Appendix S—Constraining Epidemic Type Aftershock Sequence (ETAS) Parameters from the Uniform California Earthquake Rupture Forecast, Version 3 Catalog and Validating the ETAS Model for Magnitude 6.5 or Greater Earthquakes

Operational earthquake forecasting in the Uniform California Earthquake Rupture Forecast, version 3 (UCERF3) model will be implemented using the Epidemic Type Aftershock Sequence (ETAS) model. Parameter values for the ETAS model are determined by fitting that model to the recent instrumental earthquake catalog. A grid search is done, and the loglikelihood is used as a measure of fit to estimate the best ETAS parameter values and their uncertainty, as well as to investigate trade-offs between parameters. For operational earthquake forecasts based on the ETAS model to be useful for emergency response and hazard mitigation purposes, they must accurately forecast the probability of large, potentially damaging earthquakes. Because of the relatively low rate of large earthquakes, the parameters of the ETAS model are from a catalog dominated by small earthquakes. It is, therefore, important to investigate whether the large earthquakes in California are explained adequately by the ETAS model derived from small earthquakes. First, I tested the null hypothesis that the transformed times of the magnitude greater than or equal to 6.5 (M≥6.5) events are Poissonian, which should be the case if the ETAS model successfully accounts for all earthquake clustering. Next, I studied the distribution of the ETAS intensity at the locations and times of M≥6.5 earthquakes, and test the null hypothesis that this distribution is the same as for small earthquakes, which would imply that the ETAS model forecasts the large earthquakes as well as it does for the small earthquakes. Finally, I used the ETAS model to decluster the catalog, and to test the null hypothesis that there is no residual clustering of M≥6.5 earthquakes in the declustered catalog. I cannot reject these null hypotheses, so I conclude that the ETAS model adequately models the occurrence of M≥6.5 earthquakes. Additionally, I showed that including small earthquakes in the ETAS modeling greatly improves the ability of the model to forecast large earthquakes.