Mean-field Burridge-Knopoff model for understanding earthquakes

Abstract

In this paper, I study avalanches in a mean-field spring-block model to simulate earthquake dynamics. The model is implemented in Fortran90, and the equations of motion are solved using a fourth-order Runge-Kutta method. The study begins with the analysis of a single block, where the system behaves deterministically, and the elastic rebound theory is recovered. Later, I consider a system of two interacting blocks. The introduction of interactions leads to the emergence of complex dynamics, and a period-doubling bifurcation appears as heterogeneity increases. Because of complex behaviour, a statistical analysis of earthquakes is performed using up to 400 blocks. Then, I observe that the magnitude distribution, related to the logarithm of the released energy, exhibits scale invariance, consistent with a power-law behaviour. In contrast, the recurrence time between earthquakes follows an exponential distribution, which is characteristic of a Poisson process, suggesting that earthquakes are statistically independent