1. Number of aftershocks in epidemic-type seismicity models.
- Author
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Molchan, George and Peresan, Antonella
- Subjects
- *
GEOMETRIC distribution , *POISSON distribution , *EARTHQUAKES , *DISTRIBUTION (Probability theory) , *SEISMOLOGY , *EARTHQUAKE aftershocks - Abstract
The Epidemic Type Aftershock Sequence (ETAS) model describes how an earthquake generates its own aftershocks. The regular ETAS model assumes that distribution F of the number of direct aftershocks is Poissonian, however there is evidence suggesting that a geometric distribution might be more adequate. Let |${{V}_M}({{m}_ \bullet })$| be the number of |$m > M$| aftershocks generated by |${{m}_ \bullet }$| event. In this study we consider the |${{V}_M}({{m}_ \bullet })$| distribution within Epidemic-type Seismicity models, ETAS(F). These models include the Gutenberg–Richter law for magnitude and Utsu law for average |${{m}_ \bullet }$| -productivity, but differ in the type of F distribution for the number |$v({{m}_ \bullet })$| 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. We replace the traditional |$M = {{m}_ \bullet } - \Delta $| threshold in |$\Delta $| -analysis with |$M = {{m}_a} - \Delta $| where |${{m}_a}$| is the distribution mode of the strongest aftershocks. Under these conditions we find the limit |${{V}_M}({{m}_ \bullet })$| distribution at |${{m}_ \bullet } > > 1$|. In the subcritical case, the limit distribution is extremely simple and identical to the |$v({{m}_\Delta })$| distribution with a suitable magnitude |${{m}_\Delta }$|. This result allows us to validate both the priority of the geometric distribution of F for direct aftershocks and the very concept of epidemic-type clustering on global seismicity data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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