中国大陆活动地块边界带强震震级分布特征研究
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摘要
本文利用基于广义帕累托分布的超阈值分布模型,对中国大陆活动地块边界带强震震级分布特征开展研究,给出了各活动地块边界带强震震级的广义帕累托分布参数估计。结果表明,广义帕累托分布较好地拟合了各边界带强震数据,形状参数估计均为负值,说明对应震级应有上限,因此广义帕累托分布为潜在震级上限提供了一种自然的刻画。在此基础上,估计了震级上限,并给出了分布0.99997高分位数估计,通过与历史最大震级比较发现,高分位数估计相对稳健。在地震发生过程为泊松过程假设下,推导了广义帕累托分布与广义极值分布之间的联系,揭示了一种利用强震数据推断最大震级分布的可能途径。
In this paper,we employ peaks over threshold method based on generalized Pareto distribution to analyze the characteritics of the great earthquake magnitude distributions for active tectonic boundaries in Chinese mainland.The results show that the generalized Pareto distribution is well fitting for the earthquake data,and the shape parameter estimations are negative,corresponding to finite earthquake magnitude,so the generalized Pareto distribution provides a natural description for potential upper limit earthquake magnitude.On this basis,upper limit earthquake magnitude and 0.99997 quantile are estimated.By the comparison between the historical maximum magnitude and high quantile,we find that the quantile provides much more stable and robust characteristic than the traditional absolute maximum magnitude.Under the Poisson process hypothesis,we establish the relations between the generalized Pareto distribution and the generalized extreme value distribution and propose a method for the estimation of maximum magnitude distribution with strong earthquake data.
In this paper,we employ peaks over threshold method based on generalized Pareto distribution to analyze the characteritics of the great earthquake magnitude distributions for active tectonic boundaries in Chinese mainland.The results show that the generalized Pareto distribution is well fitting for the earthquake data,and the shape parameter estimations are negative,corresponding to finite earthquake magnitude,so the generalized Pareto distribution provides a natural description for potential upper limit earthquake magnitude.On this basis,upper limit earthquake magnitude and 0.99997 quantile are estimated.By the comparison between the historical maximum magnitude and high quantile,we find that the quantile provides much more stable and robust characteristic than the traditional absolute maximum magnitude.Under the Poisson process hypothesis,we establish the relations between the generalized Pareto distribution and the generalized extreme value distribution and propose a method for the estimation of maximum magnitude distribution with strong earthquake data.
引文
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[8]Huyse L,Chen R,Stamatakos J A.Application of generalized pareto distribution to constrain uncertainty in peak ground accelerations[J].Bull.Seism.Soc.Am.,2010,100(1):87-101.
[9]张国民,张培震.“大陆强震机理与预测”中期学术进展[J].中国基础科学,2000,10:4-10.ZHANG Guomin,ZHANG Peizhen.Academic progress on the mechanism and forecast for continental strong earthquake in the first two years[J].China Basic Science,2000,10:4-10.(in Chinese)
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[12]马宏生,张国民,刘杰,等.中国大陆活动地块边界带强震活动特征的研究[J].地震地质,2006,28(1):48-60.MA Hongsheng,ZHANG Guomin,LIU Jie,et al.Research on the characteristics of large earthquake activity on the active tectonic boundaries inChinese mainland[J].Seismology and Geology,2006,28(1):48-60.(in Chinese)
[13]邵志刚,张国民,李志雄,等.中国大陆活动地块边界带地震活动过程及其趋势研究[J].地震,2008,28(3):33-42.SHAO Zhigang,ZHANG Guomin,LI Zhixiong,et al.Research on the process and tendency of seismicity along the active tectonic boundaries inChinese mainland[J].Earthquake,2008,28(3):33-42.(in Chinese)
[14]张浪平,李志雄,邵志刚,等.中国大陆活动地块边界带强震趋势研究[J].地震,2010,30(3):53-63.ZHANG Langping,LI Zhixiong SHAO Zhigang,et al.Study of strong earthquake trends on the active tectonic boundaries in Chinese mainland[J].Earthquake,2010,30(3):53-63.(in Chinese)
[15]Fisher R,Tippett L H.Limiting forms of the frequency distributions of the largest or smallest member of a sample[J].Proc.Camb.Phil.Soc.1928,24:180-190.
[16]张培震,邓起东,张国民,等.中国大陆的强震活动与活动地块[J].中国科学(D辑),2003,33(增刊):12-20.ZHANG Peizhen,DENG Qidong,ZHANG Guomin,et al.Active tectonic blocks and strong earthquakes in the continent of China[J].Science inChina(Series D),2003,46(Supppl.):13-24.(in Chinese)
[17]国家地震局震害防御司.地震工作手册[M].北京:地震出版社,1990.Department of Earthquake Disaster Prevention,State Seismological Bureau.Seismic work manual[M].Beijing:Seimological Press,1990.(in Chi-nese)
[18]陈凌,刘杰,陈颙,等.地震活动性分析中余震的删除[J].地球物理学报,1998,41(增刊):244-252.CHEN Ling,LIU Jie,CHEN Yong,et al.Aftershock deletion in seismicity analysis[J].Acta Geophysica Sinica,1998,41(Suppl.):244-252.(in Chinese)
[19]史道济.实用极值统计方法[M].天津:天津科学技术出版社,2006.SHI Daoji.Practical extremum statistical method[M].Tianjin:Tianjin Science and Technology Press,2006.(in Chinese)
[20]Cosentino P,Ficara V,Luzio D.Truncated exponential frequency-magnitude relationship in the earthquake statistics[J].Bull.Seism.Soc.Am.1977,67,1615-1623.
[21]高孟潭.贾素娟.极值理论在工程地震中的应用[J].地震学报,10(3):317-326.GAO Mengtan,JIA Sujuan.The application of extremum aralysis to earthquake engineering problems[J].Acta Seismologica Sinica,1988,10(3):317-326.
[22]陈虹,黄忠贤.应用混合极值理论及最大似然法估计中国大陆地震危险性[J].地震学报,1995,17(2):264-269.CHEN Hong,HUANG Zhongxian.Application of Gumbel mixture extreme theory and maximum likelihood to the seismic risk estimation of Chinesemainland[J].Acta Seismologica Sinica,1995,17(2):264-269.(in Chinese)
[23]钱小仕,王福昌,曹桂荣,等.广义极值分布在地震危险性分析中的应用[J].地震研究,2012,35(1):73-78.QIAN Xiaoshi,WANG Fuchang,CAO Guirong,et al.Application of the generalized extreme value distribution in seismic hazard analysis[J].Jour-nal of Seismological Research,2012,35(1):73-78.(in Chinese)
[2]陈培善,林邦慧.极值理论在中长期地震预报的应用[J].地球物理学报,1973,16:6-24.CHEN Peishan,LIN Banghui.An application of statistical theory of extreme values to moderate and interval earthquake prediction[J].Acta Geo-physica sinica,1973,16:6-24.(in Chinese)
[3]Utsu T.Representation and analysis of the earthquake size distribution:a historical review and some new approaches[J].Pure Appl.Geophys.1999,155,509-535.
[4]陈时军,王丽凤,马丽,等.关于震级频度关系的一些讨论[J].地震学报,2002,24(2):176-185.CHEN Shijun,WANG Lifeng,MA Li,et al.Argument on the magnitude-frequency relation[J].Acta Seismologica Sinica,2002,24(2):176-185.(in Chinese)
[5]Balkema A,de Haan L.Residual life time at great age[J].Annals of Probability,1974,2(5):792-804.
[6]Pickands J.Statistical inference using extreme order statistics[J].Ann.Stat.1975,3,119-131.
[7]Pisarenko V F,Sornette D.Characterization of frequency of extreme earthquake events by the generalized Pareto distribution[J].Pure Appl.Geo-phys,2003,160:2343-2364.
[8]Huyse L,Chen R,Stamatakos J A.Application of generalized pareto distribution to constrain uncertainty in peak ground accelerations[J].Bull.Seism.Soc.Am.,2010,100(1):87-101.
[9]张国民,张培震.“大陆强震机理与预测”中期学术进展[J].中国基础科学,2000,10:4-10.ZHANG Guomin,ZHANG Peizhen.Academic progress on the mechanism and forecast for continental strong earthquake in the first two years[J].China Basic Science,2000,10:4-10.(in Chinese)
[10]马宏生,张国民,刘杰,等.中国大陆及其邻区强震活动与活动地块关系研究[J].地学前缘,2003,10(特刊):74-80.MA Hongsheng,ZHANG Guomin,LIU Jie,et al.Correlation between strong earthquake activity and active crustal-block in China mainland and itsadjacent regions[J].Earth Science Frontiers,2003,10(Suppl):74-80.(in Chinese)
[11]张国民,马宏生,王辉,等.中国大陆活动地块边界带与强震活动[J].地球物理学报,2005,48(3):602-610.ZHANG Guomin,MA Hongsheng,WANG Hui,et al.Boundaries between active-tectonic blodks and strong earthquakes in the China mainland[J].Chinese J Geophys,2005,48(3):602-610.(in Chinese)
[12]马宏生,张国民,刘杰,等.中国大陆活动地块边界带强震活动特征的研究[J].地震地质,2006,28(1):48-60.MA Hongsheng,ZHANG Guomin,LIU Jie,et al.Research on the characteristics of large earthquake activity on the active tectonic boundaries inChinese mainland[J].Seismology and Geology,2006,28(1):48-60.(in Chinese)
[13]邵志刚,张国民,李志雄,等.中国大陆活动地块边界带地震活动过程及其趋势研究[J].地震,2008,28(3):33-42.SHAO Zhigang,ZHANG Guomin,LI Zhixiong,et al.Research on the process and tendency of seismicity along the active tectonic boundaries inChinese mainland[J].Earthquake,2008,28(3):33-42.(in Chinese)
[14]张浪平,李志雄,邵志刚,等.中国大陆活动地块边界带强震趋势研究[J].地震,2010,30(3):53-63.ZHANG Langping,LI Zhixiong SHAO Zhigang,et al.Study of strong earthquake trends on the active tectonic boundaries in Chinese mainland[J].Earthquake,2010,30(3):53-63.(in Chinese)
[15]Fisher R,Tippett L H.Limiting forms of the frequency distributions of the largest or smallest member of a sample[J].Proc.Camb.Phil.Soc.1928,24:180-190.
[16]张培震,邓起东,张国民,等.中国大陆的强震活动与活动地块[J].中国科学(D辑),2003,33(增刊):12-20.ZHANG Peizhen,DENG Qidong,ZHANG Guomin,et al.Active tectonic blocks and strong earthquakes in the continent of China[J].Science inChina(Series D),2003,46(Supppl.):13-24.(in Chinese)
[17]国家地震局震害防御司.地震工作手册[M].北京:地震出版社,1990.Department of Earthquake Disaster Prevention,State Seismological Bureau.Seismic work manual[M].Beijing:Seimological Press,1990.(in Chi-nese)
[18]陈凌,刘杰,陈颙,等.地震活动性分析中余震的删除[J].地球物理学报,1998,41(增刊):244-252.CHEN Ling,LIU Jie,CHEN Yong,et al.Aftershock deletion in seismicity analysis[J].Acta Geophysica Sinica,1998,41(Suppl.):244-252.(in Chinese)
[19]史道济.实用极值统计方法[M].天津:天津科学技术出版社,2006.SHI Daoji.Practical extremum statistical method[M].Tianjin:Tianjin Science and Technology Press,2006.(in Chinese)
[20]Cosentino P,Ficara V,Luzio D.Truncated exponential frequency-magnitude relationship in the earthquake statistics[J].Bull.Seism.Soc.Am.1977,67,1615-1623.
[21]高孟潭.贾素娟.极值理论在工程地震中的应用[J].地震学报,10(3):317-326.GAO Mengtan,JIA Sujuan.The application of extremum aralysis to earthquake engineering problems[J].Acta Seismologica Sinica,1988,10(3):317-326.
[22]陈虹,黄忠贤.应用混合极值理论及最大似然法估计中国大陆地震危险性[J].地震学报,1995,17(2):264-269.CHEN Hong,HUANG Zhongxian.Application of Gumbel mixture extreme theory and maximum likelihood to the seismic risk estimation of Chinesemainland[J].Acta Seismologica Sinica,1995,17(2):264-269.(in Chinese)
[23]钱小仕,王福昌,曹桂荣,等.广义极值分布在地震危险性分析中的应用[J].地震研究,2012,35(1):73-78.QIAN Xiaoshi,WANG Fuchang,CAO Guirong,et al.Application of the generalized extreme value distribution in seismic hazard analysis[J].Jour-nal of Seismological Research,2012,35(1):73-78.(in Chinese)
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