Description: The 2014 Working Group on California Earthquake Probabilities (WGCEP14) present the time-independent component of the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3), which provides authoritative estimates of the magnitude, location, and time-averaged frequency of potentially damaging earthquakes in California. The primary achievements have been to relax fault segmentation and include multifault ruptures, both limitations of UCERF2. The rates of all earthquakes are solved for simultaneously and from a broader range of data, using a system-level inversion that is both conceptually simple and extensible. The inverse problem is large and underdetermined, so a range of models is sampled using an efficient simulated annealing algorithm. The approach is more derivative than prescriptive (e.g., magnitude–frequency distributions are no longer assumed), so new analysis tools were developed for exploring solutions. Epistemic uncertainties were also accounted for using 1440 alternative logic-tree branches, necessitating access to supercomputers. The most influential uncertainties include alternative deformation models (fault slip rates), a new smoothed seismicity algorithm, alternative values for the total rate of M w ≥5 events, and different scaling relationships, virtually all of which are new. As a notable first, three deformation models are based on kinematically consistent inversions of geodetic and geologic data, also providing slip-rate constraints on faults previously excluded due to lack of geologic data. The grand inversion constitutes a system-level framework for testing hypotheses and balancing the influence of different experts. For example, we demonstrate serious challenges with the Gutenberg–Richter hypothesis for individual faults. UCERF3 is still an approximation of the system, however, and the range of models is limited (e.g., constrained to stay close to UCERF2). Nevertheless, UCERF3 removes the apparent UCERF2 overprediction of M  6.5–7 earthquake rates and also includes types of multifault ruptures seen in nature. Although UCERF3 fits the data better than UCERF2 overall, there may be areas that warrant further site-specific investigation. Supporting products may be of general interest, and we list key assumptions and avenues for future model improvements.

Description: We generalize the formulation of probabilistic seismic hazard analysis to accommodate simulation-based hazard models by expressing the joint probability distribution among the parameters of a kinematically complete earthquake rupture forecast in terms of a conditional hypocenter distribution and a conditional slip distribution. The seismological hierarchy implied by these dependencies allows the logarithmic excitation functional to be exactly and uniquely decomposed into a series of uncorrelated terms that include zero-mean averages of the site, source, hypocenter, and source-complexity effects. We use this averaging-based factorization to compare the CyberShake prototype hazard model developed by the Southern California Earthquake Center, CS11, with the empirical ground-motion prediction equations (GMPEs) of the 2008 Next Generation Attenuation (NGA08) project. For horizontal-response spectral accelerations at long periods (2–10 s), the basin and directivity effects of CS11 are substantially larger than those of the NGA08 GMPEs. Directivity–basin coupling and other 3D wave propagation effects not represented in the GMPEs contribute significantly to the excitation patterns in CS11. The total variance of the CS11 excitations is about 60% higher than the NGA root mean square (rms) at the 2 s period but almost 30% lower at 10 s. Relative to the NGA rms, the residual variance in CS11 at 2 s is larger than the aleatory variability in the NGA08 database by a factor of nearly 1.6. Recent CyberShake experiments with alternative source and structural models suggest that the high CS11 variances are due to an overestimation of the basin and directivity effects at short periods. The CyberShake site and path effects unexplained by the NGA08 models account for 40%–50% of total residual variance, suggesting that improvements to the simulation-based hazard models could reduce the aleatory variability intrinsic to the current GMPEs by as much as 25%.

Description: The Regional Earthquake Likelihood Models experiment in California tested the performance of earthquake likelihood models over a five-year period. First-order analysis showed a smoothed-seismicity model by Helmstetter et al. (2007) to be the best model. We construct optimal multiplicative hybrids involving the best individual model as a baseline and one or more conjugate models. Conjugate models are transformed using an order-preserving function. Two parameters for each conjugate model and an overall normalizing constant are fitted to optimize the hybrid model. Many two-model hybrids have an appreciable information gain (log probability gain) per earthquake relative to the best individual model. For the whole of California, the Bird and Liu (2007) Neokinema and Holliday et al. (2007) pattern informatics (PI) models both give gains close to 0.25. For southern California, the Shen et al. (2007) geodetic model gives a gain of more than 0.5, and several others give gains of about 0.2. The best three-model hybrid for the whole region has the Neokinema and PI models as conjugates. The best three-model hybrid for southern California has the Shen et al. (2007) and PI models as conjugates. The information gains of the best multiplicative hybrids are greater than those of additive hybrids constructed from the same set of models. The gains tend to be larger when the contributing models involve markedly different concepts or data. These results need to be confirmed by further prospective tests. Multiplicative hybrids will be useful for assimilating other earthquake-related observations into forecasting models and for combining forecasting models at all timescales.

Description: The Regional Earthquake Likelihood Models (RELM) working group designed a 5-year experiment to forecast the number, spatial distribution, and magnitude distribution of subsequent target earthquakes, defined to be those with magnitude ≥4.95 ( M 4.95+) in a well-defined California testing region. Included in the experiment specification were the description of the data source, the methods for data processing, and the proposed evaluation metrics. The RELM experiment began on 1 January 2006 and involved 17 time-invariant forecasts constructed by seismicity modelers; by the end of the experiment on 1 January 2011, 31 target earthquakes had occurred. We analyze the experiment outcome by applying the proposed consistency tests based on likelihood measures and additional comparison tests based on a measure of information gain. We find that the smoothed seismicity forecast by Helmstetter et al. , 2007 based on M 2+ earthquakes since 1981, is the best forecast, regardless of whether aftershocks are included in the analysis. The RELM experiment has helped to clarify ideas about testing that can be applied to more wide-ranging earthquake forecasting experiments conducted by the Collaboratory for the Study of Earthquake Predictability (CSEP). Online Material: Figures and tables showing the RELM testing region and collection region definitions, numerical results associated with the RELM experiment, and the uncorrected forecast by Ebel et al. (2007) .

Description: The assessment of earthquake forecast models for practical purposes requires more than simply checking model consistency in a statistical framework. One also needs to understand how to construct the best model for specific forecasting applications. We describe a Bayesian approach to evaluating earthquake forecasting models, and we consider related procedures for constructing ensemble forecasts. We show how evaluations based on Bayes factors, which measure the relative skill among forecasts, can be complementary to common goodness-of-fit tests used to measure the absolute consistency of forecasts with data. To construct ensemble forecasts, we consider averages across a forecast set, weighted by either posterior probabilities or inverse log-likelihoods derived during prospective earthquake forecasting experiments. We account for model correlations by conditioning weights using the Garthwaite–Mubwandarikwa capped eigenvalue scheme. We apply these methods to the Regional Earthquake Likelihood Models (RELM) five-year earthquake forecast experiment in California, and we discuss how this approach can be generalized to other ensemble forecasting applications. Specific applications of seismological importance include experiments being conducted within the Collaboratory for the Study of Earthquake Predictability (CSEP) and ensemble methods for operational earthquake forecasting. Online Material: Tables of likelihoods for each testing phase and code to analyze the RELM experiment.