Determination of the scale of coarse graining in earthquake networks

Abstract

In a recent paper (Abe S. and Suzuki N., Europhys. Lett., 65 (2004) 581), the concept of earthquake network has been introduced in order to describe the complexity of seismicity. There, the cell size, which is the scale of coarse graining needed for constructing an earthquake network, has remained as a free parameter. Here, a method is presented for determining it based on the scaling behavior of the network. Quite remarkably, both the exponent of the power law connectivity distribution and the clustering coefficient are found to approach the respective universal values and remain invariant as the cell size becomes larger than a certain value, l*, which depends on the number of events contained in the analysis, in general. This l* fixes the scale of coarse graining. Universality of the result is demonstrated for all of the networks constructed from the data independently taken from California, Japan and Iran.