Earthquake recurrence as a record breaking process

We extend the notion of waiting times for a point process to recurrent events in space-time. Earthquake B is a recurrence of a previous one, A, if no intervening earthquake happens after A and before B in the spatial disc centered on A with radius AB. The cascade of recurrent events, where each later recurrence to an event is closer in space than all previous ones, forms a sequence of records. Representing each record by a directed link between nodes defines a network of earthquakes. For Southern California, this network exhibits robust scaling laws. The rupture length emerges as a fundamental scale for distance between recurrent events. Also, the distribution of relative separations for the next record in space (time) ∼ rr (∼ tt), with δr ≈ δt ≈ 0.6. While the in-degree distribution agrees with a random network, the out-degree distribution shows large deviations from Poisson statistics. Comparison with randomized data and a theory of records for independent events occurring on a fractal shows that these statistics capture non-trivial features of the complex spatiotemporal organization of seismicity.