Richard Styron

Because of the natural variability (aleatoric uncertainty) in earthquake recurrence intervals and coseismic displacements on a fault, cumulative slip on a fault does not increase linearly or perfectly step-wise with time; instead, some amount of variability in shorter-term slip rates results. Though this variability could greatly affect the accuracy of neotectonic (i.e., late Quaternary) and paleoseismic slip rate estimates, these effects have not been quantified. In this study, idealized faults with four different, representative earthquake recurrence distributions are created with equal mean recurrence intervals (1,000 years) and coseismic slip distributions, and the variability in slip rate measurements over 500 to 100,000 year measurement windows is calculated for all faults through Monte Carlo simulations. The recurrence distributions used are quasi-periodic, unclustered and clustered lognormal distributions, and an unclustered exponential distribution. The results demonstrate that the most important parameter is the coefficient of variation (COV = standard deviation/mean) of the recurrence distributions rather than the shape of the distribution itself. Slip rate variability over short time scales (< 10,000 years or 10 mean earthquake cycles) is quite high, but decreases with time and is close to stable after ~ 40,000 years (40 mean earthquake cycles). This variability is higher for recurrence distributions with a higher COV. The natural variability in the slip rate estimates compared to the true value is then used to estimate the epistemic uncertainty in a single slip rate measurement (as one would make in a geological study) in the absence of any measurement uncertainty. This epistemic uncertainty is very high (a factor of 2 or more) for measurement windows of a few mean earthquake cycles (as in a paleoseismic slip rate estimate), but decreases rapidly to a factor of 1–2 with > 5 mean earthquake cycles (as in a neotectonic slip rate study). These uncertainties are independent of, and should be propagated with uncertainties in fault displacement and geochronologic measurements used to estimate slip rates. They may then aid in the comparison of slip rates from different methods or the evaluation of potential slip rate changes over time.