论文标题
ETAS地震性模型中的生产力
Productivity within the ETAS seismicity model
论文作者
论文摘要
可以在$ m-δ$以上的数量级事件的术语中表征一个幅度$ m $事件的生产率：这是直接“后代” $ν_δ$的数量，以及所有“后裔” $v_Δ$的数量。有证据表明，$ν_δ$和$v_δ$的离散指数分布，并具有主要幅度$ m $（余震群的情况）。我们考虑一般的流行类型余震序列（ETAS）模型，适用于$ν_δ$的任何分布。事实证明，该模型的分支结构不包括同时具有指数分布的可能性。我们已经分析研究了$V_δ$分布在广泛的ETAS模型中的特征。我们显示了$v_δ$ - 分布的尾部行为的基本差异，用于通用类型的簇和簇，具有主要的初始幅度：前一种情况下的尾巴很重，而后者则是光线。实际数据证明了这种可能性。该结果为$v_δ$的分布分析提供了理论和实用的约束。
The productivity of a magnitude $m$ event can be characterized in term of triggered events of magnitude above $m-Δ$: it is the number of direct "descendants" $ν_Δ$ and the number of all "descendants" $V_Δ$. There is evidence in favour of the discrete exponential distribution for both $ν_Δ$ and $V_Δ$ with a dominant magnitude $m$ (the case of aftershock cluster). We consider the general Epidemic Type Aftershock Sequence (ETAS) model adapted to any distribution of $ν_Δ$. It turns out that the branching structure of the model excludes the possibility of having exponential distributions for both productivity characteristics at once. We have analytically investigated the features of the $V_Δ$ distribution within a wide class of ETAS models. We show the fundamental difference in tail behavior of the $V_Δ$-distributions for general-type clusters and clusters with a dominant initial magnitude: the tail is heavy in the former case and light in the latter. The real data demonstrate the possibilities of this kind. This result provides theoretical and practical constraints for distributional analysis of $V_Δ$.
