提高规则网格最短路径方法反射波走时计算精度的走时校正技术
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摘要
最短路径射线追踪方法是计算地震波走时的主要方法之一,该方法基于惠更斯原理和费玛原理,具有稳健、适于复杂介质模型的优点.为处理方便,最短路径方法中的介质模型通常以规则网格进行剖分,界面节点(界面与网格的交点)以其邻近的模型单元节点(即边界单元节点)近似表示.界面近似将导致计算误差,对于反射波尤为严重.反射波的走时精度可通过减小网格的尺寸提高,但这样会大大增加计算时间.为高精度和高效率地计算地震反射波走时,我们提出了一种基于规则网格的走时校正技术.地震波传播至或起始于边界单元节点的走时校正为地震波传播至或起始于该边界单元节点所对应的界面节点的走时.数值模型计算结果表明,走时校正方法可使反射波的走时精度提高约1～2个数量级,而其计算时间则和常规算法基本上在相同量级.
The shortest path method is one of main approaches of calculating seismic traveltimes.The ray tracing method is based on Huygens' and Fermat's principles,and can be applied to complex velocity models due to its excellent robustness.For convenience,the velocity model is usually divided into small equal elements with a regular grid,taking the points at the centers of the elements as model nodes.Accordingly,an interface node,namely an intersection point of an interface with the model node grid,is approximately represented with its adjacent model node,which is referred to as a boundary model node.The interface approximation certainly produces traveltime errors,which is accentuated for reflection waves.The traveltime error can be reduced by decreasing the model element size,at the large cost of computation time.For efficiently calculating reflection wave traveltime with high accuracy,we put forward a traveltime correction technology which is combined with the shortest path method based on a regular grid.The traveltime of a secondary wave from or to a boundary model note is corrected to that of the wave from or to the corresponding interface node.Numerical examples show that by employing the traveltime correction technology,the traveltime accuracy of reflection waves can be improved by about 1~2 orders of magnitude while the computational time maintains the same magnitude order as that of the normal algorithm.
The shortest path method is one of main approaches of calculating seismic traveltimes.The ray tracing method is based on Huygens' and Fermat's principles,and can be applied to complex velocity models due to its excellent robustness.For convenience,the velocity model is usually divided into small equal elements with a regular grid,taking the points at the centers of the elements as model nodes.Accordingly,an interface node,namely an intersection point of an interface with the model node grid,is approximately represented with its adjacent model node,which is referred to as a boundary model node.The interface approximation certainly produces traveltime errors,which is accentuated for reflection waves.The traveltime error can be reduced by decreasing the model element size,at the large cost of computation time.For efficiently calculating reflection wave traveltime with high accuracy,we put forward a traveltime correction technology which is combined with the shortest path method based on a regular grid.The traveltime of a secondary wave from or to a boundary model note is corrected to that of the wave from or to the corresponding interface node.Numerical examples show that by employing the traveltime correction technology,the traveltime accuracy of reflection waves can be improved by about 1~2 orders of magnitude while the computational time maintains the same magnitude order as that of the normal algorithm.
引文
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[3]Zhang Z J,Klemperer S L.West-east variation in crustalthickness in northern Lhasa block,central Tibet,from deepseismic sounding data,J.Geophys.Res.,2005,110(B9),B09403.
[4]Zhang Z J,Klemperer S.Crustal structure of the TethyanHimalaya,southern Tibet:new constraints from old wide-angle seismic data.Geophys.J.Int.,2010,181(3):1247-1260.
[5]Zhang Z J,Deng Y F,Teng J W,et al.An overview of thecrustal structure of the Tibetan plateau after 35years of deepseismic soundings.Journal of Asian Earth Sciences,2011,40(4):977-989.
[6]Zhang Z J,Klemperer S.,Bai Z,et al.Crustal structure ofthe Paleozoic Kunlun orogeny from an active-source seismicprofile between Moba and Guide in East Tibet,China.Gondwana Research,2011,19(4):994-1007.
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[9]嘉世旭,刘昌铨.华北地区人工地震测深震相与地壳结构研究.地震地质,1995,17(2):97-105.Jia S X,Liu C Q.Study on the seismic phases of DSS in NorthChina.Seismology and Geology,1995,17(2):97-105.
[10]Kennett B L N,Engdahl E R.Traveltimes for global earthquakelocation and phase identification.Geophys.J.Int.,1991,105(2):429-465.
[11]Rawlinson N,Sambridge M.Seismic traveltime tomographyof the crust and lithosphere.Advances in Geophysics,2003,46:81-198.
[12]Julian B R,Gubbins D.1977.Three-dimensional seismic raytracing.Journal of Geophysics,43(1):95-114.
[13]徐涛,徐果明,高尔根,等.三维复杂介质的块状建模和试射射线追踪.地球物理学报,2004,47(6):1118-1126.Xu T,Xu G M,Gao E G,et al.Block modeling andshooting ray tracing in complex 3-D media.Chinese J.Geophys.(in Chinese),2004,47(6):1118-1126.
[14]Um J,Thurber C.1987.A fast algorithm for two-point seismicray tracing.Bulletin of the Seismological Society of America,77(3):972-986.
[15]Zhao D,Hasegawa A,Horiuchi S.Tomographic imaging ofP and S wave velocity structure beneath Northeastern Japan.Journal of Geophysical Research,1992,97(B13):19909-19928.
[16]Xu T,Xu G,Gao E,et al.Block modeling and segmentallyiterative ray tracing in complex 3Dmedia,Geophysics,2006,71(3):T41-T51.
[17]Xu T,Zhang Z,Gao E,Xu G,et al.Segmentally iterativeray tracing in complex 2D and 3D heterogeneous blockmodels,Bull.Seism.Soc.Am.,2010,100(2):841-850.
[18]Vidale J E.1988.Finite-difference calculation of traveltimes.Bulletin of the Seismological Society of America,78(6):2062-2076.
[19]Sethian J A,Popovici A M.1999.3-D traveltime computationusing fast marching method.Geophysics,64(2):516-523.
[20]Nakanishi I,Yamaguchi K.1986.A numerical experimenton nonlinear image reconstruction from first-arrival times fortwo-dimensional island arc structure.Journal of Physics ofthe.Earth,34(2):195-201.
[21]Moser T J.1991.Shortest path calculation of seismic rays.Geophysics,56(1):59-67.
[22]Cao S,Greenhalgh S.Calculation of the seismic first-breaktime field and its ray path distribution using a minimumtraveltime tree algorithm.Geophys.J.Int.,1993,114(3):593-600.
[23]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):823-832.Liu H,Meng F L,Li Y M.The interface grid method forseeking global minimum travel-time and the correspondentraypath.Chinese J.Geophys.(in Chinese),1995,38(6):823-832.
[24]Cheng N,House L.Minimum traveltime calculation in 3-Dgraph theory.Geophysics,1996,61(6):1895-1898.
[25]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):534-541.Wang H,Chang X.3-D tracing method based on graphicstructure.Chinese J.Geophys.(in Chinese),2000,43(4):534-541.
[26]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):151-157.Zhao A H,Zhang Z J,Wang G J,et al.A new scheme forfast calculation of seismic traveltimes and ray paths inheterogeneous media.ACTA seismological Sinica,2000,13(2):166-173.
[27]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):513-516.Zhao A H,Zhang Z J,Peng S P.Fast ray tracing method forconverted waves in complex media.Journal of ChinaUniversity of Mining&Technology(in Chinese),2003,32(5):513-516.
[28]Zhao A H,Zhang Z J and Teng J W,Minimum travel timetree algorithm for seismic ray tracing:improvement inefficiency.J.Geophys.Eng.,2004,1(4):245-251.
[29]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):899-904.Zhang J Z,Chen S J,Xu C W.A method of shortest pathraytracing with dynamic networks.Chinese J.Geophys.(inChinese),2004,47(5):899-904.
[30]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):1141-1147.Zhao A H,Ding Z F.A double-grid algorithm for calculatingtraveltimes of wide-angle reflection waves.Chinese J.Geophys.(in Chinese),2005,48(5):1141-1147.
[31]张美根,程冰洁,李小凡,等.一种最短路径射线追踪的快速算法.地球物理学报,2006,49(5):1467-1474.Zhang M G,Cheng B J,Li X F,et al.A fast algorithm ofshortest path ray tracing.Chinese J.Geophys.(in Chinese),2006,49(5):1467-1474.
[32]Bai C,Greenhalgh S,Zhou B.3Dray tracing using a modifiedshortest-path method.Geophysics,2007,72(4):T27-T36.
[33]Zelt C A.Modelling strategies and model assessment for wide-angle seismic traveltime data.Geophys.J.Int.,1999,139(1):183-204.
[34]Rawlinson N,Sambridge M.Wavefront evolution in stronglyheterogeneous layered media using the Fast MarchingMethod.Geophys.J.Int.,2004,156(3):631-647.
[35]成谷,张宝金.三角网格参数化在反射地震走时层析成像中的应用.中山大学学报,2006,45(5):128-132.Cheng G,Zhang B J.Application of triangle cellparameterization in travel-time tomography of reflectionseismic data.Acta Scientiarum Naturalium UniversitatisSunyatseni,2006,45(5):128-132.
[36]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.
[37]Bai C,Huang G,Zhao R.2-D/3-D irregular shortest pathray tracing for multiple arrivals and its applications.Geophys.J.Int.,2010,183(3):1596-1612.
[38]Yu S,Liu R,Cheng J.A minimum traveltime ray tracing globalalgorithm on a triangular net for propagating plane waves.Applied Geophysics,2010,7(4):348-356S.
[39]Klimes L,Kvasnicka M.3-D network ray tracing.Geophys.J.Int.,1994,116(3):726-738.
[2]Zhang Z J,Badal J,Li Y K,et al.Crust-upper mantle seismicwave velocity structure across southeastern China.Tectonophysics,2005,395(1-2):137-157.
[3]Zhang Z J,Klemperer S L.West-east variation in crustalthickness in northern Lhasa block,central Tibet,from deepseismic sounding data,J.Geophys.Res.,2005,110(B9),B09403.
[4]Zhang Z J,Klemperer S.Crustal structure of the TethyanHimalaya,southern Tibet:new constraints from old wide-angle seismic data.Geophys.J.Int.,2010,181(3):1247-1260.
[5]Zhang Z J,Deng Y F,Teng J W,et al.An overview of thecrustal structure of the Tibetan plateau after 35years of deepseismic soundings.Journal of Asian Earth Sciences,2011,40(4):977-989.
[6]Zhang Z J,Klemperer S.,Bai Z,et al.Crustal structure ofthe Paleozoic Kunlun orogeny from an active-source seismicprofile between Moba and Guide in East Tibet,China.Gondwana Research,2011,19(4):994-1007.
[7]赵荣国.震相分析是地震科学的心脏.地震地磁观测与研究,1999,20(5):121-126.Zhao R G.Phase analysis is the heart of seismology.Seismological and Geomagnetic Observation and Research,1999,20(5):121-126.
[8]赵鸿儒,孙进忠,唐文榜.全波震相分析的应用.地球物理学报,1990,33(1):54-63.Zhao H R,Sun J Z,Tang W B.The application of full wavephase analysis.Chinese J.Geophys.(in Chinese),1990,33(1):54-63.
[9]嘉世旭,刘昌铨.华北地区人工地震测深震相与地壳结构研究.地震地质,1995,17(2):97-105.Jia S X,Liu C Q.Study on the seismic phases of DSS in NorthChina.Seismology and Geology,1995,17(2):97-105.
[10]Kennett B L N,Engdahl E R.Traveltimes for global earthquakelocation and phase identification.Geophys.J.Int.,1991,105(2):429-465.
[11]Rawlinson N,Sambridge M.Seismic traveltime tomographyof the crust and lithosphere.Advances in Geophysics,2003,46:81-198.
[12]Julian B R,Gubbins D.1977.Three-dimensional seismic raytracing.Journal of Geophysics,43(1):95-114.
[13]徐涛,徐果明,高尔根,等.三维复杂介质的块状建模和试射射线追踪.地球物理学报,2004,47(6):1118-1126.Xu T,Xu G M,Gao E G,et al.Block modeling andshooting ray tracing in complex 3-D media.Chinese J.Geophys.(in Chinese),2004,47(6):1118-1126.
[14]Um J,Thurber C.1987.A fast algorithm for two-point seismicray tracing.Bulletin of the Seismological Society of America,77(3):972-986.
[15]Zhao D,Hasegawa A,Horiuchi S.Tomographic imaging ofP and S wave velocity structure beneath Northeastern Japan.Journal of Geophysical Research,1992,97(B13):19909-19928.
[16]Xu T,Xu G,Gao E,et al.Block modeling and segmentallyiterative ray tracing in complex 3Dmedia,Geophysics,2006,71(3):T41-T51.
[17]Xu T,Zhang Z,Gao E,Xu G,et al.Segmentally iterativeray tracing in complex 2D and 3D heterogeneous blockmodels,Bull.Seism.Soc.Am.,2010,100(2):841-850.
[18]Vidale J E.1988.Finite-difference calculation of traveltimes.Bulletin of the Seismological Society of America,78(6):2062-2076.
[19]Sethian J A,Popovici A M.1999.3-D traveltime computationusing fast marching method.Geophysics,64(2):516-523.
[20]Nakanishi I,Yamaguchi K.1986.A numerical experimenton nonlinear image reconstruction from first-arrival times fortwo-dimensional island arc structure.Journal of Physics ofthe.Earth,34(2):195-201.
[21]Moser T J.1991.Shortest path calculation of seismic rays.Geophysics,56(1):59-67.
[22]Cao S,Greenhalgh S.Calculation of the seismic first-breaktime field and its ray path distribution using a minimumtraveltime tree algorithm.Geophys.J.Int.,1993,114(3):593-600.
[23]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):823-832.Liu H,Meng F L,Li Y M.The interface grid method forseeking global minimum travel-time and the correspondentraypath.Chinese J.Geophys.(in Chinese),1995,38(6):823-832.
[24]Cheng N,House L.Minimum traveltime calculation in 3-Dgraph theory.Geophysics,1996,61(6):1895-1898.
[25]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):534-541.Wang H,Chang X.3-D tracing method based on graphicstructure.Chinese J.Geophys.(in Chinese),2000,43(4):534-541.
[26]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):151-157.Zhao A H,Zhang Z J,Wang G J,et al.A new scheme forfast calculation of seismic traveltimes and ray paths inheterogeneous media.ACTA seismological Sinica,2000,13(2):166-173.
[27]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):513-516.Zhao A H,Zhang Z J,Peng S P.Fast ray tracing method forconverted waves in complex media.Journal of ChinaUniversity of Mining&Technology(in Chinese),2003,32(5):513-516.
[28]Zhao A H,Zhang Z J and Teng J W,Minimum travel timetree algorithm for seismic ray tracing:improvement inefficiency.J.Geophys.Eng.,2004,1(4):245-251.
[29]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):899-904.Zhang J Z,Chen S J,Xu C W.A method of shortest pathraytracing with dynamic networks.Chinese J.Geophys.(inChinese),2004,47(5):899-904.
[30]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):1141-1147.Zhao A H,Ding Z F.A double-grid algorithm for calculatingtraveltimes of wide-angle reflection waves.Chinese J.Geophys.(in Chinese),2005,48(5):1141-1147.
[31]张美根,程冰洁,李小凡,等.一种最短路径射线追踪的快速算法.地球物理学报,2006,49(5):1467-1474.Zhang M G,Cheng B J,Li X F,et al.A fast algorithm ofshortest path ray tracing.Chinese J.Geophys.(in Chinese),2006,49(5):1467-1474.
[32]Bai C,Greenhalgh S,Zhou B.3Dray tracing using a modifiedshortest-path method.Geophysics,2007,72(4):T27-T36.
[33]Zelt C A.Modelling strategies and model assessment for wide-angle seismic traveltime data.Geophys.J.Int.,1999,139(1):183-204.
[34]Rawlinson N,Sambridge M.Wavefront evolution in stronglyheterogeneous layered media using the Fast MarchingMethod.Geophys.J.Int.,2004,156(3):631-647.
[35]成谷,张宝金.三角网格参数化在反射地震走时层析成像中的应用.中山大学学报,2006,45(5):128-132.Cheng G,Zhang B J.Application of triangle cellparameterization in travel-time tomography of reflectionseismic data.Acta Scientiarum Naturalium UniversitatisSunyatseni,2006,45(5):128-132.
[36]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.
[37]Bai C,Huang G,Zhao R.2-D/3-D irregular shortest pathray tracing for multiple arrivals and its applications.Geophys.J.Int.,2010,183(3):1596-1612.
[38]Yu S,Liu R,Cheng J.A minimum traveltime ray tracing globalalgorithm on a triangular net for propagating plane waves.Applied Geophysics,2010,7(4):348-356S.
[39]Klimes L,Kvasnicka M.3-D network ray tracing.Geophys.J.Int.,1994,116(3):726-738.
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