三维复杂速度模型的交切法地震定位
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摘要
地震定位是地震监测与减灾研究重要基础.基于均匀或横向均匀介质模型,利用震源轨迹确定震源位置的交切法具有稳健和效率高的优点,但定位精度较低,特别是震源深度.为提高震源定位精度,我们提出适用于三维复杂速度模型的地震定位交切法.将地壳速度模型由均匀或横向均匀介质模型扩展为三维复杂速度模型;均匀或横向均匀介质模型对应的原假设为球面或双曲面的震源轨迹通过最小走时树射线追踪技术予以确定.确定震源位置的震源轨迹以到时差作为约束条件;将震源定位于震源轨迹交汇最密集的点处,即总的到时差残差(RDT)最小的点处.定位结果的不确定性可通过RDT值较小节点的空间分布予以定性表示.考察了准确速度模型、扰动速度模型、扰动观测到时及地震在台网外等4种情况下改进方法的地震定位效果,结果表明改进的交切法可用于三维复杂速度模型的地震定位;综合利用P波与S波的到时差信息,可明显改善震源位置约束;使用多条震源轨迹进行定位,有助于减少由随机因素导致的定位误差.
Earthquake location is critical to the research on seismicity and disaster alleviation.The location problem can be solved by an intersection method which determines a hypocenter using its focal loci.The traditional intersection method is excellent in robustness and efficiency but deficient in location accuracy especially for hypocenter depth because it is based on homogeneous or laterally homogeneous media that are far from the real Earth.In order to eliminate the disadvantage of low accuracy,we have modified it in the suitability for 3-D complex velocity models.In the modified method,focal loci are not assumed to be spherical or hyperboloidal but exactly calculated with a minimum traveltime tree algorithm for tracing rays.The focal loci are constrained with observed arrival time differences so that the problem of origin time is evaded.The hypocenter is located at the point that the focal loci most densely intersect,namely,the point with the minimal total residual of arrival time differences(RDT).The location uncertainty is qualitatively estimated by means of the distribution of nodes where RDT is smaller.The modified intersection method is verified with an earthquake in a complex model.The location tests in different cases including accurate model,perturbed model,noisy arrival times and partial observation show that the modified location method is practical for locating earthquakes in 3-D complex velocity models;integrated utilization of arrival time differences between and of P-and S-waves can remarkably improve the constraint on the hypocenter;using more focal loci can decrease the influence of random errors on earthquake location.
Earthquake location is critical to the research on seismicity and disaster alleviation.The location problem can be solved by an intersection method which determines a hypocenter using its focal loci.The traditional intersection method is excellent in robustness and efficiency but deficient in location accuracy especially for hypocenter depth because it is based on homogeneous or laterally homogeneous media that are far from the real Earth.In order to eliminate the disadvantage of low accuracy,we have modified it in the suitability for 3-D complex velocity models.In the modified method,focal loci are not assumed to be spherical or hyperboloidal but exactly calculated with a minimum traveltime tree algorithm for tracing rays.The focal loci are constrained with observed arrival time differences so that the problem of origin time is evaded.The hypocenter is located at the point that the focal loci most densely intersect,namely,the point with the minimal total residual of arrival time differences(RDT).The location uncertainty is qualitatively estimated by means of the distribution of nodes where RDT is smaller.The modified intersection method is verified with an earthquake in a complex model.The location tests in different cases including accurate model,perturbed model,noisy arrival times and partial observation show that the modified location method is practical for locating earthquakes in 3-D complex velocity models;integrated utilization of arrival time differences between and of P-and S-waves can remarkably improve the constraint on the hypocenter;using more focal loci can decrease the influence of random errors on earthquake location.
引文
[1]田玥,陈晓非.地震定位研究综述.地球物理学进展,2002,17(1):147-155.Tian Y,Chen X F.Review of seismic location study.Progress in Geophysics(in Chinese),2002,17(1):147-155.
[2]蔡明军,山秀明,徐彦等.从误差观点综述分析地震定位方法.地震研究,2004,27(4):314-317.Cai M J,Shan X M,Xu Y,et al.Review of earthquake-locating methods from error.Journal of SeismologicalResearch(in Chinese),2004,27(4):314-317.
[3]杨文东,金星,李山有等.地震定位研究及应用综述.地震工程与工程振动,2005,25(1):14-20.Yang W D,Jin X,Li S Y,et al.Study of seismic locationmethods.Earthquake Engineering and Engineering Vibration(in Chinese),2005,25(1):14-20.
[4]Storchak D A.Results of locating the IASPEI GT(0-5)reference events using the standard ISC procedures.Phys.Earth Planet.Inter.,2006,158(1):4-13.
[5]黄媛,吴建平,张天中等.汶川8.0级大地震及其余震序列重定位研究.中国科学(D辑),2008,38(10):1250-1257.Huang Y,Wu J P,Zhang T Z,et al.Relocation of theMs8.0 Wenchuan earthquake and its aftershock sequence.Science in China(Series D)(in Chinese),2008,38(10):1250-1257.
[6]Billings S D,Sambridge M S,Kennett B L N.Errors inhypocenter location:picking,model,and magnitude dependence.Bull.Seism.Soc.Am.,1994,84(6):1978-1990.
[7]Geiger L.Probability method for the determination ofearthquake epicenters from the arrival time only.Bull.St.Louis Univ.,1912,8:60-71.
[8]Waldhauser F,Ellsworth W L.A double-differenceearthquake location algorithm:method and application to thenorthern Hayward fault,California.Bull.Seismol.Soc.Am.,2000,90(6):1353-1368.
[9]Shearer P M.Improving local earthquake location using theL1norm and waveform cross correlation:Application to theWhittier Narrows,California,aftershock sequence.J.Geophys.Res.,1997,102(B4):8269-8283.
[10]Udías A.Principles of Seismology.Cambridge:CambridgeUniversity Press,1999.
[11]Pujol J.Earthquake location tutorial:graphical approach andapproximate epicentral location techniques.Seis.Res.Lett.,2004,75(1):63-74.
[12]廉超,李胜乐,董曼等.球面交切法地震定位.大地测量与地球动力学,2006,26(2):99-103.Lian C,Li S L,Dong M,et al.Method of spherical surfaceshearing in earthquake location.Journal of Geodesy andGeodynamics(in Chinese),2006,26(2):99-103.
[13]孟玉梅,赵永,王斌.中国地震观测台网地震速报定位偏差的分析.地震,2001,21(3):65-69.Meng Y M,Zhao Y,Wang B.The analysis on deviation ofrapid location by China Seismic Observational Network.Earthquake(in Chinese),2001,21(3):65-69.
[14]宋锐,顾小红,王永力等.国家数字地震台网中心实时处理及大地震速报软件系统.地震,2001,21(4):47-59.Song R,Gu X H,Wang Y L,et al.The software system forreal-time processing and large earthquake rapid determinationof NCDSN.Earthquake(in Chinese),2001,21(4):47-59.
[15]张中杰,滕吉文,张霖斌等.地球深部研究的复杂性及其对策.地球物理学进展,1996,11(3):10-20.Zhang Z J,Teng J W,Zhang L B,et al.The complexity inthe study of earth depth and its countermeasure.Progress inGeophysics(in Chinese),1996,11(3):10-20.
[16]Zhang Z J,Badal J,Li Y K,et al.Crust-upper mantle seismicvelocity structure across southeastern China.Tectonophysics,2005,395(1-2):137-157.
[17]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,doi:10.1029/2004JB003139.
[18]Zhang Z J,Yang L Q,Teng J W,et al.An overview of theearth crust under China.Earth Science Reviews,2011,104(1-3):143-166.
[19]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.
[20]滕吉文,王夫运,赵文智等.鄂尔多斯盆地上地壳速度分布与沉积建造和结晶基底起伏的构造研究.地球物理学报,2008,51(6):1753-1766.Teng J W,Wang F Y,Zhao W Z,et al.Velocity distributionof upper crust,undulation of sedimentary formation andcrystalline basement beneath the Ordos basin in North China.Chinese J.Geophys.(in Chinese),2008,51(6):1753-1766.
[21]Chen H,Chiu J M,Pujol J,et al.A simple algorithm forlocal earthquake location using 3DVPand VS models:testexamples in the central United States and in central easternTaiwan.Bull.Seismol.Soc.Am.,2006,96(1):288-305.
[22]Zhao A H,Ding Z F.An intersection method for locatingearthquakes in complex velocity models.Applied Geophysics,2007,4(4):294-300.
[23]Nakanishi I,Yamaguchi K.A numerical experiment onnonlinear image reconstruction from first-arrival times fortwo-dimensional island arc structure.J.Phys.Earth,1986,34(2):195-201.
[24]Dijkstra E W.A note on two problems in connection withgraphs.Numer.Math.,1959,1(2)269-271.
[25]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59-67.
[26]Cao S H,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.
[27]Fischer R,Lees J M.Shortest path ray tracing with sparsegraphs.Geophysics,1993,58(7):987-996.
[28]Klimes L,Kvasnicka M.3-D network ray tracing.Geophys.J.Int.,1994,116(3):726-738.
[29]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.
[30]Cheng N,House L.Minimum traveltime calculation in 3-Dgraph theory.Geophysics,1996,61(6):1895-1898.
[31]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 ray tracing method based on graphicstructure.Chinese J.Geophys.(in Chinese),2000,43(4):534-541.
[32]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 Seismologica Sinica(in Chinese),2000,13(2):167-173.
[33]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.
[34]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 raytracing algorithm of wavefront expanding withinterface points as secondary sources.Chinese J.Geophys.(in Chinese),2006,49(4):1169-1175.
[35]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.
[36]Bai C,Greenhalgh S,Zhou B.3D ray tracing using amodified shortest-path method.Geophysics,2007,72(4):T27-T36.
[37]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.
[38]Zhao A H,Zhang Z J,Teng J W.Minimum travel time treealgorithm for seismic ray tracing:improvement in efficiency.J.Geophy.Eng.,2004,1(4):245-251.
[39]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):702-707.Zhao A H,Zhang Z J.Fast calculation of converted wavetraveltime in 3-D complex media.Chinese J.Geophys.(inChinese),2004,47(4):702-707.
[40]赵爱华,丁志峰,孙为国等.复杂介质地震定位中震源轨迹的计算.地球物理学报,2008,51(4):1188-1195.Zhao A H,Ding Z F,Sun W G,et al.Calculation of focalloci for earthquake location in complex media.Chinese J.Geophys.(in Chinese),2008,51(4):1188-1195.
[41]Zhao A H,Ding Z F.Earthquake location in transverselyisotropic media with a tilted symmetry axis.J.Seismology,2009,13(2):301-311.
[42]Gajewski D,Tessmer E.Reverse modelling for seismic eventcharacterization.Geophys.J.Int.,2005,163(1):276-284.
[2]蔡明军,山秀明,徐彦等.从误差观点综述分析地震定位方法.地震研究,2004,27(4):314-317.Cai M J,Shan X M,Xu Y,et al.Review of earthquake-locating methods from error.Journal of SeismologicalResearch(in Chinese),2004,27(4):314-317.
[3]杨文东,金星,李山有等.地震定位研究及应用综述.地震工程与工程振动,2005,25(1):14-20.Yang W D,Jin X,Li S Y,et al.Study of seismic locationmethods.Earthquake Engineering and Engineering Vibration(in Chinese),2005,25(1):14-20.
[4]Storchak D A.Results of locating the IASPEI GT(0-5)reference events using the standard ISC procedures.Phys.Earth Planet.Inter.,2006,158(1):4-13.
[5]黄媛,吴建平,张天中等.汶川8.0级大地震及其余震序列重定位研究.中国科学(D辑),2008,38(10):1250-1257.Huang Y,Wu J P,Zhang T Z,et al.Relocation of theMs8.0 Wenchuan earthquake and its aftershock sequence.Science in China(Series D)(in Chinese),2008,38(10):1250-1257.
[6]Billings S D,Sambridge M S,Kennett B L N.Errors inhypocenter location:picking,model,and magnitude dependence.Bull.Seism.Soc.Am.,1994,84(6):1978-1990.
[7]Geiger L.Probability method for the determination ofearthquake epicenters from the arrival time only.Bull.St.Louis Univ.,1912,8:60-71.
[8]Waldhauser F,Ellsworth W L.A double-differenceearthquake location algorithm:method and application to thenorthern Hayward fault,California.Bull.Seismol.Soc.Am.,2000,90(6):1353-1368.
[9]Shearer P M.Improving local earthquake location using theL1norm and waveform cross correlation:Application to theWhittier Narrows,California,aftershock sequence.J.Geophys.Res.,1997,102(B4):8269-8283.
[10]Udías A.Principles of Seismology.Cambridge:CambridgeUniversity Press,1999.
[11]Pujol J.Earthquake location tutorial:graphical approach andapproximate epicentral location techniques.Seis.Res.Lett.,2004,75(1):63-74.
[12]廉超,李胜乐,董曼等.球面交切法地震定位.大地测量与地球动力学,2006,26(2):99-103.Lian C,Li S L,Dong M,et al.Method of spherical surfaceshearing in earthquake location.Journal of Geodesy andGeodynamics(in Chinese),2006,26(2):99-103.
[13]孟玉梅,赵永,王斌.中国地震观测台网地震速报定位偏差的分析.地震,2001,21(3):65-69.Meng Y M,Zhao Y,Wang B.The analysis on deviation ofrapid location by China Seismic Observational Network.Earthquake(in Chinese),2001,21(3):65-69.
[14]宋锐,顾小红,王永力等.国家数字地震台网中心实时处理及大地震速报软件系统.地震,2001,21(4):47-59.Song R,Gu X H,Wang Y L,et al.The software system forreal-time processing and large earthquake rapid determinationof NCDSN.Earthquake(in Chinese),2001,21(4):47-59.
[15]张中杰,滕吉文,张霖斌等.地球深部研究的复杂性及其对策.地球物理学进展,1996,11(3):10-20.Zhang Z J,Teng J W,Zhang L B,et al.The complexity inthe study of earth depth and its countermeasure.Progress inGeophysics(in Chinese),1996,11(3):10-20.
[16]Zhang Z J,Badal J,Li Y K,et al.Crust-upper mantle seismicvelocity structure across southeastern China.Tectonophysics,2005,395(1-2):137-157.
[17]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,doi:10.1029/2004JB003139.
[18]Zhang Z J,Yang L Q,Teng J W,et al.An overview of theearth crust under China.Earth Science Reviews,2011,104(1-3):143-166.
[19]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.
[20]滕吉文,王夫运,赵文智等.鄂尔多斯盆地上地壳速度分布与沉积建造和结晶基底起伏的构造研究.地球物理学报,2008,51(6):1753-1766.Teng J W,Wang F Y,Zhao W Z,et al.Velocity distributionof upper crust,undulation of sedimentary formation andcrystalline basement beneath the Ordos basin in North China.Chinese J.Geophys.(in Chinese),2008,51(6):1753-1766.
[21]Chen H,Chiu J M,Pujol J,et al.A simple algorithm forlocal earthquake location using 3DVPand VS models:testexamples in the central United States and in central easternTaiwan.Bull.Seismol.Soc.Am.,2006,96(1):288-305.
[22]Zhao A H,Ding Z F.An intersection method for locatingearthquakes in complex velocity models.Applied Geophysics,2007,4(4):294-300.
[23]Nakanishi I,Yamaguchi K.A numerical experiment onnonlinear image reconstruction from first-arrival times fortwo-dimensional island arc structure.J.Phys.Earth,1986,34(2):195-201.
[24]Dijkstra E W.A note on two problems in connection withgraphs.Numer.Math.,1959,1(2)269-271.
[25]Moser T J.Shortest path calculation of seismic rays.Geophysics,1991,56(1):59-67.
[26]Cao S H,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.
[27]Fischer R,Lees J M.Shortest path ray tracing with sparsegraphs.Geophysics,1993,58(7):987-996.
[28]Klimes L,Kvasnicka M.3-D network ray tracing.Geophys.J.Int.,1994,116(3):726-738.
[29]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.
[30]Cheng N,House L.Minimum traveltime calculation in 3-Dgraph theory.Geophysics,1996,61(6):1895-1898.
[31]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 ray tracing method based on graphicstructure.Chinese J.Geophys.(in Chinese),2000,43(4):534-541.
[32]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 Seismologica Sinica(in Chinese),2000,13(2):167-173.
[33]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.
[34]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 raytracing algorithm of wavefront expanding withinterface points as secondary sources.Chinese J.Geophys.(in Chinese),2006,49(4):1169-1175.
[35]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.
[36]Bai C,Greenhalgh S,Zhou B.3D ray tracing using amodified shortest-path method.Geophysics,2007,72(4):T27-T36.
[37]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.
[38]Zhao A H,Zhang Z J,Teng J W.Minimum travel time treealgorithm for seismic ray tracing:improvement in efficiency.J.Geophy.Eng.,2004,1(4):245-251.
[39]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):702-707.Zhao A H,Zhang Z J.Fast calculation of converted wavetraveltime in 3-D complex media.Chinese J.Geophys.(inChinese),2004,47(4):702-707.
[40]赵爱华,丁志峰,孙为国等.复杂介质地震定位中震源轨迹的计算.地球物理学报,2008,51(4):1188-1195.Zhao A H,Ding Z F,Sun W G,et al.Calculation of focalloci for earthquake location in complex media.Chinese J.Geophys.(in Chinese),2008,51(4):1188-1195.
[41]Zhao A H,Ding Z F.Earthquake location in transverselyisotropic media with a tilted symmetry axis.J.Seismology,2009,13(2):301-311.
[42]Gajewski D,Tessmer E.Reverse modelling for seismic eventcharacterization.Geophys.J.Int.,2005,163(1):276-284.
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