基于激发振幅成像条件的探地雷达逆时偏移成像
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摘要
针对基于互相关成像条件的探地雷达(GPR)逆时偏移计算效率低、存储量大及易产生低频假象的不足,本文将激发振幅成像条件应用于GPR逆时偏移成像中.通过在源点电磁波场正向传播过程计算每个网格点的能量密度,并保存最大能量密度的时刻和相应的电磁波场值;在接收点电磁波场逆向传播过程提取每个网格点最大能量密度时刻及对应的电磁波场值,并利用保存的最大能量源点电磁波场及走时做归一化,从而获得了依赖反射系数成像剖面,避免了源点正向传播电磁波场的存储和重建.此外,为了提高电磁波场的模拟精度,采用了基于三角形剖分的时间域有限单元法(FETD)计算电磁波正向和逆向传播过程.最后通过模型试算表明:激发振幅成像条件相比于归一化互相关成像条件,成像结果低频噪声更弱,空间分辨率更高,计算效率提高了近2倍.
In order to overcome the shortcoming of lower calculation efficiency,larger storage and low frequency illusion,which can be easily produced in Ground Penetrating Radar(GPR)reverse time migration(RTM)based on normalized correlation imaging condition,a stable excitation amplitude imaging condition for GPR reverse time migration is proposed.In the propagation of the source electromagnetic wave filed extrapolation along apositive time axis,the energy density for total grids are computed at each time step,and the travel time as well as electromagnetic wavefiled values corresponding to the maximum energy density are stored to extract and normalize the receiver electromagnetic wave field,the imaging profile which rely on reflectance can be obtained.Compared to the normalized cross-correlation(NC)imaging condition,this strategy will save agreat amount of memory resource and significantly improve the computational efficiency for RTM.In order to improve the simulation accuracy of electromagnetic wavefield,the finite element timedomain(FETD)method based on triangulation is used to calculate the forward and reverse propagation process of electromagnetic wave.At last the feasibility and accuracy of the proposed GPR RTM algorithm are validated by numerical tests of inclined model and fluctuation interface model by compared with the results of RTM based on the NC imaging condition.The compared results demonstrated that the RTM based on the excitation imaging condition has a higher spatial resolution and can produce less low-frequency artifacts compared with the RTM results based on NC imaging condition.Moreover,the calculation efficiency of the excitation imaging condition has improved nearly 2 times because computer storage capacity due to that it needs not to store source electromagnetic field.
In order to overcome the shortcoming of lower calculation efficiency,larger storage and low frequency illusion,which can be easily produced in Ground Penetrating Radar(GPR)reverse time migration(RTM)based on normalized correlation imaging condition,a stable excitation amplitude imaging condition for GPR reverse time migration is proposed.In the propagation of the source electromagnetic wave filed extrapolation along apositive time axis,the energy density for total grids are computed at each time step,and the travel time as well as electromagnetic wavefiled values corresponding to the maximum energy density are stored to extract and normalize the receiver electromagnetic wave field,the imaging profile which rely on reflectance can be obtained.Compared to the normalized cross-correlation(NC)imaging condition,this strategy will save agreat amount of memory resource and significantly improve the computational efficiency for RTM.In order to improve the simulation accuracy of electromagnetic wavefield,the finite element timedomain(FETD)method based on triangulation is used to calculate the forward and reverse propagation process of electromagnetic wave.At last the feasibility and accuracy of the proposed GPR RTM algorithm are validated by numerical tests of inclined model and fluctuation interface model by compared with the results of RTM based on the NC imaging condition.The compared results demonstrated that the RTM based on the excitation imaging condition has a higher spatial resolution and can produce less low-frequency artifacts compared with the RTM results based on NC imaging condition.Moreover,the calculation efficiency of the excitation imaging condition has improved nearly 2 times because computer storage capacity due to that it needs not to store source electromagnetic field.
引文
Bitri A,Grandjean G.1998.Frequency-wavenumber modelling and migration of 2D GPR data in moderately heterogeneous dispersivemedia.Geophysical Prospecting,46(3):287-301.
Bradford J H.2015.Reverse-time prestack depth migration of GPRdata from topography for amplitude reconstruction in complex environments.Journal of Earth Science,26(6):791-798.
Chang W F,McMechan G A.1986.Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,51(1):67-84.
Chattopadhyay S,McMechan G A.2008.Imaging conditions for prestack reverse-time migration.Geophysics,73(3):S81-S89.
Chen T,He B S.2014.A normalized wavefield separation crosscorrelation imaging condition for reverse time migration based on Poynting vector.Applied Geophysics(in Chinese),11(2):158-166.
Claerbout J F.1971.Toward a unified theory of reflector mapping.Geophysics,36(3):467-481.
Dai Q W,Wang H H,Feng D S,et al.2012.Finite element numerical simulation for GPR based on quadratic interpolation.Progress in Geophysics(in Chinese),27(2):736-743,doi:10.6038/j.issn.1004-2903.2012.02.041.
Di Q Y,Xu K,Wang M Y.2000.The attenuated radar wave migration with finite element method.Chinese Journal of Geophysics(in Chinese),43(2):257-263.
Drossaert F H,Giannopoulos A.2007.A nonsplit complex frequency-shifted PML based on recursive integration for FDTDmodeling of elastic waves.Geophysics,72(2):T9-T17.
Feng D S,Dai Q W.2008.The migration of GPR three dimension wave equation in wavelets domain.Chinese Journal of Geophysics(in Chinese),51(2):566-574.
Feng D S,Zhang B,Dai Q W,et al.2011.The application of the improved linear transformation of finite difference migration based on the velocity estimation in the GPR date processing.Chinese Journal of Geophysics(in Chinese),54(5):1340-1347,doi:10.3969/j.issn.0001-5733.2011.05.023.
Fisher E,McMechan G A,Annan A P,et al.1992.Examples of reverse-time migration of single-channel,ground-penetrating radar profiles.Geophysics,57(4):577-586.
Fletcher R P,Du X,Fowler P J.2009.Reverse time migration in tilted transversely isotropic(TTI)media.Geophysics,74(6):WCA179-WCA187.
Fu L,Liu S X,Liu L B,et al.2014.Airborne ground penetrating radar numerical simulation and reverse time migration.Chinese Journal of Geophysics(in Chinese),57(5):1636-1646,doi:10.6038/cjg20140526.
Gu B L,Liu Y S,Ma X N,et al.2014.A modified excitation amplitude imaging condition for prestack reverse time migration.Exploration Geophysics,46(4):359-370.
Leuschen C J,Plumb R G.2000.A matched-filter approach to wave migration.Journal of Applied Geophysics,43(2-4):271-280.
Leuschen C J,Plumb R G.2001.A matched-filter-based reversetime migration algorithm for ground-penetrating radar data.IEEE Transactions on Geoscience and Remote Sensing,39(5):929-936.
Li J,Zeng Z F,Wu F S,et al.2010.Study of three dimension highorder FDTD simulation for GPR.Chinese Journal of Geophysics(in Chinese),53(4):974-981,doi:10.3969/j.issn.0001-5733.2010.04.022.
Liu H W,Liu H,Zhou Z,et al.2010.The problems of denoise and storage in seismic reverse time migration.Chinese Journal of Geophysics(in Chinese),53(9):2171-2180,doi:10.3969/j.issn.0001-5733.2010.09.017.
Liu S X,Lei L L,Fu L,et al.2014.Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data.Journal of Applied Geophysics,107:1-7.
Liu Y J,Li Z C.2015.Least-squares reverse-time migration with extended imaging condition.Chinese Journal of Geophysics(in Chinese),58(10):3771-3782,doi:10.6038/cjg20151027.
Lopera O,Slob E C,Milisavljevic N,et al.2007.Filtering soil surface and antenna effects from GPR data to enhance landmine detection.IEEE Transactions on Geoscience and Remote Sensing,45(3):707-717.
Lu X L,Qian R Y,Liu L B.2016.Ground-penetrating radar finitedifference reverse time migration from irregular surface by flattening surface topography.∥2016 16th International Conference on Ground Penetrating Radar(GPR).Hong Kong,China:IEEE,1-5.
Moran M L,Greenfield R J,Arcone S A,et al.2000.Multidimensional GPR array processing using Kirchhoff migration.Journal of Applied Geophysics,43(2-4):281-295.
Mulder W A,Plessix R E.2004.A comparison between one-way and two-way wave-equation migration.Geophysics,69(6):1491-1504.
Nguyen B D,McMechan G A.2012.Excitation amplitude imaging condition for prestack reverse-time migration.Geophysics,78(1):S37-S46.
Nguyen B D,McMechan G A.2014.Five ways to avoid storing source wavefield snapshots in 2Delastic prestack reverse time migration.Geophysics,80(1):S1-S18.
Schleicher J,Costa J C,Novais A.2008.A comparison of imaging conditions for wave-equation shot-profile migration.Geophysics,73(6):S219-S227.
Sena A R,Stoffa P L,Sen M K.2006.Split-step Fourier migration of GPR data in lossy media.Geophysics,71(4):K77-K91.
Streich R,Van Der Kruk J,Green A G.2007.Vector-migration of standard copolarized 3DGPR data.Geophysics,72(5):J65-J75.
Symes W W.2007.Reverse time migration with optimal checkpointing.Geophysics,72(5):SM213-SM221.
Wang H H,Dai Q W.2013.Finite element numerical simulation for GPR based on UPML boundary condition.The Chinese Journal of Nonferrous Metals(in Chinese),23(7):2003-2011.
Wang H H,Dai Q W.2014.Finite element method GPR forward simulation in dispersive medium.Journalo f Central South University(Science and Technology)(in Chinese),45(3):790-797.
Xu S Z.1994.Finite Element Method in Geophysics(in Chinese).Beijing:Science Press.
Yoon K,Marfurt K J.2006.Reverse-time migration using thePoynting vector.Exploration Geophysics,37(1):102-107.
Zhang Z,Liu Y S,Xu T,et al.2013.A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation.Chinese Journal of Geophysics(in Chinese),56(10):3523-3533,doi:10.6038/cjg20131027.
Zhu T Y,Harris J M,Biondi B.2014.Q-compensated reverse-time migration.Geophysics,79(3):S77-S87.
Zhu W Q,Huang Q H.2016.Attenuation compensated reverse time migration method of ground penetrating radar signals.Chinese Journal of Geophysics(in Chinese),59(10):3909-3916,doi:10.6038/cjg20161034.
Zhuge X,Yarovoy A G,Savelyev T,et al.2010.Modified Kirchhoff migration for UWB MIMO array-based radar imaging.IEEETransactions on Geoscience and Remote Sensing,48(6):2692-2703.
陈婷,何兵寿.2014.基于Poynting矢量的归一化波场分离互相关逆时偏移成像条件.应用地球物理,11(2):158-166.
戴前伟,王洪华,冯德山等.2012.基于双二次插值的探地雷达有限元数值模拟.地球物理学进展,27(2):736-743,doi:10.6038/j.issn.1004-2903.2012.02.041.
底青云,许琨,王妙月.2000.衰减雷达波有限元偏移.地球物理学报,43(2):257-263.
冯德山,戴前伟.2008.探地雷达小波域三维波动方程偏移.地球物理学报,51(2):566-574.
冯德山,张彬,戴前伟等.2011.基于速度估计的改进型线性变换有限差分偏移在探地雷达中的应用.地球物理学报,54(5):1340-1347,doi:10.3969/j.issn.0001-5733.2011.05.023.
傅磊,刘四新,刘澜波等.2014.机载探地雷达数值模拟及逆时偏移成像.地球物理学报,57(5):1636-1646,doi:10.6038/cjg20140526.
李静,曾昭发,吴丰收等.2010.探地雷达三维高阶时域有限差分法模拟研究.地球物理学报,53(4):974-981,doi:10.3969/j.issn.0001-5733.2010.04.022.
刘红伟,刘洪,邹振等.2010.地震叠前逆时偏移中的去噪与存储.地球物理学报,53(9):2171-2180,doi:10.3969/j.issn.0001-5733.2010.09.017.
刘玉金,李振春.2015.扩展成像条件下的最小二乘逆时偏移.地球物理学报,58(10):3771-3782,doi:10.6038/cjg20151027.
王洪华,戴前伟.2013.基于UPML吸收边界条件的GPR有限元数值模拟.中国有色金属学报,23(7):2003-2011.
王洪华,戴前伟.2014.频散介质中探地雷达有限元法正演模拟.中南大学学报(自然科学版),45(3):790-797.
徐世浙.1994.地球物理中的有限单元法.北京:科学出版社.(请核对英文信息)
张智,刘有山,徐涛等.2013.弹性波逆时偏移中的稳定激发振幅成像条件.地球物理学报,56(10):3523-3533,doi:10.6038/cjg20131027.
朱尉强,黄清华.2016.探地雷达衰减补偿逆时偏移成像方法.地球物理学报,59(10):3909-3916,doi:10.6038/cjg20161034.
Bradford J H.2015.Reverse-time prestack depth migration of GPRdata from topography for amplitude reconstruction in complex environments.Journal of Earth Science,26(6):791-798.
Chang W F,McMechan G A.1986.Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition.Geophysics,51(1):67-84.
Chattopadhyay S,McMechan G A.2008.Imaging conditions for prestack reverse-time migration.Geophysics,73(3):S81-S89.
Chen T,He B S.2014.A normalized wavefield separation crosscorrelation imaging condition for reverse time migration based on Poynting vector.Applied Geophysics(in Chinese),11(2):158-166.
Claerbout J F.1971.Toward a unified theory of reflector mapping.Geophysics,36(3):467-481.
Dai Q W,Wang H H,Feng D S,et al.2012.Finite element numerical simulation for GPR based on quadratic interpolation.Progress in Geophysics(in Chinese),27(2):736-743,doi:10.6038/j.issn.1004-2903.2012.02.041.
Di Q Y,Xu K,Wang M Y.2000.The attenuated radar wave migration with finite element method.Chinese Journal of Geophysics(in Chinese),43(2):257-263.
Drossaert F H,Giannopoulos A.2007.A nonsplit complex frequency-shifted PML based on recursive integration for FDTDmodeling of elastic waves.Geophysics,72(2):T9-T17.
Feng D S,Dai Q W.2008.The migration of GPR three dimension wave equation in wavelets domain.Chinese Journal of Geophysics(in Chinese),51(2):566-574.
Feng D S,Zhang B,Dai Q W,et al.2011.The application of the improved linear transformation of finite difference migration based on the velocity estimation in the GPR date processing.Chinese Journal of Geophysics(in Chinese),54(5):1340-1347,doi:10.3969/j.issn.0001-5733.2011.05.023.
Fisher E,McMechan G A,Annan A P,et al.1992.Examples of reverse-time migration of single-channel,ground-penetrating radar profiles.Geophysics,57(4):577-586.
Fletcher R P,Du X,Fowler P J.2009.Reverse time migration in tilted transversely isotropic(TTI)media.Geophysics,74(6):WCA179-WCA187.
Fu L,Liu S X,Liu L B,et al.2014.Airborne ground penetrating radar numerical simulation and reverse time migration.Chinese Journal of Geophysics(in Chinese),57(5):1636-1646,doi:10.6038/cjg20140526.
Gu B L,Liu Y S,Ma X N,et al.2014.A modified excitation amplitude imaging condition for prestack reverse time migration.Exploration Geophysics,46(4):359-370.
Leuschen C J,Plumb R G.2000.A matched-filter approach to wave migration.Journal of Applied Geophysics,43(2-4):271-280.
Leuschen C J,Plumb R G.2001.A matched-filter-based reversetime migration algorithm for ground-penetrating radar data.IEEE Transactions on Geoscience and Remote Sensing,39(5):929-936.
Li J,Zeng Z F,Wu F S,et al.2010.Study of three dimension highorder FDTD simulation for GPR.Chinese Journal of Geophysics(in Chinese),53(4):974-981,doi:10.3969/j.issn.0001-5733.2010.04.022.
Liu H W,Liu H,Zhou Z,et al.2010.The problems of denoise and storage in seismic reverse time migration.Chinese Journal of Geophysics(in Chinese),53(9):2171-2180,doi:10.3969/j.issn.0001-5733.2010.09.017.
Liu S X,Lei L L,Fu L,et al.2014.Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data.Journal of Applied Geophysics,107:1-7.
Liu Y J,Li Z C.2015.Least-squares reverse-time migration with extended imaging condition.Chinese Journal of Geophysics(in Chinese),58(10):3771-3782,doi:10.6038/cjg20151027.
Lopera O,Slob E C,Milisavljevic N,et al.2007.Filtering soil surface and antenna effects from GPR data to enhance landmine detection.IEEE Transactions on Geoscience and Remote Sensing,45(3):707-717.
Lu X L,Qian R Y,Liu L B.2016.Ground-penetrating radar finitedifference reverse time migration from irregular surface by flattening surface topography.∥2016 16th International Conference on Ground Penetrating Radar(GPR).Hong Kong,China:IEEE,1-5.
Moran M L,Greenfield R J,Arcone S A,et al.2000.Multidimensional GPR array processing using Kirchhoff migration.Journal of Applied Geophysics,43(2-4):281-295.
Mulder W A,Plessix R E.2004.A comparison between one-way and two-way wave-equation migration.Geophysics,69(6):1491-1504.
Nguyen B D,McMechan G A.2012.Excitation amplitude imaging condition for prestack reverse-time migration.Geophysics,78(1):S37-S46.
Nguyen B D,McMechan G A.2014.Five ways to avoid storing source wavefield snapshots in 2Delastic prestack reverse time migration.Geophysics,80(1):S1-S18.
Schleicher J,Costa J C,Novais A.2008.A comparison of imaging conditions for wave-equation shot-profile migration.Geophysics,73(6):S219-S227.
Sena A R,Stoffa P L,Sen M K.2006.Split-step Fourier migration of GPR data in lossy media.Geophysics,71(4):K77-K91.
Streich R,Van Der Kruk J,Green A G.2007.Vector-migration of standard copolarized 3DGPR data.Geophysics,72(5):J65-J75.
Symes W W.2007.Reverse time migration with optimal checkpointing.Geophysics,72(5):SM213-SM221.
Wang H H,Dai Q W.2013.Finite element numerical simulation for GPR based on UPML boundary condition.The Chinese Journal of Nonferrous Metals(in Chinese),23(7):2003-2011.
Wang H H,Dai Q W.2014.Finite element method GPR forward simulation in dispersive medium.Journalo f Central South University(Science and Technology)(in Chinese),45(3):790-797.
Xu S Z.1994.Finite Element Method in Geophysics(in Chinese).Beijing:Science Press.
Yoon K,Marfurt K J.2006.Reverse-time migration using thePoynting vector.Exploration Geophysics,37(1):102-107.
Zhang Z,Liu Y S,Xu T,et al.2013.A stable excitation amplitude imaging condition for reverse time migration in elastic wave equation.Chinese Journal of Geophysics(in Chinese),56(10):3523-3533,doi:10.6038/cjg20131027.
Zhu T Y,Harris J M,Biondi B.2014.Q-compensated reverse-time migration.Geophysics,79(3):S77-S87.
Zhu W Q,Huang Q H.2016.Attenuation compensated reverse time migration method of ground penetrating radar signals.Chinese Journal of Geophysics(in Chinese),59(10):3909-3916,doi:10.6038/cjg20161034.
Zhuge X,Yarovoy A G,Savelyev T,et al.2010.Modified Kirchhoff migration for UWB MIMO array-based radar imaging.IEEETransactions on Geoscience and Remote Sensing,48(6):2692-2703.
陈婷,何兵寿.2014.基于Poynting矢量的归一化波场分离互相关逆时偏移成像条件.应用地球物理,11(2):158-166.
戴前伟,王洪华,冯德山等.2012.基于双二次插值的探地雷达有限元数值模拟.地球物理学进展,27(2):736-743,doi:10.6038/j.issn.1004-2903.2012.02.041.
底青云,许琨,王妙月.2000.衰减雷达波有限元偏移.地球物理学报,43(2):257-263.
冯德山,戴前伟.2008.探地雷达小波域三维波动方程偏移.地球物理学报,51(2):566-574.
冯德山,张彬,戴前伟等.2011.基于速度估计的改进型线性变换有限差分偏移在探地雷达中的应用.地球物理学报,54(5):1340-1347,doi:10.3969/j.issn.0001-5733.2011.05.023.
傅磊,刘四新,刘澜波等.2014.机载探地雷达数值模拟及逆时偏移成像.地球物理学报,57(5):1636-1646,doi:10.6038/cjg20140526.
李静,曾昭发,吴丰收等.2010.探地雷达三维高阶时域有限差分法模拟研究.地球物理学报,53(4):974-981,doi:10.3969/j.issn.0001-5733.2010.04.022.
刘红伟,刘洪,邹振等.2010.地震叠前逆时偏移中的去噪与存储.地球物理学报,53(9):2171-2180,doi:10.3969/j.issn.0001-5733.2010.09.017.
刘玉金,李振春.2015.扩展成像条件下的最小二乘逆时偏移.地球物理学报,58(10):3771-3782,doi:10.6038/cjg20151027.
王洪华,戴前伟.2013.基于UPML吸收边界条件的GPR有限元数值模拟.中国有色金属学报,23(7):2003-2011.
王洪华,戴前伟.2014.频散介质中探地雷达有限元法正演模拟.中南大学学报(自然科学版),45(3):790-797.
徐世浙.1994.地球物理中的有限单元法.北京:科学出版社.(请核对英文信息)
张智,刘有山,徐涛等.2013.弹性波逆时偏移中的稳定激发振幅成像条件.地球物理学报,56(10):3523-3533,doi:10.6038/cjg20131027.
朱尉强,黄清华.2016.探地雷达衰减补偿逆时偏移成像方法.地球物理学报,59(10):3909-3916,doi:10.6038/cjg20161034.