A hidden Markov model for earthquake prediction

Abstract

Earthquake occurrence is well-known to be associated with structural changes in underground dynamics, such as stress level and strength of electromagnetic signals. While the causation between earthquake occurrence and underground dynamics remains elusive, the modeling of changes in underground dynamics can provide insights on earthquake occurrence. However, underground dynamics are usually difficult to measure accurately or even unobservable. In order to model and examine the effect of the changes in unobservable underground dynamics on earthquake occurrence, we propose a novel model for earthquake prediction by introducing a latent Markov process to describe the underground dynamics. In particular, the model is capable of predicting the change-in-state of the hidden Markov chain, and thus can predict the time and magnitude of future earthquake occurrences simultaneously. Simulation studies and applications on a real earthquake dataset indicate that the proposed model successfully predicts future earthquake occurrences. Theoretical results, including the stationarity and ergodicity of the proposed model, as well as consistency and asymptotic normality of model parameter estimation, are provided.