Variation of the Gutenberg-Richter b values and nontrivial temporal correlations in a Spring-Block Model for earthquakes

We show that a two-dimensional spring-block model for earthquakes is equivalent to a continuous, nonconservative cellular automaton model. The level of conservation is a function of the relevant elastic parameters describing the model. The model exhibits power law distributions for the energy released during an earthquake. The corresponding exponent is not universal. It is a function of the level of conservation. Thus the observed variation in the b value in the Gutenberg-Richter law could be explained by a variation in the elastic parameters. We address the problem of the boundary conditions and display results for two extreme possibilities. Furthermore, we discuss the correlation in the interoccurrence time of earthquakes. The model exhibits the features of real earthquakes: the occurrence of small earthquakes is random, while the larger earthquakes seem to be bunched. Primarily, the results of our work indicate that the dynamic of earthquakes is intimately related to the nonconservative nature of the model, which gives birth to both the change in the exponent and the correlations in interoccurrence time.