起伏海底界面上覆液相弹性介质的海底电缆数据正演模拟与波形分离方法（英文）
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摘要
在海洋地震勘探中,海底电缆技术能够准确记录多分量地震波场。但地震波在海洋上覆液相弹性介质环境中的传播无法用单一的波动方程进行稳定地模拟,而且当海底界面为起伏构造时,常规有限差分格式无法准确地对声波波场传递到弹性波波场的过程进行模拟。因此,提出了一种曲坐标系下的声弹耦合方程正演模拟及纵横波矢量分解方法。该方法将起伏海底界面的上覆液相弹性介质剖分为正交曲网格,并采用坐标旋转将笛卡尔坐标系下的起伏海底界面映射为曲坐标系下的水平海底界面,在上覆液相介质和下伏固相介质中分别采用曲坐标系下的声波方程和弹性波方程进行模拟,在起伏海底界面处,提出了一种曲坐标系下的声-弹耦合控制方程将两种方程的声压和应力结合起来。在数值离散时,引入了一种全交错网格机制提高数值模拟的稳定性。基于上述研究,推导了一种曲坐标系下分离的纵波方程和横波方程,实现了曲坐标系下纵横波矢量分解。分别采用理论推导和数值测试证明了该方法的正确性。
In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P-and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P-and S-wave equations in the curvilinear coordinates system are derived to realize the P-and S-wave separation method.
In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P-and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P-and S-wave equations in the curvilinear coordinates system are derived to realize the P-and S-wave separation method.
引文
Aki,K.,and Richards,P.,2002,Quantitative seismology(second edition):University Science Books.
Bernth,H.,and Chapman,C.,2011,A comparison of the dispersion relations for anisotropic elastodynamic finitedifference grids:Geophysics,76(3),WA43-WA50.
Carcione,J.M.,and Helle,H.B.,2004,The physics and simulation of wave propagation at the ocean bottom:Geophysics,69(3),825-839.
Choi,Y.,Min,D.J.,and Shin,C.,2008,Two-dimensional waveform inversion of multi-component data in acoustic-elastic coupled media:Geophysical Prospecting,56(6),863-881.
Dahake,G.,and Gracewski,S.M.,1997,Finite difference predictions of P-SV wave propagation inside submerged solids.I.Liquid-solid interface conditions:The Journal of the Acoustical Society of America,102(4),2125-2137.
Dai,Y.J.,2005,Research and application of wave field separation technology of multi-wave reflection seismic exploration data acquisition:Master Thesis,Central South University,Changsha.
Dankbaar,J.W.M.,1985,Separation of P-and S waves:Geophysical Prospecting,33(7),970-986.
Devaney,A.J.,and Oristagliot,M.L.,1986,A planewave decomposition for elastic wave fields applied to the separation of P-waves and S-waves in vector seismic data:Geophysics,51(2),419-423.
Du,Q.Z.,Zhang,M.Q.,Chen,X.R.,Gong,X.F.,and Guo,C.F.,2014,True-amplitude wavefield separation using staggered-grid interpolation in the wavenumber domain:Applied Geophysics,11(4),437-446.
Falk,J.,Tessmer,E.,and Gajewski,D.,1998,Efficient finite-difference modelling of seismic waves using locally adjustable time steps:Geophysical Journal International,46(6),603-616.
Fornberg,B.,1988,The pseudospectral method:accurate representation of interfaces in elastic wave calculations:Geophysics,53(5),625-637.
Hestholm,S.O.,and Ruud,B.O.,1994,2D finitedifference elastic wave modelling including surface topography:Geophysical Prospecting,42(5),371-390.
Huang,J.P.,Qu,Y.M.,Li,Q.Y.,Li,Z.C.,Li,G.L.,Bu,C.C.,and Teng,H.H.,2015,Variable-coordinate forward modeling of irregular surface based on dual-variable grid:Applied Geophysics,12(1),101-110.
Jastram,C.,and Behle,A.,1992,Acoustic modeling on a vertically varying grid:Geophysical Prospecting,40(2),157-169.
Jastram,C.,and Tessmer,E.,1994,Elastic modeling on a grid with vertically varying spacing:Geophysical Prospecting,42(4),357-370.
Komatitsch,D.,Barnes,C.,and Tromp,J.,2000,Wave propagation near a fluid-solid interface:A spectralelement approach:Geophysics,65(2),623-631.
Komatitsch,D.,and Tromp,J.,2002,Spectral-element simulations of global seismic wave propagation-I.Validation:Geophys.J.Int.149(2),390-412.
Lan,H.Q.,and Zhang,Z.J.,2012,Research on seismic survey design for doubly complex areas,Applied Geophysics,9(3),301-312.
Lebedev,V.I.,1964,Difference analogues of orthogonal decompositions,basic differential operators and some boundary problems of mathematical physics:USSRComputational Mathematics and Mathematical Physics,4(3),36-45.
Levander,A.,1988,Fourth-order finite-difference P-SVseismograms:Geophysics,53(11),1425-1436.
Li,Z.C.,Zhang,H.,Liu,Q.M.,and Han,W.G.,2007,Numieric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm:Oil Geophysical Prospecting,42(5),510-515.
Lu,J.,and Wang,Y.,and Yao,C.,2012,Separating P-and S-waves in an affine coordinate system:J.Geophys.Eng.,9(1),12-18.
Ma,J.T.,Sen,K.M.,Chen,X.H.,and Yao,F.C.,2011,OBC multiple attenuation technique using SRME theory:Chinese J.Geophys.(in Chinese),54(11),2960-2966.
Mirko,V.D.B.,2006,PP/PS Wavefield separation by independent component analysis:Geophys.J.Int.,166(1),339-348.
Moczo,P.,Bystricky,E.,Kristek,J.,Carcione,J.M.,and Bouchon,M.,1997,Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures:Bull.seism.Soc.Am.,87(5),1305-1323.
Qu,Y.,Huang,J.,Li,Z.,Li,Q.,Zhao,J.,and Li,X.,2015,Elastic wave modeling and pre-stack reverse time migration of irregular free-surface based on layered mapping method:Chinese J.Geophys.,58(8),2896-2911.
Qu,Y.,Huang,J.,Li,Z.,and Li,J.,2017,A hybrid grid method in an auxiliary coordinate system for irregular fluid-solid interface modeling:Geophys.J.Int.,208(3),1540-1556.
Qu,Y.,Li,Z.,Huang,J.,and Li,J.,2017,Elastic full waveform inversion for surface topography:Geophysics,82(5),R269-R285.
Qu,Y.,Li,Z.,and Huang,J.,Li,J.,2018,Multi-scale full waveform inversion for areas with irregular surface topography in anauxiliary coordinate system:Exploration Geophysics.,49(1),70-82.
Soares,J.D.,and Mansur,W.J.,2006,Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method:Journal of Computational Physics,219(2),498-512.
Sun,R.,Chow,J.,and Chen,K.J.,2001,Phase correction in separating P-and S-waves in elastic data:Geophysics,66(5),1515-1518.
Sun,R.,McMechan,G.A.,and Chuang,H.,2011,Amplitude balancing in separating P-and S-waves in 2Dand 3D elastic seismic data:Geophysics,76(3),S103-S113.
Tessmer,E.,2000,Seismic finite-difference modeling with spatially varying time steps:Geophysics,65(4),1290-1293.
Tessmer,E.,Kosloff,D.,and Behle,A.,1992,Elastic wave propagation simulation in the presence of surface topography:Geophysical Journal International,108(2),621-632.
Tessmer,E.,and Kosloff,D.,1994,3D elastic modelling with surface topography by a Chebychev spectral method:Geophysics,59(3),464-473.
Virieux,J.,1984,SH-wave propagation in heterogeneous media:velocity-stress finite-difference method:Geophysics,49(11),1933-1957.
Virieux,J.,1986,P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method:Geophysics,51(4),889-901.
Wang,Y.B.,Satish,C.S.,and Penny J.B.,2002,Separation of P-and SV-wavefields from multicomponent seismic data in theτ-p domain:Geophys.J.Int.,151(2),663-672.
Yang,J.J.,He B.S.,and Zhang J.Z.,2014,Multicomponent seismic forward modeling of gas hydrates beneath the seafloor:Applied Geophysics,11(4),418-428.
Yang,J.H.,Liu,T.,Tang,G.Y.,and Hu,T.Y.,2009,Modeling seismic wave propagation within complex structures:Applied Geophysics,6(1),30-41.
Zhang,B.Q.,Zhou,H.,Li,G.F.,and Guo,J.Q.,2016,Geophone-seabed coupling effect and its correction:Applied Geophysics,13(1),145-155.
Zhang,J.,2004,Wave propagation across fluid-solid interfaces:a grid method approach:Geophysical Journal International,159(1),240-252.
Bernth,H.,and Chapman,C.,2011,A comparison of the dispersion relations for anisotropic elastodynamic finitedifference grids:Geophysics,76(3),WA43-WA50.
Carcione,J.M.,and Helle,H.B.,2004,The physics and simulation of wave propagation at the ocean bottom:Geophysics,69(3),825-839.
Choi,Y.,Min,D.J.,and Shin,C.,2008,Two-dimensional waveform inversion of multi-component data in acoustic-elastic coupled media:Geophysical Prospecting,56(6),863-881.
Dahake,G.,and Gracewski,S.M.,1997,Finite difference predictions of P-SV wave propagation inside submerged solids.I.Liquid-solid interface conditions:The Journal of the Acoustical Society of America,102(4),2125-2137.
Dai,Y.J.,2005,Research and application of wave field separation technology of multi-wave reflection seismic exploration data acquisition:Master Thesis,Central South University,Changsha.
Dankbaar,J.W.M.,1985,Separation of P-and S waves:Geophysical Prospecting,33(7),970-986.
Devaney,A.J.,and Oristagliot,M.L.,1986,A planewave decomposition for elastic wave fields applied to the separation of P-waves and S-waves in vector seismic data:Geophysics,51(2),419-423.
Du,Q.Z.,Zhang,M.Q.,Chen,X.R.,Gong,X.F.,and Guo,C.F.,2014,True-amplitude wavefield separation using staggered-grid interpolation in the wavenumber domain:Applied Geophysics,11(4),437-446.
Falk,J.,Tessmer,E.,and Gajewski,D.,1998,Efficient finite-difference modelling of seismic waves using locally adjustable time steps:Geophysical Journal International,46(6),603-616.
Fornberg,B.,1988,The pseudospectral method:accurate representation of interfaces in elastic wave calculations:Geophysics,53(5),625-637.
Hestholm,S.O.,and Ruud,B.O.,1994,2D finitedifference elastic wave modelling including surface topography:Geophysical Prospecting,42(5),371-390.
Huang,J.P.,Qu,Y.M.,Li,Q.Y.,Li,Z.C.,Li,G.L.,Bu,C.C.,and Teng,H.H.,2015,Variable-coordinate forward modeling of irregular surface based on dual-variable grid:Applied Geophysics,12(1),101-110.
Jastram,C.,and Behle,A.,1992,Acoustic modeling on a vertically varying grid:Geophysical Prospecting,40(2),157-169.
Jastram,C.,and Tessmer,E.,1994,Elastic modeling on a grid with vertically varying spacing:Geophysical Prospecting,42(4),357-370.
Komatitsch,D.,Barnes,C.,and Tromp,J.,2000,Wave propagation near a fluid-solid interface:A spectralelement approach:Geophysics,65(2),623-631.
Komatitsch,D.,and Tromp,J.,2002,Spectral-element simulations of global seismic wave propagation-I.Validation:Geophys.J.Int.149(2),390-412.
Lan,H.Q.,and Zhang,Z.J.,2012,Research on seismic survey design for doubly complex areas,Applied Geophysics,9(3),301-312.
Lebedev,V.I.,1964,Difference analogues of orthogonal decompositions,basic differential operators and some boundary problems of mathematical physics:USSRComputational Mathematics and Mathematical Physics,4(3),36-45.
Levander,A.,1988,Fourth-order finite-difference P-SVseismograms:Geophysics,53(11),1425-1436.
Li,Z.C.,Zhang,H.,Liu,Q.M.,and Han,W.G.,2007,Numieric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm:Oil Geophysical Prospecting,42(5),510-515.
Lu,J.,and Wang,Y.,and Yao,C.,2012,Separating P-and S-waves in an affine coordinate system:J.Geophys.Eng.,9(1),12-18.
Ma,J.T.,Sen,K.M.,Chen,X.H.,and Yao,F.C.,2011,OBC multiple attenuation technique using SRME theory:Chinese J.Geophys.(in Chinese),54(11),2960-2966.
Mirko,V.D.B.,2006,PP/PS Wavefield separation by independent component analysis:Geophys.J.Int.,166(1),339-348.
Moczo,P.,Bystricky,E.,Kristek,J.,Carcione,J.M.,and Bouchon,M.,1997,Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures:Bull.seism.Soc.Am.,87(5),1305-1323.
Qu,Y.,Huang,J.,Li,Z.,Li,Q.,Zhao,J.,and Li,X.,2015,Elastic wave modeling and pre-stack reverse time migration of irregular free-surface based on layered mapping method:Chinese J.Geophys.,58(8),2896-2911.
Qu,Y.,Huang,J.,Li,Z.,and Li,J.,2017,A hybrid grid method in an auxiliary coordinate system for irregular fluid-solid interface modeling:Geophys.J.Int.,208(3),1540-1556.
Qu,Y.,Li,Z.,Huang,J.,and Li,J.,2017,Elastic full waveform inversion for surface topography:Geophysics,82(5),R269-R285.
Qu,Y.,Li,Z.,and Huang,J.,Li,J.,2018,Multi-scale full waveform inversion for areas with irregular surface topography in anauxiliary coordinate system:Exploration Geophysics.,49(1),70-82.
Soares,J.D.,and Mansur,W.J.,2006,Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method:Journal of Computational Physics,219(2),498-512.
Sun,R.,Chow,J.,and Chen,K.J.,2001,Phase correction in separating P-and S-waves in elastic data:Geophysics,66(5),1515-1518.
Sun,R.,McMechan,G.A.,and Chuang,H.,2011,Amplitude balancing in separating P-and S-waves in 2Dand 3D elastic seismic data:Geophysics,76(3),S103-S113.
Tessmer,E.,2000,Seismic finite-difference modeling with spatially varying time steps:Geophysics,65(4),1290-1293.
Tessmer,E.,Kosloff,D.,and Behle,A.,1992,Elastic wave propagation simulation in the presence of surface topography:Geophysical Journal International,108(2),621-632.
Tessmer,E.,and Kosloff,D.,1994,3D elastic modelling with surface topography by a Chebychev spectral method:Geophysics,59(3),464-473.
Virieux,J.,1984,SH-wave propagation in heterogeneous media:velocity-stress finite-difference method:Geophysics,49(11),1933-1957.
Virieux,J.,1986,P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method:Geophysics,51(4),889-901.
Wang,Y.B.,Satish,C.S.,and Penny J.B.,2002,Separation of P-and SV-wavefields from multicomponent seismic data in theτ-p domain:Geophys.J.Int.,151(2),663-672.
Yang,J.J.,He B.S.,and Zhang J.Z.,2014,Multicomponent seismic forward modeling of gas hydrates beneath the seafloor:Applied Geophysics,11(4),418-428.
Yang,J.H.,Liu,T.,Tang,G.Y.,and Hu,T.Y.,2009,Modeling seismic wave propagation within complex structures:Applied Geophysics,6(1),30-41.
Zhang,B.Q.,Zhou,H.,Li,G.F.,and Guo,J.Q.,2016,Geophone-seabed coupling effect and its correction:Applied Geophysics,13(1),145-155.
Zhang,J.,2004,Wave propagation across fluid-solid interfaces:a grid method approach:Geophysical Journal International,159(1),240-252.