三维起伏地表条件下地震波走时计算的不等距迎风差分法
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摘要
三维起伏地表条件下的地震波走时计算技术是研究三维起伏地表地区很多地震数据处理技术的基础性工具.为了获得适应于任意三维起伏地表且计算精度高的走时算法,提出三维不等距迎风差分法.该方法采用不等距网格剖分三维起伏地表模型,通过在迎风差分格式中引入不等距差分格式、Huygens原理及Fermat原理来建立地表附近的局部走时计算公式,并通过在窄带技术中设定新的网格节点类型来获得三维起伏地表条件下算法的整体实现步骤.精度及算例分析表明:三维不等距迎风差分法具有很高的计算精度且能够适应于任意三维起伏地表模型.
The traveltime computation scheme in a 3D undulating surface condition has a great significance to some 3D seismic data processing techniques in complex topographical regions.To obtain a traveltime computation algorithm that can treat the 3D complex topography with high accuracy and good flexibility,we present an upwind finite difference method with nonuniform grid spacing.We use the grid with nonuniform grid spacing for dividing the velocity model.For obtaining the local traveltime computation formulas,we synthetically introduce the finite difference scheme with nonuniform grid spacing,Huygens principle and Fermat principle into the conventional upwind finite difference scheme.To build up the implementation steps,we propose a new narrow-band technique in complex topographical conditions by improving the conventional narrow-band technique.The accuracy analysis and an example show that the new method can treat any 3D complex topography problems with high accuracy.
The traveltime computation scheme in a 3D undulating surface condition has a great significance to some 3D seismic data processing techniques in complex topographical regions.To obtain a traveltime computation algorithm that can treat the 3D complex topography with high accuracy and good flexibility,we present an upwind finite difference method with nonuniform grid spacing.We use the grid with nonuniform grid spacing for dividing the velocity model.For obtaining the local traveltime computation formulas,we synthetically introduce the finite difference scheme with nonuniform grid spacing,Huygens principle and Fermat principle into the conventional upwind finite difference scheme.To build up the implementation steps,we propose a new narrow-band technique in complex topographical conditions by improving the conventional narrow-band technique.The accuracy analysis and an example show that the new method can treat any 3D complex topography problems with high accuracy.
引文
[1]孙建国.复杂地表条件下地球物理场数值模拟方法评述.世界地质,2007,26(3):345-362.Sun J G.Methods for numerical modeling of geophysicalfields under complex topographical conditions:a criticalreview.Global Geology(in Chinese),2007,26(3):345-362.
[2]Sun J G.True-amplitude weight functions in 3Dlimited-aperture migration revisited.Geophysics,2004,69(4):1025-1036.
[3]Sun J G.Limited-aperture migration.Geophysics,2000,65(2):584-595.
[4]Sun J G.On the aperture effect in 3D Kirchhoff-typemigration.Geophysical Prospecting,1999,47(5):1045-1076.
[5]Sun J G.On the limited aperture migration in twodimensions.Geophysics,1998,63(5):984-994.
[6]井西利,杨长春,王世清.一种改进的地震反射层析成像方法.地球物理学报,2007,50(6):1831-1836.Jing X L,Yang C C,Wang S S.A improved seismic reflectiontomographic method.Chinese J.Geophys.(in Chinese),2007,50(6):1831-1836.
[7]瞿辰,周蕙兰,赵大鹏.使用纵波和横波走时层析成像研究菲律宾海板块西边缘带和南海地区的深部结构.地球物理学报,2007,50(6):1757-1768.Qu C,Zhou H L,Zhao D P.Deep structure beneath the westmargin of Philippine Sea Plate and South China Sea from Pand S wave travel time tomography.Chinese J.Geophys.(inChinese),2007,50(6):1757-1768
[8]Julian B R,Gubbins D.Three-dimensional seismic raytracing.J.Geophys.,1977,43:95-113.
[9]Vinje V,Iversen E,Gjystdal H.Traveltime and amplitudeestimation using wavefront construction.Geophysics,1993,58(8):1157-1166.
[10]Han F X,Sun J G,Sun Z Q,et al.Positioning of grid pointsin wavefront construction.Applied Geophysics,2009,6(3):248-258.
[11]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59-67.
[12]张美根,贾豫葛,王妙月等.界面二次源波前扩展法全局最小走时射线追踪技术.地球物理学报,2006,49(4):1169-1175.Zhang M G,Jia Y G,Wang M Y,et al.A global minimumtraveltime ray tracing algorithm of wavefront expanding withinterface points as secondary sources.Chinese J.Geophys.(in Chinese),2006,49(4):1169-1175.
[13]Asakawa E,Wanaka T.Seismic ray tracing using lineartraveltime interpolation.Geophysical Prospecting,1993,41(1):99-111.
[14]Wang H Z,Ma Z T.Traveltime calculation in 3Dmedia witharbitray velocity distribution.69th Ann.Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1999:1778-1781.
[15]秦孟兆,陈景波.Maslov渐近理论与辛几何算法.地球物理学报,2000,43(4):523-533.Qin M Z,Chen J B.Maslov asymptotic theory and symplecticalgorithm.Chinese J.Geophys.(in Chinese),2000,43(4):523-533.
[16]高亮李幼铭,陈旭荣等.地震射线辛几何算法初探.地球物理学报,2000,43(3):402-409.Gao L,Li Y M,Chen X R,et al.An attempt to seismic raytracing with symplectic algorithm.Chinese J.Geophys.(inChinese),2000,43(3):402-409.
[17]Vidale J E.Finite-difference calculation of travel times.Bull.Seism.Soc.Am.,1988,78(6):2062-2076.
[18]Sethian J A,Popovici A M.3-D traveltime computation usingthe fast marching method.Geophysics,1999,64(2):516-523.
[19]Sethian J A.Fast marching methods.SIAM Review,1999,41(2):199-235.
[20]Rawlinson N,Sambridge M.Wave front evolution instrongly heterogeneous layered mediausing the fast marchingmethod.Geophys.J.Int.,2004,156(3):631-647.
[21]Rawlinson N,Sambridge M.Multiple reflection andtransmission phases in complex layered media using amultistage fast marching method.Geophysics,2004,69(5):1338-1350.
[22]Sun J G,Yang H,Han F X.A finite-difference scheme forsolving the eikonal equation with varying grid spacing.77thAnn.Internat.Mtg.,Soc.Expl.Geophys.,ExpandedAbstracts,2007:2120-2124.
[23]蒋先艺.基于二维与三维复杂结构模型正演的地震数据采集设计方法研究[博士论文].成都:成都理工大学地球物理学院,2004.Jiang X Y.The study of seismic acquisition method based onmodeling of 2Dand 3Dcomplex geologic structure[Ph.D.thesis](in Chinese).Chengdu:College of Geophysics ofChengdu University of Technology,2004.
[24]刘少勇,王华忠,张兵.起伏地表Kirchhoff积分法叠前深度偏移方法研究与应用.∥2010年国际石油地球物理技术交流会会议专刊.北京:科学出版社,2010:49-54.Liu S Y,Wang H Z,Zhang B.Kirchhoff integral PSDM forrugged topography:technology and application.∥Conferenceon Exploration Geophysics in the West of China(inChinese).Beijing:Science Press,2010:49-54.
[25]白超英,黄国娇,李忠生.三维复杂层状介质中多震相走时联合反演成像.地球物理学报,2011,54(1):182-192.Bai C Y,Huang G J,Li Z S.Simultaneous inversioncombining multiple-phase traveltimes within 3D complexlayered media.Chinese J.Geophys.(in Chinese),2011,54(1):182-192.
[26]Sun J G,Sun Z Q,Han F X.A finite difference scheme forsolving the eikonal equation including surface topography.79th Ann.Internat.Mtg.,Expl.Geophys.,ExpandedAbstracts,2009:2667-2671.
[27]Sun J G,Sun Z Q,Han F X.A finite difference scheme forsolving the eikonal equation including surface topography.Geophysics,2011,76(4):T53-T63.
[28]Sethian J A,Popovici A M.3-D traveltime computation usingthe fast marching method.Geophysics,1999,64(2):516-523.
[2]Sun J G.True-amplitude weight functions in 3Dlimited-aperture migration revisited.Geophysics,2004,69(4):1025-1036.
[3]Sun J G.Limited-aperture migration.Geophysics,2000,65(2):584-595.
[4]Sun J G.On the aperture effect in 3D Kirchhoff-typemigration.Geophysical Prospecting,1999,47(5):1045-1076.
[5]Sun J G.On the limited aperture migration in twodimensions.Geophysics,1998,63(5):984-994.
[6]井西利,杨长春,王世清.一种改进的地震反射层析成像方法.地球物理学报,2007,50(6):1831-1836.Jing X L,Yang C C,Wang S S.A improved seismic reflectiontomographic method.Chinese J.Geophys.(in Chinese),2007,50(6):1831-1836.
[7]瞿辰,周蕙兰,赵大鹏.使用纵波和横波走时层析成像研究菲律宾海板块西边缘带和南海地区的深部结构.地球物理学报,2007,50(6):1757-1768.Qu C,Zhou H L,Zhao D P.Deep structure beneath the westmargin of Philippine Sea Plate and South China Sea from Pand S wave travel time tomography.Chinese J.Geophys.(inChinese),2007,50(6):1757-1768
[8]Julian B R,Gubbins D.Three-dimensional seismic raytracing.J.Geophys.,1977,43:95-113.
[9]Vinje V,Iversen E,Gjystdal H.Traveltime and amplitudeestimation using wavefront construction.Geophysics,1993,58(8):1157-1166.
[10]Han F X,Sun J G,Sun Z Q,et al.Positioning of grid pointsin wavefront construction.Applied Geophysics,2009,6(3):248-258.
[11]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59-67.
[12]张美根,贾豫葛,王妙月等.界面二次源波前扩展法全局最小走时射线追踪技术.地球物理学报,2006,49(4):1169-1175.Zhang M G,Jia Y G,Wang M Y,et al.A global minimumtraveltime ray tracing algorithm of wavefront expanding withinterface points as secondary sources.Chinese J.Geophys.(in Chinese),2006,49(4):1169-1175.
[13]Asakawa E,Wanaka T.Seismic ray tracing using lineartraveltime interpolation.Geophysical Prospecting,1993,41(1):99-111.
[14]Wang H Z,Ma Z T.Traveltime calculation in 3Dmedia witharbitray velocity distribution.69th Ann.Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1999:1778-1781.
[15]秦孟兆,陈景波.Maslov渐近理论与辛几何算法.地球物理学报,2000,43(4):523-533.Qin M Z,Chen J B.Maslov asymptotic theory and symplecticalgorithm.Chinese J.Geophys.(in Chinese),2000,43(4):523-533.
[16]高亮李幼铭,陈旭荣等.地震射线辛几何算法初探.地球物理学报,2000,43(3):402-409.Gao L,Li Y M,Chen X R,et al.An attempt to seismic raytracing with symplectic algorithm.Chinese J.Geophys.(inChinese),2000,43(3):402-409.
[17]Vidale J E.Finite-difference calculation of travel times.Bull.Seism.Soc.Am.,1988,78(6):2062-2076.
[18]Sethian J A,Popovici A M.3-D traveltime computation usingthe fast marching method.Geophysics,1999,64(2):516-523.
[19]Sethian J A.Fast marching methods.SIAM Review,1999,41(2):199-235.
[20]Rawlinson N,Sambridge M.Wave front evolution instrongly heterogeneous layered mediausing the fast marchingmethod.Geophys.J.Int.,2004,156(3):631-647.
[21]Rawlinson N,Sambridge M.Multiple reflection andtransmission phases in complex layered media using amultistage fast marching method.Geophysics,2004,69(5):1338-1350.
[22]Sun J G,Yang H,Han F X.A finite-difference scheme forsolving the eikonal equation with varying grid spacing.77thAnn.Internat.Mtg.,Soc.Expl.Geophys.,ExpandedAbstracts,2007:2120-2124.
[23]蒋先艺.基于二维与三维复杂结构模型正演的地震数据采集设计方法研究[博士论文].成都:成都理工大学地球物理学院,2004.Jiang X Y.The study of seismic acquisition method based onmodeling of 2Dand 3Dcomplex geologic structure[Ph.D.thesis](in Chinese).Chengdu:College of Geophysics ofChengdu University of Technology,2004.
[24]刘少勇,王华忠,张兵.起伏地表Kirchhoff积分法叠前深度偏移方法研究与应用.∥2010年国际石油地球物理技术交流会会议专刊.北京:科学出版社,2010:49-54.Liu S Y,Wang H Z,Zhang B.Kirchhoff integral PSDM forrugged topography:technology and application.∥Conferenceon Exploration Geophysics in the West of China(inChinese).Beijing:Science Press,2010:49-54.
[25]白超英,黄国娇,李忠生.三维复杂层状介质中多震相走时联合反演成像.地球物理学报,2011,54(1):182-192.Bai C Y,Huang G J,Li Z S.Simultaneous inversioncombining multiple-phase traveltimes within 3D complexlayered media.Chinese J.Geophys.(in Chinese),2011,54(1):182-192.
[26]Sun J G,Sun Z Q,Han F X.A finite difference scheme forsolving the eikonal equation including surface topography.79th Ann.Internat.Mtg.,Expl.Geophys.,ExpandedAbstracts,2009:2667-2671.
[27]Sun J G,Sun Z Q,Han F X.A finite difference scheme forsolving the eikonal equation including surface topography.Geophysics,2011,76(4):T53-T63.
[28]Sethian J A,Popovici A M.3-D traveltime computation usingthe fast marching method.Geophysics,1999,64(2):516-523.
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