Abstract

We present a method for estimating earthquake time dependence in probabilistic seismic hazard analysis; this method uses the fault‐slip rate and available information about the amount of time that has elapsed since the most recent event (tMRE). We call this estimate the Equivalent Poisson Hazard Ratio (EPHR) because it adjusts the corresponding time‐independent (Poisson) hazard estimate. Other inputs include generalized distributions for the possible average displacement per event and the recurrence model coefficient of variation. Lognormal, Brownian passage time, and Weibull time‐dependent recurrence models are considered. We illustrate the method with two faults that are located on the central California coast. One of these faults, the Hosgri fault, slips at a nominal rate of 1.7 (0.72.7)  mm/yr. As such, for a credible average slip per event of up to a few meters, the best minimum limiting value of tMRE=242  yrs is a significant fraction of the expected recurrence interval. For the Hosgri fault, we find a weighted mean EPHR of 1.24 (1.09–1.33). The second of the faults, the Los Osos fault, slips more slowly at 0.26 (0.180.36)  mm/yr. Corresponding average recurrence intervals are long compared with the minimum tMRE=242  yrs and yield a small weighted mean EPHR estimate of 1.03 (1.02–1.04). Although the mean is near unity, the EPHR distribution is useful for capturing uncertainty. Expressed as a three‐point approximation, EPHR values of 0.26, 1.16, and 1.54 can be carried forward with corresponding weights of 0.25, 0.50, and 0.25, respectively. This is a measure of the epistemic uncertainty in regards to the Los Osos fault and whether it is early, about due, or past due when considering its average recurrence interval. For faults with low slip rates, even limiting evidence about the tMRE from paleoseismic investigation can significantly improve the mean EHPR estimate.

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