Assimilation of deterministic multicycle earthquake simulations into probabilistic rupture forecasts

SUMMARY A problem of growing importance in earthquake forecasting is how to compare probabilistic forecasting models with deterministic physical simulations and extract physical insights from their differences. Here, we compare the time-independent Uniform California Earthquake Rupture Forecast Version 3 with a long earthquake catalogue simulated by the multicycle Rate-State Quake Simulator (RSQSim). Shaw et al. generated a million-year rupture catalogue for California from RSQSim simulations based on Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3) fault geometries and slip rates and found that the shaking hazard from the synthetic catalogue was in good agreement with the UCERF3 hazard maps. We take this model-to-model comparison to the more granular level of individual faults and ruptures. We map RSQSim ruptures from the Shaw18 catalogue onto equivalent UCERF3 ruptures by maximizing the mapping efficiency and ensuring that every RSQSim realizations is associated with a unique UCERF3 rupture. The full UCERF3 logic tree is used to approximate the prior distributions of individual rupture rates and fault subsection participation rates as independent gamma distributions. We formally test the ontological null hypothesis (ONH) that the empirical RSQSim rupture counts are statistically consistent with the UCERF3 rate distributions, given the sampling uncertainty of the RSQSim catalogue and the epistemic uncertainty of the UCERF3 model. Testing individual rupture rates provides little evidence either for or against the ONH, owing to the predominance of large ruptures with low recurrence rates. However, at the subsection level, the statistically significant discrepancies are much more common than expected under the ONH. We obtain a 25 per cent failure rate at the 5 per cent significance level and a 15 per cent failure rate at 1 per cent level. The false discovery rates estimated by q-value calculations are low, so we can be confident that the same subsections would likely fail if tested against an independent million-year catalogue generated by the same RSQSim model. Bayesian recalibration of the UCERF3 priors using the empirical RSQSim rates yields Gamma posterior distributions that can be derived analytically. The results of testing and recalibration, taken together, quantify how well RSQSim rupture rates agree with, and differ from, the UCERF3 forecast rates. We find that some of the discrepancies can be attributed to the differences in slip rates that drive the models, whereas others are governed by the RSQSim fault dynamics absent from UCERF3.