2024/03/27 by G. M. Molchan, Molchan, G.
Computer Science · Earth and Planetary Sciences · #Anomaly Detection Techniques and Applications #FOS: Physical sciences #G.3 #Geophysics (physics.geo-ph) #H.1 #J.2 #earthquake and tectonic studies
paper · pdf · doi:10.48550/arxiv.2403.18526
openalex publication_date 2024/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let VM,(m0) be the number of m>M aftershocks caused by m0 event. We consider the VM,(m0) 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=m0-Δ, we consider M=ma-Δ, where ma is the mode in the distribution of the strongest aftershock. Under these conditions we find the limit VM,(m0) distribution at m0≫1. In the subcritical case, the limit distribution is extremely simple and identical to the v(mΔ) distribution with a suitable magnitude m=mΔ. 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.