Number of aftershocks in epidemic-type seismicity models
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910420680310784 |
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| author | Molchan, G. |
| author_facet | Molchan, G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Number of aftershocks in epidemic-type seismicity models Molchan, G. Geophysics G.3 G.3; J.2; H.1 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. |
| title | Number of aftershocks in epidemic-type seismicity models |
| topic | Geophysics G.3 G.3; J.2; H.1 |
| url | https://arxiv.org/abs/2403.18526 |