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Bayesian ETAS for Improved Earthquake Rate Models for the Pacific Northwest

Max Schneider, Peter Guttorp, Nicholas J. van der Elst, Michael J. Barall, Andrew J. Michael, Jeanne L. Hardebeck, & Morgan T. Page

Submitted September 11, 2022, SCEC Contribution #12235, 2022 SCEC Annual Meeting Poster #201

The Pacific Northwest (PNW) has substantial earthquake risk, both due to the Cascadia megathrust fault and other fault systems under the region’s population centers. Forecasts of aftershocks following future large earthquakes will thus be desirable and require statistical models calibrated to a catalog of the PNW’s past earthquakes and aftershock sequences. This is complicated by the fact that the PNW contains multiple tectonic regimes hypothesized to have different aftershock dynamics as well as frequent swarms. We use the Epidemic-Type Aftershock Sequence (ETAS) model to describe the characteristics of earthquakes and aftershocks for the PNW, accounting for these different types of seismicity. Typically, maximum likelihood estimation (MLE) is used to fit ETAS to an earthquake catalog; however, the ETAS likelihood suffers from flatness near its optima, parameter correlation and numerical instability, making likelihood-based estimates far from robust. We present a Bayesian procedure for ETAS estimation, such that parameter estimates and uncertainty can be robustly quantified, even for small and complex catalogs like the PNW. The procedure is conditional on associating aftershocks with the correct mainshock; this latent structure and posterior distributions for the ETAS parameters are estimated iteratively. We use the procedure to model the earthquakes of the continental PNW, using a new catalog formed by algorithmically combining US and Canadian data sources and then identifying earthquake swarms. We perform a completeness analysis that supports two complete subcatalogs split by latitude, and with differing start years and magnitudes of completeness. While ETAS parameter MLEs are unstable and depend on both the optimization procedure and its initial values, Bayesian estimates are insensitive to these choices. Bayesian estimates also fit the subcatalogs better than do MLEs. We use the Bayesian method to rigorously estimate ETAS parameters and their uncertainty when including swarms in the model, modelling across different tectonic regimes and complete subcatalogs, as well as from catalog measurement error. Many parameter estimates change substantially when considering these catalog issues, indicating their importance for seismicity rate modelling and aftershock forecasting in the PNW.

Key Words
ETAS, Pacific Northwest, Cascadia, statistical seismology, aftershock forecasts, Bayesian statistics

Schneider, M., Guttorp, P., van der Elst, N. J., Barall, M. J., Michael, A. J., Hardebeck, J. L., & Page, M. T. (2022, 09). Bayesian ETAS for Improved Earthquake Rate Models for the Pacific Northwest. Poster Presentation at 2022 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)