交错网格中基于波数域插值的波场分离方法研究（英文）
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摘要
应用多分量地震资料进行成像时通常需要先做波场分离,然后再对分离的波型进行成像。其中,波场分离可以在空间域或波数域实现。然而,由于用交错网格有限差分进行弹性波场数值模拟时,用来进行波数域波场分离的质点振动速度分量定义在不同网格节点上,本文提出了利用波数域插值方法来估算同一网格节点所需质点振动速度值;进而给出了先进行波数域插值后进行波场分离的波数域保幅波场分离方案。数值实验结果表明波数域插值方法具有较高的插值精度且保幅波场分离方法具有较好的保幅性,将本文方法进一步应用于弹性波逆时偏移可以获得保幅性较好的成像结果且对存在一定程度速度误差情况具有较好的适应性。
Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.
Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.
引文
Aki,K.,and Richards,P.G.,2002,Quantitative Seismology(2nd ed).California:University Science Books.
Chattopadhyay,S.,and Mc Mechan,G.A.,2008,Imaging conditions for prestack everse-time migration:Geophysics,73(3),S81–S89.
Dellinger,J.,1991,Anisotropic Seismic Wave Propagation[Doctor’s thesis].California:Stanford University,65–69.
Dellinger,J.,and Etgen,J.,1990,Wavefield separation in two-dimensional anisotropic media:Geophysics,55(7),914–919.
Devaney,A.J.,Oristagliot,M.L.,1986,A plane-wave decomposition for elastic wave fields applied to the separation of P-waves and S-waves in vector seismicdata:Geophysics,51(2),419–423.
Dong,L.G.,Ma Z.T.,Cao,J.Z.,Wang,H.Z.,Geng,J.H.,Lei,B.,and Xu,S.Y.,2000,A staggered-grid high-order difference method of one-order elastic wave equation:Chinese J.Geophys(in Chinese),43(3),411–419.
Du,Q.,Gong,X.,Zhang,M.,Zhu,Y.T.,and Fang,G.,2014,3D PS-wave imaging with elastic reverse-time migration:Geophysics,79(5),S173–S184.
Du,Q.Z.,Zhu,Y.T.,and Ba,J.,2012,Polarity reversal correction for elastic reverse time migration:Geophysics,77(2),S31–S41.
Etgen,J.T.,1988,Prestacked migration of P-and SV waves:58th Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,972–975.
Feng,X.,Zhang,X.W.,Liu,C.,Wang,D.,and Yang,Q.J.,2011,Separating P-P and P-SV wave by parabolic Radon transform with multiple coherence:Chinese J.Geophys(in Chinese),54(2),304–309.
Li,Z.Y.,Liang,G.H.,and Gu,B.L.,2013,Improved method of separating P-and S-waves using divergence and curl:Chinese J.Geophys(in Chinese),56(6),2012–2022.
Liu,Y.,2014,Optimal staggered-grid finite-difference schemes based on least squares for wave equation modeling:Geophysical Journal International,197(2),1033–1047.
Madariaga,R.,1976,Dynamics of an expanding circular fault:Bull.Seismol.Soc.Am.,66(3),639–666.
Martin,G.S.,Wiley,R.,and Marfurt,K.J.,2006,Marmousi 2:An elastic upgrade for Marmousi:The Leading Edge,25,156–166.
Moczo,P.,Kristek,J.,Vavrycuk,V.,Archuleta,R.J.,and Halada,L.,2002,3D heterogeneous staggered-grid finite difference modeling of seismic motion with volume andarithmetic averaging of elastic moduli and densities:Bull.Seismol.Soc.Am.,92(8),3042–3066.
Oristaglio,M.L.,Devany,A.J.,and Track,A.,1985,Separation of P-waves and S-waves in borehole seismicdata:55th Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,52–55.
Schleicher,J.,Costa,J.C.,and Novais,A.,2008,A comparison of imaging conditions for wave-equationshot-profile migration:Geophysics,73(6),S219–S227.
Sun,R.,1999,Separating P-and S-waves in a prestack 2-dimensional elastics eismogram:6 1th EAGE Conference & Exhibition,Extended Abstracts,6–23.
Sun,R.,Chow,J.D.,and Chen,K.J.,2001,Phase correction in separating P-and S-waves in elastic data:Geophysics,66(5),1515–1518.
Sun,R.,Mc Mechan,G.A.,and Chuang,H.H.,2011,Amplitude balancing in separating P-and S-waves in 2Dand 3D elastic data:Geophysics,76(3),S103–S113.
Sun,R.,Mc Mechan,G.A.,Hsiao,H.S.,and Chow,J.,2004,Separating P-and S-waves in prestack 3D elastic seismograms using divergence and curl:Geophysics,69(1),286–297.
Virieux,J.,1984,SH-wave propagation in heterogeneousm edia:velocity-stress finite-difference method:Geophysics,49(11),1933–1957.
Virieux,J.,1986,P-SV wave propagation in heterogeneousm edia:velocity-stress finite-difference method:Geophysics,51(4),889–901.
Yan,J.,and Sava,P.,2009a,Elastic wave-mode separation for VTI media:Geophysics,74(5),WB19–WB32.
Yan,J.,and Sava,P.,2009b,Elastic wave mode separation for TTI media:79th Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,1197–1021.
Yan,J.,and Sava,P.,2009c,3D elastic wave mode separation for TTI media:79th A Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,4294–4298.
Yao,D.Z.,Zhou,X.X.,and Zhong,B.S.,1993,Method for separating out P-wave or S-wave in VSP data and itsapplication:OGP(in Chinese),28(5),623–628.
Yoon,K.,and Marfurt,K.J.,2006,Reverse-time migrationusing the Poynting vector:Exploration Geophysics,37(1),102–107.
Zhang,G.Q.,and Zhou,H.B.,1995,Separating compressional wave from shear wave in surface seismic records:OGP(in Chinese),30(2),181–191.
Zhang,M.,Du,Q.Z.,Fang,G.,Gong,X.F.,and Zhu,Y.T.,2013,Phase correction of elastic reverse time migration section:83rd Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,1713–1717.
Zhang,Q.S.,and Mc Mechan,G.A.,2010,2D and3D elastic wavefield vector decomposition in the wave number domain for VTI media:Geophysics,75(3),D13–D26.
Zhang,Y.,and Sun,J.,2009,Practical issues of reverse time migration:True-amplitude gathers,noise removal and harmonic-source encoding:First Break,27(1),53–60.
Chattopadhyay,S.,and Mc Mechan,G.A.,2008,Imaging conditions for prestack everse-time migration:Geophysics,73(3),S81–S89.
Dellinger,J.,1991,Anisotropic Seismic Wave Propagation[Doctor’s thesis].California:Stanford University,65–69.
Dellinger,J.,and Etgen,J.,1990,Wavefield separation in two-dimensional anisotropic media:Geophysics,55(7),914–919.
Devaney,A.J.,Oristagliot,M.L.,1986,A plane-wave decomposition for elastic wave fields applied to the separation of P-waves and S-waves in vector seismicdata:Geophysics,51(2),419–423.
Dong,L.G.,Ma Z.T.,Cao,J.Z.,Wang,H.Z.,Geng,J.H.,Lei,B.,and Xu,S.Y.,2000,A staggered-grid high-order difference method of one-order elastic wave equation:Chinese J.Geophys(in Chinese),43(3),411–419.
Du,Q.,Gong,X.,Zhang,M.,Zhu,Y.T.,and Fang,G.,2014,3D PS-wave imaging with elastic reverse-time migration:Geophysics,79(5),S173–S184.
Du,Q.Z.,Zhu,Y.T.,and Ba,J.,2012,Polarity reversal correction for elastic reverse time migration:Geophysics,77(2),S31–S41.
Etgen,J.T.,1988,Prestacked migration of P-and SV waves:58th Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,972–975.
Feng,X.,Zhang,X.W.,Liu,C.,Wang,D.,and Yang,Q.J.,2011,Separating P-P and P-SV wave by parabolic Radon transform with multiple coherence:Chinese J.Geophys(in Chinese),54(2),304–309.
Li,Z.Y.,Liang,G.H.,and Gu,B.L.,2013,Improved method of separating P-and S-waves using divergence and curl:Chinese J.Geophys(in Chinese),56(6),2012–2022.
Liu,Y.,2014,Optimal staggered-grid finite-difference schemes based on least squares for wave equation modeling:Geophysical Journal International,197(2),1033–1047.
Madariaga,R.,1976,Dynamics of an expanding circular fault:Bull.Seismol.Soc.Am.,66(3),639–666.
Martin,G.S.,Wiley,R.,and Marfurt,K.J.,2006,Marmousi 2:An elastic upgrade for Marmousi:The Leading Edge,25,156–166.
Moczo,P.,Kristek,J.,Vavrycuk,V.,Archuleta,R.J.,and Halada,L.,2002,3D heterogeneous staggered-grid finite difference modeling of seismic motion with volume andarithmetic averaging of elastic moduli and densities:Bull.Seismol.Soc.Am.,92(8),3042–3066.
Oristaglio,M.L.,Devany,A.J.,and Track,A.,1985,Separation of P-waves and S-waves in borehole seismicdata:55th Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,52–55.
Schleicher,J.,Costa,J.C.,and Novais,A.,2008,A comparison of imaging conditions for wave-equationshot-profile migration:Geophysics,73(6),S219–S227.
Sun,R.,1999,Separating P-and S-waves in a prestack 2-dimensional elastics eismogram:6 1th EAGE Conference & Exhibition,Extended Abstracts,6–23.
Sun,R.,Chow,J.D.,and Chen,K.J.,2001,Phase correction in separating P-and S-waves in elastic data:Geophysics,66(5),1515–1518.
Sun,R.,Mc Mechan,G.A.,and Chuang,H.H.,2011,Amplitude balancing in separating P-and S-waves in 2Dand 3D elastic data:Geophysics,76(3),S103–S113.
Sun,R.,Mc Mechan,G.A.,Hsiao,H.S.,and Chow,J.,2004,Separating P-and S-waves in prestack 3D elastic seismograms using divergence and curl:Geophysics,69(1),286–297.
Virieux,J.,1984,SH-wave propagation in heterogeneousm edia:velocity-stress finite-difference method:Geophysics,49(11),1933–1957.
Virieux,J.,1986,P-SV wave propagation in heterogeneousm edia:velocity-stress finite-difference method:Geophysics,51(4),889–901.
Yan,J.,and Sava,P.,2009a,Elastic wave-mode separation for VTI media:Geophysics,74(5),WB19–WB32.
Yan,J.,and Sava,P.,2009b,Elastic wave mode separation for TTI media:79th Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,1197–1021.
Yan,J.,and Sava,P.,2009c,3D elastic wave mode separation for TTI media:79th A Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,4294–4298.
Yao,D.Z.,Zhou,X.X.,and Zhong,B.S.,1993,Method for separating out P-wave or S-wave in VSP data and itsapplication:OGP(in Chinese),28(5),623–628.
Yoon,K.,and Marfurt,K.J.,2006,Reverse-time migrationusing the Poynting vector:Exploration Geophysics,37(1),102–107.
Zhang,G.Q.,and Zhou,H.B.,1995,Separating compressional wave from shear wave in surface seismic records:OGP(in Chinese),30(2),181–191.
Zhang,M.,Du,Q.Z.,Fang,G.,Gong,X.F.,and Zhu,Y.T.,2013,Phase correction of elastic reverse time migration section:83rd Ann.Internat Mtg.,Soc.of Expl.Geophys.,Expanded Abstract,1713–1717.
Zhang,Q.S.,and Mc Mechan,G.A.,2010,2D and3D elastic wavefield vector decomposition in the wave number domain for VTI media:Geophysics,75(3),D13–D26.
Zhang,Y.,and Sun,J.,2009,Practical issues of reverse time migration:True-amplitude gathers,noise removal and harmonic-source encoding:First Break,27(1),53–60.
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