PHYSlCA ELSEVIER Physica A 229 (1996) 530-539 Dynamical models of earthquakes Hiizu Nakanishi 2 Department of Physics, Faculty of Science and Technology, Keio University, Yokohama 223, Japan Abstract Recent results on the uniform one-dimensional chain of spring-block model for earthquakes are reviewed. A two-dimensional extension of the model is also discussed and some important parameters are estimated. 1. Introduction Earthquakes are, as we all know, one of the most drastic phenomena that are hap- pening on the earth. Due to the development of plate tectonics, basic mechanism of earthquakes is now understood as the fracture phenomenon in the earth crust. Most im- portant questions for ordinary people are, of course, when and where big earthquakes will occur, but it is fair to say that answering to such questions is still not possible in practical sense. On the other hand, earthquakes have some interesting features if they are regarded as a physical phenomenon, and there arise more academic questions to ask for better understanding of the phenomenon. (1) Why are there many power laws in the earthquakes? - One of the most well- known properties is the Gutenberg-Richter law [1], which says that the smaller the earthquakes are, the more frequent they occur, and the frequency distribution of the earthquake size follows a power law. Another power law holds for the frequency decay of aftershocks after big earthquakes; It has been observed that aftershock rate decays as 1/t in most cases (Omori law)[2]. It is also claimed that epicenters of earthquakes form a fractal structure which leads to a power law for the spatial correlation of epicenter. Invited paper presented at the Second IUPAP Topical Conferenceand Third Taipei International Symposium on Statistical Physics: Nonlinear and Random Processes, 18-24 July 1995, Academia Sinica, Taipei, Taiwan. The Proceedings has already been published in Physica A 221 (1995) Nos. 1-3. 2 Present address: Department of Physics, Kyushu University 33, Fukuoka 812-81, Japan. 0378-4371/96/$15.00 (~) 1996 Elsevier Science B.V. All rights reserved Pll S0378-4371 (96)00040-4