Risk implications of Poisson assumptions and declustering inferred from a fully time-dependent earthquake forecast

Abstract

We use the Third Uniform California Earthquake Rupture Forecast Epidemic Type Aftershock Sequence model, which is fully time-dependent in terms of including spatiotemporal clustering, to evaluate the effects of the Poisson assumption and declustering algorithms on statewide loss exceedance curves. The model is simulation based, meaning it produces synthetic catalogs that exhibit realistic behavior with respect to aftershocks and multi-fault earthquakes. A Poisson version of the model was constructed by randomizing event times, and the influence of two declustering algorithms was examined as well. We demonstrate that the probability of one-or-more loss exceedances (occurrence exceedance probability) is greater for the Poisson model because it has fewer seismically quiet time windows. The discrepancy between dollar loss estimates with a given exceedance probability is up to a factor of 32% but varies depending on the loss threshold (the x-axis value) and the forecast duration (we examined a range between 24 h and 50 years, with the discrepancy for the latter being negligible). We discuss how the one-or-more loss exceedance metric is questionable because it ignores all but the maximum loss experienced in each timeframe. An alternative metric based on total aggregate loss in each time window (aggregate exceedance probability) was therefore also examined, for which the Poisson model again implies higher risk at intermediate losses but lower risk at higher losses (because large, triggered events now contribute to total aggregate losses for the fully time-dependent model). We also argue that declustering is not a scientifically justifiable way to deal with full time dependence, in agreement with a chorus from other recent studies. It is difficult to draw generally applicable conclusions from our study, in part because application specific details will likely be important, but our results highlight how full time dependence can be reckoned with once authoritative forecast models are made available.