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大多数概率地震危险性分析方法要求知道至少3个震源参数,即平均地震活动率λ、古登堡—里克特b值和地区特征(孕震源)的最大可能震级mmax。目前,所有使用这3个参数的地震危险性评估方法几乎都明确地假定这3个参数在时间和空间上保持不变。但是,对大多数地震目录更细致的分析表明,地震活动率λ和古登堡—里克特b值都存在显著的时空变化。本文,这些地震危险性参数的最大似然估计考虑目录的不完整性、震级测定的不确定性以及所用地震发生模型的不确定性。通过假定平均地震活动率λ和古登堡—里克特b值为伽马分布的随机变量引入地震发生模型的不确定性。该方法扩展了经典的古登堡—里克特的频度—震级关系,地震数量按对应的复合量泊松分布(Benjamin,1968;Campbell,1982,1983)。使用所提出的方法估计了在南非当代历史上经历最强、破坏性最大地震,即1969年9月29日M_W6.3塞里斯—塔尔巴赫地震地区的地震活动性参数。结果表明引入地震发生模型的不确定性会减小平均复发周期,使所估计的地震危险性增大。此外,研究证实考虑震级的不确定性则作用相反,即那会增大复发周期或等效地减小估计的地震危险性。
Most methods of probabilistic seismic hazard analysis require knowledge of at least 3 source parameters, namely, the mean seismic activity rate λ, the Gutenberg-Richter b-value, and the maximum possible magnitude mmax of regional features (seismogenic sources). At present, almost all seismic risk assessment methods using these three parameters explicitly assume that the three parameters remain unchanged in time and space. However, a more detailed analysis of most earthquake catalogs shows that both the seismic activity rate λ and Gutenberg-Richet b values have significant temporal and spatial variations. In this paper, the maximum likelihood estimates of these seismic hazard parameters account for the incompleteness of catalogs, the uncertainty of magnitude determination, and the uncertainty of the seismogenic models used. The uncertainty of the earthquake occurrence model was introduced by assuming that the mean seismic activity rate λ and the Gutenberg-Ricote b value are random variables with gamma distribution. This method extends the frequency-magnitude relationship of the classical Gutenberg-Richterian earthquake with the corresponding complex Poisson distribution (Benjamin, 1968; Campbell, 1982, 1983). The proposed method was used to estimate the seismicity parameters of the area which experienced the strongest and most destructive earthquake in the contemporary history of South Africa, the M_W6.3 Seychelles-Tulbagh earthquake on September 29, 1969. The results show that the introduction of the uncertainty of the earthquake occurrence model will reduce the average recurrence period, so that the estimated seismic risk increases. In addition, the study confirms that the uncertainty in magnitude is the opposite, ie it increases the recurrence period or equivalently reduces the estimated seismic risk.