Methodology for Including Path Effects Due to 3D Velocity Structure in Nonergodic Ground-Motion Models

A new approach is developed to incorporate the anisotropic path effects in ground motions due to the 3D velocity structure into nonergodic ground-motion models (GMMs) using the varying coefficient model (VCM) in a two-step process. The first step uses the VCM to estimate the spatially varying path term for each site separately with the spatial correlation based on the separation between earthquakes. The model for the correlation length varies as a function of rupture distance to reflect that, for a given separation between events, the path effects are more similar for longer path lengths. The second step uses the step-1 VCM results as the input to estimate path terms for a specific source location for any site location. The final model is a smooth spatially varying nonergodic path term that can be applied to any source-site pair. An example application of the proposed method using a subset of 600 scenarios of the v15.4 CyberShake simulation for T = 3 s response spectral values shows that nonergodic path terms can be significant, ranging from -0.8 to 0.8 ln units, which corresponds to factors of 0.45-2.23 in the median ground motion compared to the ergodic approach. With nonergodic path terms, the single-path aleatory variability for the nonergodic GMM is reduced to 0.34 ln units as compared to 0.52 ln units for single-station sigma without systematic path effects. A comparison of probabilistic hazards shows that the proposed approach leads to a nonergodic GMM that can capture the path effects seen in the CyberShake simulations in terms of both the median and the aleatory standard deviation. The resulting nonergodic GMM extends the applicability of the 3D simulation results to site-source pairs in the region and not limited to the locations of the simulations, making the simulation results more practical to use in seismic hazard studies.