任意各向异性介质中三维可控源音频大地电磁正演模拟
|
摘要
在一些地层层理发育的地区,地下介质存在显著的电各向异性,此时基于各向同性模型解释含各向异性效应的可控源音频大地电磁(CSAMT)测深观测数据会导致错误的结果.本文通过引入3×3的对称正定张量表征电导率各向异性,采用非结构四面体网格和矢量有限元方法离散电场满足的矢量Helmholtz方程,并将电磁场源等效为系列电偶极子,实现任意各向异性介质中CSAMT高效数值模拟.本文首先通过层状各向异性模型检验三维有限元算法的精度和有效性,进一步建立三维地电模型研究异常体各向异性和围岩各向异性对CSAMT响应的影响,最后使用视电阻率极性图来识别各向异性电导率主轴方向.数值模拟结果表明,各向异性电导率对CSAMT视电阻率幅值及分布规律都有很大影响,视电阻率极性图能够很好地识别各向异性主轴方向.
Controlled-source audio-frequency magnetotellurics(CSAMT)is playing an important role in shallow subsurface exploration.Most current three-dimensional(3D)forward modeling for CSAMT are based on an isotropic earth model which neglects the electrical anisotropy in the earth.Here we implement a 3Dvector finite-element modeling algorithm to solve the frequencydomain Helmholtz equation for the total electrical field and analyze the effect of earth anisotropy on tensor CSAMT apparent resistivity responses.First we introduce a 3×3 positive-definite conductivity tensor to represent the arbitrarilyelectrical anisotropy.Then we discretize the weak-form of vector Helmholtz equation with an unstructured tetrahedral grid and lowest order of Nédélec vector basis functions.Besides,we approximate the horizontal transmitting sources for CSAMT by a series of electrical dipoles and solve the final system of equations with the direct solver MUMPS that can speed up the forward modeling while guaranteeing the numerical precision.We compare our 3D numerical results with one-dimensional solutions for a layered anisotropic earth to verify the accuracy and reliability of the proposed 3D anisotropic finite element algorithm.To further explore the anisotropic effect of a 3D anomalous body and host rock,we design a conductive brick model embedded in a homogeneous half-space.Then,we rotate the principal conductivity tensor of the anomalous body and host rock around x-axis and z-axis separately,and simulate the apparent resistivity for tensor CSAMT.Numerical results show that both the amplitude and distribution pattern of the CSAMT apparent resistivity vary with the anisotropic conductivity tensors.To recognize the electrical anisotropy of the earth,we show the CSAMT apparent resistivity in polar plots,thus one can clearly identify the principal axis of the anisotropic conductivity.
Controlled-source audio-frequency magnetotellurics(CSAMT)is playing an important role in shallow subsurface exploration.Most current three-dimensional(3D)forward modeling for CSAMT are based on an isotropic earth model which neglects the electrical anisotropy in the earth.Here we implement a 3Dvector finite-element modeling algorithm to solve the frequencydomain Helmholtz equation for the total electrical field and analyze the effect of earth anisotropy on tensor CSAMT apparent resistivity responses.First we introduce a 3×3 positive-definite conductivity tensor to represent the arbitrarilyelectrical anisotropy.Then we discretize the weak-form of vector Helmholtz equation with an unstructured tetrahedral grid and lowest order of Nédélec vector basis functions.Besides,we approximate the horizontal transmitting sources for CSAMT by a series of electrical dipoles and solve the final system of equations with the direct solver MUMPS that can speed up the forward modeling while guaranteeing the numerical precision.We compare our 3D numerical results with one-dimensional solutions for a layered anisotropic earth to verify the accuracy and reliability of the proposed 3D anisotropic finite element algorithm.To further explore the anisotropic effect of a 3D anomalous body and host rock,we design a conductive brick model embedded in a homogeneous half-space.Then,we rotate the principal conductivity tensor of the anomalous body and host rock around x-axis and z-axis separately,and simulate the apparent resistivity for tensor CSAMT.Numerical results show that both the amplitude and distribution pattern of the CSAMT apparent resistivity vary with the anisotropic conductivity tensors.To recognize the electrical anisotropy of the earth,we show the CSAMT apparent resistivity in polar plots,thus one can clearly identify the principal axis of the anisotropic conductivity.
引文
Amestoy P R,Guermouche A,L′Excellent J Y,et al.2006.Hybrid scheduling for the parallel solution of linear systems.Parallel Computing,32(2):136-156.
Cao Q,Lin C H,Tan H D,et al.2016.Occam inversion of CSAMT data in layered media with azimuthal anisotropy.Geophysical and Geochemical Exploration(in Chinese),40(3):594-602,doi:10.11720/wtyht.2016.3.23.
Chen G B.2009.Integral equation method for 3-D electromagnetic modeling in layered anisotropic earth and its applications[Ph.D.thesis](in Chinese).Changchun:Jilin University.
Deng J Z,Tan H D,Chen H,et al.2011.CSAMT 3D modeling using staggered-grid finite difference method.Progress in Geophysics(in Chinese),26(6):2026-2032,doi:10.3969/j.issn.1004-2903.2011.06.017.
Di Q Y,Unsworth M,Wang M Y.2004.2.5-D CSAMT modeling with the finite element method over 2-D complex earth media.Chinese Journal of Geophysics(in Chinese),47(4):723-730.
Han B,Hu X Y,Huang Y F,et al.2015.3-D frequency-domain CSEM modeling using aparallel direct solver.Chinese Journal of Geophysics(in Chinese),58(8):2812-2826,doi:10.6038/cjg20150816.
Hu Y C,Li T L,Fan C S,et al.2015.Three-dimensional tensorcontrolled-source electromagnetic modeling based on the vector finiteelement method.AppliedG eophysics,12(1):35-46,doi:10.1007/s11770-014-0469-1.
Jin J M.2014.The Finite Element Method in Electromagnetics.3rd ed.Hoboken,NJ:Wiley-IEEE Press.
Lei D.2010.Studies and applications of 2-D CSAMT modeling and inversion with a dipole source and topography.Chinese Journal of Geophysics(in Chinese),53(4):982-993,doi:10.3969/j.issn.0001-5733.2010.04.023.
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 X B,Oskooi B,Pedersen L B.2000.Inversion of controlledsource tensor magnetotelluric data for a layered earth with azimuthal anisotropy.Geophysics,65(2):452-464.
Liu Y H,Yin C C.2014.3Danisotropic modeling for airborne EMsystems using finite-difference method.Journal of Applied Geophysics,109:186-194.
Nédélec J C.1980.Mixed finite elements in瓗3.Numerische Mathematik,35(3):315-341.
Qi Y F,Yin C C,Liu Y H,et al.2017.3Dtime-domain airborne EM full-wave forward modeling based on instantaneous current pulse.Chinese Journal of Geophysics(in Chinese),60(1):369-382,doi:10.6038/cjg20170131.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013.A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling.Geophysical Journal International,194(2):700-718,doi:10.1093/gji/ggt154.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2014.A finiteelement-based domain-decomposition approach for plane wave3Delectromagnetic modeling.Geophysics,79(6):E255-E268,doi:10.1190/GEO2013-0376.1.
Wang Y L,Di Q Y,Wang R.2017.Three-dimensional modeling ofcontrolled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid.Chinese Journal of Geophysics(in Chinese),60(3):1158-1167,doi:10.6038/cjg20170326.
Yin C,Maurer H M.2001.Electromagnetic induction in a layered earth with arbitrary anisotropy.Geophysics,66(5):1405-1416,doi:10.1190/1.1487086.
Yin C C.2000.Geoelectrical inversion for a one-dimensional anisotropic model and inherent non-uniqueness.Geophysical Journal International,140(1):11-23,doi:10.1046/j.1365-246x.2000.00974.x.
Yin C C,Fraser D C.2004.The effect of the electrical anisotropy on the response of helicopter-borne frequency-domain electromagnetic systems.Geophysical Prospecting,52(5):399-416.
Yin C C.2006.MMT forward modeling for a layered earth with arbitrary anisotropy.Geophysics,71(3):G115-G128.
Zhou J M,Wang J X,Shang Q L,et al.2014.Regularized inversion of controlled source audio-frequency magnetotelluric data in horizontally layered transversely isotropic media.Journal of Geophysics and Engineering,11(2):025003,doi:10.1088/1742-2132/11/2/025003.
曹强,林昌洪,谭捍东等.2016.可控源音频大地电磁法方位非各向同性层状介质Occam反演.物探与化探,40(3):594-602,doi:10.11720/wtyht.2016.3.23.
陈桂波.2009.各向异性地层中电磁场三维数值模拟的积分方程算法及其应用[博士论文].长春:吉林大学.
邓居智,谭捍东,陈辉等.2011.CSAMT三维交错采样有限差分数值模拟.地球物理学进展,26(6):2026-2032,doi:10.3969/j.issn.1004-2903.2011.06.017.
底青云,Unsworth M,王妙月.2004.复杂介质有限元法2.5维可控源音频大地电磁法数值模拟.地球物理学报,47(4):723-730.
韩波,胡祥云,黄一凡等.2015.基于并行化直接解法的频率域可控源电磁三维正演.地球物理学报,58(8):2812-2826,doi:10.6038/cjg20150816.
雷达.2010.起伏地形下CSAMT二维正反演研究与应用.地球物理学报,53(4):982-993,doi:10.3969/j.issn.0001-5733.2010.04.023.
齐彦福,殷长春,刘云鹤等.2017.基于瞬时电流脉冲的三维时间域航空电磁全波形正演模拟.地球物理学报,60(1):369-382,doi:10.6038/cjg20170131.
汤井田,何继善.2005.可控源音频大地电磁法及其应用.长沙:中南大学出版社.
王亚璐,底青云,王若.2017.三维CSAMT法非结构化网格有限元数值模拟.地球物理学报,60(3):1158-1167,doi:10.6038/cjg20170326.
Cao Q,Lin C H,Tan H D,et al.2016.Occam inversion of CSAMT data in layered media with azimuthal anisotropy.Geophysical and Geochemical Exploration(in Chinese),40(3):594-602,doi:10.11720/wtyht.2016.3.23.
Chen G B.2009.Integral equation method for 3-D electromagnetic modeling in layered anisotropic earth and its applications[Ph.D.thesis](in Chinese).Changchun:Jilin University.
Deng J Z,Tan H D,Chen H,et al.2011.CSAMT 3D modeling using staggered-grid finite difference method.Progress in Geophysics(in Chinese),26(6):2026-2032,doi:10.3969/j.issn.1004-2903.2011.06.017.
Di Q Y,Unsworth M,Wang M Y.2004.2.5-D CSAMT modeling with the finite element method over 2-D complex earth media.Chinese Journal of Geophysics(in Chinese),47(4):723-730.
Han B,Hu X Y,Huang Y F,et al.2015.3-D frequency-domain CSEM modeling using aparallel direct solver.Chinese Journal of Geophysics(in Chinese),58(8):2812-2826,doi:10.6038/cjg20150816.
Hu Y C,Li T L,Fan C S,et al.2015.Three-dimensional tensorcontrolled-source electromagnetic modeling based on the vector finiteelement method.AppliedG eophysics,12(1):35-46,doi:10.1007/s11770-014-0469-1.
Jin J M.2014.The Finite Element Method in Electromagnetics.3rd ed.Hoboken,NJ:Wiley-IEEE Press.
Lei D.2010.Studies and applications of 2-D CSAMT modeling and inversion with a dipole source and topography.Chinese Journal of Geophysics(in Chinese),53(4):982-993,doi:10.3969/j.issn.0001-5733.2010.04.023.
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 X B,Oskooi B,Pedersen L B.2000.Inversion of controlledsource tensor magnetotelluric data for a layered earth with azimuthal anisotropy.Geophysics,65(2):452-464.
Liu Y H,Yin C C.2014.3Danisotropic modeling for airborne EMsystems using finite-difference method.Journal of Applied Geophysics,109:186-194.
Nédélec J C.1980.Mixed finite elements in瓗3.Numerische Mathematik,35(3):315-341.
Qi Y F,Yin C C,Liu Y H,et al.2017.3Dtime-domain airborne EM full-wave forward modeling based on instantaneous current pulse.Chinese Journal of Geophysics(in Chinese),60(1):369-382,doi:10.6038/cjg20170131.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013.A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling.Geophysical Journal International,194(2):700-718,doi:10.1093/gji/ggt154.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2014.A finiteelement-based domain-decomposition approach for plane wave3Delectromagnetic modeling.Geophysics,79(6):E255-E268,doi:10.1190/GEO2013-0376.1.
Wang Y L,Di Q Y,Wang R.2017.Three-dimensional modeling ofcontrolled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid.Chinese Journal of Geophysics(in Chinese),60(3):1158-1167,doi:10.6038/cjg20170326.
Yin C,Maurer H M.2001.Electromagnetic induction in a layered earth with arbitrary anisotropy.Geophysics,66(5):1405-1416,doi:10.1190/1.1487086.
Yin C C.2000.Geoelectrical inversion for a one-dimensional anisotropic model and inherent non-uniqueness.Geophysical Journal International,140(1):11-23,doi:10.1046/j.1365-246x.2000.00974.x.
Yin C C,Fraser D C.2004.The effect of the electrical anisotropy on the response of helicopter-borne frequency-domain electromagnetic systems.Geophysical Prospecting,52(5):399-416.
Yin C C.2006.MMT forward modeling for a layered earth with arbitrary anisotropy.Geophysics,71(3):G115-G128.
Zhou J M,Wang J X,Shang Q L,et al.2014.Regularized inversion of controlled source audio-frequency magnetotelluric data in horizontally layered transversely isotropic media.Journal of Geophysics and Engineering,11(2):025003,doi:10.1088/1742-2132/11/2/025003.
曹强,林昌洪,谭捍东等.2016.可控源音频大地电磁法方位非各向同性层状介质Occam反演.物探与化探,40(3):594-602,doi:10.11720/wtyht.2016.3.23.
陈桂波.2009.各向异性地层中电磁场三维数值模拟的积分方程算法及其应用[博士论文].长春:吉林大学.
邓居智,谭捍东,陈辉等.2011.CSAMT三维交错采样有限差分数值模拟.地球物理学进展,26(6):2026-2032,doi:10.3969/j.issn.1004-2903.2011.06.017.
底青云,Unsworth M,王妙月.2004.复杂介质有限元法2.5维可控源音频大地电磁法数值模拟.地球物理学报,47(4):723-730.
韩波,胡祥云,黄一凡等.2015.基于并行化直接解法的频率域可控源电磁三维正演.地球物理学报,58(8):2812-2826,doi:10.6038/cjg20150816.
雷达.2010.起伏地形下CSAMT二维正反演研究与应用.地球物理学报,53(4):982-993,doi:10.3969/j.issn.0001-5733.2010.04.023.
齐彦福,殷长春,刘云鹤等.2017.基于瞬时电流脉冲的三维时间域航空电磁全波形正演模拟.地球物理学报,60(1):369-382,doi:10.6038/cjg20170131.
汤井田,何继善.2005.可控源音频大地电磁法及其应用.长沙:中南大学出版社.
王亚璐,底青云,王若.2017.三维CSAMT法非结构化网格有限元数值模拟.地球物理学报,60(3):1158-1167,doi:10.6038/cjg20170326.