Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part II: Analysis of Paleoseismic Excavation Data and Earthquake Behavior along the Central and Southern San Andreas Fault

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.

Calibration of cosmogenic 36Cl production rates from Ca and K spallation in lava flows from Mt. Etna (38°N, Italy) and Payun Matru (36°S, Argentina)

“…This approach has already been successfully applied in archeology, paleontology and in paleoseismology (e.g. Buck and Bard, 2007;Hilley and Young, 2008). In geochronology the approach has been used to reconcile and combine ages originating from various methods (Muzikar and Granger, 2006).…”

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

“…[21] To determine the amount of overlap between paleoearthquake PDFs from different investigation sites, we use two measures of overlap described by Hilley and Young [2008b] to compare paleoearthquake PDFs on the San Andreas Fault. The first measure is a modification of the "mean event overlap," where we calculate the cumulative probability of the 2s range of each PDF that falls in the 2s range of the other.…”

“…Our correlation of the paleoearthquake PDFs in the paleoearthquake model is shown in Figure 5, and plausible correlating earthquakes are listed in Table 5. To investigate how well the correlated paleoearthquake PDFs correspond to each other, we extend the "weighted range overlap" described by Hilley and Young [2008b] to take into account more than two PDFs. We call the percentage of the multiple PDFs that overlap the collective weighted range overlap, and the period over which they overlap the collective weighted age range.…”

Recent topographic evolution and erosion of the deglaciated Washington Cascades inferred from a stochastic landscape evolution model

“…The statistical approaches using Bayes' theorem such as brute‐force, Metropolis‐Hastings, and Markov‐Chain Monte Carlo algorithms have been applied to geomorphic studies to calibrate parameters in experiments and numerical models [ Vrugt et al ., ; Hilley et al ., ; Hobley et al ., ; Pelletier et al ., ]. We adopt the procedure described in Hilley and Young [, ] and Hilley et al . [] but implement brute‐force exhaustive sampling instead of Metropolis‐Hastings Markov‐Chain Monte Carlo sampling method.…”

“…To examine the uncertainties within model parameters and the covariations between them, we estimate the joint probability distribution of five parameters using Bayes' theorem [ Bayes , ; Hilley and Young , , ; Hilley et al ., ]. Based on Bayes' theorem, we can calculate the a posteriori probability density function (pdf) of the model parameters P ( m | x ), the conditional probability of the model parameters that are taken into account by observation data sets.…”