基于广义帕累托分布的地震震级分布尾部特征分析
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摘要
极值理论在地震危险性分析中有着重要应用,发震震级超过某一阈值的超出量分布可以近似为广义帕累托分布.基于广义帕累托分布给出了若干地震活动性参数的估计公式,包括强震震级分布、地震复发周期和重现水平、期望重现震级、地震危险性概率和潜在震级上限等;以云南地区震级资料为基础数据,讨论了阈值选取、模型拟合诊断和参数估计;在此基础上计算了该地区的地震活动性参数.结果表明,广义帕累托分布较好地刻画了强震震级分布,通过超阈值(POT)模型计算的复发周期与实际复发间隔统计基本一致,高分位数估计在一定阈值范围内表现稳定,为工程抗震中潜在震级上限的确定提供了一种途径.
Extreme value theory in seismic risk analysis has important application, and the excess of earthquake magnitude distribution over a threshold can be approximated by generalized Pareto distribution. Based on the generalized Pareto distribution, we developed several estimation formulas of seismic activity parameters, including strong earthquake magnitude distribution, earthquake recurrence period and return level, expected recurrence magnitude, probability of seismic risk and maximum earthquake magnitude; then, based on historical seismic data in Yunnan region, we discussed how to choose the threshold value, model fitting diagnosis and parameter estimation. Finally we calculated seismicity parameters in the region. The results show that generalized Pareto distribution characterized strong earthquake magnitude distribution quite satisfactorily, the recurrence periods by POT (peaks over threshold method) model agree with the actual recurrence interval statistics, and the high quantile is stable within a specific threshold range. So the generalized Pareto distribution is a possible approach to determining the potential upper limit earthquake magnitude in engineering seismology.
Extreme value theory in seismic risk analysis has important application, and the excess of earthquake magnitude distribution over a threshold can be approximated by generalized Pareto distribution. Based on the generalized Pareto distribution, we developed several estimation formulas of seismic activity parameters, including strong earthquake magnitude distribution, earthquake recurrence period and return level, expected recurrence magnitude, probability of seismic risk and maximum earthquake magnitude; then, based on historical seismic data in Yunnan region, we discussed how to choose the threshold value, model fitting diagnosis and parameter estimation. Finally we calculated seismicity parameters in the region. The results show that generalized Pareto distribution characterized strong earthquake magnitude distribution quite satisfactorily, the recurrence periods by POT (peaks over threshold method) model agree with the actual recurrence interval statistics, and the high quantile is stable within a specific threshold range. So the generalized Pareto distribution is a possible approach to determining the potential upper limit earthquake magnitude in engineering seismology.
引文
①马瑾,等.2005.中国地震目录.中国地震局地质研究所.[2011-11-09]http:∥westdc.westgis.ac.cn/data/236a607a-245f-4444-ba4c-f7cccfd53271.
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陈虹,黄忠贤.1995.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,17(2):264--269.
陈凌,刘杰,陈颙,陈龙生.1998.地震活动性分析中余震的删除[J].地球物理学报,41(增刊):244--252.
陈培善,林邦慧.1973.极值理论在中长期地震预报中的应用[J].地球物理学报,16(1):6--24.
陈颙,陈凌.1999.地震危险性分析中最大地震震级的确定[J].地球物理学报,42(3):351--357.
高孟潭,贾素娟.1988.极值理论在工程地震中的应用[J].地震学报,10(3):317--326.
黄玮琼,李文香,曹学峰.1994.中国大陆地震资料完整性研究之二:分区地震资料基本完整的起始年分布图[J].地震学报,16(4):423--432.
皇甫岗,李中华.2010.20世纪云南地区地震记录完全性评价[J].地震研究,33(1):1--6.
贾素娟,鄢家全.1996.利用历史地震影响烈度的统计特性进行地震区划[J].地震研究,19(3):277--285.
钱小仕,王福昌,曹桂荣,任晴晴.2012.广义极值分布在地震危险性分析中的应用[J].地震研究,35(1):73--78.
冉洪流.2009.潜在震源区震级上限不确定性研究[J].地震学报,31(4):396--402.
史道济.2006.实用极值统计方法[M].天津:天津科学技术出版社:83--85.
苏有锦,李中华.2011.云南地区6级以上强震时间分布特征及其概率预测模型研究[J].地震研究,34(1):1--7.
汪素云,高阿甲,冯义钧,和锐.2010.中国地震目录间的对比及标准化[J].地震,30(2):38--45.
Balkema A A,de Haan L.1974.Residual life time at great age[J].Ann Probab,2(5):792--804.
Cosentino P,Ficara V,Luzio D.1977.Truncated exponential frequency-magnitude relationship in the earthquake statis-tics[J].Bull Seism Soc Amer,67(6):1615--1623.
Epstein B,Lomnitz C.1966.A model for the occurrence of the largest earthquakes[J].Nature,211(5052):954--956.
Fisher R,Tippett L H.1928.Limiting forms of the frequency distributions of the largest or smallest member of a sample[J].Proc Camb Phil Soc,24(2):180--190.
Gutenberg B,Richter C.1956.Earthquake magnitude,intensity,energy,and acceleration,partⅡ[J].Bull Seism SocAmer,46(2):105--145.
Huyse L,Chen R,Stamatakos J A.2010.Application of generalized pareto distribution to constrain uncertainty in peakground accelerations[J].Bull Seism Soc Amer,100(1):87--101.
Pickands J.1975.Statistical inference using extreme order statistics[J].Ann Stat,3(1):119--131.
Pisarenko V F,Sornette D.2003.Characterization of frequency of extreme earthquake events by the generalized paretodistribution[J].Pure Appl Geophys,160(12):2343--2364.
Yegulalp T M,Kuo J A.1974.Statistical prediction of the occurrence of maximum magnitude earthquakes[J].BullSeism Soc Amer,64(2):393--414.
②中国地震台网中心.2012.中国地震台网(CSN)地震目录.中国地震台网中心.[2011-11-15]http:∥www.csndmc.ac.cn/newweb/catalog_direct_link.htm.
陈虹,黄忠贤.1995.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,17(2):264--269.
陈凌,刘杰,陈颙,陈龙生.1998.地震活动性分析中余震的删除[J].地球物理学报,41(增刊):244--252.
陈培善,林邦慧.1973.极值理论在中长期地震预报中的应用[J].地球物理学报,16(1):6--24.
陈颙,陈凌.1999.地震危险性分析中最大地震震级的确定[J].地球物理学报,42(3):351--357.
高孟潭,贾素娟.1988.极值理论在工程地震中的应用[J].地震学报,10(3):317--326.
黄玮琼,李文香,曹学峰.1994.中国大陆地震资料完整性研究之二:分区地震资料基本完整的起始年分布图[J].地震学报,16(4):423--432.
皇甫岗,李中华.2010.20世纪云南地区地震记录完全性评价[J].地震研究,33(1):1--6.
贾素娟,鄢家全.1996.利用历史地震影响烈度的统计特性进行地震区划[J].地震研究,19(3):277--285.
钱小仕,王福昌,曹桂荣,任晴晴.2012.广义极值分布在地震危险性分析中的应用[J].地震研究,35(1):73--78.
冉洪流.2009.潜在震源区震级上限不确定性研究[J].地震学报,31(4):396--402.
史道济.2006.实用极值统计方法[M].天津:天津科学技术出版社:83--85.
苏有锦,李中华.2011.云南地区6级以上强震时间分布特征及其概率预测模型研究[J].地震研究,34(1):1--7.
汪素云,高阿甲,冯义钧,和锐.2010.中国地震目录间的对比及标准化[J].地震,30(2):38--45.
Balkema A A,de Haan L.1974.Residual life time at great age[J].Ann Probab,2(5):792--804.
Cosentino P,Ficara V,Luzio D.1977.Truncated exponential frequency-magnitude relationship in the earthquake statis-tics[J].Bull Seism Soc Amer,67(6):1615--1623.
Epstein B,Lomnitz C.1966.A model for the occurrence of the largest earthquakes[J].Nature,211(5052):954--956.
Fisher R,Tippett L H.1928.Limiting forms of the frequency distributions of the largest or smallest member of a sample[J].Proc Camb Phil Soc,24(2):180--190.
Gutenberg B,Richter C.1956.Earthquake magnitude,intensity,energy,and acceleration,partⅡ[J].Bull Seism SocAmer,46(2):105--145.
Huyse L,Chen R,Stamatakos J A.2010.Application of generalized pareto distribution to constrain uncertainty in peakground accelerations[J].Bull Seism Soc Amer,100(1):87--101.
Pickands J.1975.Statistical inference using extreme order statistics[J].Ann Stat,3(1):119--131.
Pisarenko V F,Sornette D.2003.Characterization of frequency of extreme earthquake events by the generalized paretodistribution[J].Pure Appl Geophys,160(12):2343--2364.
Yegulalp T M,Kuo J A.1974.Statistical prediction of the occurrence of maximum magnitude earthquakes[J].BullSeism Soc Amer,64(2):393--414.
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