Adaptive estimation of the Gutenberg–Richter b value using a state space model and particle filtering

Abstract

Earthquakes follow an exponential distribution referred to as the Gutenberg–Richter law, which is characterized by the b value that represents a ratio of the number of large earthquakes to that of small earthquakes. Spatial and temporal variation in the b value is important for assessing the probability of a larger earthquake. Conventionally, the b value is obtained by a maximum-likelihood estimation based on past earthquakes with a certain sample size. To properly assess the occurrence of earthquakes and understand their dynamics, determining this parameter with a statistically optimal method is important. Here, we discuss a method that uses a state space model and a particle filter, as a framework for time-series data, to estimate temporal variation in the b value. We then compared our output with that of a conventional method using data of earthquakes that occurred in Tohoku and Kumamoto regions in Japan. Our results indicate that the proposed method has the advantage of estimating temporal variation of the b value and forecasting magnitude. Moreover, our research suggests no heightened probability of a large earthquake in the Tohoku region, in contrast to previous studies. Simultaneously, there is the potential of a large earthquake in the Kumamoto region, emphasizing the need for enhanced monitoring.