发震时间的指数分布、Gamma分布和Weibull分布之间关系的研究

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.