Bimodal Recurrence Pattern of Tsunamis in South‐Central Chile: A Statistical Exploration of Paleotsunami Data

Abstract

To improve tsunami hazard assessment, paleotsunami research aims at extending the time span of a region s historical tsunami record to provide a greater number of interevent periods to investigate. With 17 tsunami deposits, that is, 16 interevent periods, the sedimentary record of Lake Huelde in south-central Chile belongs to the longest paleotsunami records from a coastal subduction zone setting. The compiled interevent periods of the Lake Huelde paleotsunami record show a complex bimodal recurrence pattern. The null hypothesis that the underlying process is a time-independent (memoryless) Poissonian process can be rejected by use of the Cox and Oakes test for exponentiality. By creating six different synthetic recurrence patterns based on statistical principles and real-world examples, we explore the reliability of simple descriptive statistical metrics. The results reveal that the level of certainty for mean interevent period or variability of the process varies strongly with sample size and underlying process, for example, rupture behavior. Of the investigated recurrence patterns, the simplest, that is, a normal distribution, is described with reasonable reliability with only three interevent periods. The required number of interevent periods needed increases with recurrence pattern complexity and/or time independence, that is, the most complex model is a supercycle model, which reaches the same level of reliability only after 100 interevent periods. We argue that the current best practice of reporting the mean interevent period with 1 sigma or 2 sigma ranges of the sample can be misleading for tsunami or seismic hazard assessment without considering the sample size and the possible underlying process. This becomes strikingly obvious when considering that the mean interevent period of the Lake Huelde record of similar to 325 yrs coincides with the antimode at similar to 315 yrs, that is, the least likely between the two modes of 115 and 490 yrs. The implications for south-central Chile are that the probability for a tsunami in the next 50 yrs is 11.6%, which decreases to only 5.2% if 250 yrs elapse without tsunami occurrence. This decrease in probability would be unaccounted for with a classical hazard assessment, for example, assuming Poissonian behavior. We conclude with four requisites for a robust recurrence pattern: (1) good age control, (2) a stable sensitivity of the record to be impacted by and preserve traces of the event, (3) continuity in the record, and (4) a sufficient sample size given the expected underlying process.