Estimating background activity based on interevent-time distribution

The statistics of time delays between successive earthquakes has recently been claimed to be universal and to show the existence of clustering beyond the duration of aftershock bursts. We demonstrate that these claims are unjustified. Stochastic simulations with Poissonian background activity and triggered Omori-type aftershock sequences are shown to reproduce the interevent-time distributions observed on different spatial and magnitude scales in California. Thus the empirical distribution can be explained without any additional long-term clustering. Furthermore, we find that the shape of the interevent-time distribution, which can be approximated by the gamma distribution, is determined by the percentage of main-shocks in the catalog. This percentage can be calculated by the mean and variance of the interevent times and varies between 5% and 90% for different regions in California. Our investigation of stochastic simulations indicates that the interevent-time distribution provides a nonparametric reconstruction of the mainshock magnitude-frequency distribution that is superior to standard declustering algorithm.