非椭圆各向异性介质高阶优化走时计算方法及应用
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摘要
随着地震勘探的深入,对勘探精度的要求越来越高,目前,提高勘探精度的主要方法之一就是提高地震波走时计算的精度,地震走时精度直接影响如动校正、静校正和偏移成像质量.根据地质模型假设条件的不同,有不同的走时计算方法,常用的有各向同性介质假设和各向异性介质假设条件下的走时计算方法,各向异性假设具有比各向同性假设更好的适用性,具有更高的走时计算精度,能够满足大偏移距和高陡构造情况下成像的要求.本文根据Alkhalifah的VTI介质中走时计算方法,以Fomel的TI介质中群速度的计算为基础,利用各向异性介质中Snell定律,提出了在非椭圆各向异性介质中的高阶优化走时计算方法,通过理论和实际数据的应用,表明该方法克服了常规各向异性走时方法中不能够计算大偏深比情况下地震波走时的缺点,具有走时计算精度高、便于实际应用等特点,对叠加和偏移成像有广阔的应用.
With the progress in seismic exploration,the need for accuracy is more essential.One of the methods in improving the accuracy of the exploration is to improve the accuracy of traveltime,which affacts the stack,statics and migration in the seismic data processing.According to the assumption of the medium,such as the isotropic medium and the anisotropic medium,there are different methods in calculating traveltime.The algorithm of traveltime based on the anisotropic medium is more applicable and accurate than the algorithm based on the isotropic medium,and it can settle with the traveltime for the deep dip or the large offset seismic easily.This paper,using the group velocity of anisotropy from Fomel's and Snell's law in anisotropy,deals with the traveltime based on the method of Alkhalifah,and develops a new high-order optimized algorithm for the anelliptical anisotropic medium.After application for the theoretical model and raw seimic data,the method in this paper succeeds in dealing with the weakness of the conventional method not computing the taveltime in the large-offset-deepth ratios seismic data,and it is more accurate and useful in the stack and imaging.
With the progress in seismic exploration,the need for accuracy is more essential.One of the methods in improving the accuracy of the exploration is to improve the accuracy of traveltime,which affacts the stack,statics and migration in the seismic data processing.According to the assumption of the medium,such as the isotropic medium and the anisotropic medium,there are different methods in calculating traveltime.The algorithm of traveltime based on the anisotropic medium is more applicable and accurate than the algorithm based on the isotropic medium,and it can settle with the traveltime for the deep dip or the large offset seismic easily.This paper,using the group velocity of anisotropy from Fomel's and Snell's law in anisotropy,deals with the traveltime based on the method of Alkhalifah,and develops a new high-order optimized algorithm for the anelliptical anisotropic medium.After application for the theoretical model and raw seimic data,the method in this paper succeeds in dealing with the weakness of the conventional method not computing the taveltime in the large-offset-deepth ratios seismic data,and it is more accurate and useful in the stack and imaging.
引文
[1]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[2]Tsvankin I.P-wave signatures and notation for transverselyisotropic media:An overview.Geophysics,1996,61(2):467-483.
[3]Tsvankin I.Inversion of reflection traveltime for transverseisotropic media.Geophysics,1995,60(1):268-284.
[4]Tsvankin I.Seismic Signatures and Analysis of Reflection Datain Anisotropic Media.Netherlands:Elsevier Science PublishngCompany,Inc,2005.
[5]Alkhalifah T.Prestack phase-shift migration of separate offsets.Geophysics,2000,65(4):1179-1194.
[6]Alkhalifah T.The offset-midpoint traveltime pyramid intransversely isotropic media.Geophysics,2000,65(4):1316-1325.
[7]Alkhalifah T.Acoustic approximations for processing intransversely isotropic media.Geophysics,1998,63(2):623-631.
[8]Alkhalifah T,Tsvankin I.Velocity analysis for transverselyisotropic media.Geophysics,1995,60(5):1550-1566.
[9]Alkhalifah T,Larner,K.Migration error in transverselyisotropic media.Geophysics,1994,59(9):1405-1418.
[10]Alkhalifah T.Transformation to zero offset in transverselyisotropic media.Geophysics,1996,61(4):947-963.
[11]Alkhalifah T.Traveltime computation with the linearizedeikonal equation for anisotropic media.GeophysicalProspecting,2002,50(4):373-382.
[12]Alkhalifah T.Kirchhoff time migration for transverselyisotropic media:an application to Trinidada data.Geophysics,2006,71(1):S29-S35.
[13]Alkhalifa T,Rampton D.Seismic anisotropy in Trinidad:Anew tool for lithology prediction.The Leading Edge,2001,20(4):105-113.
[14]Banik N C.Velocity anisotropy of shales and depth estimationin the North Sea Basin.Geophysics,1984,49(9):1411-1419
[15]Grechka V,Tsvankin I.Feasibility of nonhyperbolic moveoutinversion in transversely isotropic media.Geophysics,1998,63(3):957-969.
[16]Llya T,Leon T.Nonhyperbolic reflection moveout inanisotropic.Geophysics,1994,59(5):1550-1556.
[17]Pech A,Tsvankin I.Quartic moveout coefficient for a dippingazimuthally anisotropic layer.Geophysics,2004,69(3):699-707.
[18]Pech A,Tsvankin I,Grechka V.Quartic moveout coefficient,3-D description and application to titled Ti media.Geophysics,2003,68(5):1600-1610.
[19]Risto S.Technological leap in time processing focuses the datathroughout anisotropic media:special topic:seismicprocessing.First Break,2001,19(11):612-617.
[20]Stovas A,Ursin,B.Reflection and transmission responses oflayered transversely isotropic visco-elastic media.Geophys.Prospect.,2003,51(5):447-477.
[21]Stovas A,Ursin B.New travel-time approximations for atransversely isotropic medium.J.Geophys.Eng.,2004,1(2):128-133.
[22]Grechka V,Tsvankin I.Feasibility of nonhyperbolic moveoutinversion in transversely isotropic media.Geophysics,1998,63(3):957-969.
[23]Grechka V,Pech A.P-wave quartic reflection moveout inweakly anisotropic dipping layer.//SEG/Houston 2005,Annual Meeting,ANI 1.7:116-119.
[24]卢明辉,唐建侯,胡彬等.VTI介质P波非双曲时差分析.地球物理学进展,2005,20(2):328-331.Lu M H,Tang J H,Hu B,et al.Analysis of P-Wavenonhyperbolic reflection moveout in VTI media.Progress inGeophysics(in Chinese),2005,20(2):328-331.
[25]尤建军,常旭,刘伊克.VTI介质长偏移距非双曲动校正公式优化.地球物理学报,2006,49(6):1770-1778.You J J,Chang X,Liu Y K.Optimization of nonhyperbolicmoveout correction equation of long-offset seismic data inVTI media.Chinese J.Geophys.(in Chinese),2006,49(6):1770-1778.
[26]苑书金,董敏煜.各向异性介质中的P波旅行时反演.物探化探计算技术,2000,22(4):312-315.Yuan S J,Dong M Y.The inversion of P-wave traveltimes foranisotropic media.Computing Techniques for Geophysical andGeochemical Exploration(in Chinese),2000,22(4):312-315.
[27]张文生,何樵登.横向各向同性介质中的反射波时距曲线.石油物探,1997,36(2):15-24.Zhang W S,He J D.Reflection time-distance curves intransversely isotropic media.Geophysical Prospecting forPetroleum(in Chinese),1997,36(2):15-24.
[28]张超英,李守林,王光杰等.几种弱各向异性中qP波速度与偏振异常分析.石油物探,2001,40(1):33-40.Zhang C Y,Li S L,Wang G J,et al.Velocity and polarizationanomaly for qP wave in several weak anisotropic media.Geophysical Prospecting for Petroleum(in Chinese),2001,40(1):33-40.
[29]孙福利,杨长春,陈雨红等.弱各向异性介质中qP波的一阶射线追踪.地球物理学进展,2009,24(1):35-41.Sun F L,Yang C C,Chen Y H,et al.First-order Ray-tracingfor qP waves in weakly anisotropic media.Progress inGeophysics(in Chinese),2009,24(1):35-41.
[30]范桃园,杨长春,王真理等.复杂地质层面的网格化模型及两点射线追踪方法.地球物理学进展,2009,24(1):118-123.Fan T Y,Yang C C,Wang Z L,et al.Surface meshing and 3-Dtwo-point ray tracing in complex geology structure.Progressin Geophysics(in Chinese),2009,24(1):118-123.
[31]朱童,李小凡,张美根等.各向异性介质地震波场的优化褶积微分算子法数值模拟.地球物理学进展,2010,25(5):1568-1576.Zhu T,Li X F,Zhang M G,et al.Numerical modelling ofseismic wave fields in anisotropic media by using an optimalconvolutional differentiator.Progress in Geophysics(inChinese),2010,25(5):1568-1576.
[32]李波涛,杨长春,陈雨红等.基于波前面三角形网格剖分的波前重建法三维射线追踪.地球物理学进展,2009,24(2):507-512.Li B T,Yang C C,Chen Y H,et al.3Dwavefront constructionmethod ray tracing based on triangular grids layout onwavefront.Progress in Geophysics(in Chinese),2009,24(2):507-512.
[33]鲁彬,周立发,王兴春等.迭代法在三维网络模型最短路径射线追踪中的应用.地球物理学进展,2010,25(2)533-537.Lu B,Zhou L F,Wang X C,et al.A method of shortest pathraytracing using iterative optimization in a 3Dgrid model.Progress in Geophysics(in Chinese),2010,25(2):533-537.
[34]田晓峰,张先康,杨卓欣等.反射波走时高阶多项式拟合在三维地震透射中的应用.地球物理学进展,2007,22(3):913-918.Tian X F,Zhang X K,Yang Z X,et al.Fitting a high-orderpolynomial to reflection times and its application to three-dimensional seismic transmission.Progress in Geophysics(inChinese),2007,22(3):913-918.
[35]王建立,方正茂,杨长春等.高阶优化走时计算方法及在地震成像中的应用.石油地球物理勘探,2012,47(1):63-67.Wang J L,Fang Z M,Yang C C,et al.A high order optimizedtraveltime algorithm and its applicatipons in seismic imaging.Oil Geophysical Prospecting(in Chinese),2012,47(1):63-67.
[36]Fomel S.On anelliptic approximations for qP velocities in VTImedia.Geophys.Prosp.,2004,52(3):247-259.
[37]Michael A.A generalized form of Snell’s law in anisotropicmedia.Geophysics,2000,65(2):632-637.
[2]Tsvankin I.P-wave signatures and notation for transverselyisotropic media:An overview.Geophysics,1996,61(2):467-483.
[3]Tsvankin I.Inversion of reflection traveltime for transverseisotropic media.Geophysics,1995,60(1):268-284.
[4]Tsvankin I.Seismic Signatures and Analysis of Reflection Datain Anisotropic Media.Netherlands:Elsevier Science PublishngCompany,Inc,2005.
[5]Alkhalifah T.Prestack phase-shift migration of separate offsets.Geophysics,2000,65(4):1179-1194.
[6]Alkhalifah T.The offset-midpoint traveltime pyramid intransversely isotropic media.Geophysics,2000,65(4):1316-1325.
[7]Alkhalifah T.Acoustic approximations for processing intransversely isotropic media.Geophysics,1998,63(2):623-631.
[8]Alkhalifah T,Tsvankin I.Velocity analysis for transverselyisotropic media.Geophysics,1995,60(5):1550-1566.
[9]Alkhalifah T,Larner,K.Migration error in transverselyisotropic media.Geophysics,1994,59(9):1405-1418.
[10]Alkhalifah T.Transformation to zero offset in transverselyisotropic media.Geophysics,1996,61(4):947-963.
[11]Alkhalifah T.Traveltime computation with the linearizedeikonal equation for anisotropic media.GeophysicalProspecting,2002,50(4):373-382.
[12]Alkhalifah T.Kirchhoff time migration for transverselyisotropic media:an application to Trinidada data.Geophysics,2006,71(1):S29-S35.
[13]Alkhalifa T,Rampton D.Seismic anisotropy in Trinidad:Anew tool for lithology prediction.The Leading Edge,2001,20(4):105-113.
[14]Banik N C.Velocity anisotropy of shales and depth estimationin the North Sea Basin.Geophysics,1984,49(9):1411-1419
[15]Grechka V,Tsvankin I.Feasibility of nonhyperbolic moveoutinversion in transversely isotropic media.Geophysics,1998,63(3):957-969.
[16]Llya T,Leon T.Nonhyperbolic reflection moveout inanisotropic.Geophysics,1994,59(5):1550-1556.
[17]Pech A,Tsvankin I.Quartic moveout coefficient for a dippingazimuthally anisotropic layer.Geophysics,2004,69(3):699-707.
[18]Pech A,Tsvankin I,Grechka V.Quartic moveout coefficient,3-D description and application to titled Ti media.Geophysics,2003,68(5):1600-1610.
[19]Risto S.Technological leap in time processing focuses the datathroughout anisotropic media:special topic:seismicprocessing.First Break,2001,19(11):612-617.
[20]Stovas A,Ursin,B.Reflection and transmission responses oflayered transversely isotropic visco-elastic media.Geophys.Prospect.,2003,51(5):447-477.
[21]Stovas A,Ursin B.New travel-time approximations for atransversely isotropic medium.J.Geophys.Eng.,2004,1(2):128-133.
[22]Grechka V,Tsvankin I.Feasibility of nonhyperbolic moveoutinversion in transversely isotropic media.Geophysics,1998,63(3):957-969.
[23]Grechka V,Pech A.P-wave quartic reflection moveout inweakly anisotropic dipping layer.//SEG/Houston 2005,Annual Meeting,ANI 1.7:116-119.
[24]卢明辉,唐建侯,胡彬等.VTI介质P波非双曲时差分析.地球物理学进展,2005,20(2):328-331.Lu M H,Tang J H,Hu B,et al.Analysis of P-Wavenonhyperbolic reflection moveout in VTI media.Progress inGeophysics(in Chinese),2005,20(2):328-331.
[25]尤建军,常旭,刘伊克.VTI介质长偏移距非双曲动校正公式优化.地球物理学报,2006,49(6):1770-1778.You J J,Chang X,Liu Y K.Optimization of nonhyperbolicmoveout correction equation of long-offset seismic data inVTI media.Chinese J.Geophys.(in Chinese),2006,49(6):1770-1778.
[26]苑书金,董敏煜.各向异性介质中的P波旅行时反演.物探化探计算技术,2000,22(4):312-315.Yuan S J,Dong M Y.The inversion of P-wave traveltimes foranisotropic media.Computing Techniques for Geophysical andGeochemical Exploration(in Chinese),2000,22(4):312-315.
[27]张文生,何樵登.横向各向同性介质中的反射波时距曲线.石油物探,1997,36(2):15-24.Zhang W S,He J D.Reflection time-distance curves intransversely isotropic media.Geophysical Prospecting forPetroleum(in Chinese),1997,36(2):15-24.
[28]张超英,李守林,王光杰等.几种弱各向异性中qP波速度与偏振异常分析.石油物探,2001,40(1):33-40.Zhang C Y,Li S L,Wang G J,et al.Velocity and polarizationanomaly for qP wave in several weak anisotropic media.Geophysical Prospecting for Petroleum(in Chinese),2001,40(1):33-40.
[29]孙福利,杨长春,陈雨红等.弱各向异性介质中qP波的一阶射线追踪.地球物理学进展,2009,24(1):35-41.Sun F L,Yang C C,Chen Y H,et al.First-order Ray-tracingfor qP waves in weakly anisotropic media.Progress inGeophysics(in Chinese),2009,24(1):35-41.
[30]范桃园,杨长春,王真理等.复杂地质层面的网格化模型及两点射线追踪方法.地球物理学进展,2009,24(1):118-123.Fan T Y,Yang C C,Wang Z L,et al.Surface meshing and 3-Dtwo-point ray tracing in complex geology structure.Progressin Geophysics(in Chinese),2009,24(1):118-123.
[31]朱童,李小凡,张美根等.各向异性介质地震波场的优化褶积微分算子法数值模拟.地球物理学进展,2010,25(5):1568-1576.Zhu T,Li X F,Zhang M G,et al.Numerical modelling ofseismic wave fields in anisotropic media by using an optimalconvolutional differentiator.Progress in Geophysics(inChinese),2010,25(5):1568-1576.
[32]李波涛,杨长春,陈雨红等.基于波前面三角形网格剖分的波前重建法三维射线追踪.地球物理学进展,2009,24(2):507-512.Li B T,Yang C C,Chen Y H,et al.3Dwavefront constructionmethod ray tracing based on triangular grids layout onwavefront.Progress in Geophysics(in Chinese),2009,24(2):507-512.
[33]鲁彬,周立发,王兴春等.迭代法在三维网络模型最短路径射线追踪中的应用.地球物理学进展,2010,25(2)533-537.Lu B,Zhou L F,Wang X C,et al.A method of shortest pathraytracing using iterative optimization in a 3Dgrid model.Progress in Geophysics(in Chinese),2010,25(2):533-537.
[34]田晓峰,张先康,杨卓欣等.反射波走时高阶多项式拟合在三维地震透射中的应用.地球物理学进展,2007,22(3):913-918.Tian X F,Zhang X K,Yang Z X,et al.Fitting a high-orderpolynomial to reflection times and its application to three-dimensional seismic transmission.Progress in Geophysics(inChinese),2007,22(3):913-918.
[35]王建立,方正茂,杨长春等.高阶优化走时计算方法及在地震成像中的应用.石油地球物理勘探,2012,47(1):63-67.Wang J L,Fang Z M,Yang C C,et al.A high order optimizedtraveltime algorithm and its applicatipons in seismic imaging.Oil Geophysical Prospecting(in Chinese),2012,47(1):63-67.
[36]Fomel S.On anelliptic approximations for qP velocities in VTImedia.Geophys.Prosp.,2004,52(3):247-259.
[37]Michael A.A generalized form of Snell’s law in anisotropicmedia.Geophysics,2000,65(2):632-637.
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