Triggering cascades and statistical properties of aftershocks

Abstract

Applying a simple general procedure for identifying aftershocks, we investigate their statistical properties for a high‐resolution earthquake catalog covering Southern California. We compare our results with those obtained by using other methods in order to show which features truly characterize aftershock sequences and which depend on the definition of aftershocks. Features robust across methods include thepvalue in the Omori‐Utsu law for large main shocks, Båth's law, and the productivity law with an exponent smaller than thebvalue in the Gutenberg‐Richter law. The identification of a typical aftershock distance with the rupture length is a feature we confirm as well as a power law decay in the spatial distribution of aftershocks with an exponent less than 2. Other results we obtain, but not common to all other works including Marsan and Lengliné (2008), Hainzl and Marsan (2008), and Zhuang et al. (2008), are (a)pvalues that do not increase with the main shock magnitude; (b) the duration of bare aftershock sequences that scales with the main shock magnitude; (c) an additional power law in the temporal variation, at intermediate times, in the rate of aftershocks for main shocks of small and intermediate magnitude; and (d) abvalue for the Gutenberg‐Richter law of background events that is sensibly larger than that of aftershocks. Tests on synthetic catalogs generated by the epidemic‐type aftershock sequence model corroborate the validity of our approach.