Complex Network of Earthquakes: Universal Law for Waiting Internal Time in Seismicity

Seismic data are mapped to growing random networks. Vertices and edges of such networks correspond to coarse-grained events and event-event correlations, respectively. This approach turned out to reveal many new aspects of complexity of seismicity. The earthquake networks were found to be complex networks, being scale-free, smallworld and hierarchically organized, each of which has its own implication in view of seismology. In studies of seismicity, one can consider two different kinds of time: one is the conventional time, and the other is the internal time. Let {t₁,t₂,...,t_N} be the conventional occurrence times of N earthquakes contained in the dataset to be analyzed. In this case, the internal time is simply the label n of t_n(n=1,2,...,N ), n which is henceforth referred to as the "event time". Carbone et al. show that "unified scaling law" for conventional waiting times of earthquakes claimed by Bak et al. is actually not universal. We show that, in contrast to the conventional waiting time, the waiting "event time" obeys a power law. This implies the existence of temporal long-range correlations in terms of the event time with no sharp decay of the crossover type. The discovered power-law waiting event-time distribution turns out to be universal in the sense that it takes the same form for seismicities in California, Japan and Iran. In particular, the parameters contained in the distribution take the common values in all these geographical regions. An implication of this result to the procedure of constructing earthquake networks is discussed.