Earthquake networks based on space–time influence domain

• A new earthquake network construction method based on space–time influence domain is proposed.
• The influence domain is determined by the magnitude of each event in the catalog.
• The earthquake network constructed by our method is proved to be scale-free.
• The earthquake network constructed by our method is proved to be small-world.
• The Omori Law for aftershocks emerges as a result of our analysis.

A new construction method of earthquake networks based on the theory of complex networks is presented in this paper. We propose a space–time influence domain for each earthquake to quantify the subsequence of earthquakes which are directly influenced by the former earthquake. The size of the domain is according to the magnitude of earthquake. In this way, the seismic data in the region of California are mapped to a topology of earthquake network. It is discovered that the earthquake networks in different time spans behave as scale-free networks. This result can be interpreted in terms of the Gutenberg–Richter law. Discovery of small-world characteristic is also reported on the earthquake network constructed by our method. The Omori law emerges as a feature of seismicity for the out-going links of the network. These characteristics highlight a novel aspect of seismicity as a complex phenomenon and will help us to reveal the internal mechanism of seismic system.