Power law distributions of seismic rates

We report an empirical determination of the probability density functions Pdata(r) of the number r of earthquakes in finite space–time windows for the California catalog for different space (5 × 5 to 50 × 50 km2) and time intervals (0.1 to 1000 days). The data can be represented by asymptotic power law tails together with several cross-overs reasonably explained by one of the most used reference model in seismology (ETAS), which assumes that each earthquake can trigger other earthquakes according to complex cascades. These results are useful to constrain the physics of earthquakes and to estimate the performance of forecasting models of seismicity.