基于非结构双网格的2D RMT双参数同步反演研究
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摘要
Radio-magnetotelluric(RMT)是以无线电发射机为信号源的一种地球物理勘探方法,近年来被广泛应用于数米至数十米内的近地表工程和环境地球物理勘探.目前,各类电磁资料的反演均是以寻求满足目标拟合差的地下介质电阻率分布为目的.然而,对于勘探频率为10～300kHz的RMT数据,由介电常数所引起的波动场在总场中的比例可达20%以上,在这种情况下,忽略介电常数,仅通过电阻率参数的反演来进行数据拟合势必降低反演资料解释的准确性.为解决这一问题,本文研究了基于电阻率-介电常数的双参数同步反演算法.构建了一个全新的双参数目标函数,并推导了双参数反演迭代方程组;通过灵敏度分析,研究了电阻率和介电常数对正演响应的影响,并据此提出相对电导率的概念,统一了反演参数的灵敏度;通过理论模型分析了参考频率、双参数正则化因子对反演结果的影响,并给出了一般性的参数优选方案.此外,为了能够灵活处理复杂地形,本文采用非结构的正反演双网格进行模型离散,并通过局部加密技术保证反演的速度和精度.最后,对一带地形的理论模型分别进行了单参数和双参数反演,结果表明单参数反演无法正确反映出地电信息,而双参数反演能够准确得到异常的分布,验证了本文所开发的双参数反演程序的有效性.
The radio-magnetotelluric(RMT)method is an electromagnetic method that employs the signals from remote radio transmitters.As a kind of near-surface geophysical prospecting method,RMT is widely used for engineering and environmental exploration in recent years.Atpresent,most geophysical inversion for electromagnetic data is aimed at the reconstruction of the resistivity and make the forward responses fit the observed data.However,the percentage of wave field which caused by permittivity in the total field can be up to 20% for the RMT data which collected at the frequency ranges from 10～300 kHz.Inversion for reconstructing a resistivity model but neglecting the effect of permittivity may lead to a false interpretation.To solve this problem,this paper presents an algorithm for the simultaneous inversion of the dielectric permittivity and the electrical resistivity dual-parameters.We developed a new dual-parameters based objective function and derived the dual-parameters inverse equations.With sensitivity analysis,we evaluated the effect of the resistivity and permittivity on the forward responses,proposed the concept of the relative electrical conductivity and unified the scale of the sensitivity of the two parameters.We studied the effect of reference frequency and the two regularization factors on the inversion results,put forward an optimum parameter selection scheme in the general cases.Based on unstructured triangle meshes,our code can model arbitrary surface topography.The local refinement technology was used for mesh discretization,which improved the speed and accuracy of inversion procedure.At last,the reliability and effectiveness of our dual-parameters inversion program are demonstrated by synthetic examples.Data with topography are inversed by both ordinary and our new schemes.The ordinary resistivity inversion cannot reflect the anomalous body correctly,while our dual-parameters inversion can provide better results.
The radio-magnetotelluric(RMT)method is an electromagnetic method that employs the signals from remote radio transmitters.As a kind of near-surface geophysical prospecting method,RMT is widely used for engineering and environmental exploration in recent years.Atpresent,most geophysical inversion for electromagnetic data is aimed at the reconstruction of the resistivity and make the forward responses fit the observed data.However,the percentage of wave field which caused by permittivity in the total field can be up to 20% for the RMT data which collected at the frequency ranges from 10～300 kHz.Inversion for reconstructing a resistivity model but neglecting the effect of permittivity may lead to a false interpretation.To solve this problem,this paper presents an algorithm for the simultaneous inversion of the dielectric permittivity and the electrical resistivity dual-parameters.We developed a new dual-parameters based objective function and derived the dual-parameters inverse equations.With sensitivity analysis,we evaluated the effect of the resistivity and permittivity on the forward responses,proposed the concept of the relative electrical conductivity and unified the scale of the sensitivity of the two parameters.We studied the effect of reference frequency and the two regularization factors on the inversion results,put forward an optimum parameter selection scheme in the general cases.Based on unstructured triangle meshes,our code can model arbitrary surface topography.The local refinement technology was used for mesh discretization,which improved the speed and accuracy of inversion procedure.At last,the reliability and effectiveness of our dual-parameters inversion program are demonstrated by synthetic examples.Data with topography are inversed by both ordinary and our new schemes.The ordinary resistivity inversion cannot reflect the anomalous body correctly,while our dual-parameters inversion can provide better results.
引文
Bastani M.2001.EnviroMT-a new controlled source/radio magnetotelluric system[Ph.D.thesis].Uppsala:Acta Universitatis Upsaliensis.
Bastani M,Malehmir A,Ismail N,et al.2009.Delineating hydrothermal stockwork copper deposits using controlled-source and radio-magnetotelluric methods:A case study from northeast Iran.Geophysics,74(5):B167-B181.
Bastani M,Persson L,Beiki M,et al.2013.A radio magnetotelluric study to evaluate the extents of a limestone quarry in Estonia.Geophysical Prospecting,61(3):678-687.
Busch S,Van Der Kruk J,Bikowski J,et al.2012.Quantitative permittivity and conductivity estimation using full-waveform inversion of on-ground GPR data.Geophysics,77(6):H79-H91.
Candansayar M E,Tezkan B A.2006.A comparison of different radiomagnetotelluric data inversion methods for buried waste sites.Journal of Applied Geophysics,58(3):218-231.
Candansayar M E,Tezkan B.2008.Two-dimensional joint inversion of radiomagnetotelluric and direct current resistivity data.Geophysical Prospecting,56(5):737-749.
Chave A D,Jones A G.2012.The Magnetotelluric Method:Theory and Practice.Cambridge:Cambridge University Press.
Da Gomes M G,Souto R P,De Athayde A S,et al.2014.Estimating dielectric permittivity and electric conductivity from simulated multichannel GPR pulses using aco and quasi-newton inversion techniques.Revista Brasileira de Geofísica,32(4):595-614.
Günther T,Rucker C,Spitzer K.2006.Three-dimensional modeling and inversion of dc resistivity data incorporating topography-II.Inversion.Geophysical Journal International,166(2):506-517.
Han Q,Hu X Y,Cheng Z P,et al.2015.A study of twodimensional MT inversion with steep topography using the adaptive unstructured finite element method.Chinese Journal of Geophysics(in Chinese),58(12):4675-4684,doi:10.6038/cjg20151228.
Ismail N,Schwarz G,Pedersen L B.2011.Investigation of groundwater resources using controlled-source radio magnetotellurics(CSRMT)in glacial deposits in Heby,Sweden.Journal of Applied Geophysics,73(1):74-83.
Kalscheuer T,Pedersen L B,Siripunvaraporn W.2008.Radiomagnetotelluric two-dimensional forward and inverse modelling accounting for displacement currents.Geophysical Journal International,175(2):486-514.
LavouéF,Brossier R,Métivier L,et al.2014.Two-dimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data:A frequency-domain quasi-Newton approach.Geophysical Journal International,197(1):248-268.
Li G,Xiao X,Tang J T,et al.2017.Near-source noise suppression of AMT by compressive sensing and mathematical morphology filtering.Applied Geophysics,14(4):581-589.
Li J,Zhang X,Gong J Z,et al.2018.Signal-noise identification of magnetotelluric signals using fractal-entropy and clustering algorithm for targeted de-noising.Fractals,26(2):1840011,doi:10.1142/S0218348X1840011X.
Li J,Zhang X,Tang J T,et al.2019.Audio magnetotelluric based on multifractal spectrum and matching pursuit.Fractals,27(1):1940007,doi:10.1142/S0218348X19400073.
Linde N,Pedersen L B.2004.Characterization of a fractured granite using radio magnetotelluric(RMT)data.Geophysics,69(5):1155-1165.
Meles G A,Van Der Kruk J,Greenhalgh S A,et al.2010.A new vector waveform inversion algorithm for simultaneous updating of conductivity and permittivity parameters from combination crosshole/borehole-to-surface GPR data.IEEETransactionson GeoscienceandRemoteSensing,48(9):3391-3407.
Newman G A,Recher S,Tezkan B,et al.2003.3Dinversion of a scalar radio magnetotelluric field data set.Geophysics,68(3):791-802.
Operto S,Gholami Y,Prieux V,et al.2013.A guided tour of multiparameter full-waveform inversion for multicomponent data:From theory to practice.The Leading Edge,32(9):1040-1054.
Pedersen L,Bastani M,Dynesius L.2005.Groundwater exploration using combined controlled-source and radiomagnetotelluric techniques.Geophysics,70(10):G8-G15.
Pedersen L,Bastani M,Dynesius L.2006.Some characteristics of the electromagnetic field from radio transmitters in Europe.Geophysics,71(6):G279-G284.
Persson L.2001.Plane wave electromagnetic measurements for imaging fracture zones[Ph.D.thesis].Uppsala:Acta Universitatis Upsaliensis.
Persson L,Pedersen B.2002.The importance of displacement currents in RMT measurements in high resistivity environments.Journal of Applied Geophysics,51(1):11-20.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013a.A goaloriented adaptive finite-element approach for plane wave 3-Delectromagnetic modeling.Geophysical Journal International,194(2):700-718.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013b.Boundary element solutions for broad-band 3-D geo-electromagnetic problems accelerated by an adaptive multilevel fast multipole method.Geophysical Journal International,192(2):473-499.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2014a.A finiteelement-based domain-decomposition approach for plane wave3Delectromagnetic modeling.Geophysics,79(6):E255-E268.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2014b.A hybrid boundary element-finite element approach to modeling plane wave 3D electromagnetic induction responses in the Earth.Journal of Computational Physics,258:705-717.
Shewchuk J.1996.Triangle:Engineering a 2Dquality mesh generator and Delaunay triangulator.Lecture Notes in Computer Science,1148:203-222.
Tezkan B,Goldman M,Greinwald S,et al.1996.Joint application of radiomagnetotellurics and transient electromagnetics to the investigation of a waste deposit in Cologne(Germany).Journal of Applied Geophysics,34(3):199-212.
Tezkan B,H9rdt A,Gobashy M.2000.Two-dimensional radiomagnetotelluric investigation of industrial and domestic waste sites in Germany.Journal of Applied Geophysics,44(2-3):237-256.
Tezkan B,Georgescu P,Fauzi U.2005 A radiomagnetotelluric survey on an oil-contaminated area near the Brazi Refinery,Romania.Geophysical Prospecting,53(3):311-323.
Tezkan B,Saraev A.2008.A new broadband radiomagnetotelluric instrument:Applications to near surface investigations.Near Surface Geophysics,6(4):245-252.
Turberg P,Müller I,Flury F.1994.Hydrogeological investigation of porous environments by radio magnetotelluric-resistivity(RMT-R 12-240kHz).Journal of Applied Geophysics,31(1-4):133-143.
Wu X P,Liu Y,Wang W.2015.3Dresistivity inversion incorporating topography based on unstructured meshes.Chinese Journal of Geophysics(in Chinese),58(8):2706-2717,doi:10.6038/cjg20150808.
Yuan Y,Tang J T,Ren Z Y,et al.2015.Two-dimensional complicated radio-magnetotelluric finite-element modeling using unstructured grids.Chinese Journal of Geophysics(in Chinese),58(12):4685-4695,doi:10.6038/cjg20151229.
韩骑,胡祥云,程正璞等.2015.自适应非结构有限元MT二维起伏地形正反演研究.地球物理学报,58(12):4675-4684,doi:10.6038/cjg20151228.
吴小平,刘洋,王威.2015.基于非结构网格的电阻率三维带地形反演.地球物理学报,58(8):2706-2717,doi:10.6038/cjg20150808.
原源,汤井田,任政勇等.2015.基于非结构化网格的任意复杂2DRMT有限元模拟.地球物理学报,58(12):4685-4695,doi:10.6038/cjg20151229.
Bastani M,Malehmir A,Ismail N,et al.2009.Delineating hydrothermal stockwork copper deposits using controlled-source and radio-magnetotelluric methods:A case study from northeast Iran.Geophysics,74(5):B167-B181.
Bastani M,Persson L,Beiki M,et al.2013.A radio magnetotelluric study to evaluate the extents of a limestone quarry in Estonia.Geophysical Prospecting,61(3):678-687.
Busch S,Van Der Kruk J,Bikowski J,et al.2012.Quantitative permittivity and conductivity estimation using full-waveform inversion of on-ground GPR data.Geophysics,77(6):H79-H91.
Candansayar M E,Tezkan B A.2006.A comparison of different radiomagnetotelluric data inversion methods for buried waste sites.Journal of Applied Geophysics,58(3):218-231.
Candansayar M E,Tezkan B.2008.Two-dimensional joint inversion of radiomagnetotelluric and direct current resistivity data.Geophysical Prospecting,56(5):737-749.
Chave A D,Jones A G.2012.The Magnetotelluric Method:Theory and Practice.Cambridge:Cambridge University Press.
Da Gomes M G,Souto R P,De Athayde A S,et al.2014.Estimating dielectric permittivity and electric conductivity from simulated multichannel GPR pulses using aco and quasi-newton inversion techniques.Revista Brasileira de Geofísica,32(4):595-614.
Günther T,Rucker C,Spitzer K.2006.Three-dimensional modeling and inversion of dc resistivity data incorporating topography-II.Inversion.Geophysical Journal International,166(2):506-517.
Han Q,Hu X Y,Cheng Z P,et al.2015.A study of twodimensional MT inversion with steep topography using the adaptive unstructured finite element method.Chinese Journal of Geophysics(in Chinese),58(12):4675-4684,doi:10.6038/cjg20151228.
Ismail N,Schwarz G,Pedersen L B.2011.Investigation of groundwater resources using controlled-source radio magnetotellurics(CSRMT)in glacial deposits in Heby,Sweden.Journal of Applied Geophysics,73(1):74-83.
Kalscheuer T,Pedersen L B,Siripunvaraporn W.2008.Radiomagnetotelluric two-dimensional forward and inverse modelling accounting for displacement currents.Geophysical Journal International,175(2):486-514.
LavouéF,Brossier R,Métivier L,et al.2014.Two-dimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data:A frequency-domain quasi-Newton approach.Geophysical Journal International,197(1):248-268.
Li G,Xiao X,Tang J T,et al.2017.Near-source noise suppression of AMT by compressive sensing and mathematical morphology filtering.Applied Geophysics,14(4):581-589.
Li J,Zhang X,Gong J Z,et al.2018.Signal-noise identification of magnetotelluric signals using fractal-entropy and clustering algorithm for targeted de-noising.Fractals,26(2):1840011,doi:10.1142/S0218348X1840011X.
Li J,Zhang X,Tang J T,et al.2019.Audio magnetotelluric based on multifractal spectrum and matching pursuit.Fractals,27(1):1940007,doi:10.1142/S0218348X19400073.
Linde N,Pedersen L B.2004.Characterization of a fractured granite using radio magnetotelluric(RMT)data.Geophysics,69(5):1155-1165.
Meles G A,Van Der Kruk J,Greenhalgh S A,et al.2010.A new vector waveform inversion algorithm for simultaneous updating of conductivity and permittivity parameters from combination crosshole/borehole-to-surface GPR data.IEEETransactionson GeoscienceandRemoteSensing,48(9):3391-3407.
Newman G A,Recher S,Tezkan B,et al.2003.3Dinversion of a scalar radio magnetotelluric field data set.Geophysics,68(3):791-802.
Operto S,Gholami Y,Prieux V,et al.2013.A guided tour of multiparameter full-waveform inversion for multicomponent data:From theory to practice.The Leading Edge,32(9):1040-1054.
Pedersen L,Bastani M,Dynesius L.2005.Groundwater exploration using combined controlled-source and radiomagnetotelluric techniques.Geophysics,70(10):G8-G15.
Pedersen L,Bastani M,Dynesius L.2006.Some characteristics of the electromagnetic field from radio transmitters in Europe.Geophysics,71(6):G279-G284.
Persson L.2001.Plane wave electromagnetic measurements for imaging fracture zones[Ph.D.thesis].Uppsala:Acta Universitatis Upsaliensis.
Persson L,Pedersen B.2002.The importance of displacement currents in RMT measurements in high resistivity environments.Journal of Applied Geophysics,51(1):11-20.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013a.A goaloriented adaptive finite-element approach for plane wave 3-Delectromagnetic modeling.Geophysical Journal International,194(2):700-718.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2013b.Boundary element solutions for broad-band 3-D geo-electromagnetic problems accelerated by an adaptive multilevel fast multipole method.Geophysical Journal International,192(2):473-499.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2014a.A finiteelement-based domain-decomposition approach for plane wave3Delectromagnetic modeling.Geophysics,79(6):E255-E268.
Ren Z Y,Kalscheuer T,Greenhalgh S,et al.2014b.A hybrid boundary element-finite element approach to modeling plane wave 3D electromagnetic induction responses in the Earth.Journal of Computational Physics,258:705-717.
Shewchuk J.1996.Triangle:Engineering a 2Dquality mesh generator and Delaunay triangulator.Lecture Notes in Computer Science,1148:203-222.
Tezkan B,Goldman M,Greinwald S,et al.1996.Joint application of radiomagnetotellurics and transient electromagnetics to the investigation of a waste deposit in Cologne(Germany).Journal of Applied Geophysics,34(3):199-212.
Tezkan B,H9rdt A,Gobashy M.2000.Two-dimensional radiomagnetotelluric investigation of industrial and domestic waste sites in Germany.Journal of Applied Geophysics,44(2-3):237-256.
Tezkan B,Georgescu P,Fauzi U.2005 A radiomagnetotelluric survey on an oil-contaminated area near the Brazi Refinery,Romania.Geophysical Prospecting,53(3):311-323.
Tezkan B,Saraev A.2008.A new broadband radiomagnetotelluric instrument:Applications to near surface investigations.Near Surface Geophysics,6(4):245-252.
Turberg P,Müller I,Flury F.1994.Hydrogeological investigation of porous environments by radio magnetotelluric-resistivity(RMT-R 12-240kHz).Journal of Applied Geophysics,31(1-4):133-143.
Wu X P,Liu Y,Wang W.2015.3Dresistivity inversion incorporating topography based on unstructured meshes.Chinese Journal of Geophysics(in Chinese),58(8):2706-2717,doi:10.6038/cjg20150808.
Yuan Y,Tang J T,Ren Z Y,et al.2015.Two-dimensional complicated radio-magnetotelluric finite-element modeling using unstructured grids.Chinese Journal of Geophysics(in Chinese),58(12):4685-4695,doi:10.6038/cjg20151229.
韩骑,胡祥云,程正璞等.2015.自适应非结构有限元MT二维起伏地形正反演研究.地球物理学报,58(12):4675-4684,doi:10.6038/cjg20151228.
吴小平,刘洋,王威.2015.基于非结构网格的电阻率三维带地形反演.地球物理学报,58(8):2706-2717,doi:10.6038/cjg20150808.
原源,汤井田,任政勇等.2015.基于非结构化网格的任意复杂2DRMT有限元模拟.地球物理学报,58(12):4685-4695,doi:10.6038/cjg20151229.