Unified Scaling Law for Earthquakes

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter $b$ value, the exponent $-1\mathrm{}$ of the Omori law for aftershocks, and the fractal dimension $d_f$ of earthquakes appear as critical indices.