Nonextensive Analysis of Aftershocks Following Moderate Earthquakes in Tien Shan and North Pamir

Abstract

Aftershock sequences have been identified for 60 earthquakes (K ≥ 11) from the catalog of the Institute of Seismology, National Academy of Sciences, Kyrgyz Republic (to be referred to as KIS in what follows). The catalog includes 56 259 events that have occurred in Tien Shan and North Pamir during the period from 1980 to 2001. We have obtained some statistical characteristics of the catalog and determined its completely reported part. A map of seismic activity has been made. We determined some parameters of main events and aftershock sequences. The lowest number of aftershocks was 3 events, the largest number was 2370, the shortest duration of the aftershock process was 2 days and the longest 2046 days. The earthquake catalog and the aftershock sequences were treated from the standpoint of nonequilibrium thermodynamics using the Tsallis statistic (the parameters q and a). We sought to obtain a description of earthquakes over energy using a modified stick-slip earthquake source model and the principle of maximum entropy. This approach was used to obtain a quantitative estimate of the nonextensive Tsallis parameter q for seismicity, as well as to estimate the variation of that parameter just before a large earthquake and during aftershocks. It was shown that seismicity is a system with memory and long-range spatial correlations. The Tsallis parameter q for aftershock sequences exceeds the value of q based on the entire catalog, thus indicating an unstable state of the earthquake-generating system during aftershocks. One observed a sharp increase in the Tsallis parameter q in an area that includes the precursory area before the main event and a sharp drop at once after it, gradually returning to the average level observed before the main event.