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本文应用最大熵原理确定震级概率密度分布函数P(M)=βe~(-βM)/(e~(-βM_o)-e~(-βM_u)) M_o≤M_(?)(1)这里 M_o 是非负震级下限,M_u 是震级上限,参数β可由1/β+(M_oe~(-βM_o)-M_ue~(-βM_u)/(e~(-βM_o)-e~(-βM_u)=(?)(2)确定。用数值方法求解方程(2)并且把β的数值代入方程(1),得到震级 M 的最小无偏概率密度分布。这种分布是与 M_o、M_u 以及平均震级(?)的可利用信息相一致的。震级大于或等于 M 的地震数N(M)=T(e~(-βM)-e~(-βM_u))/(e~(-βM_o)-e~(-βM_u))(3)这里 T 是 M≥M_o 的地震总数。当 M_o→0并且 M_u→∞时,(3)式简化为N(M)=Te~(-βM)(4)方程(4)精确地等价于古登堡—李克特关系log N=α-bM(5)只需令a=log T,并且b=β/ln 10。本文把基于最大熵原理得到的重复关系与全球 M_s≥7、全国 M_s≥6以及鄂尔多斯地块周边 M_s≥5级的地震观测资料作了对比。结果表明,在较大的震级跨度范围内,应用最大熵原理得到的重复关系与实际资料更为吻合。最后求得了各级地震的复发周期。上述结果显然可应用于地震危险性分析中。
In this paper, we use the principle of maximum entropy to determine the probability density distribution function of magnitude (M) = βe ~ (-βM) / (e ~ (-βM_o) -e ~ (-βM_u)) M_o≤M_ (?) The lower limit of the negative magnitude, M_u is the upper limit of the magnitude, and the parameter β can be calculated from 1 / β + (M_oe ~ (-βM_o) -M_ue ~ (-βM_u) / (e ~ (-βM_o) -e ~ (-βM_u) = (2) and substituting the value of β into equation (1) yields the minimum unbiased probability density distribution for magnitude M. This distribution is related to M_o, M_u, and the average magnitude (?) (M) = T (e ~ (-βM) -e ~ (-βM_u)) / (e ~ (-βM_o) -e ~ (-βM_u)) which is consistent with the use information, ) (3) where T is the total number of earthquakes with M≥M_o (3) is simplified to N (M) = Te ~ (-βM) when M_o → 0 and M_u → ∞. Equivalent to Gutenberg-Likert log N = α-bM (5), we only need to make a = log T, and b = β / ln 10. In this paper, the relationship between the repeated relations based on maximum entropy principle and global M_s ≥ 7, the national M_s≥6 and the M_s≥5 earthquakes around Ordos block are compared.The results show that in the range of large magnitude span, Which is more consistent with the actual data.Finally, the recurrence cycles of all levels of earthquakes are obtained.The above results are obviously applicable to the seismic hazard analysis.