Abstract
Abstract. Because of the natural (aleatoric) variability 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 (1000 years) and coseismic slip distributions, and the variability in slip rate estimates over 500- to 100 000-year measurement windows is calculated for all faults through Monte Carlo simulations. Slip rates are calculated as net offset divided by elapsed time, as in a typical neotectonic study. 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 (CV = standard deviation ∕ mean) of the recurrence distributions rather than the shape of the distribution itself. Slip rate variability over short timescales (< 5000 years or 5 mean earthquake cycles) is quite high, varying by a factor of 3 or more from the mean, 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 CV. 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.
Highlights
Fault slip rates are generally estimated by dividing measurements of the offset of geologic marker features by the time over which that offset accumulated
Due to progressive erosion of geologic markers and the challenge of dating many late Pliocene to early Quaternary units, geologists often have no choice but to choose late Pleistocene to Holocene markers to date
This work seeks to evaluate the effect of natural variability in earthquake recurrence intervals on slip rate measurements
Summary
Fault slip rates are generally estimated by dividing measurements of the offset of geologic marker features by the time over which that offset accumulated (it is not currently possible to measure a slip rate directly, though the term “slip rate measurement” may be used to compare to a simulated or modeled value). Due to progressive erosion of geologic markers and the challenge of dating many late Pliocene to early Quaternary units (which are too old for radiocarbon and many cosmogenic nuclide systems), geologists often have no choice but to choose late Pleistocene to Holocene markers to date These units may be more desirable targets if the scientists are primarily concerned with estimating the contemporary slip rate on a fault with a slip rate that may vary over Quaternary timescales (e.g., Rittase et al, 2014; Zinke et al, 2018). The measured slip rate may deviate from the time-averaged rate based on the amount of natural variability in the earthquake cycle, given successive events from the tails of the recurrence interval or displacement distributions. The study is geared towards providing useful heuristic bounds on the aleatoric variability and epistemic uncertainty of late Quaternary slip rate estimates for fault geologists, probabilistic seismic hazard modelers, and others for whom such uncertainties are important
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