A partially nonergodic ground-motion model for Fourier amplitude spectra for the San Francisco Bay area, California, USA

Abstract

We develop a partially nonergodic ground-motion model (GMM) for Fourier amplitude spectra for the San Francisco Bay Area, California, USA, using the Bayless and Abrahamson (2019) GMM as a reference ergodic GMM and developing location-dependent adjustments to the predicted median and variance. We compile regional ground-motion data from moment magnitude (𝑀 w ) >3 earthquakes occurring during 2000–2022 for which magnitude information is available in the U.S. Geological Survey Comprehensive Catalog (Guy et al., 2015). The data set predominantly consists of records from 𝑀 w 3.5–4.5 earthquakes but includes three well-recorded 𝑀 w > 5 events. Ground-motion residuals are evaluated using the time-averaged shear-wave velocity in the top 30 m (𝑉 S30 ) from the California-specific map of Thompson et al. (2018) and basin-depth site parameters from the seismic velocity model of Aagaard and Hirakawa (2021). The 𝑉 S30 dependence and basin-depth scaling of the reference ergodic GMM of Bayless and Abrahamson (2019) are evaluated and modified with the updated data set. We compute maps of site adjustments using a varying-coefficient model that considers the spatial correlation structure and uncertainties at each observation location. The spatial covariance model is developed using ground-motion residuals that are standardized by the uncertainty model, which allows for consideration of the aleatory variability in developing the site adjustments. The covariance model is fit considering the means and standard deviations of the site terms at all locations. The use of partially nonergodic median adjustments results in modified variance components of the within-event variability. Due to the low number of large-magnitude earthquakes that control seismic hazard in the data set, we do not modify between-event variance; however, we present adjustments to site-to-site variability for use in partially nonergodic hazard assessments.