评B.Epstein关于地震震级分布的统计模型/
A COMMENT ON THE EPSTEIN'S MODEL FOR THE MAGNITUDE OF EARTHQUAKES
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摘要: 本文指出 B.Epstein提出的地震震级分布函数G(y)=exp(——e-y),y0并不是Ⅰ型极大值分布函数,而是泊松指数型复合极值分布,这是因为G(y)在y=0处有跃度e-.当地震资料中有某一年无震时,Epstein方法就不适用了。为此,本文不但给出更一般的理论和方法,而且提出一种新的计算方法。它与台风导致的海洋波高分布的计算是相似的。此法对地震资料较少的地区将有明显的优越性。Abstract: In this paper the author points out that G(y)=exp( - e-y), y0, the distribution of magnitude of earthquakes, suggested by B. Epstein is not the Type I distribution of the largest value, but is the Type Poisson-Bxponential compound distribution of extreme value because the Epstein's distribution has a saltus e- at y=0. The method suggested by B. Epstein is not feasible if no earthquake is observed in a year from all data.The precent author not only gives the general theory and method, but also proposes a new method which is similar to the computation of the height of typhoon wave in ocean. This method has advantage for the area where earthquakes are observed not very often.
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[1] B. Epstein and C. Lommitz, A model for the oceurrexice of large earthquakes, Nature, 211, 5052952——956, 1966.
[2] 陈培善、林邦慧,极值理论在中长期地震预报中的应用,地球物理学报,16, 6——24, 1973,
[3] 马逢时、刘德辅,复合极值分布理论及其应用,应用数学学报,2, 4, 366——375, 1979.
[4] 马逢时、刘德辅,海洋工程建筑中设计波高淮算的新方法,科学通报,24, 1, 33——37, 1979.
[5] Liu Tehfu(刘德辅)and Ma Fengshi(马逢时)Prediction of extreme heights and wind velocities, Journal of the Wateuway, Port, Coastal and Ocean Division,A SCE, 106, ww4, 469——479.Nov.. 1980.
[6] E. J. Gumbel. Statistics of Ytremes, Columbia Lniversi Press. 1958.[1] B. Epstein and C. Lommitz, A model for the oceurrexice of large earthquakes, Nature, 211, 5052952——956, 1966.
[2] 陈培善、林邦慧,极值理论在中长期地震预报中的应用,地球物理学报,16, 6——24, 1973,
[3] 马逢时、刘德辅,复合极值分布理论及其应用,应用数学学报,2, 4, 366——375, 1979.
[4] 马逢时、刘德辅,海洋工程建筑中设计波高淮算的新方法,科学通报,24, 1, 33——37, 1979.
[5] Liu Tehfu(刘德辅)and Ma Fengshi(马逢时)Prediction of extreme heights and wind velocities, Journal of the Wateuway, Port, Coastal and Ocean Division,A SCE, 106, ww4, 469——479.Nov.. 1980.
[6] E. J. Gumbel. Statistics of Ytremes, Columbia Lniversi Press. 1958.
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