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arXiv · 2403.18526

Number of aftershocks in epidemic-type seismicity models

G. Molchan
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Abstract

Let $V_M,(m_0)$ be the number of m>M aftershocks caused by $m_0$ event. We consider the $V_M,(m_0)$ distribution within epidemic-type seismicity models, ETAS(F). These models include the Gutenberg-Richter law for magnitude and Utsu law for average productivity of m0, but differ in the type of F distribution for the number v(m0) of direct aftershocks. The class of F is quite broad and includes both the Poisson distribution, which is the basis for the regular ETAS model, and its possible alternative, the Geometric distribution. Instead of the traditional threshold $M=m_0-Δ$, we consider $M=m_a-Δ$, where $m_a$ is the mode in the distribution of the strongest aftershock. Under these conditions we find the limit $V_M,(m_0)$ distribution at $m_0\gg1$. In the subcritical case, the limit distribution is extremely simple and identical to the $v(m_Δ)$ distribution with a suitable magnitude $m=m_Δ$. Theoretical results of this kind are lacking even for the regular ETAS model. Our results provide an additional opportunity to test the type of F-distribution, Bath law, and the very concept of epidemic-type clustering.

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G. Molchan. 2024-04-24. Number of aftershocks in epidemic-type seismicity models. https://arxiv.org/abs/2403.18526

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