The impact of earthquake cycle variability on neotectonic and paleoseismic slip rate estimates

Abstract

Abstract. 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 5 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 10 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 15 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.

Seismic Hazard Analyses From Geologic and Geomorphic Data: Current and Future Challenges

“…It can often also be difficult to tightly constrain the age of seismic events that produced the faulted feature, and this lack of event timing can introduce uncertainty into the slip rate estimate. For example, the slip rate estimate could be biased if there is a significant time lapse between the age constraints available for the initial formation of the undeformed feature and the time of the earthquake that offset it (i.e., an open interval) (Styron, 2019).…”

“…Slip rates derived from short paleoseismic records (less than five earthquake cycles) can also be subject to inaccuracies resulting from averaging a very small number of earthquakes from a system that may have high variance (Nicol et al, 2009; Weldon, 2011). This bias is diminished over longer paleoseismic records, as the number of sampled earthquakes increases and the total rate converges toward the mean (Grant Ludwig et al, 2019; Styron, 2019).…”

“…However, the open intervals bracketing all of the earthquakes responsible for the observed deformation are not easily quantified and removed from the slip rate estimate in these types of studies. If more than 5–10 mean earthquake cycles have transpired since the creation of the offset marker, the open intervals and variation of earthquake recurrence times will not dramatically affect the resulting slip rate estimate, but shorter‐term slip rate estimates may be inaccurate by a large factor and become biased (Styron, 2019).…”

“…Although there are advantages and disadvantages to slip rates spanning short‐term (<5 earthquake cycles) and long‐term (>5 earthquake cycles) slip rates from any method, longer‐term rates should be more accurate than shorter‐term estimates (Grant Ludwig et al, 2019; Styron, 2019) unless there is evidence for substantial earthquake clustering or temporal variation in slip rate. Quaternary geologic slip rates based on offset markers can be biased by the unknown duration of open intervals, but this effect is lessened over longer periods of time so long as there has not been substantial variation in fault slip throughout the measurement time.…”

Offset Channels May Not Accurately Record Strike‐Slip Fault Displacement: Evidence From Landscape Evolution Models

“…Most faults lack detailed records of multiple earthquakes, and some faults have only a few data points at sites measured over tens to hundreds of kilometers of distance along fault length. Statistical analysis suggests at least five earthquake cycles must be measured to accurately estimate slip rate (Styron, ). However, earthquake recurrence intervals on major faults range from 10 2 to10 3 years and in some cases exceed 10 4 years (e.g., Koehler & Wesnousky, ; Pérouse & Wernicke, ; Wesnousky, ), whereas a long observation period for geodetic methods is on the order of 2 decades.…”