电性任意各向异性且分块连续变化CSAMT三维有限元数值模拟
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摘要
考虑地球介质电导率任意各向异性且随空间位置连续变化的情况,本文实现了直接求解电磁场的可控源音频大地电磁测深(CSAMT)三维有限元数值模拟.首先给出了电导率任意各向异性介质中CSAMT二次电场满足的控制方程及其相应变分问题,然后采用任意六面体单元对研究区域进行剖分,在网格单元中对任意各向异性电导率进行线性插值,解决了实际工作中岩矿石电导率各向异性且连续变化的情况,将变分问题转化为线性代数方程组的求解.电导率各向异性且连续变化一维模型三维有限元数值模拟结果与电导率各向异性且分层均匀渐进模型解析解结果对比验证了方法的有效性;三维地电模型电导率随位置线性变化且各向同性、主轴各向异性、方位各向异性和倾斜各向异性的数值模拟结果表明,电导率各向异性且连续变化对CSAMT视电阻率和相位数据均有明显的影响.
Considering that the conductivity of the earth medium is arbitrarily anisotropic and continuously changes with spatial position,this work makes three-dimensional CSAMT finite element numerical simulation to resolve the electromagnetic field directly.Firstly,we give the governing equation and its corresponding variational problem of CSAMT secondary electric field in an arbitrary anisotropic conductive medium.Then,the study area is divided into many elements of arbitrary hexahedral shape.In each element,the tri-line interpolation is performed for the arbitrary anisotropic conductivity parameter to simulate the arbitrary anisotropy and continuous change of rock and ore conductivity.The variational problem is transformed into solution of a linear algebraic equation set.Three-dimensional finite element numerical simulation results of an one-dimension conductivity model with anisotropy and continuous change are compared with analytical solution results of an anisotropic and layered progressive conductivity-model to verify the effectiveness of the method.Forward calculation is carried out on other three-dimensional geoelectric models,in which the electrical conductivity varies linearly with position and the medium is isotropic,principal axis anisotropic,azimuthal anisotropic and oblique anisotropic,respectively.Results show that the electrical conductivity anisotropy and continuous change have prominent influence on CSAMT apparent resistivity and phase data.
Considering that the conductivity of the earth medium is arbitrarily anisotropic and continuously changes with spatial position,this work makes three-dimensional CSAMT finite element numerical simulation to resolve the electromagnetic field directly.Firstly,we give the governing equation and its corresponding variational problem of CSAMT secondary electric field in an arbitrary anisotropic conductive medium.Then,the study area is divided into many elements of arbitrary hexahedral shape.In each element,the tri-line interpolation is performed for the arbitrary anisotropic conductivity parameter to simulate the arbitrary anisotropy and continuous change of rock and ore conductivity.The variational problem is transformed into solution of a linear algebraic equation set.Three-dimensional finite element numerical simulation results of an one-dimension conductivity model with anisotropy and continuous change are compared with analytical solution results of an anisotropic and layered progressive conductivity-model to verify the effectiveness of the method.Forward calculation is carried out on other three-dimensional geoelectric models,in which the electrical conductivity varies linearly with position and the medium is isotropic,principal axis anisotropic,azimuthal anisotropic and oblique anisotropic,respectively.Results show that the electrical conductivity anisotropy and continuous change have prominent influence on CSAMT apparent resistivity and phase data.
引文
Ansari S,Farquharson C G.2014.3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids.Geophysics,79(4):E149-E165．
Avdeev D,Knizhnik S.2009.3Dintegral equation modeling with a linear dependence on dimensions.Geophysics,74(5):F89-F94．
Badea E A,Everett M E,Newman G A,et al.2001.Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials.Geophysics,66(3):786-799．
Ben F,Liu Y H,Huang W,et al.2016.MCSEM Responses for Anisotropic Media in Shallow Water.Journal of Jilin University(Earth Science Edition)(in Chinese),46(2):581-593．
Boerner D E,Wright J A,Thurlow J G,et al.1993.Tensor CSAMTstudies at the Buchans Mine in central Newfoundland.Geophysics,58(1):12-19．
Borner R U.2010.Numerical modelling in geo-electromagnetics:Advances and challenges.Surveys in Geophysics,31(2):225-245．
Chen G B,Wang H N,Yao J J,et al.2009.Three-dimensional numerical modeling of marine controlled-source electromagnetic responses in a layered anisotropic seabed using integral equation method.Acta Physica Sinica(in Chinese),58(6):3848-3857．
Fu C M,Di Q Y,An Z G.2013.Application of the CSAMT method to groundwater exploration in a metropolitan environment.Geophysics,78(5):B201-B209．
Grayver A V,Kolev T V.2015.Large-scale 3Dgeoelectromagnetic modeling using parallel adaptive high-order finite element method.Geophysics,80(6):E277-E291．
Grayver A V,Bürg M.2014.Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method.Geophysical Journal International,198(1):110-125．
Herwanger J V,Pain C C,Binley A,et al.2004.Anisotropic resistivity tomography.Geophysical Journal International,158(2):409-425．
Hou J S,Mallan R K,Torres-Verdín C.2006.Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials.Geophysics,71(5):G225-G233．
Hu X Y,Peng R H,Wu G J,et al.2013.Mineral Exploration using CSAMT data:Application to Longmen region metallogenic belt,Guangdong Province,China.Geophysics,78(3):B111-B119．
Jahandari H,Farquharson C G.2014.A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids.Geophysics,79(6):E287-E302．
Jin J M.2002.The Finite Element Method in Electromagnetics.2nd ed.New York:Wiley-IEEE Press．
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．
Kong F N,Johnstad S E,Rsten T,et al.2008.A 2.5Dfiniteelement-modeling difference method for marine CSEM modeling in stratified anisotropic media.Geophysics,73(1):F9-F19．
Li J H,Farquharson C G,Hu X Y.2016.A vector finite element solver of three-dimensional modelling for a long grounded wire source based on total electric field.Chinese Journal of Geophysics(in Chinese),59(4):1521-1534,doi:10.6038/cjg20160432．
Li X B,Pedersen L B.1991.The electromagnetic response of an azimuthally anisotropic half-space.Geophysics,56(9):1462-1473．
Li X B,Pedersen L B.1992.Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy.Geophysical Journal International,111(1):91-103．
Li Y,Lin P R,Liu W Q,et al.2017.2.5-D numerical simulation of the marine controlled-source electromagnetic method based on isoparametric FEM for the conductivity orthotropic medium.Chinese Journal of Geophysics(in Chinese),60(2):748-765,doi:10.6038/cjg20170226．
Li Y G,Dai S K.2011.Finite element modelling of marine controlled-source electromagnetic responses in two-dimensional dipping anisotropic conductivity structures.Geophysical Journal International,185(2):622-636．
Li Y G,Luo M,Pei J X.2013.Adaptive finite element modeling of marine controlled-source electromagnetic fields in two-dimensional general anisotropic media.Journal of Ocean University of China,12(1):1-5．
Linde N,Pedersen L B.2004.Evidence of electrical anisotropy in limestone formations using the RMT technique.Geophysics,69(4):909-916．
Lseth L O,Ursin B.2007.Electromagnetic fields in planarly layered anisotropic media.Geophysical Journal International,170(1):44-80．
Negi J G,Saraf P D.1992.Anisotropy in Geoelectromagnetism(in Chinese).Zou Y H,Chen D Z,trans.Beijing:Geological Publishing House．
Newman G A,Commer M,Carazzone J J.2010.Imaging CSEMdata in the presence of electrical anisotropy.Geophysics,75(2):F51-F61．
Puzyrev V,Koldan J,De La Puente J,et al.2013.A parallel finiteelement method for three-dimensional controlled-source electromagnetic forward modelling.Geophysical Journal International,193(2):678-693．
Ruan B Y,Xu S Z.1998.FEM for modeling resistivity sounding on2-D geoelectric model with line variation of conductivity within each block.Earth Science-Journal of China University of Geosciences(in Chinese),23(3):303-307．
Schwarzbach C,B9rner R U,Spitzer K.2011.Three-dimensional adaptive higher order finite element simulation for geoelectromagnetics-a marine CSEM example.Geophysical Journal International,187(1):63-74．
Streich R,Becken M.2011.Sensitivity of controlled-source electromagnetic fields in planarly layered media.Geophysical Journal International,187(2):705-728．
Tang W W,Liu J X,Tong X Z.2013.Finite element forward modeling on line source of FCSEM for continuous conductivity.Journal of Jilin University(Earth Science Edition)(in Chinese),43(5):1646-1654．
Tsili W,Fang S.2001.3-D electromagnetic anisotropy modeling using finite differences.Geophysics,66(5):1386-1398．
Wang X J,He L F,Chen L,et al.2017.Mapping deeply buried karst cavities using controlled-source audio magnetotellurics:Acase history of a tunnel investigation in southwest China.Geophysics,82(1):EN1-EN11．
Wannamaker P E.1997.Tensor CSAMT survey over the Sulphur Springs thermal area,Valles Caldera,New Mexico,United States of America,Part I:Implications for structure of the western caldera.Geophysics,62(2):451-465．
Yang J,Liu Y,Wu X P.2015.3Dsimulation of marine CSEMusing vector finite element method on unstructured grids.Chinese Journal of Geophysics(in Chinese),58(8):2827-2838,doi:10.6038/cjg20150817．
Yin C C.1997.Electromagnetic Induction in A Layered Conductor with Arbitrary Anisotropy.Aufl-G9ttingen:Cuvillier Verlag．
Yin C C,Ben F,Liu Y H,et al.2014.MCSEM 3D modeling for arbitrarily anisotropic media.Chinese Journal of Geophysics(in Chinese),57(12):4110-4122,doi:10.6038/cjg20141222．
Zhang Y J,Sun Q.2007.Preconditioned bi-conjugate gradient method of large-scale complex linear equations.Computer Engineering and Applications(in Chinese),43(36):19-20．
Zhou J M,Zhang Y,Wang H N,et al.2014.Efficient simulation of three-dimensional marine controlled-source electromagnetic response in anisotropic formation by means of coupled potential finite volume method.Acta Physica Sinica(in Chinese),63(15):159101．
Negi J G,Saraf P D.1992．大地介质电磁各向异性问题．邹永辉，陈德志译．北京：地质出版社．
贲放，刘云鹤，黄威等．2016．各向异性介质中的浅海海洋可控源电磁响应特征．吉林大学学报（地球科学版），46(2):581-593．
陈桂波，汪宏年，姚敬金等．2009．各向异性海底地层海洋可控源电磁响应三维积分方程法数值模拟．物理学报，58(6):3848-3857．
李建慧，Farquharson C G，胡祥云等．2016．基于电场总场矢量有限元法的接地长导线源三维正演．地球物理学报，59(4):1521-1534,doi:10.6038/cjg20160432．
李勇，林品荣，刘卫强等．2017.2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟．地球物理学报，60(2):748-765,doi:10.6038/cjg20170226．
阮百尧，徐世浙．1998．电导率分块线性变化二维地电断面电阻率测深有限元数值模拟．地球科学-中国地质大学学报，23(3):303-307．
汤文武，柳建新，童孝忠．2013．电导率连续变化的线源FCSEM有限元正演模拟．吉林大学学报（地球科学版），43(5):1646-1654．
杨军，刘颖，吴小平．2015．海洋可控源电磁三维非结构矢量有限元数值模拟．地球物理学报，58(8):2827-2838,doi:10.6038/cjg20150817．
殷长春，贲放，刘云鹤等．2014．三维任意各向异性介质中海洋可控源电磁法正演研究．地球物理学报，57(12):4110-4122,doi:10.6038/cjg20141222．
张永杰，孙秦．2007．大型复线性方程组预处理双共轭梯度法．计算工程与应用，43(36):19-20．
周建美，张烨，汪宏年等．2014．耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应．物理学报，63(15):159101.
Avdeev D,Knizhnik S.2009.3Dintegral equation modeling with a linear dependence on dimensions.Geophysics,74(5):F89-F94．
Badea E A,Everett M E,Newman G A,et al.2001.Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials.Geophysics,66(3):786-799．
Ben F,Liu Y H,Huang W,et al.2016.MCSEM Responses for Anisotropic Media in Shallow Water.Journal of Jilin University(Earth Science Edition)(in Chinese),46(2):581-593．
Boerner D E,Wright J A,Thurlow J G,et al.1993.Tensor CSAMTstudies at the Buchans Mine in central Newfoundland.Geophysics,58(1):12-19．
Borner R U.2010.Numerical modelling in geo-electromagnetics:Advances and challenges.Surveys in Geophysics,31(2):225-245．
Chen G B,Wang H N,Yao J J,et al.2009.Three-dimensional numerical modeling of marine controlled-source electromagnetic responses in a layered anisotropic seabed using integral equation method.Acta Physica Sinica(in Chinese),58(6):3848-3857．
Fu C M,Di Q Y,An Z G.2013.Application of the CSAMT method to groundwater exploration in a metropolitan environment.Geophysics,78(5):B201-B209．
Grayver A V,Kolev T V.2015.Large-scale 3Dgeoelectromagnetic modeling using parallel adaptive high-order finite element method.Geophysics,80(6):E277-E291．
Grayver A V,Bürg M.2014.Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method.Geophysical Journal International,198(1):110-125．
Herwanger J V,Pain C C,Binley A,et al.2004.Anisotropic resistivity tomography.Geophysical Journal International,158(2):409-425．
Hou J S,Mallan R K,Torres-Verdín C.2006.Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials.Geophysics,71(5):G225-G233．
Hu X Y,Peng R H,Wu G J,et al.2013.Mineral Exploration using CSAMT data:Application to Longmen region metallogenic belt,Guangdong Province,China.Geophysics,78(3):B111-B119．
Jahandari H,Farquharson C G.2014.A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids.Geophysics,79(6):E287-E302．
Jin J M.2002.The Finite Element Method in Electromagnetics.2nd ed.New York:Wiley-IEEE Press．
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．
Kong F N,Johnstad S E,Rsten T,et al.2008.A 2.5Dfiniteelement-modeling difference method for marine CSEM modeling in stratified anisotropic media.Geophysics,73(1):F9-F19．
Li J H,Farquharson C G,Hu X Y.2016.A vector finite element solver of three-dimensional modelling for a long grounded wire source based on total electric field.Chinese Journal of Geophysics(in Chinese),59(4):1521-1534,doi:10.6038/cjg20160432．
Li X B,Pedersen L B.1991.The electromagnetic response of an azimuthally anisotropic half-space.Geophysics,56(9):1462-1473．
Li X B,Pedersen L B.1992.Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy.Geophysical Journal International,111(1):91-103．
Li Y,Lin P R,Liu W Q,et al.2017.2.5-D numerical simulation of the marine controlled-source electromagnetic method based on isoparametric FEM for the conductivity orthotropic medium.Chinese Journal of Geophysics(in Chinese),60(2):748-765,doi:10.6038/cjg20170226．
Li Y G,Dai S K.2011.Finite element modelling of marine controlled-source electromagnetic responses in two-dimensional dipping anisotropic conductivity structures.Geophysical Journal International,185(2):622-636．
Li Y G,Luo M,Pei J X.2013.Adaptive finite element modeling of marine controlled-source electromagnetic fields in two-dimensional general anisotropic media.Journal of Ocean University of China,12(1):1-5．
Linde N,Pedersen L B.2004.Evidence of electrical anisotropy in limestone formations using the RMT technique.Geophysics,69(4):909-916．
Lseth L O,Ursin B.2007.Electromagnetic fields in planarly layered anisotropic media.Geophysical Journal International,170(1):44-80．
Negi J G,Saraf P D.1992.Anisotropy in Geoelectromagnetism(in Chinese).Zou Y H,Chen D Z,trans.Beijing:Geological Publishing House．
Newman G A,Commer M,Carazzone J J.2010.Imaging CSEMdata in the presence of electrical anisotropy.Geophysics,75(2):F51-F61．
Puzyrev V,Koldan J,De La Puente J,et al.2013.A parallel finiteelement method for three-dimensional controlled-source electromagnetic forward modelling.Geophysical Journal International,193(2):678-693．
Ruan B Y,Xu S Z.1998.FEM for modeling resistivity sounding on2-D geoelectric model with line variation of conductivity within each block.Earth Science-Journal of China University of Geosciences(in Chinese),23(3):303-307．
Schwarzbach C,B9rner R U,Spitzer K.2011.Three-dimensional adaptive higher order finite element simulation for geoelectromagnetics-a marine CSEM example.Geophysical Journal International,187(1):63-74．
Streich R,Becken M.2011.Sensitivity of controlled-source electromagnetic fields in planarly layered media.Geophysical Journal International,187(2):705-728．
Tang W W,Liu J X,Tong X Z.2013.Finite element forward modeling on line source of FCSEM for continuous conductivity.Journal of Jilin University(Earth Science Edition)(in Chinese),43(5):1646-1654．
Tsili W,Fang S.2001.3-D electromagnetic anisotropy modeling using finite differences.Geophysics,66(5):1386-1398．
Wang X J,He L F,Chen L,et al.2017.Mapping deeply buried karst cavities using controlled-source audio magnetotellurics:Acase history of a tunnel investigation in southwest China.Geophysics,82(1):EN1-EN11．
Wannamaker P E.1997.Tensor CSAMT survey over the Sulphur Springs thermal area,Valles Caldera,New Mexico,United States of America,Part I:Implications for structure of the western caldera.Geophysics,62(2):451-465．
Yang J,Liu Y,Wu X P.2015.3Dsimulation of marine CSEMusing vector finite element method on unstructured grids.Chinese Journal of Geophysics(in Chinese),58(8):2827-2838,doi:10.6038/cjg20150817．
Yin C C.1997.Electromagnetic Induction in A Layered Conductor with Arbitrary Anisotropy.Aufl-G9ttingen:Cuvillier Verlag．
Yin C C,Ben F,Liu Y H,et al.2014.MCSEM 3D modeling for arbitrarily anisotropic media.Chinese Journal of Geophysics(in Chinese),57(12):4110-4122,doi:10.6038/cjg20141222．
Zhang Y J,Sun Q.2007.Preconditioned bi-conjugate gradient method of large-scale complex linear equations.Computer Engineering and Applications(in Chinese),43(36):19-20．
Zhou J M,Zhang Y,Wang H N,et al.2014.Efficient simulation of three-dimensional marine controlled-source electromagnetic response in anisotropic formation by means of coupled potential finite volume method.Acta Physica Sinica(in Chinese),63(15):159101．
Negi J G,Saraf P D.1992．大地介质电磁各向异性问题．邹永辉，陈德志译．北京：地质出版社．
贲放，刘云鹤，黄威等．2016．各向异性介质中的浅海海洋可控源电磁响应特征．吉林大学学报（地球科学版），46(2):581-593．
陈桂波，汪宏年，姚敬金等．2009．各向异性海底地层海洋可控源电磁响应三维积分方程法数值模拟．物理学报，58(6):3848-3857．
李建慧，Farquharson C G，胡祥云等．2016．基于电场总场矢量有限元法的接地长导线源三维正演．地球物理学报，59(4):1521-1534,doi:10.6038/cjg20160432．
李勇，林品荣，刘卫强等．2017.2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟．地球物理学报，60(2):748-765,doi:10.6038/cjg20170226．
阮百尧，徐世浙．1998．电导率分块线性变化二维地电断面电阻率测深有限元数值模拟．地球科学-中国地质大学学报，23(3):303-307．
汤文武，柳建新，童孝忠．2013．电导率连续变化的线源FCSEM有限元正演模拟．吉林大学学报（地球科学版），43(5):1646-1654．
杨军，刘颖，吴小平．2015．海洋可控源电磁三维非结构矢量有限元数值模拟．地球物理学报，58(8):2827-2838,doi:10.6038/cjg20150817．
殷长春，贲放，刘云鹤等．2014．三维任意各向异性介质中海洋可控源电磁法正演研究．地球物理学报，57(12):4110-4122,doi:10.6038/cjg20141222．
张永杰，孙秦．2007．大型复线性方程组预处理双共轭梯度法．计算工程与应用，43(36):19-20．
周建美，张烨，汪宏年等．2014．耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应．物理学报，63(15):159101.
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