Unified scaling law for waiting times between seismic events

The statistical properties of seismic time series, including both sequences of aftershocks, and patterns of occurrence of mainshocks, are studied. In this case, the universality claimed by Bak et al. (Phys. Rev. Lett. 88 (2002) 178501) about the waiting times between earthquakes, has not been found. Looking for a different law, we show that the behavior of the surviving function $P(\\tau)$ of inter-event times $\\tau$ satisfy a simple relation, with two free parameter, which generalizes Omori's law also to catalogues of main earthquakes. Moreover we observe that the $P(\\tau)$ calculated for all catalogues we investigate, collapse to a single curve when suitably scaled. This is an indication that the above relation expresses a unified scaling law for seismic events whatever their origin. On the base of this relation it results that the seismic event occurrence pattern within a given seismogenetic area, significantly departs from a Poissonian distribution.