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 (PSHAs). 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 a prior distribution imposed on a Gaussian Process. 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. This study 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, verification of what is recovered by the VCM from CyberShake simulations is straightforward. We found that the site effects in CyberShake datasets can be reliably estimated by the VCM. However, the densely-located self-similar events in CyberShake datasets along pre-defined faults violate the isotropic assumption underlying the VCM, thus preventing 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, which is most likely due to other unmodeled effects and inappropriate assumption of wave-propagation path. Instead, a midpoint approach that only considers the aggregated path effects can better recover the strong anelastic attenuation within basins by fixing the correlation length of path effects. Lessons learned in this study not only provide guidance for future applications of VCM to both simulation and empirical datasets, but will also guide further development of the technique, with emphasis on the recovery of path effects.