Unified scaling law for earthquakes

We propose and verify a unified scaling law that provides a framework for viewing the probability of the occurrence of earthquakes in a given region and for a given cutoff magnitude. The law shows that earthquakes occur in hierarchical correlated clusters, which overlap with other spatially separated correlated clusters for large enough time periods and areas. For a small enough region and time-scale, only a single correlated group can be sampled. The law links together the Gutenberg--Richter Law, the Omori Law of aftershocks, and the fractal dimensions of the faults. The Omori Law is shown to be the short time limit of general hierarchical phenomenon containing the statistics of both "main shocks" and "aftershocks," indicating that they are created by the same mechanism.