Cellular Automaton and Markov Chains: A Study of Earthquake Dynamics

Abstract

Many models exist to study earthquake fault systems to gain a fundamental understanding of the dynamic processes that occur during an earthquake. We study cellular automata (CA) models to replicate a simple earthquake fault model. We find that the dynamics of a CA model can be simplified to a statistical Markov process. This offers a new insight into how an earthquake sequence may develop and suggests that some underlying processes are more probable than others. We compare the Markov model to the CA model and find that they are in good agreement. Lastly, we implement heterogeneities into the CA model as varied structures which complicate model dynamics. We find heterogeneities generate swarm events and temporal clustering visible within their time series. Therefore, the overall shape and slope of the frequency-size relation is modified. This suggests that scaling depends on the underlying spatial distribution of heterogeneities. A fundamental understanding of the basic processes can help predict the behavior of more complex mixed systems, which is the ultimate goal of this project.