Abstract

This paper considers the global statistics of times of largest aftershocks relative to the times of the corresponding main shocks. A large data set was used to show that the time-dependent distribution of largest aftershocks obeys a power law distribution. This is analogous to the Omori law for the sequence of all aftershocks. It is also shown that the times of the second, etc., largest aftershocks obey the same distribution. Thereby, we have confirmed the hypothesis that the times and magnitudes in an aftershock sequence are independent and make a good case for the Reasenberg–Jones representation of the aftershock process as a superposition of the Omori–Utsu law and the Gutenberg–Richter relation. Events that are smaller than the largest in an aftershock sequence show no delay relative to the largest event; this rejects the idea of the aftershock process as a direct failure cascade involving gradual transitions from larger to lesser scales, which imposes certain restrictions on the widely popular stochastic models of aftershock generation as branching processes. The above result is important in practice for prediction of aftershock activity and for assessing the hazard of large aftershocks.

中文翻译：

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大地震后余震的全球统计：时间和大小的独立性

摘要

本文考虑了最大余震时间相对于相应主震时间的全球统计数据。大数据集用于显示最大余震的时间相关分布服从幂律分布。这类似于所有余震序列的大森定律。还显示出第二次等最大余震的时间服从相同的分布。因此，我们已经证实了这样一个假设，即余震序列中的时间和幅度是独立的，并为Reasenberg-Jones表示余震过程作为Omori-Utsu定律和Gutenberg-Richter关系的叠加提供了很好的例证。小于余震序列中最大事件的事件相对于最大事件没有延迟。这拒绝了余震过程的想法，因为它是一个直接的故障级联，涉及从较大规模到较小规模的逐渐过渡，这对作为分支过程的余震产生的广泛流行的随机模型施加了一定的限制。上述结果在实践中对于预测余震活动和评估大余震的危害非常重要。