Lessons Learned from Applying Varying Coefficient Model to Controlled Simulation Datasets

The development of site- and path-specific (i.e., non-ergodic) ground motion models (GMMs) can drastically improve the accuracy of probabilistic seismic hazard analyses (PSHA). The Varying Coefficient Model (VCM) is a novel technique for developing non-ergodic GMMs, which puts epistemic uncertainty into spatially varying coefficients. The coefficients at nearby locations are correlated by placing a Gaussian process prior on them. The correlation structure is determined by the data, and later used to predict coefficients and their epistemic uncertainties at new locations. It is important to carefully verify the technique before its results can be accepted by the engineering community. In this study, we used a series of simulation-based controlled ground motion datasets from CyberShake to test a modified VCM technique, which partitions the epistemic uncertainty into spatially varying source, site and path terms. Because the simulation parameters (inputs) are known, it is straightforward to verify what is recovered by the VCM from CyberShake simulation. We find that the site effects in CyberShake datasets can be reliably recovered by the VCM. However, the densely-located self-similar events in CyberShake datasets lead to large correlation lengths, which violates the isotropic assumption underlying the method and prevents the VCM from capturing the genuine source effects. For path effects, cell-specific attenuation approaches fail to recover the anelastic attenuation pattern of the 3D velocity model, most likely due to inappropriate assumption of point sources and straight-line wave propagation. Instead, a midpoint approach that only considers the aggregated path effects can better recover the strong attenuation within basins by fixing the correlation length of path effects. Lessons learned in this study not only provide important guidance for future applications of VCM to both simulation and empirical datasets, but also help further development of the technique, notably for the recovery of path effects.