基于局部余弦基小波束的观测系统沉降法叠前深度偏移
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摘要
将局部余弦基小波束波场分解、传播与观测系统沉降法叠前深度偏移相结合,推导了源-检波器观测系统沉降法传播算子.本算法中,先对频率域的共点源和共点检波器道集做局部余弦小波束分解,然后分别沿共小波束源和共小波束检波器在深度方向延拓得到下一层波场.每个深度的波场,都等效于把源和检波器放在该层后所能接收到的地震记录,每点的像值由炮点和检波点重合时的零时刻波场值给出.通过二维SEG/EAGE盐丘模型和Marmousi模型的偏移成像结果验证该方法理论推导的正确性.另外,结果显示该方法继承了小波束域波场延拓在速度扰动较大情况下波传播及成像精度高的优点.
In this work,we combine the local perturbation beamlet migration theory and the concept of survey sinking prestack depth migration.We prove the equivalence between the propagators in source-receiver survey sinking migration and the shot domain beamlet migration.In this algorithm,the frequency domain common point source and point receiver wavefield is first decomposed by the local cosine basis along common sources and receivers,and then the decomposed wavefield is downward-continued to the next depth along common beamlet-sources and beamlet-receivers subsequently.The propagated wavefield is equivalent to the data that would have been received if all sources and receivers were placed at the current depth.The migrated image is evaluated at zero time and zero offset.Numerical tests on synthetic data of the 2D SEG/EAGE salt model and the Marmousi model demonstrate the validity of the theory and the good accuracy of the beamlet method on strong contrast velocity model and complex geology structures.
In this work,we combine the local perturbation beamlet migration theory and the concept of survey sinking prestack depth migration.We prove the equivalence between the propagators in source-receiver survey sinking migration and the shot domain beamlet migration.In this algorithm,the frequency domain common point source and point receiver wavefield is first decomposed by the local cosine basis along common sources and receivers,and then the decomposed wavefield is downward-continued to the next depth along common beamlet-sources and beamlet-receivers subsequently.The propagated wavefield is equivalent to the data that would have been received if all sources and receivers were placed at the current depth.The migrated image is evaluated at zero time and zero offset.Numerical tests on synthetic data of the 2D SEG/EAGE salt model and the Marmousi model demonstrate the validity of the theory and the good accuracy of the beamlet method on strong contrast velocity model and complex geology structures.
引文
[1]Biondi B L.3D seismic imaging.SEG Investigations inGeophysics,No.14,2006.
[2]Claerbout J F.Imaging the Earth′s Interior.Cambridge:Blackwell Scientific Publications,1985.
[3]Yilmaz O,Claerbout J F.Prestack partial migration.Geophysics,1980,45(12):1753-1779.
[4]Popovici A M.Prestack migration by split-step DSR.Geophysics,1996,61(5):1412-1416.
[5]Jin S W,Mosher C C,Wu R S.Offset-domain pseudo-screenprestack depth migration.Geophysics,2002,67(6):1985-1902.
[6]Biondi B,Palacharla G.3-D prestack migration of common-azimuth data.Geophysics,1996,61(6):1822-1832.
[7]Biondi B,Fomel S,Chemingui N.Azimuth moveout for 3-Dprestack imaging.Geophysics,1998,63(2):574-588.
[8]孙沛勇,张叔伦.双平方根叠前深度偏移的广义高阶屏方法.石油地球物理勘探,2001,36(4):398-407.Sun P Y,Zhang S L.Generalized high-order screen methodfor pre-stack depth migration by double-square-root.OilGeophysical Prospecting(in Chinese),2001,36(4):398-407.
[9]程玖兵,王华忠,马在田.双平方根方程三维叠前深度偏移.地球物理学报,2003,46(5):676-683.Cheng J B,Wang H Z,Ma Z T.Double square root equation3D prestack depth migration.Chinese J.Geophys.(inChinese),2003,46(5):676-683.
[10]程玖兵,王华忠,马在田.窄方位地震数据双平方根方程偏移方法探讨.地球物理学报,2005,48(2):399-405.Cheng J B,Wang H Z,Ma Z T.Double square root equationmigration methods of narrow azimuth seismic data.ChineseJ.Geophys.(in Chinese),2005,48(2):399-405.
[11]刘定进,印兴耀.基于双平方根方程的保幅地震偏移.石油地球物理勘探,2007,42(1):11-16.Liu D J,Yin X Y.Amplitude-preserved seismic migrationbased on double square root.Oil Geophysical Prospecting(in Chinese),2007,42(1):11-16.
[12]Kosloff D D,Baysal E.Migration with the full acoustic waveequation.Geophysics,1983,48(6):677-687.
[13]Sandberg K,Beylkin G.Full-wave-equation depth extrapolationfor migration.Geophysics,2009,74(6):WCA121-WCA128.
[14]Alkhalifah T,Formel S.Source-receiver two-way waveextrapolation for prestack exploding-reflector modeling andmigration.∥80th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2010:2950-2954.
[15]Wu R S,Wang Y Z,Gao J H.Beamlet migration based onlocal perturbation theory.∥70th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2000:1008-1011.
[16]陈凌.小波束域波场的分解、传播及在地震偏移成像中的应用[博士论文].北京:中国地震局地球物理研究所,2002.Chen L.Beamlet-domain wavefield decomposition,propagationand it application in seismic migration/imaging[Ph.D thesis](inChinese).Beijing:Institute of Geophysics,China SeismologicalBureau,2002.
[17]高静怀,周艳辉,毛剑等.局部角度域波传播步进算法研究.地球物理学报,2007,50(1):248-259.Gao J H,Zhou Y H,Mao J,et al.A wave propagationmethod in local angle domain.Chinese J.Geophys.(in Chinese),2007,50(1):248-259.
[18]陈凌,吴如山,陈颙.基于Gabor-Daubechies小波束域波场外推的散射系数矩阵的计算及其应用.地球物理学报,2004,47(2):289-298.Chen L,Wu R S,Chen Y.Construction and application oflocal scattering matrix based on wavefield extrapolation in theGabor-Daubechies beamlet domain.Chinese J.Geophys.(inChinese),2004,47(2):289-298.
[19]陈凌,吴如山,王伟军.基于Gabor-Daubechies小波束叠前深度偏移的角度域共成像道集.地球物理学报,2004,47(5):876-885.Chen L,Wu R S,Wang W J.Common angle image gathersobtained from Gabor-Daubechies beamlet prestack depthmigration.Chinese J.Geophys.(in Chinese),2004,47(5):876-885.
[20]Luo M Q,Jin S W.Offset-domain LCB beamlet prestackdepth migration.∥76th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2006:2494-2497.
[21]Wu R S,Wang Y Z,Luo,M Q.Beamlet migration usinglocal cosine basis.Geophysics,2008,73(5):207-217.
[22]Coifman R R,Meyer Y.Remaxques sur 1′analyse de Fourieràfêngtre.Comptes Rendus de l′Académie des Sciences série1,mathématique,1991,312(3):259-261.Coifman R R,Meyer Y.Remarks on windowed Fourieranalysis.Comptes Rendus de l′Académie des Sciences série1,mathématique,1991,312(3):259-261.
[23]Mallat S.A Wavelet Tour of Signal Processing.2nd ed.SanDiego:Academic Press,1999.
[24]Hua B L,Williamson P,Zhang L B,et al.3-D prestackdepth migration with survey sinking operator in source-geophone and midpoint-offset hybrid domain.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2007:2270-2273.
[25]Biondi B.Equivalence of source-receiver migration and shot-profile migration.Geophysics,2003,68(4):1340-1347.
[26]Sava P,Hill S J.Overview and classification of wavefieldseismic imaging methods.The Leading Edge,2009,28(2):170-183.
[2]Claerbout J F.Imaging the Earth′s Interior.Cambridge:Blackwell Scientific Publications,1985.
[3]Yilmaz O,Claerbout J F.Prestack partial migration.Geophysics,1980,45(12):1753-1779.
[4]Popovici A M.Prestack migration by split-step DSR.Geophysics,1996,61(5):1412-1416.
[5]Jin S W,Mosher C C,Wu R S.Offset-domain pseudo-screenprestack depth migration.Geophysics,2002,67(6):1985-1902.
[6]Biondi B,Palacharla G.3-D prestack migration of common-azimuth data.Geophysics,1996,61(6):1822-1832.
[7]Biondi B,Fomel S,Chemingui N.Azimuth moveout for 3-Dprestack imaging.Geophysics,1998,63(2):574-588.
[8]孙沛勇,张叔伦.双平方根叠前深度偏移的广义高阶屏方法.石油地球物理勘探,2001,36(4):398-407.Sun P Y,Zhang S L.Generalized high-order screen methodfor pre-stack depth migration by double-square-root.OilGeophysical Prospecting(in Chinese),2001,36(4):398-407.
[9]程玖兵,王华忠,马在田.双平方根方程三维叠前深度偏移.地球物理学报,2003,46(5):676-683.Cheng J B,Wang H Z,Ma Z T.Double square root equation3D prestack depth migration.Chinese J.Geophys.(inChinese),2003,46(5):676-683.
[10]程玖兵,王华忠,马在田.窄方位地震数据双平方根方程偏移方法探讨.地球物理学报,2005,48(2):399-405.Cheng J B,Wang H Z,Ma Z T.Double square root equationmigration methods of narrow azimuth seismic data.ChineseJ.Geophys.(in Chinese),2005,48(2):399-405.
[11]刘定进,印兴耀.基于双平方根方程的保幅地震偏移.石油地球物理勘探,2007,42(1):11-16.Liu D J,Yin X Y.Amplitude-preserved seismic migrationbased on double square root.Oil Geophysical Prospecting(in Chinese),2007,42(1):11-16.
[12]Kosloff D D,Baysal E.Migration with the full acoustic waveequation.Geophysics,1983,48(6):677-687.
[13]Sandberg K,Beylkin G.Full-wave-equation depth extrapolationfor migration.Geophysics,2009,74(6):WCA121-WCA128.
[14]Alkhalifah T,Formel S.Source-receiver two-way waveextrapolation for prestack exploding-reflector modeling andmigration.∥80th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2010:2950-2954.
[15]Wu R S,Wang Y Z,Gao J H.Beamlet migration based onlocal perturbation theory.∥70th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2000:1008-1011.
[16]陈凌.小波束域波场的分解、传播及在地震偏移成像中的应用[博士论文].北京:中国地震局地球物理研究所,2002.Chen L.Beamlet-domain wavefield decomposition,propagationand it application in seismic migration/imaging[Ph.D thesis](inChinese).Beijing:Institute of Geophysics,China SeismologicalBureau,2002.
[17]高静怀,周艳辉,毛剑等.局部角度域波传播步进算法研究.地球物理学报,2007,50(1):248-259.Gao J H,Zhou Y H,Mao J,et al.A wave propagationmethod in local angle domain.Chinese J.Geophys.(in Chinese),2007,50(1):248-259.
[18]陈凌,吴如山,陈颙.基于Gabor-Daubechies小波束域波场外推的散射系数矩阵的计算及其应用.地球物理学报,2004,47(2):289-298.Chen L,Wu R S,Chen Y.Construction and application oflocal scattering matrix based on wavefield extrapolation in theGabor-Daubechies beamlet domain.Chinese J.Geophys.(inChinese),2004,47(2):289-298.
[19]陈凌,吴如山,王伟军.基于Gabor-Daubechies小波束叠前深度偏移的角度域共成像道集.地球物理学报,2004,47(5):876-885.Chen L,Wu R S,Wang W J.Common angle image gathersobtained from Gabor-Daubechies beamlet prestack depthmigration.Chinese J.Geophys.(in Chinese),2004,47(5):876-885.
[20]Luo M Q,Jin S W.Offset-domain LCB beamlet prestackdepth migration.∥76th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2006:2494-2497.
[21]Wu R S,Wang Y Z,Luo,M Q.Beamlet migration usinglocal cosine basis.Geophysics,2008,73(5):207-217.
[22]Coifman R R,Meyer Y.Remaxques sur 1′analyse de Fourieràfêngtre.Comptes Rendus de l′Académie des Sciences série1,mathématique,1991,312(3):259-261.Coifman R R,Meyer Y.Remarks on windowed Fourieranalysis.Comptes Rendus de l′Académie des Sciences série1,mathématique,1991,312(3):259-261.
[23]Mallat S.A Wavelet Tour of Signal Processing.2nd ed.SanDiego:Academic Press,1999.
[24]Hua B L,Williamson P,Zhang L B,et al.3-D prestackdepth migration with survey sinking operator in source-geophone and midpoint-offset hybrid domain.∥77th Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2007:2270-2273.
[25]Biondi B.Equivalence of source-receiver migration and shot-profile migration.Geophysics,2003,68(4):1340-1347.
[26]Sava P,Hill S J.Overview and classification of wavefieldseismic imaging methods.The Leading Edge,2009,28(2):170-183.
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