Bayesian forecasting of the recurrent earthquakes and its predictive performance for a small sample size

This study is concerned with the probability forecast by the Brownian Passage Time (BPT) model especially in case where only a few records of recurrent earthquakes from an active fault are available. We adopt the Bayesian predictive distribution that takes the relevant prior information and all possibilities for model parameters into account. We utilize the size of single-event displacements U and the slip rate V across the segment to calculate the mean recurrence time T=U/V that the past recurrence intervals are distributed around as Figure 1. We then make use of the best fitted prior distribution for the BPT variation coefficient (the shape parameter, α) selected by the Akaike Bayesian information criterion (ABIC), while the ERC uses the same common estimate α=0.24. Applying this prior distribution, we can see that α takes various values among the faults but has some locational tendencies from Figure 2. For example, α values tend to be higher in the center of Honshu island where the faults are densely populated. We compare the goodness of fit and probability forecasts between the conventional models and our proposed model by historical or simulated datasets. The Bayesian predictor shows very stable and superior performance for small samples or variant recurrence times. Figure 1: The relation between mean recurrence time from slip data and past recurrence intervals with error bars.

Figure 2: The map of active faults in land and subduction-zones in Japan, whose colors show the Bayes estimates of variation coefficient α.