NON-ERGODIC FAS GROUND-MOTION MODEL FOR CALIFORNIA

A new non-ergodic Fourier effective amplitude spectrum (EAS) ground-motion model (GMM) for California is presented in this study. The model of this study is developed as a varying-coefficient model (VCM) following the Landwehr et al, 2016 [1] framework. The Bayless and Abrahamson [2] EAS global ergodic GMM was used as the base model for the average source, site, and distance terms for California. This base GMM was then modified to incorporate non-ergodic coefficients for the path, site, and constant terms. The mean values of the non-ergodic coefficients and the epistemic uncertainty in the non-ergodic coefficients vary spatially to capture the spatial variations in the systematic path and site effects through California. A Gaussian process [3] was used to model the spatial correlation structure of the coefficients. The motivations for developing an EAS GMM rather than a spectral acceleration GMM include the straight forward consideration of constraints based on seismological theory and the Fourier transform (FT) being a linear operator. The seismological constraints are used to guide the scaling of the median ground-motion when outside the well-constrained dataset. The linear properties of the FT allow the incorporation of small magnitude earthquakes when estimating the non-ergodic coefficients, which is more difficult for a pseudo-spectral acceleration (PSA) GMM because the response spectrum is a non-linear operation. The mean value and epistemic uncertainty of the spatially varying coefficients are determined for a 5km grid spacing. The non-ergodic total aleatory standard deviation is approximately 40% smaller than the total aleatory standard deviation of the ergodic GMM. This reduction in aleatory variability has a significant impact on hazard calculations at large return periods. In areas with available ground-motion data, the epistemic uncertainty of the non-ergodic coefficients is small and the mean estimates of the coefficients deviate from the ergodic coefficients, representing the systematic path and site effects. In areas with no data from past earthquakes, the mean coefficients become equal to the ergodic model but with large epistemic uncertainty. The next step is to use the non-ergodic EAS GMM to create a synthetic dataset for magnitudes and distances typical for engineering projects, then use this dataset in combination with random vibration ration theory to develop a non-ergodic PSA GMM.