Long-Term b Value Variations of Shallow Earthquakes in New Zealand: A HMM-Based Analysis

Abstract

The magnitude–frequency relationship is a fundamental statistic in seismology. Customarily, the temporal variations of b values in the magnitude–frequency distribution are demonstrated via “sliding-window” approach. However, the window size is often only tuned empirically, which may cause difficulties in interpretation of b value variability. In this study, a continuous-time hidden Markov model (HMM) is applied to characterize b value variations of New Zealand shallow earthquakes over decades. HMM-based approach to the b value estimation has some appealing properties over the popular sliding-window approach. The estimation of b value is stable over a range of magnitude thresholds, which is ideal for the interpretation of b value variability. The overall b values of medium and large earthquakes across North Island and northern South Island in New Zealand vary roughly at a decade scale. It is noteworthy that periods of low b values are typically associated with the occurrences of major large earthquakes. The overall temporal variations of b values seem prevailing over many grids in space as evidenced by a comparison of spatial b values in many grids made between two periods with low or high b values, respectively. We also carry out a pre-seismic b value analysis for recent Darfield earthquake and Cook Strait swarm. it is suggested that the mainshock rupture is nucleated at the margin of or right at low b value asperities. In addition, short period of pre-seismic b value decrease is observed in both cases. The overall time-varying behavior of b values over decades is an indication of broad scale of time-varying behavior associated with subduction process, probably related to the convergence rate of the plates. The advance in the method of b value estimation will enhance our understanding of earthquake occurrence and may lead to improved risk forecasting.