Performance Evaluation Metrics for Velocity Models Used for Numerical Simulations of Ground Motions for Seismic Hazard Applications

Abstract The exponential growth in numerical capabilities for 3D, regional-scale physics-based simulations is driving their adoption in seismic hazard analyses as a complement to empirical ground-motion models (GMMs); however, this transition is impeded by the fundamental question of whether the quality of simulation inputs can yield more accurate ground-motion predictions than ergodic GMMs. This study proposes a systematic framework for evaluating the performance of regional-scale velocity models used in numerical ground-motion simulations. Two complementary metrics are introduced: (1) Fourier amplitude spectra (FAS) across a range of frequencies, quantifying the model’s ability to reproduce ground motions at different characteristic length scales, and (2) waveform duration, which serves as a proxy for the temporal phasing distribution of the simulated wavefields. Residuals are defined relative to recorded data and a reference ergodic GMM, enabling the assessment of systematic bias, variability, and source–site-specific accuracy. This methodology is applied to the velocity model developed for the San Francisco Bay area by the U.S. Geological Survey. For this example, the median bias in FAS is not significantly different from zero, indicating no systematic bias in the median amplitudes of the simulated ground motions. The variability of the simulated waveforms is consistently lower than observed, suggesting the model is overly smooth at the investigated scales. For frequencies below 0.5 Hz, the simulations provide more accurate source–site-specific predictions of the FAS than ergodic GMMs; however, the GMM performs better at higher frequencies. In addition, the waveform duration in the simulations is, on average, 35% shorter than that of the recordings. These results emphasize the need to incorporate finer-scale characterizations to improve both amplitude and timing/phasing features of simulated ground motions. The presented evaluation methodology provides a quantitative basis for evaluating velocity models and identifying the frequency bands over which physics-based simulations can reliably supplement or replace traditional GMMs in seismic hazard analyses.