Scale-free network of earthquakes

¹ Institute of Physics, University of Tsukuba - Ibaraki 305-8571, Japan
² College of Science and Technology, Nihon University - Chiba 274-8501, Japan

Received: 12 May 2003
Accepted: 2 December 2003

Abstract

The district of Southern California and Japan are divided into small cubic cells, each of which is regarded as a vertex of a graph if earthquakes occur therein. Two successive earthquakes define an edge or a loop, which may replace the complex fault-fault interaction. In this way, the seismic data are mapped to a random graph. It is discovered that an evolving random graph associated with earthquakes behaves as a scale-free network of the Barabási-Albert type. The distributions of connectivities in the graphs thus constructed are found to decay as a power law, showing a novel feature of earthquake as a complex critical phenomenon. This result can be interpreted in view of the facts that the frequency of earthquakes with large values of moment also decays as a power law (the Gutenberg-Richter law) and aftershocks associated with a mainshock tend to return to the locus of the mainshock, contributing to the large degree of connectivity of the vertex of the mainshock. Thus, a mainshock plays the role of a “hub”. It is also found that the exponent of the distribution of connectivities is characteristic for the plate under investigation.