Scale-free network of earthquakesS. Abe1 and N. Suzuki2
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 in final form 2 December 2003)
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.
89.75.Da - Systems obeying scaling laws.
05.65.+b - Self-organized systems.
91.30.-f - Seismology.
© EDP Sciences 2004