横向各向同性介质中地震波走时模拟
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摘要
横向各向同性介质是地球内部广泛分布的一种各向异性介质.针对这种介质,我们对各向同性介质的最小走时树走时模拟方法进行了推广,推广后的方法可适用于非均匀、对称轴任意倾斜的横向各向同性介质模型.为保证计算效率,最小走时树的构建采用了一种子波传播区域随地震波传播动态变化的改进算法.对于弱各向异性介质,我们使用了一种新的地震波群速度近似表示方法,该方法基于用射线角近似表示相角的思想,对3种地震波(qP,qSV和qSH)均有较好的精度.应用本文地震波走时模拟方法对均匀介质、横向非均匀介质模型进行了计算,并将后者结果与弹性波方程有限元方法的模拟结果进行了对比,结果表明两者符合得很好.本文方法可用于横向各向同性介质的深度偏移及地震层析成像的深入研究.
The minimum traveltime tree algorithm for tracing rays in isotropic media is extended to transversely isotropic(TI) media,which exist extensively in the Earth.The extended algorithm is suitable to heterogeneous TI media with tilted axes of symmetry.Construction of the minimum traveltime tree is implemented efficiently with a modified algorithm in which propagation areas of secondary waves are not fixed but adjusted dynamically with spread of seismic waves in media.As for weakly anisotropic media,we use a new approximate formula of group velocity in terms of ray angle.The approximate velocity formula is based on the expression of phase angle in terms of ray angle,and fits well the exact values for three independent modes of seismic waves(qP,qSV and qSH).Homogeneous and heterogeneous models are calculated with the extended minimum traveltime tree algorithm.We compare our results corresponding to the heterogeneous model with those obtained by a finite-element method for elastic anisotropic waves and find that they are in excellent agreement.The extended ray tracing method can be applied to further researches on depth migration and seismic tomography for TI media.
The minimum traveltime tree algorithm for tracing rays in isotropic media is extended to transversely isotropic(TI) media,which exist extensively in the Earth.The extended algorithm is suitable to heterogeneous TI media with tilted axes of symmetry.Construction of the minimum traveltime tree is implemented efficiently with a modified algorithm in which propagation areas of secondary waves are not fixed but adjusted dynamically with spread of seismic waves in media.As for weakly anisotropic media,we use a new approximate formula of group velocity in terms of ray angle.The approximate velocity formula is based on the expression of phase angle in terms of ray angle,and fits well the exact values for three independent modes of seismic waves(qP,qSV and qSH).Homogeneous and heterogeneous models are calculated with the extended minimum traveltime tree algorithm.We compare our results corresponding to the heterogeneous model with those obtained by a finite-element method for elastic anisotropic waves and find that they are in excellent agreement.The extended ray tracing method can be applied to further researches on depth migration and seismic tomography for TI media.
引文
[1]滕吉文,张中杰,王爱武等.弹性介质各向异性研究沿革现状与问题.地球物理学进展,1992,7(4):14~28Teng J W,Zhang Z J,Wang A W,et al.The study of anisotropy inelastic medium:evolution,present situation and questions.Progressin Geophysics(in Chinese),1992,7(4):14~28
[2]黄晓葛,白武明.地震波各向异性的研究进展.地球物理学进展,1999,14(3):54~65Huang X G,Bai W M.Research on seismic anisotropy—a review.Progress in Geophysics(in Chinese),1999,14(3):54~65
[3]张中杰.地震各向异性研究进展.地球物理学进展,2002,17图6图4模型射线追踪方法计算结果与弹性波有限元方法模拟结果的比较a)震源波形;(b)t=0.45 s时Z分量的快照及qP波走时等值线;(c)t=0.9 s时X分量的快照及qSV波走时等值线.Fig.6 Comparison between the results calculated with the ray tracing method and afinite-element forward modeling method of elastic waves for the model in Fig.4(a)Waveform of the seismic source;(b)Snapshot ofZcomponent and the traveltime contour of qP waveatt=0.45 s;(c)Snapshot ofXcomponent and the traveltime contour of qSV wave att=0.9 s.(2):281~293Zhang Z J.A review of the seismic anisotropy and its applications.Progress in Geophysics(in Chinese),2002,17(2):281~293
[4]高原.地震各向异性研究进展—参加2001年IAGA-IASPEI会议总结.地球物理学进展,2002,17(2):360~364Gao Y.Development of seismic anisotropy:from the 2001 IAGA-IASPEI Joint Scientific Assembly.Progress in Geophysics(inChinese),2002,17(2):360~364
[5]张中杰.多分量地震资料的各向异性处理与解释方法.哈尔滨:黑龙江教育出版社,2002Zhang Z J.Multi-component Seismic Data Processing andInterpretation for Anisotropy(in Chinese).Harbin:HeilongjiangEducation Press,2002
[6]Mourad A,Deschamps M.Lamb’s problem for an anisotropic half-space studied by the Cagniard de Hoop method.J.Acoust.Soc.Am.1995,97(5):3194~3197
[7]Sena A G.Seismic traveltime equations for azimuthally anisotropicand isotropic media:Estimation of interval elastic properties.Geophysics,1991,56(12):2090~2101
[8]Alkhalifah T,Tsvankin I.Velocity analysis for transversely isotropicmedia.Geophysics,1995,60(5):1550~1566
[9]Cˇerven V.Seismic rays and rays intensities in inhomogeneousanisotropic media.Geophys.J.Roy.Astr.Soc.,1972,29(1):1~13
[10]Cˇerven V.Seismic Ray Theory.Cambridge:Cambridge UniversityPress,2001
[11]Farra V.First-order ray tracing for qS waves in inhomogeneous weaklyanisotropic media.Geophys.J.Int.2005,161(2):309~324
[12]P encˇík I,Farra V.First-order ray tracing for qP waves ininhomogeneous weakly anisotropic media.Geophysics,2005,70(6):D65~D75
[13]Grechka V Y,McMechan G A.3-D tow-point ray tracing forheterogeneous,weakly transversely isotropic media.Geophysics,1996,61(6):1883~1894
[14]Coman R,Gajewski D.Traveltime computation by wavefront-orientated ray tracing.Geophysical Prospecting,2005,53(1):23~36
[15]Gibson Jr R L,Durussel V,Lee K.Modeling and velocity analysiswith a wavefront-construction algorithm for anisotropic media.Geophysics,2005,70(4):T63~T74
[16]Ettrich N,Gajewski D.Traveltime computation by perturbation withFD-eikonal solvers in isotropic and weakly anisotropic media.Geophysics,1998,63(3):1066~1078
[17]Alkhalifah T.Traveltime computation with the linearized eikonalequation for anisotropic media.Geophysical Prospecting,2002,50(4):373~382
[18]Schneider Jr W A.Linearization of the P-wave eikonal equation forweak vertical transverse isotropy.Geophysics,2003,68(3):1075~1082
[19]Faria E L,Stoffa P L.Traveltime computation in transverselyisotropic media.Geophysics,1994,59(2):272~281
[20]Cardarelli E,Cerreto A.Ray tracing in elliptical anisotropic mediausing the linear traveltime interpolation(LTI)method applied totraveltime seismic tomography.Geophysical Prospecting,2002,50(1):55~72
[21]Kumar D,Sen M K,Ferguson R J.Traveltime calculation andprestack depth migration in tilted transversely isotropic media.Geophysics,2004,69(1):37~44
[22]Qin Y,Zhang Z,Li S.CDP mapping in tilted transversely isotropic(TTI)media.Part I:Method and effectiveness.GeophysicalProspecting,2003,51(4):315~324
[23]Zhou B,Greenhalgh S A.‘Shortest path’ray tracing for most general2D/3D anisotropic media.J.Geophys.Eng.2005,2(1):54~63
[24]Julian B R,Gubbins D.Three-dimensional seismic ray tracing.J.Geophys.,1977,43(1):95~114
[25]Vidale J E.Finite-difference calculation of traveltimes.Bull.Seis.Soc.Am.,1988,78(6):2062~2076
[26]Vidale J E.Finite-difference calculation of traveltimes in threedimensions.Geophysics,1990,55(5):521~526
[27]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution of theeikonal equation along expanding wavefronts.Geophysics,1992,57(3):478~487
[28]Sethian J A,Popovici A M.3-D traveltime computation using the fastmarching method.Geophysics,1999,64(2):516~523
[29]Nakanishi I,Yamaguchi K.A numerical experiment on nonlinearimage reconstruction from first-arrival times for two-dimensional islandarc structure.J.Phys.Earth,1986,34(2):195~201
[30]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59~67
[31]黄联捷,李幼铭,吴如山.用于图像重建的波前法射线追踪.地球物理学报,1992,35(2):223~233Huang L J,Li Y M,Wu R S.The wave-front ray tracing method forimage reconstruction.Chinese J.Geophys.(in Chinese),1992,35(2):223~233
[32]Cao S,Greenhalgh S.Calculation of the seismic first-break time fieldand its ray path distribution using a minimum traveltime treealgorithm.Geophys.J.Int.,1993,114(3):593~600
[33]Fischer R,Lees J M.Shortest path ray tracing with sparse graphs.Geophysics,1993,58(7):987~996
[34]Klimes L,Kvasnicka M.3-D network ray tracing.Geophys.J.Int.,1994,116(3):726~738
[35]刘洪,孟凡林,李幼铭.计算最小走时和射线路径的界面网全局方法.地球物理学报,1995,38(6):823~832Liu H,Meng F L,Li Y M.The interface grid method for seekingglobal minimum travel-time and the correspondent raypath.ChineseJ.Geophys.(in Chinese),1995,38(6):823~832
[36]Cheng N,House L.Minimum traveltime calculation in 3-D graphtheory.Geophysics,1996,61(6):1895~1898
[37]王辉,常旭.基于图形结构的三维射线追踪方法.地球物理学报,2000,43(4):534~541Wang H,Chang X.3-D tracing method based on graphic structure.Chinese J.Geophys.(in Chinese),2000,43(4):534~541
[38]赵爱华,张中杰,王光杰等.非均匀介质中地震波走时与射线路径快速计算技术.地震学报,2000,22(2):151~157Zhao A H,Zhang Z J,Wang G J,et al.A new scheme for fastcalculation of seismic traveltimes and ray paths in heterogeneousmedia.Acta Seismological Sinica,2000,13(2):166~173
[39]赵爱华,张中杰,彭苏萍.复杂地质模型转换波快速射线追踪方法.中国矿业大学学报,2003,32(5):513~516Zhao A H,Zhang Z J,Peng S P.Fast ray tracing method forconverted waves in complex media.Journal of China University ofMining&Technology(in Chinese),2003,32(5):513~516
[40]赵爱华,张中杰.三维复杂介质中转换波走时快速计算.地球物理学报,2004,47(4):702~707Zhao A H,Zhang Z J.Fast calculation of converted wave traveltimesin 3-D complex media.Chinese J.Geophys.(in Chinese),2004,47(4):702~707
[41]Zhao A H,Zhang Z J,Teng J W.Minimum travel time tree algorithmfor seismic ray tracing:improvement in efficiency.J.Geophys.Eng.,2004,1(4):245~251
[42]张建中,陈世军,徐初伟.动态网络最短路径射线追踪.地球物理学报,2004,47(5):899~904Zhang J Z,Chen S J,Xu C W.A method of shortest path raytracingwith dynamic networks.Chinese J.Geophys.(in Chinese),2004,47(5):899~904
[43]赵爱华,丁志峰.宽角反射地震波走时模拟的双重网格法.地球物理学报,2005,48(5):1141~1147Zhao A H,Ding Z F.A double-grid algorithm for calculatingtraveltimes of wide-angle reflection waves.Chinese J.Geophys.(inChinese),2005,48(5):1141~1147
[44]Daley P F,Hron F.Reflection and transmission coefficients fortransversely isotropic media.Bull.Seis.Soc.Am.,1977,67(3):661~675
[45]Berryman J G.Long-wave elastic anisotropy in transversely isotropicmedia.Geophysics,1979,44(5):896~917
[46]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954~1966
[47]Byun B S,Corrigan D,Gaiser J E.Anisotropic velocity analysis forlithology discrimination.Geophysics,1989,54(12):1564~1574
[48]赵爱华,丁志峰.一种弱各向异性介质地震波群速度的近似表示新方法.地球物理学进展,2005,20(4):916~919Zhao A H,Ding Z F.New approximate expressions of seismic groupvelocities for weakly anisotropic media.Progress in Geophysics(inChinese),2005,20(4):916~919
[49]徐,杨长春,刘洪等.射线追踪的微变网格方法.地球物理学报,1996,39(1):97~102Xu S,Yang C C,Liu H,et al.A grid-changeable method for raytracing.Chinese J.Geophys.(in Chinese),1996,39(1):97~102
[50]张美根,王妙月,李小凡等.各向异性弹性波场的有限元数值模拟.地球物理学进展,2002,17(3):384~389Zhang M G,Wang M Y,Li X F,et al.Finite element forwardmodeling of anisotropic elastic waves.Progress in Geophysics(inChinese),2002,17(3):384~389
[2]黄晓葛,白武明.地震波各向异性的研究进展.地球物理学进展,1999,14(3):54~65Huang X G,Bai W M.Research on seismic anisotropy—a review.Progress in Geophysics(in Chinese),1999,14(3):54~65
[3]张中杰.地震各向异性研究进展.地球物理学进展,2002,17图6图4模型射线追踪方法计算结果与弹性波有限元方法模拟结果的比较a)震源波形;(b)t=0.45 s时Z分量的快照及qP波走时等值线;(c)t=0.9 s时X分量的快照及qSV波走时等值线.Fig.6 Comparison between the results calculated with the ray tracing method and afinite-element forward modeling method of elastic waves for the model in Fig.4(a)Waveform of the seismic source;(b)Snapshot ofZcomponent and the traveltime contour of qP waveatt=0.45 s;(c)Snapshot ofXcomponent and the traveltime contour of qSV wave att=0.9 s.(2):281~293Zhang Z J.A review of the seismic anisotropy and its applications.Progress in Geophysics(in Chinese),2002,17(2):281~293
[4]高原.地震各向异性研究进展—参加2001年IAGA-IASPEI会议总结.地球物理学进展,2002,17(2):360~364Gao Y.Development of seismic anisotropy:from the 2001 IAGA-IASPEI Joint Scientific Assembly.Progress in Geophysics(inChinese),2002,17(2):360~364
[5]张中杰.多分量地震资料的各向异性处理与解释方法.哈尔滨:黑龙江教育出版社,2002Zhang Z J.Multi-component Seismic Data Processing andInterpretation for Anisotropy(in Chinese).Harbin:HeilongjiangEducation Press,2002
[6]Mourad A,Deschamps M.Lamb’s problem for an anisotropic half-space studied by the Cagniard de Hoop method.J.Acoust.Soc.Am.1995,97(5):3194~3197
[7]Sena A G.Seismic traveltime equations for azimuthally anisotropicand isotropic media:Estimation of interval elastic properties.Geophysics,1991,56(12):2090~2101
[8]Alkhalifah T,Tsvankin I.Velocity analysis for transversely isotropicmedia.Geophysics,1995,60(5):1550~1566
[9]Cˇerven V.Seismic rays and rays intensities in inhomogeneousanisotropic media.Geophys.J.Roy.Astr.Soc.,1972,29(1):1~13
[10]Cˇerven V.Seismic Ray Theory.Cambridge:Cambridge UniversityPress,2001
[11]Farra V.First-order ray tracing for qS waves in inhomogeneous weaklyanisotropic media.Geophys.J.Int.2005,161(2):309~324
[12]P encˇík I,Farra V.First-order ray tracing for qP waves ininhomogeneous weakly anisotropic media.Geophysics,2005,70(6):D65~D75
[13]Grechka V Y,McMechan G A.3-D tow-point ray tracing forheterogeneous,weakly transversely isotropic media.Geophysics,1996,61(6):1883~1894
[14]Coman R,Gajewski D.Traveltime computation by wavefront-orientated ray tracing.Geophysical Prospecting,2005,53(1):23~36
[15]Gibson Jr R L,Durussel V,Lee K.Modeling and velocity analysiswith a wavefront-construction algorithm for anisotropic media.Geophysics,2005,70(4):T63~T74
[16]Ettrich N,Gajewski D.Traveltime computation by perturbation withFD-eikonal solvers in isotropic and weakly anisotropic media.Geophysics,1998,63(3):1066~1078
[17]Alkhalifah T.Traveltime computation with the linearized eikonalequation for anisotropic media.Geophysical Prospecting,2002,50(4):373~382
[18]Schneider Jr W A.Linearization of the P-wave eikonal equation forweak vertical transverse isotropy.Geophysics,2003,68(3):1075~1082
[19]Faria E L,Stoffa P L.Traveltime computation in transverselyisotropic media.Geophysics,1994,59(2):272~281
[20]Cardarelli E,Cerreto A.Ray tracing in elliptical anisotropic mediausing the linear traveltime interpolation(LTI)method applied totraveltime seismic tomography.Geophysical Prospecting,2002,50(1):55~72
[21]Kumar D,Sen M K,Ferguson R J.Traveltime calculation andprestack depth migration in tilted transversely isotropic media.Geophysics,2004,69(1):37~44
[22]Qin Y,Zhang Z,Li S.CDP mapping in tilted transversely isotropic(TTI)media.Part I:Method and effectiveness.GeophysicalProspecting,2003,51(4):315~324
[23]Zhou B,Greenhalgh S A.‘Shortest path’ray tracing for most general2D/3D anisotropic media.J.Geophys.Eng.2005,2(1):54~63
[24]Julian B R,Gubbins D.Three-dimensional seismic ray tracing.J.Geophys.,1977,43(1):95~114
[25]Vidale J E.Finite-difference calculation of traveltimes.Bull.Seis.Soc.Am.,1988,78(6):2062~2076
[26]Vidale J E.Finite-difference calculation of traveltimes in threedimensions.Geophysics,1990,55(5):521~526
[27]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution of theeikonal equation along expanding wavefronts.Geophysics,1992,57(3):478~487
[28]Sethian J A,Popovici A M.3-D traveltime computation using the fastmarching method.Geophysics,1999,64(2):516~523
[29]Nakanishi I,Yamaguchi K.A numerical experiment on nonlinearimage reconstruction from first-arrival times for two-dimensional islandarc structure.J.Phys.Earth,1986,34(2):195~201
[30]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59~67
[31]黄联捷,李幼铭,吴如山.用于图像重建的波前法射线追踪.地球物理学报,1992,35(2):223~233Huang L J,Li Y M,Wu R S.The wave-front ray tracing method forimage reconstruction.Chinese J.Geophys.(in Chinese),1992,35(2):223~233
[32]Cao S,Greenhalgh S.Calculation of the seismic first-break time fieldand its ray path distribution using a minimum traveltime treealgorithm.Geophys.J.Int.,1993,114(3):593~600
[33]Fischer R,Lees J M.Shortest path ray tracing with sparse graphs.Geophysics,1993,58(7):987~996
[34]Klimes L,Kvasnicka M.3-D network ray tracing.Geophys.J.Int.,1994,116(3):726~738
[35]刘洪,孟凡林,李幼铭.计算最小走时和射线路径的界面网全局方法.地球物理学报,1995,38(6):823~832Liu H,Meng F L,Li Y M.The interface grid method for seekingglobal minimum travel-time and the correspondent raypath.ChineseJ.Geophys.(in Chinese),1995,38(6):823~832
[36]Cheng N,House L.Minimum traveltime calculation in 3-D graphtheory.Geophysics,1996,61(6):1895~1898
[37]王辉,常旭.基于图形结构的三维射线追踪方法.地球物理学报,2000,43(4):534~541Wang H,Chang X.3-D tracing method based on graphic structure.Chinese J.Geophys.(in Chinese),2000,43(4):534~541
[38]赵爱华,张中杰,王光杰等.非均匀介质中地震波走时与射线路径快速计算技术.地震学报,2000,22(2):151~157Zhao A H,Zhang Z J,Wang G J,et al.A new scheme for fastcalculation of seismic traveltimes and ray paths in heterogeneousmedia.Acta Seismological Sinica,2000,13(2):166~173
[39]赵爱华,张中杰,彭苏萍.复杂地质模型转换波快速射线追踪方法.中国矿业大学学报,2003,32(5):513~516Zhao A H,Zhang Z J,Peng S P.Fast ray tracing method forconverted waves in complex media.Journal of China University ofMining&Technology(in Chinese),2003,32(5):513~516
[40]赵爱华,张中杰.三维复杂介质中转换波走时快速计算.地球物理学报,2004,47(4):702~707Zhao A H,Zhang Z J.Fast calculation of converted wave traveltimesin 3-D complex media.Chinese J.Geophys.(in Chinese),2004,47(4):702~707
[41]Zhao A H,Zhang Z J,Teng J W.Minimum travel time tree algorithmfor seismic ray tracing:improvement in efficiency.J.Geophys.Eng.,2004,1(4):245~251
[42]张建中,陈世军,徐初伟.动态网络最短路径射线追踪.地球物理学报,2004,47(5):899~904Zhang J Z,Chen S J,Xu C W.A method of shortest path raytracingwith dynamic networks.Chinese J.Geophys.(in Chinese),2004,47(5):899~904
[43]赵爱华,丁志峰.宽角反射地震波走时模拟的双重网格法.地球物理学报,2005,48(5):1141~1147Zhao A H,Ding Z F.A double-grid algorithm for calculatingtraveltimes of wide-angle reflection waves.Chinese J.Geophys.(inChinese),2005,48(5):1141~1147
[44]Daley P F,Hron F.Reflection and transmission coefficients fortransversely isotropic media.Bull.Seis.Soc.Am.,1977,67(3):661~675
[45]Berryman J G.Long-wave elastic anisotropy in transversely isotropicmedia.Geophysics,1979,44(5):896~917
[46]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954~1966
[47]Byun B S,Corrigan D,Gaiser J E.Anisotropic velocity analysis forlithology discrimination.Geophysics,1989,54(12):1564~1574
[48]赵爱华,丁志峰.一种弱各向异性介质地震波群速度的近似表示新方法.地球物理学进展,2005,20(4):916~919Zhao A H,Ding Z F.New approximate expressions of seismic groupvelocities for weakly anisotropic media.Progress in Geophysics(inChinese),2005,20(4):916~919
[49]徐,杨长春,刘洪等.射线追踪的微变网格方法.地球物理学报,1996,39(1):97~102Xu S,Yang C C,Liu H,et al.A grid-changeable method for raytracing.Chinese J.Geophys.(in Chinese),1996,39(1):97~102
[50]张美根,王妙月,李小凡等.各向异性弹性波场的有限元数值模拟.地球物理学进展,2002,17(3):384~389Zhang M G,Wang M Y,Li X F,et al.Finite element forwardmodeling of anisotropic elastic waves.Progress in Geophysics(inChinese),2002,17(3):384~389
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