Comparison of Probabilistic Seismic-Hazard Models Using Averaging-Based Factorization

We generalize the formulation of probabilistic seismic hazard analysis to accommodate simulation-based hazard models by expressing the joint probability dis-tribution 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 excita-tion 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 Cyber-Shake prototype hazard model developed by the Southern California Earthquake Center, CS11, with the empirical ground-motion prediction equations (GMPEs) of the 2008Next Generation Attenuation (NGA08) project. For horizontal-response spec-tral 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 signifi-cantly 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 theNGA 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 NGA08models 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%.