Foundations of earthquake statistics in view of non-stationary chaos theory(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Abstract

This paper is dedicated to the memory of a dear friend of ours, Professor Shuichi Tasaki. He left us many excellent works in the field of nonequilibrium statistical mechanics with his broad interests, and he always encouraged us to challenge to new problems in complex nonlinear systems, which often reveal anomalous fluctuations, characteristic scalings, etc. In this paper we discuss a simple dynamical model which reproduces a sequence of empirical laws in seismic statistics, and derive a universal relation that connects two important statistical laws; the Gutenberg-Richter distribution and the interoccurrence time distribution. These results imply that the seismic statistics can be well understood in terms of the stationary-nonstationary chaos transition near the critical regime. The results derived from the Data-Catalog in Japan, California, and Taiwan (JMA, SCDEC, TCMA), which support the universal relation, are briefly discussed.