Size dependence of the Burridge-Knopoff model

Abstract

Earthquakes are not periodic phenomena and their size distribution obeys the power law, the so-called Gutenberg-Richter's law [1, 2]. It is well known that the Gutenberg-Richter's law is reproduced by the Burridge-Knopoff model [3], which is a kind of spring-block model between two tectonic plates. The mechanism of the Gutenberg-Richter's law is usually explained in the context of self-organized criticality (SOC) proposed by Bak et al. [4]. It is observed in recent research, however, that the deviation from the Gutenberg-Richter's law becomes larger for longer faults [5]. We simulated numerically the Burridge-Knopoff model in one dimension with special attention to the dependence on the model size, that is the number of blocks. It is shown that the range where the power law holds becomes narrower as the number of blocks increases [6]. We also discuss the relation between the dimensionality of the system and the size distribution.