Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part I: Evaluation of New Bayesian Markov-Chain Monte Carlo Simulation Methods Applied to Excavations with Continuous Peat Growth

Abstract

Determining the timing of paleoearthquakes is a central goal of paleoseismology and serves as an important input to seismic hazard evaluations. Herein, we develop a Bayesian statistical method for refining the ages of strata and earthquakes and calculating the recurrence of earthquakes based on data from paleoseismic excavations. Our work extends previous paleoseismic Bayesian modeling by simultaneously calculating the joint posterior probability density of recurrence intervals, earthquake ages, and layer ages. To estimate this joint posterior density, we employed the Metropolis-Hastings Markov-Chain Monte Carlo (MCMC) sampling method. We used the Wrightwood paleoseismic excavation site as a test bed for our method by comparing the results derived from our simulation to those of previous studies. We found that for stratigraphic order constraints, our results agreed well with previously used methods; however, when peat growth was used to constrain the minimum time that separates layers from one another, a systematic aging of strata in the lower portion of the stratigraphic column resulted. Inspection of our results indicated that, rather than representing a minimum time that separates layers, peat growth instead determined the strata's ages exactly when a constant peat-growth rate was prescribed. Using this information, we developed a new method of improving layer age, earthquake age, and recurrence interval estimates at sites where peat-bearing layers are present. This method generally produces layer-age estimates with less variance than previous methods and requires that both proximal stratigraphic constraints and trenchwide constraints be obeyed. The benchmarking of the MCMC simulation results shows that simulation provides an effective and efficient way of improving estimates of layer ages, earthquake ages, and recurrence intervals.

The sensitivity of turbidity currents to mass and momentum exchanges between these underflows and their surroundings

“…In this view, uncertainty in flow dynamics primarily results from uncertainties in the empirical relationships that describe how the flow interacts with its surroundings. For this reason, we characterize uncertainties in sediment and clear‐water entrainment relationships using a Bayesian Metropolis‐Hastings sampler [e.g., Hilley and Young , 2008]. We define the goodness of fit in terms of the reduced χ 2 statistic as [e.g., Hilley et al , 2009; Pollitz , 2003]: where DOF = n − m .…”

“…We define the goodness of fit in terms of the reduced χ 2 statistic as [e.g., Hilley et al , 2009; Pollitz , 2003]: where DOF = n − m . Here, mod x is the modeled value for each data point given a set of model parameters, measured x is the value of each data point, measured σ 2 is the variance of each data point, n is the number of measured values, m is the number of free model parameters, and DOF is the degrees of freedom [e.g., Hilley and Young , 2008; Hilley et al , 2010].…”

Recent behavior of the North Anatolian Fault: Insights from an integrated paleoseismological data set

“…In such models, the posteriors can be unrealistically shifted away from each other [Steier and Rom, 2000]. We note that Biasi et al [2002] and Hilley and Young [2008a] did not use boundaries in their formulations, although Hilley and Young [2008a] observed a systematic aging of posterior layer PDFs with age in sequences ending with a known historical earthquake where the additional constraint of a minimum amount of time between layers (based on peat growth rates) was applied.…”

“…We use a method similar to that of Lienkaemper and Bronk Ramsey [2009] to build the OxCal files. Each of the models uses stratigraphic ordering constraints; this utilizes the logic that samples from a given layer must be older than samples from the layer above [Biasi et al, 2002;Hilley and Young, 2008a]. In OxCal, this is achieved by entering the constraining dates, from oldest to youngest, in a "Sequence.…”

“…Paleoseismic investigations determine the approximate timing of surface-rupturing earthquakes using geological and geomorphological evidence along with Quaternary dating methods [e.g., McCalpin, 1996]. But not all surface-rupturing earthquakes are recognized by paleoseismology [Yeats, 2007] and the procedure for considering Quaternary dating data has been evolving over recent decades [e.g., Biasi and Weldon, 1994;Biasi et al, 2002;Hilley and Young, 2008a], which influences how we determine the timing of paleoearthquakes. Therefore, the results from existing paleoseismic investigations have been determined using slightly different methodologies, making it dubious to draw comparisons between them.…”