Improving Uncertainty Quantification and Visualization for Spatiotemporal Earthquake Rate Models for the Pacific Northwest

The Pacific Northwest (PNW) has substantial earthquake risk, both due to the offshore Cascadia megathrust fault but also other fault systems that produce earthquakes under the region's population centers. Forecasts of aftershocks following large earthquakes are thus highly desirable and require statistical models of 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 two types of earthquake clustering (aftershock sequences and swarms). The Epidemic-Type Aftershock Sequence (ETAS) model is a top-performing spatiotemporal point process model which describes the dynamics of earthquakes and aftershocks in a seismic region using a set of parameters. Typically, maximum likelihood estimation 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 less reliable. 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 knowing which earthquakes triggered which aftershocks; this latent structure and the ETAS parameters are estimated iteratively. The procedure uses a Gibbs sampler to conditionally estimate the posterior distributions of each part of the model. We simulate several synthetic catalogs and test the modelling procedure, showing well-mixed posterior distributions centered on true parameter values. We also use the procedure to model the continental PNW, using a new catalog formed by algorthmically combining US and Canadian data sources and then, identifying and removing earthquake swarms. While 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 catalog better than do MLEs. We use the Bayesian method to quantify the uncertainty in ETAS estimates when including swarms in the model or modelling across different tectonic regimes, as well as from catalog measurement error. Seismicity rate estimates and the earthquake forecasts they yield vary spatially and are usually represented as heat maps. While the visualization literature suggests that displaying forecast uncertainty improves understanding in users of forecast maps, research on uncertainty visualization (UV) is missing from earthquake science. In a pre-registered online experiment, we test the effectiveness of three UV techniques for displaying uncertainty in aftershock forecasts. Participants completed two map-reading tasks and a comparative judgment task, which demonstrated how successful a visualization was in reaching two key communication goals: indicating where many aftershocks and no aftershocks are likely (sure bets) and where the forecast is low but the uncertainty is high enough to imply potential risk (surprises). All visualizations performed equally well in the goal of communicating sure bet situations. But the visualization mapping the lower and upper bounds of an uncertainty interval was substantially better than the other map designs at communicating potential surprises. We discuss the implications of these experimental results for the communication of uncertainty in aftershock forecast maps.

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