Slip‐size‐dependent renewal processes and Bayesian inferences for uncertainties

Abstract

This paper is initially concerned with uncertainty of hazard estimates using renewal process models where the parameters are poorly constrained because of the scarcity of large earthquakes occurring along the same fault segment. A Bayesian inference is adopted, taking account of the whole likelihood function of the parameters. Also, new statistical models are considered which make use of knowledge on the slip associated with earthquake ruptures, may help to improve the hazard estimate in a positive way. Including these models, the predictive efficiency is compared by using the Akaike's Bayesian information criterion (ABIC). Three data sets are analyzed for the illustrations. The Brownian Passage Time (BPT) model is selected to fit the first data set, consisting of 10 historical great earthquakes from Nanaki trough in Japan. However, its predictive hazard function shows a large uncertainty (>100 years) of likely occurrence time around 2070. The second data set consists of the last three events of the first data set but associated with record of slip sizes, for which the ABIC selected the extended lognormal renewal process model where the time intervals between successive events are normalized by the corresponding slip sizes of the starting events of the intervals. The estimated predictive hazard function implies that the next event is likely to occur around 2040 ± 10. The last data set, consisting of 4 events with estimated occurrence times and slip sizes from a submarine fault. The ABIC selected the slip‐size‐dependent BPT model for this data. This model indicates that the likelihood of occurrence time of the next event is decreasing from now, and the period of its half decay is more than several hundred years. For the data sets of the last two examples, it was also shown that the slip size records are useful for better prediction of the next event.