# Bimodal Recurrence Pattern of Tsunamis in south central Chile: a statistical exploration of paleotsunami data

To improve tsunami hazard assessment, paleotsunami research aims at extending the time span of a region’s historical tsunami record in order to provide a greater number of inter-event periods to investigate. With seventeen tsunami deposits, i.e. sixteen inter-event 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 inter-event 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 inter-event period or variability of the process varies strongly with sample size and underlying process, e.g. rupture behavior. Of the investigated recurrence patterns, the simplest, i.e. a normal distribution, is described with reasonable reliability with only 3 inter-event periods. The required number of inter-event periods needed increases with recurrence pattern complexity and/or time-independence, i.e. the most complex model is a supercycle model, which reaches the same level of reliability only after 100 inter-event periods. We argue that the current best practice of reporting the mean inter-event period with 1σ- or 2σ-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 inter-event period of the Lake Huelde record of ~325 years, coincides with the anti-mode at ~315 years, i.e. the least likely between the two modes of 115 years and 490 years. The implications for south central Chile are that the probability for a tsunami in the next 50 years is 11.6%, which decreases to only 5.2%, if 250 years elapse without tsunami occurrence. This decrease in probability would be unaccounted for with a classical hazard assessment, e.g. assuming Poissonian behavior. We conclude with four requisites for a robust recurrence pattern: i) good age control, ii) a stable sensitivity of the record to be impacted by and preserve traces of the event, iii) continuity in the record, and iv) a sufficient sample size given the expected underlying process.

Kempf et al. manuscript - post-print.docx — application/vnd.openxmlformats-officedocument.wordprocessingml.document, 7.14 MB (7482765 bytes)