Uncertainty in recurrence rates of large magnitude events due to short historic catalogs

Abstract

Seismic hazard analysis requires knowledge of the recurrence rates of large magnitude earthquakes that drive the hazard at low probabilities of interest for seismic design. Earthquake recurrence is usually determined through studies of the historic earthquake catalogue for a given region. Reliable historic catalogues generally span time periods of 100–200 years in North America, while large magnitude events (M ≥ 7) have recurrence rates on the order of hundreds or thousands of years in many areas, resulting in large uncertainty in recurrence rates for large events. Using Monte Carlo techniques and assuming typical recurrence parameters, we simulate earthquake catalogues that span long periods of time. We then split these catalogues into smaller catalogues spanning 100–200 years that mimic the length of historic catalogues. For each of these simulated “historic” catalogues, a recurrence rate for large magnitude events is determined. By comparing recurrence rates from one historic-length catalogue to another, we quantify the uncertainty associated with determining recurrence rates from short historic catalogues. The use of simulations to explore the uncertainty (rather than analytical solutions) allows us flexibility to consider issues such as the relative contributions of aleatory versus epistemic uncertainty, and the influence of fitting method, as well as lending insight into extreme-event statistics. The uncertainty in recurrence rates of large (M > 7) events is about a factor of two in regions of high seismicity, due to the shortness of historic catalogues. This uncertainty increases greatly with decreasing seismic activity. Uncertainty is dependent on the length of the catalogue as well as the fitting method used (least squares vs. maximum likelihood). Examination of 90th percentile recurrence rates reveals that epistemic uncertainty in the true parameters may cause recurrence rates determined from historic catalogues to be uncertain by a factor greater than 50.