In this paper,based on the threedimensional finite-difference forward modeling of arbitrary anisotropic models,we analyzed how the scales and anisotropic parameters of anomalous bodies influence impedance phases with the examples of upper-lower structure.In all the models,the lower anomalous body is apparently larger than the upper one in scale or in a layer.If the upper anomalous body has a great difference in its horizontal length and can be treated as quasi two-dimensional structure,the model is easier to produce PROQ phenomenon.If the upper anomalous body shows similar length in both horizontaldirections and can be considered as regular three-dimensional structure,it needs higher anisotropic ratio in anisotropic bodies to generate PROQ effect.Under the same conditions,increasing anisotropic ratio will be prone to PROQ;variations in anisotropic strike will influence the range of PROQ areas directly.We adopted and extended the approximately analytical analysis of PROQ in two-dimensional conditions,and further built an indicator function including the anisotropic conductivity,anisotropic strike,and host conductivity to interpret PROQ phenomenon in quasi twodimensional or two-dimensional cases intuitively.
The PROQ(Phase Roll out of Quadrant)phenomenon in magnetotelluric observed data may be caused by different electrical resistivity structure.In this paper,based on the threedimensional finite-difference forward modeling of arbitrary anisotropic models,we analyzed how the scales and anisotropic parameters of anomalous bodies influence impedance phases with the examples of upper-lower structure.In all the models,the lower anomalous body is apparently larger than the upper one in scale or in a layer.If the upper anomalous body has a great difference in its horizontal length and can be treated as quasi two-dimensional structure,the model is easier to produce PROQ phenomenon.If the upper anomalous body shows similar length in both horizontaldirections and can be considered as regular three-dimensional structure,it needs higher anisotropic ratio in anisotropic bodies to generate PROQ effect.Under the same conditions,increasing anisotropic ratio will be prone to PROQ;variations in anisotropic strike will influence the range of PROQ areas directly.We adopted and extended the approximately analytical analysis of PROQ in two-dimensional conditions,and further built an indicator function including the anisotropic conductivity,anisotropic strike,and host conductivity to interpret PROQ phenomenon in quasi twodimensional or two-dimensional cases intuitively.
引文
Chen X,Weckmann U,Tietze K.2009.From forward modelling of MTphases over 90°towards 2Danisotropic inversion.∥SchmuckerWeidelt-Colloquium für Elektromagnetische Tiefenforschung,Heimvolkshochschule am Seddiner See.Germany.
Cherevatova M,Smirnov M Y,Jones A G,et al.2015.Magnetotelluric array data analysis from north-west Fennoscandia.Tectonophysics,653:1-19,doi:10.1016/j.tecto.2014.12.023.
Chouteau M,Tournerie B.2000.Analysis of magnetotelluric data showing phase rolling out of quadrant(PROQ).∥70th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,344-346,doi:10.1190/1.1816062.
de Lugo P,Kriegshuser B,Finateu C.2013.Phase roll out of quadrant effect in MT data from a gold prospect.∥13th International Congress of the Brazilian Geophysical Society.Rio de Janeiro,Brazil:SEG,doi:10.1190/sbgf2013-161.
Heise W,Pous J.2003.Anomalous phases exceeding 90°in magnetotellurics:anisotropic model studies and a field example.Geophysical Journal International,155(1):308-318,doi:10.1046/j.1365-246X.2003.02050.x.
Hu X Y,Huo G P,Gao R,et al.2013.The magnetotelluric anisotropic two-dimensional simulation and case analysis.Chinese Journal of Geophysics(in Chinese),56(12):4268-4277,doi:10.6038/cjg20131229.
Huo G P,Hu X Y,Huang Y F,et al.2015.MT modeling for twodimensional anisotropic conductivity structure with topography and examples of comparative analyses.Chinese Journal of Geophysics(in Chinese),58(12):4696-4708,doi:10.6038/cjg20151230.
Ichihara H,Mogi T,Yamaya Y.2013.Three-dimensional resistivity modelling of a seismogenic area in an oblique subduction zone in the western Kurile arc:constraints from anomalous magnetotelluric phases.Tectonophysics,603:114-122,doi:10.1016/j.tecto.2013.05.020.
Jones A G,Kurtz R D,Oldenburg D W,et al.1988.Magnetotelluric observations along the lithoprobe southeastern Canadian Cordilleran Transect.Geophysical Research Letters,15(7):677-680.
Jones A G.2012.Distortion decomposition of the magnetotelluric impedance tensors from a one-dimensional anisotropic Earth.Geophysical Journal International,189(1):268-284,doi:10.1111/j.1365-246X.2012.05362.x.
Junge A.2016.3D anisotropic modelling and EM transfer functions.∥The 23rd Electromagnetic Induction Workshop.Chiang Mai,Thailand.
Kühn C,Küster J,Brasse H.2014.Three-dimensional inversion of magnetotelluric data from the Central Andean continental margin.Earth,Planets and Space,66:112,doi:10.1186/1880-5981-66-112.
Kumar G P,Manglik A.2012.Electrical anisotropy in the Main Central Thrust Zone of the Sikkim Himalaya:inference from anomalous MT phase.Journal of Asian Earth Sciences,57:120-127,doi:10.1016/j.jseaes.2012.06.017.
Kuzmin A,Luisier M,Schenk O.2013.Fast methods for computing selected elements of the Green′s function in massively parallel nanoelectronic device simulations.∥Wolf F,Mohr B,Ney D Aeds.Euro-Par 2013Parallel Processing.Berlin:Springer,8097:533-544,doi:10.1007/978-3-642-40047-6_54.
Lezaeta P,Haak V.2003.Beyond magnetotelluric decomposition:induction,current channeling,and magnetotelluric phases over90°.Journal of Geophysical Research:Solid Earth,108(B6):2305,doi:10.1029/2001JB000990.
Li Y G.2002.A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures.Geophysical Journal International,148(3):389-401,doi:10.1046/j.1365-246x.2002.01570.x.
Livelybrooks D,Mareschal M,Blais E,et al.1996.Magnetotelluric delineation of the Trillabelle massive sulfide body in Sudbury,Ontario.Geophysics,61(4):971-986,doi:10.1190/1.1444046.
Martí A.2014.The role of electrical anisotropy in magnetotelluric responses:from modelling and dimensionality analysis to inversion and interpretation.Surveys in Geophysics,35(1):179-218,doi:10.1007/s10712-013-9233-3.
Martinelli P,Osella A.1997.MT forward modeling of 3-D anisotropic electrical conductivity structures using the Rayleigh-Fourier method.Journal of Geomagnetism and Geoelectricity,49(11-12):1499-1518.
Newman G A,Alumbaugh D L.2002.Three-dimensional induction logging problems,part 2:a finite-difference solution.Geophysics,67(2):484-491,doi:10.1190/1.1468608.
Pek J,Verner T.1997.Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media.Geophysical Journal International,128(3):505-521,doi:10.1111/j.1365-246X.1997.tb05314.x.
Qin C,Wang X B,Zhao N.2017.Parallel three-dimensional forward modeling and inversion of magnetotelluric based on a secondary field approach.Chinese Journal of Geophysics(in Chinese),60(6):2456-2468,doi:10.6038/cjg20170633.
Qin L J,Yang C F,Chen K.2013.Quasi-analytic solution of 2-Dmagnetotelluric fields on an axially anisotropic infinite fault.Geophysical Journal International,192(1):67-74,doi:10.1093/gji/ggs018.
Reddy I K,Rankin D.1975.Magnetotelluric response of laterally inhomogeneous and anisotropic media.Geophysics,40(6):1035-1045,doi:10.1190/1.1440579.
Schenk O,Grtner K.2004.Solving unsymmetric sparse systems of linear equations with PARDISO.Future Generation Computer Systems,20(3):475-487,doi:10.1016/j.future.2003.07.011.
Shao G H,Xiao Q B.2016.Model for phase rolling out of quadrant magnetotelluric data-an example from north to the Hexi corridor.Progress in Geophysics(in Chinese),31(4):1480-1491,doi:10.6038/pg20160410.
Siripunvaraporn W,Egbert G,Lenbury Y.2002.Numerical accuracy of magnetotelluric modeling:a comparison of finite difference approximations.Earth,Planets and Space,54(6):721-725,doi:10.1186/BF03351724.
Tan H D,Yu Q F,Booker J,et al.2003.Magnetotelluric threedimensional modeling using the staggered-grid finite difference method.Chinese Journal of Geophysics(in Chinese),46(5):705-711,doi:10.3321/j.issn:0001-5733.2003.05.019.
Vaittinen K,Korja T,Kaikkonen P,et al.2012.High-resolution magnetotelluric studies of the Archaean-Proterozoic border zone in the Fennoscandian Shield,Finland.GeophysicalJournal International,188(3):908-924,doi:10.1111/j.1365-246X.2011.05300.x.
Weckmann U,Ritter O,Haak V.2003.A magnetotelluric study of the Damara Belt in Namibia:2.MT phases over 90°reveal the internal structure of the Waterberg Fault/Omaruru Lineament.Physics of the Earth and Planetary Interiors,138(2):91-112,doi:10.1016/S0031-9201(03)00079-7.
Weidelt P.1999.3D conductivity models:implications of electrical anisotropy.∥Oristaglio M,Spies B eds.Three-Dimensional Electromagnetics.New York:Society of Exploration Geophysicists Publishers,119-137.
Weiss C J,Newman G A.2002.Electromagnetic induction in a fully3-D anisotropic earth.Geophysics,67(4):1104-1114,doi:10.1190/1.1500371.
Xiao Q B,Zhang J,Zhao G Z,et al.2013.Electrical resistivity structures northeast of the Eastern Kunlun Fault in the
Northeastern Tibet:Tectonic implications.Tectonophysics,601:125-138,doi:10.1016/j.tecto.2013.05.003.
Xiao Q B,Shao G H,Liu-Zeng J,et al.2015.Eastern termination of the Altyn Tagh Fault,western China:constraints from a magnetotelluric survey.Journal of Geophysical Research:Solid Earth,120(5):2838-2858,doi:10.1002/2014JB011363.
Xiao Q B,Shao G H,Yu G,et al.2016.Electrical resistivity structures of the Kunlun-Qaidam-Qilian system at the northern Tibet and their tectonic implications.Physics of the Earth and Planetary Interiors,255:1-17,doi:10.1016/j.pepi.2016.03.011.
Xu Z,Li Y.2016.Three-dimensional finite element modelling of magnetotelluric fields in general anisotropic media.∥Proceedings of the 23rd Electromagnetic Induction Workshop.Chiang Mai,Thailand.
Yee K S.1966.Numerical solution of initial boundary value problems involving Maxwell′s equations in isotropic media.IEEE Transactions on Antennas&Propagation,14(3):302-307,doi:10.1109/TAP.1966.1138693.
Yu G,Xiao Q B,Zhao G Z,et al.2018.Three-dimensional magnetotelluric responses for arbitrary electrically anisotropic media and a practical application.Geophysical Prospecting,66:1764-1783,doi:10.1111/1365-2478.12690.
胡祥云,霍光谱,高锐等.2013.大地电磁各向异性二维模拟及实例分析.地球物理学报,56(12):4268-4277,doi:10.6038/cjg20131229.
霍光谱,胡祥云,黄一凡等.2015.带地形的大地电磁各向异性二维模拟及实例对比分析.地球物理学报,58(12):4696-4708,doi:10.6038/cjg20151230.
秦策,王绪本,赵宁.2017.基于二次场方法的并行三维大地电磁正反演研究.地球物理学报,60(6):2456-4268,doi:10.6038/cjg20170633.
邵贵航,肖骑彬.2016.相位超象限大地电磁观测数据的模型研究---以河西走廊北侧为例.地球物理学进展,31(4):1480-1491,doi:10.6038/pg20160410.
谭捍东,余钦范,Booker J等.2003.大地电磁法三维交错采样有限差分数值模拟.地球物理学报,46(5):705-711,doi:10.3321/j.issn:0001-5733.2003.05.019.
Cherevatova M,Smirnov M Y,Jones A G,et al.2015.Magnetotelluric array data analysis from north-west Fennoscandia.Tectonophysics,653:1-19,doi:10.1016/j.tecto.2014.12.023.
Chouteau M,Tournerie B.2000.Analysis of magnetotelluric data showing phase rolling out of quadrant(PROQ).∥70th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,344-346,doi:10.1190/1.1816062.
de Lugo P,Kriegshuser B,Finateu C.2013.Phase roll out of quadrant effect in MT data from a gold prospect.∥13th International Congress of the Brazilian Geophysical Society.Rio de Janeiro,Brazil:SEG,doi:10.1190/sbgf2013-161.
Heise W,Pous J.2003.Anomalous phases exceeding 90°in magnetotellurics:anisotropic model studies and a field example.Geophysical Journal International,155(1):308-318,doi:10.1046/j.1365-246X.2003.02050.x.
Hu X Y,Huo G P,Gao R,et al.2013.The magnetotelluric anisotropic two-dimensional simulation and case analysis.Chinese Journal of Geophysics(in Chinese),56(12):4268-4277,doi:10.6038/cjg20131229.
Huo G P,Hu X Y,Huang Y F,et al.2015.MT modeling for twodimensional anisotropic conductivity structure with topography and examples of comparative analyses.Chinese Journal of Geophysics(in Chinese),58(12):4696-4708,doi:10.6038/cjg20151230.
Ichihara H,Mogi T,Yamaya Y.2013.Three-dimensional resistivity modelling of a seismogenic area in an oblique subduction zone in the western Kurile arc:constraints from anomalous magnetotelluric phases.Tectonophysics,603:114-122,doi:10.1016/j.tecto.2013.05.020.
Jones A G,Kurtz R D,Oldenburg D W,et al.1988.Magnetotelluric observations along the lithoprobe southeastern Canadian Cordilleran Transect.Geophysical Research Letters,15(7):677-680.
Jones A G.2012.Distortion decomposition of the magnetotelluric impedance tensors from a one-dimensional anisotropic Earth.Geophysical Journal International,189(1):268-284,doi:10.1111/j.1365-246X.2012.05362.x.
Junge A.2016.3D anisotropic modelling and EM transfer functions.∥The 23rd Electromagnetic Induction Workshop.Chiang Mai,Thailand.
Kühn C,Küster J,Brasse H.2014.Three-dimensional inversion of magnetotelluric data from the Central Andean continental margin.Earth,Planets and Space,66:112,doi:10.1186/1880-5981-66-112.
Kumar G P,Manglik A.2012.Electrical anisotropy in the Main Central Thrust Zone of the Sikkim Himalaya:inference from anomalous MT phase.Journal of Asian Earth Sciences,57:120-127,doi:10.1016/j.jseaes.2012.06.017.
Kuzmin A,Luisier M,Schenk O.2013.Fast methods for computing selected elements of the Green′s function in massively parallel nanoelectronic device simulations.∥Wolf F,Mohr B,Ney D Aeds.Euro-Par 2013Parallel Processing.Berlin:Springer,8097:533-544,doi:10.1007/978-3-642-40047-6_54.
Lezaeta P,Haak V.2003.Beyond magnetotelluric decomposition:induction,current channeling,and magnetotelluric phases over90°.Journal of Geophysical Research:Solid Earth,108(B6):2305,doi:10.1029/2001JB000990.
Li Y G.2002.A finite-element algorithm for electromagnetic induction in two-dimensional anisotropic conductivity structures.Geophysical Journal International,148(3):389-401,doi:10.1046/j.1365-246x.2002.01570.x.
Livelybrooks D,Mareschal M,Blais E,et al.1996.Magnetotelluric delineation of the Trillabelle massive sulfide body in Sudbury,Ontario.Geophysics,61(4):971-986,doi:10.1190/1.1444046.
Martí A.2014.The role of electrical anisotropy in magnetotelluric responses:from modelling and dimensionality analysis to inversion and interpretation.Surveys in Geophysics,35(1):179-218,doi:10.1007/s10712-013-9233-3.
Martinelli P,Osella A.1997.MT forward modeling of 3-D anisotropic electrical conductivity structures using the Rayleigh-Fourier method.Journal of Geomagnetism and Geoelectricity,49(11-12):1499-1518.
Newman G A,Alumbaugh D L.2002.Three-dimensional induction logging problems,part 2:a finite-difference solution.Geophysics,67(2):484-491,doi:10.1190/1.1468608.
Pek J,Verner T.1997.Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media.Geophysical Journal International,128(3):505-521,doi:10.1111/j.1365-246X.1997.tb05314.x.
Qin C,Wang X B,Zhao N.2017.Parallel three-dimensional forward modeling and inversion of magnetotelluric based on a secondary field approach.Chinese Journal of Geophysics(in Chinese),60(6):2456-2468,doi:10.6038/cjg20170633.
Qin L J,Yang C F,Chen K.2013.Quasi-analytic solution of 2-Dmagnetotelluric fields on an axially anisotropic infinite fault.Geophysical Journal International,192(1):67-74,doi:10.1093/gji/ggs018.
Reddy I K,Rankin D.1975.Magnetotelluric response of laterally inhomogeneous and anisotropic media.Geophysics,40(6):1035-1045,doi:10.1190/1.1440579.
Schenk O,Grtner K.2004.Solving unsymmetric sparse systems of linear equations with PARDISO.Future Generation Computer Systems,20(3):475-487,doi:10.1016/j.future.2003.07.011.
Shao G H,Xiao Q B.2016.Model for phase rolling out of quadrant magnetotelluric data-an example from north to the Hexi corridor.Progress in Geophysics(in Chinese),31(4):1480-1491,doi:10.6038/pg20160410.
Siripunvaraporn W,Egbert G,Lenbury Y.2002.Numerical accuracy of magnetotelluric modeling:a comparison of finite difference approximations.Earth,Planets and Space,54(6):721-725,doi:10.1186/BF03351724.
Tan H D,Yu Q F,Booker J,et al.2003.Magnetotelluric threedimensional modeling using the staggered-grid finite difference method.Chinese Journal of Geophysics(in Chinese),46(5):705-711,doi:10.3321/j.issn:0001-5733.2003.05.019.
Vaittinen K,Korja T,Kaikkonen P,et al.2012.High-resolution magnetotelluric studies of the Archaean-Proterozoic border zone in the Fennoscandian Shield,Finland.GeophysicalJournal International,188(3):908-924,doi:10.1111/j.1365-246X.2011.05300.x.
Weckmann U,Ritter O,Haak V.2003.A magnetotelluric study of the Damara Belt in Namibia:2.MT phases over 90°reveal the internal structure of the Waterberg Fault/Omaruru Lineament.Physics of the Earth and Planetary Interiors,138(2):91-112,doi:10.1016/S0031-9201(03)00079-7.
Weidelt P.1999.3D conductivity models:implications of electrical anisotropy.∥Oristaglio M,Spies B eds.Three-Dimensional Electromagnetics.New York:Society of Exploration Geophysicists Publishers,119-137.
Weiss C J,Newman G A.2002.Electromagnetic induction in a fully3-D anisotropic earth.Geophysics,67(4):1104-1114,doi:10.1190/1.1500371.
Xiao Q B,Zhang J,Zhao G Z,et al.2013.Electrical resistivity structures northeast of the Eastern Kunlun Fault in the
Northeastern Tibet:Tectonic implications.Tectonophysics,601:125-138,doi:10.1016/j.tecto.2013.05.003.
Xiao Q B,Shao G H,Liu-Zeng J,et al.2015.Eastern termination of the Altyn Tagh Fault,western China:constraints from a magnetotelluric survey.Journal of Geophysical Research:Solid Earth,120(5):2838-2858,doi:10.1002/2014JB011363.
Xiao Q B,Shao G H,Yu G,et al.2016.Electrical resistivity structures of the Kunlun-Qaidam-Qilian system at the northern Tibet and their tectonic implications.Physics of the Earth and Planetary Interiors,255:1-17,doi:10.1016/j.pepi.2016.03.011.
Xu Z,Li Y.2016.Three-dimensional finite element modelling of magnetotelluric fields in general anisotropic media.∥Proceedings of the 23rd Electromagnetic Induction Workshop.Chiang Mai,Thailand.
Yee K S.1966.Numerical solution of initial boundary value problems involving Maxwell′s equations in isotropic media.IEEE Transactions on Antennas&Propagation,14(3):302-307,doi:10.1109/TAP.1966.1138693.
Yu G,Xiao Q B,Zhao G Z,et al.2018.Three-dimensional magnetotelluric responses for arbitrary electrically anisotropic media and a practical application.Geophysical Prospecting,66:1764-1783,doi:10.1111/1365-2478.12690.
胡祥云,霍光谱,高锐等.2013.大地电磁各向异性二维模拟及实例分析.地球物理学报,56(12):4268-4277,doi:10.6038/cjg20131229.
霍光谱,胡祥云,黄一凡等.2015.带地形的大地电磁各向异性二维模拟及实例对比分析.地球物理学报,58(12):4696-4708,doi:10.6038/cjg20151230.
秦策,王绪本,赵宁.2017.基于二次场方法的并行三维大地电磁正反演研究.地球物理学报,60(6):2456-4268,doi:10.6038/cjg20170633.
邵贵航,肖骑彬.2016.相位超象限大地电磁观测数据的模型研究---以河西走廊北侧为例.地球物理学进展,31(4):1480-1491,doi:10.6038/pg20160410.
谭捍东,余钦范,Booker J等.2003.大地电磁法三维交错采样有限差分数值模拟.地球物理学报,46(5):705-711,doi:10.3321/j.issn:0001-5733.2003.05.019.