Scale-free networks of earthquakes and aftershocks.

We propose a metric to quantify correlations between earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks, or aftershocks emerges automatically without imposing predetermined space-time windows. In the simplest network construction, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent gamma=2.0(1). The original Omori law with p=1 emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The broad distribution of distances between earthquakes and their linked aftershocks suggests that aftershock collection with fixed space windows is not appropriate.