On the scaling behavior of the earthquake inter-time distribution: Influence of large shocks and time scales in the Omori law

Abstract

We present a study of the earthquake inter-time distribution \linebreak $ D(\Delta t)$ for a California catalog in temporal periods of short duration $ T$ . We compare experimental results with theoretical predictions and analytical approximate solutions. For the majority of intervals, rescaling inter-times by the average rate leads to collapse of the distributions $ D(\Delta t)$ on a universal curve, whose functional form is well fitted by a Gamma distribution. The remaining intervals, exhibiting a more complex $ D(\Delta t)$ , are all characterized by the presence of large shocks. These results can be understood in terms of the relevance of the ratio between the characteristic time $ c$ in the Omori law and $ T$ : Intervals with Gamma-like behavior are indeed characterized by a vanishing $ c/T$ . The above features are also investigated by means of numerical simulations of the ETAS model. This study shows that collapse of $ D(\Delta t)$ is also observed in numerical catalogs, however the fit with a Gamma distribution is possible only assuming that $ c$ depends on the mainshock magnitude $ m$ . This result confirms that the dependence of $ c$ on $ m$ , previously observed for $ m>6$ mainshocks, extends also to small $ m>2$ .