基于奇异值谱约束的叠前平面波最小二乘逆时偏移方法（英文）
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摘要
最小二乘偏移能够压制不规则地震数据偏移时产生的偏移假象,但存在计算量巨大、收敛速度缓慢等问题。为了快速地压制偏移噪音,发展了基于奇异值谱约束的叠前平面波最小二乘逆时偏移方法(Plane-wave prestack least-squares reverse time migration,PLSRTM)。一方面,通过奇异值谱分析(Singular spectrum analysis,SSA)方法对角度域共成像点道集(Take-Off Angle Domain Common-Image Gathers,TADCIGs)进行预处理,以压制偏移假象,同时引入随机奇异值分解减小SSA的计算量。另一方面,由于偏移速度不准确时叠加成像结果不能有效地压制偏移噪音,将相邻角度平面波偏移结果的差异作为正则化约束加入误差泛函,以改善这一问题。对Marmousi模型数据的成像测试结果表明该方法能够快速压制平面波道集及不规则地震数据偏移产生的偏移假象,改善PLSRTM的成像质量;当偏移速度不准确时,该方法能够得到偏移噪音更少、构造更加连续的成像结果。
Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration(PLSRTM) method with singular spectrum constraint. Singular spectrum analysis(SSA) is used in the preconditioning of the take-off angle-domain common-image gathers(TADCIGs). In addition, we adopt randomized singular value decomposition(RSVD) to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition(SVD) of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.
Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration(PLSRTM) method with singular spectrum constraint. Singular spectrum analysis(SSA) is used in the preconditioning of the take-off angle-domain common-image gathers(TADCIGs). In addition, we adopt randomized singular value decomposition(RSVD) to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition(SVD) of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.
引文
Chemingui,N.,van Borselen,R.,and Orlovich,M.,2007,3D plane-wave migration of wide-azimuth data:77th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,2195-2199.
Chen,Y.,Yuan,J.,Zu,S.,et al.,2015,Seismic imaging of simultaneous-source data using constrained least-squares reverse time migration:Journal of Applied Geophysics,114,32-35.
Dai,W.,Fowler,P.,and Schuster,G.T.,2012,Multisource least-squares reverse time migration:Geophysical Prospecting,60(4),681-695.
Dai,W.,and Schuster,G.T.,2013,Plane-wave leastsquares reverse-time migration:Geophysics,78(4),5165-5177.
Du,Q.Z.,Sun,R.Y.,Qin,T.,et al.,2010,A study of perfectly matched layers for joint multicomponent reverse-time migration:Applied Geophysics,7(2),166-173.
Dutta,G.,and Schuster,G.T.,2014,Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation:Geophysics,79(6),S251-S262.
Dutta,G.,Giboli,M.,Williamson,P.,and Shuster,G.,T.,2015,Least-squares reverse time migration with factorization-free priorconditioning:85th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,4270-4275.
Dutta,G.,and Schuster,G.T.,2015,Sparse leastsquares reverse time migration using seislets:85th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,4232-4237.
Etgen,J.T.,2005,How many angles do we really need for delayed-shot migration:75th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,1985-1988.
Fan,J.W.,Li,Z.C.,Zhang,K.,et al.,2016,Multisource least-squares reverse-time migration with structureoriented filtering:Applied Geophysics,13(3),491-499.
Herrmann,F.J.,and Brown,C.R.,2009,Curvelet-based migration preconditioning and scaling:Geophysics,74(4),A41-A46.
Hestenes,M.R.,and Stiefel,E.,1952,Methods of conjugate gradients for solving linear systems:Journal of Research of the National Bureau of Standards,49,409-436.
Huang,J.,Li,Z.,Kong,X.,et al.,2013,A study of leastsquares migration imaging method for fractured-type carbonate reservoir:Chinese J.Geophys.(in Chinese),56(5),1716-1725.
Huang,J.,Li,C.,Wang,R.,and Li,Q.,2015,Planewave least-squares reverse time migration for rugged topography:Journal of Earth Science,26(4),471-480.
Huang,W.,Wang,R.,Chen,Y.,et al.,2016,Damped multichannel singular spectrum analysis for 3D random noise attenuation:Geophysics,81(4),V261-V270.
Krebs,J.R.,Anderson,J.E.,Hinkley,D.,et al.,2009,Fast full-wavefield seismic inversion using encoded sources:Geophysics,74(6),WCC177-WCC188.
Kuehl,H.,and Sacchi,M.D.,2003,Least-squares waveequation migration for AVP/AVA inversion:Geophysics,68(1),262-273.
Li,C.,Huang,J.,Li,Z.,et al.,2016a,Plane-wave leastsquare reverse time migration with encoding strategies,Journal of Seismic Exploration,25,177-197.
Li,C.,Huang,J.,Li,Z.,and Wang,R.,2016b.Leastsquares migration of simultaneous source data with singular spectrum regularization:SPG/SEG 2016International Geophysical Conference,Society of Exploration Geophysicists and Society of Petroleum Geophysicists,579-581.
Li,Q.Y.,Huang,J.P.,Li,Z.C.,et al.,2014a,Multisource least-squares reverse-time migration in the presence of topography on body-fitted grids,76th EAGE Conference and Exhibition EAGE,Extended Abstracts.
Li,Z.C.,Guo,Z.B.,and Tian,K.,2014b,Least-square reverse time migration in visco-acoustic medium:Chinese J.Geophys(in Chinese),1,79-94.
Liu,G.C.,Chen,X.H.,Song,J.Y.,and Rui,Z.H.,2012,A stabilized least-squares imaging condition with a structure constraint:Applied Geophysics,9(4),459-467.
Liu,Y.J.,Li,Z.C.,Wu,D.,et al.,2013,The research on local slope constrained least-square migration:Chinese J.Geophys(in Chinese),56(3),1003-1011.
Liu,Y.J.,and Li,Z.C.,2015,Least-squares reverse-time migration with extended imaging condition:Chinese J.Geophys(in Chinese),58(10),3771-3782.
Nemeth,T.,Wu,C.,and Schuster,G.T.,1999,Leastsquares migration of incomplete reflection data,Geophysics,64(1),208-221.
Oropeza,V.,2010,The singular spectrum analysis method and its application to seismic data denoising and reconstruction:PhD Thesis,University of Alberta.
Oropeza,V.,and Sacchi,M.,2010,A randomized SVD for multichannel singular spectrum analysis(MSSA)noise attenuation:80th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,3539-3544.
Oropeza,V.,and Sacchi,M.,2011,Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis:Geophysics,76,V25-V32.
Rokhlin,V.,Szlam,A.,and Tygert,M.,2009,A randomized algorithm for principal component analysis:SIAM Journal on Matrix Analysis and Applications,31,1100-1124.
Sacchi,M.,2009,FX Singular Spectrum Analysis:CSPG CSEG CWLS Convention,392-395.
Schuster,G.T.,Wang,X.,Huang,Y.,et al.,2011,Theory of multisource crosstalk reduction by phase-encoded statics:Geophysical Journal International,184,1289-1303.
Stanton,A.,and Sacchi,M.,2015,Least squares wave equation migration of elastic data,77th Annual International Conference and Exhibition,EAGE,Extended Abstracts,116-121.
Tan,S.,and Huang,L.,2014,Least-squares reverse-time migration with a wavefield-separation imaging condition and updated source wavefields:Geophysics,79(5),S195-S205.
Xue,Z.,Chen,Y.,Fomel,S.,and Sun,J.,2015,Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping regularization:Geophysics,81(1),S11-S20.
Zhang,Y.,Sun,J.,Notfors,C.,et al.,2005,Delayed-shot3D depth migration:Geophysics,70(6),E21-E28.
Zhao,Y.,Liu,Y.,and Ren,Z.M.,2014,Viscoacoustic prestack reverse time migration based on the optimal time-space domain high-order finite-difference method:Applied Geophysics,11(1),50-62.
Zhou,H.M.,Chen,S.C.,Ren,H.R.,et al.,2014,Oneway wave equation least-squares migration based on illumination compensation:Chinese Journal of Geophysics(in Chinese),57(8),2644-2655.
Chen,Y.,Yuan,J.,Zu,S.,et al.,2015,Seismic imaging of simultaneous-source data using constrained least-squares reverse time migration:Journal of Applied Geophysics,114,32-35.
Dai,W.,Fowler,P.,and Schuster,G.T.,2012,Multisource least-squares reverse time migration:Geophysical Prospecting,60(4),681-695.
Dai,W.,and Schuster,G.T.,2013,Plane-wave leastsquares reverse-time migration:Geophysics,78(4),5165-5177.
Du,Q.Z.,Sun,R.Y.,Qin,T.,et al.,2010,A study of perfectly matched layers for joint multicomponent reverse-time migration:Applied Geophysics,7(2),166-173.
Dutta,G.,and Schuster,G.T.,2014,Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation:Geophysics,79(6),S251-S262.
Dutta,G.,Giboli,M.,Williamson,P.,and Shuster,G.,T.,2015,Least-squares reverse time migration with factorization-free priorconditioning:85th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,4270-4275.
Dutta,G.,and Schuster,G.T.,2015,Sparse leastsquares reverse time migration using seislets:85th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,4232-4237.
Etgen,J.T.,2005,How many angles do we really need for delayed-shot migration:75th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,1985-1988.
Fan,J.W.,Li,Z.C.,Zhang,K.,et al.,2016,Multisource least-squares reverse-time migration with structureoriented filtering:Applied Geophysics,13(3),491-499.
Herrmann,F.J.,and Brown,C.R.,2009,Curvelet-based migration preconditioning and scaling:Geophysics,74(4),A41-A46.
Hestenes,M.R.,and Stiefel,E.,1952,Methods of conjugate gradients for solving linear systems:Journal of Research of the National Bureau of Standards,49,409-436.
Huang,J.,Li,Z.,Kong,X.,et al.,2013,A study of leastsquares migration imaging method for fractured-type carbonate reservoir:Chinese J.Geophys.(in Chinese),56(5),1716-1725.
Huang,J.,Li,C.,Wang,R.,and Li,Q.,2015,Planewave least-squares reverse time migration for rugged topography:Journal of Earth Science,26(4),471-480.
Huang,W.,Wang,R.,Chen,Y.,et al.,2016,Damped multichannel singular spectrum analysis for 3D random noise attenuation:Geophysics,81(4),V261-V270.
Krebs,J.R.,Anderson,J.E.,Hinkley,D.,et al.,2009,Fast full-wavefield seismic inversion using encoded sources:Geophysics,74(6),WCC177-WCC188.
Kuehl,H.,and Sacchi,M.D.,2003,Least-squares waveequation migration for AVP/AVA inversion:Geophysics,68(1),262-273.
Li,C.,Huang,J.,Li,Z.,et al.,2016a,Plane-wave leastsquare reverse time migration with encoding strategies,Journal of Seismic Exploration,25,177-197.
Li,C.,Huang,J.,Li,Z.,and Wang,R.,2016b.Leastsquares migration of simultaneous source data with singular spectrum regularization:SPG/SEG 2016International Geophysical Conference,Society of Exploration Geophysicists and Society of Petroleum Geophysicists,579-581.
Li,Q.Y.,Huang,J.P.,Li,Z.C.,et al.,2014a,Multisource least-squares reverse-time migration in the presence of topography on body-fitted grids,76th EAGE Conference and Exhibition EAGE,Extended Abstracts.
Li,Z.C.,Guo,Z.B.,and Tian,K.,2014b,Least-square reverse time migration in visco-acoustic medium:Chinese J.Geophys(in Chinese),1,79-94.
Liu,G.C.,Chen,X.H.,Song,J.Y.,and Rui,Z.H.,2012,A stabilized least-squares imaging condition with a structure constraint:Applied Geophysics,9(4),459-467.
Liu,Y.J.,Li,Z.C.,Wu,D.,et al.,2013,The research on local slope constrained least-square migration:Chinese J.Geophys(in Chinese),56(3),1003-1011.
Liu,Y.J.,and Li,Z.C.,2015,Least-squares reverse-time migration with extended imaging condition:Chinese J.Geophys(in Chinese),58(10),3771-3782.
Nemeth,T.,Wu,C.,and Schuster,G.T.,1999,Leastsquares migration of incomplete reflection data,Geophysics,64(1),208-221.
Oropeza,V.,2010,The singular spectrum analysis method and its application to seismic data denoising and reconstruction:PhD Thesis,University of Alberta.
Oropeza,V.,and Sacchi,M.,2010,A randomized SVD for multichannel singular spectrum analysis(MSSA)noise attenuation:80th Annual International Meeting,Society of Exploration Geophysicists,Expanded Abstracts,3539-3544.
Oropeza,V.,and Sacchi,M.,2011,Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis:Geophysics,76,V25-V32.
Rokhlin,V.,Szlam,A.,and Tygert,M.,2009,A randomized algorithm for principal component analysis:SIAM Journal on Matrix Analysis and Applications,31,1100-1124.
Sacchi,M.,2009,FX Singular Spectrum Analysis:CSPG CSEG CWLS Convention,392-395.
Schuster,G.T.,Wang,X.,Huang,Y.,et al.,2011,Theory of multisource crosstalk reduction by phase-encoded statics:Geophysical Journal International,184,1289-1303.
Stanton,A.,and Sacchi,M.,2015,Least squares wave equation migration of elastic data,77th Annual International Conference and Exhibition,EAGE,Extended Abstracts,116-121.
Tan,S.,and Huang,L.,2014,Least-squares reverse-time migration with a wavefield-separation imaging condition and updated source wavefields:Geophysics,79(5),S195-S205.
Xue,Z.,Chen,Y.,Fomel,S.,and Sun,J.,2015,Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping regularization:Geophysics,81(1),S11-S20.
Zhang,Y.,Sun,J.,Notfors,C.,et al.,2005,Delayed-shot3D depth migration:Geophysics,70(6),E21-E28.
Zhao,Y.,Liu,Y.,and Ren,Z.M.,2014,Viscoacoustic prestack reverse time migration based on the optimal time-space domain high-order finite-difference method:Applied Geophysics,11(1),50-62.
Zhou,H.M.,Chen,S.C.,Ren,H.R.,et al.,2014,Oneway wave equation least-squares migration based on illumination compensation:Chinese Journal of Geophysics(in Chinese),57(8),2644-2655.