Empirical ground-motion models for horizontal Fourier amplitude spectra from fixed-effects and mixed-effects analyses of the NGA-West2 database

This article presents the development of ground-motion models (GMMs) of Fourier amplitude spectra for frequencies of 0.1–20 Hz and its potential extrapolation to 100 Hz at near-source distances using the effective amplitude spectrum (EAS) ordinates developed for the NGA-West2 project and the metadata and functional form from our previous NGA-West2 GMMs. We developed the GMMs using three different approaches to study the impact of including random effects in the model development: (1) fixed-effects regression (i.e. no random effects), (2) mixed-effects regression with events as a random effect, and (3) mixed-effects regression with both events and sites as random effects. Goodness-of-fit metrics show that the GMMs were improved with the addition of each random effect. We found the variance components other than the between-site standard deviation to be magnitude-dependent, which we estimated using Bayesian inference to incorporate uncertainty in the random-effects and within-group variability. As a result, our aleatory standard deviations are larger than residual-based standard deviations that ignore uncertainty in these terms. The GMMs predict a slight spectral sag at intermediate frequencies and large magnitudes that becomes more pronounced with increasing magnitude, consistent with other empirical analyses and ground-motion simulations available in the literature. We recommend use of the GMM that includes both event and site terms because of its appropriate modeling of repeatable effects. We present the other GMMs to demonstrate how each model is improved as random effects are added and to facilitate their comparison with other models that use a similar random-effects structure.