发震时间的指数分布、Gamma分布和Weibull分布之间关系的研究
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摘要
从理论上讨论了地震发生时间研究中常见的指数分布、Gamma分布和 Weibull分布模型之间的相互关系及其所反映的地震序列的特征。同时 ,对工程地震和地震预报中常见的危险函数所反映的地震特征作了分析。指出了指数分布、Gamma分布所反映的地震序列的内涵及统计时应注意的问题。利用华北地区历史地震资料 (M>4 .7)进行了分时段齐次统计的示范实例化分析 ,结果表明 :对地震序列分时段齐次化统计能表述地震发生的不均匀现象 ,且处理简便。
In interarrival time analysis for earthquake occurrence, the exponent, Gamma and Weibull distribution are usually used. In this paper, the mathematical relations of these distributions and some features in earthquake sequence are studied. Risk function, which is usually used in engineering seismic hazard analysis and earthquake prediction, and its meaning are analyzed. We also indicate what problems concerning distributions in seismic statistics researchers should pay attention to. At last, the demonstrational calculation of the North China seismic data shows that the hypothesis of segmented time homogeneity might be better than the hypothsis total time homogeneity in seismic statistics.
In interarrival time analysis for earthquake occurrence, the exponent, Gamma and Weibull distribution are usually used. In this paper, the mathematical relations of these distributions and some features in earthquake sequence are studied. Risk function, which is usually used in engineering seismic hazard analysis and earthquake prediction, and its meaning are analyzed. We also indicate what problems concerning distributions in seismic statistics researchers should pay attention to. At last, the demonstrational calculation of the North China seismic data shows that the hypothesis of segmented time homogeneity might be better than the hypothsis total time homogeneity in seismic statistics.
引文
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2 张国民,傅征祥.华北强震的时间分布及物理解释.地球物理学报,1985,28(6):569～578.
3 BufeC G,HarshP W,BurfordR O.Steady- state seismic slip-A precise recurrence model.Geophys.Res.Lett.1977,4,91～94.
4 KiremidjianA S,AnagnosT.StochasticSlip-Predictable model for earthquake occurrences.BSSA.,1984,74(2):739～755.
5 AnagnosT,KirenidjianA S.StochasticTime-Predictable model for earthquake occurrences.BSSA.,1984,74(6):2593～2611.
6 MulargiaF,GasperiniP.Evaluation of the applicability of the time- and slip- predictable earthquake re-currence models toItalian seismicity.Geophys.J.Int,1995,120.,453～473.
7 王炜,刘震华.地震时间间隔的统计分布及其地震危险度D值在华北大震前的异常变化.地震学报,1987,9(2):113～126.
8 金学申,等.韦布尔分布在地震危险性分析中的应用.见:中国地震区划文集,北京:地震出版社,1993,131～137.
9 王阜.地震发生的概率模型及其在地震危险性分析中的应用.见:中国地震局工程力学研究所博士学位论文,哈尔滨,1987.
10 陈汉尧,胡聿贤.泊松与更新复合模型及其在地震危险性分析中的应用.地震学报,1992,14(增刊):676～682.
11 周荫清.随机过程导论.北京:北京航空学院出版社,1987.
12 张尧庭.数据的统计处理和解释.北京:中国标准出版社,1997,54～57.
13 D.L.斯奈德.随机点过程(梁之舜,邓永录译).北京:人民教育出版社,1982.
14 李玉亚.可靠性数学.武汉:华中理工大学出版社,1990.
15 高维明.地震危险性区划中的空转换原则[A],胡聿贤.地震危险性分析中的综合概率法[C].北京:地震出版社,1990,94～111.
16 龚平.非齐次复合Poisson地震发生概率模型研究.地震,2000,20(3):73～81.
1中国地震简目(公元前780～公元1986年,M >4.7),《中国地震简目》汇编组,1988年10月
2 张国民,傅征祥.华北强震的时间分布及物理解释.地球物理学报,1985,28(6):569～578.
3 BufeC G,HarshP W,BurfordR O.Steady- state seismic slip-A precise recurrence model.Geophys.Res.Lett.1977,4,91～94.
4 KiremidjianA S,AnagnosT.StochasticSlip-Predictable model for earthquake occurrences.BSSA.,1984,74(2):739～755.
5 AnagnosT,KirenidjianA S.StochasticTime-Predictable model for earthquake occurrences.BSSA.,1984,74(6):2593～2611.
6 MulargiaF,GasperiniP.Evaluation of the applicability of the time- and slip- predictable earthquake re-currence models toItalian seismicity.Geophys.J.Int,1995,120.,453～473.
7 王炜,刘震华.地震时间间隔的统计分布及其地震危险度D值在华北大震前的异常变化.地震学报,1987,9(2):113～126.
8 金学申,等.韦布尔分布在地震危险性分析中的应用.见:中国地震区划文集,北京:地震出版社,1993,131～137.
9 王阜.地震发生的概率模型及其在地震危险性分析中的应用.见:中国地震局工程力学研究所博士学位论文,哈尔滨,1987.
10 陈汉尧,胡聿贤.泊松与更新复合模型及其在地震危险性分析中的应用.地震学报,1992,14(增刊):676～682.
11 周荫清.随机过程导论.北京:北京航空学院出版社,1987.
12 张尧庭.数据的统计处理和解释.北京:中国标准出版社,1997,54～57.
13 D.L.斯奈德.随机点过程(梁之舜,邓永录译).北京:人民教育出版社,1982.
14 李玉亚.可靠性数学.武汉:华中理工大学出版社,1990.
15 高维明.地震危险性区划中的空转换原则[A],胡聿贤.地震危险性分析中的综合概率法[C].北京:地震出版社,1990,94～111.
16 龚平.非齐次复合Poisson地震发生概率模型研究.地震,2000,20(3):73～81.
1中国地震简目(公元前780～公元1986年,M >4.7),《中国地震简目》汇编组,1988年10月
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