Three topics related to seismic hazard estimation are presented in this study: a non-ergodic ground-motion model (GMM) for California, an approach to adjust a GMM for the site conditions in Pacific North West, and a fault displacement model.

A new approach is used in the development of a fully non-ergodic GMM for pseudo-spectral accelerations (PSa).First, a non-ergodic effective Fourier amplitude spectrum (EAS) GMM is derived, and then, through random vibration theory (RVT), it is converted to a PSa non-ergodic GMM. The advantage of this two-step approach is that it can better capture the non-ergodic source, path, and site effects through the small magnitude earthquakes. Fourier transform is a linear operator, and therefore, the non-ergodic effects from the small magnitude events can be applied directly to the large magnitude earthquakes. The Bayless and Abrahamson (2019b) ergodic EAS GMM is used as a backbone for the non-ergodic EAS GMM; the non-ergodic effects related to the source and site are modeled as spatially varying coefficients, and the non-ergodic effects related to the path are captured through a cell-specific anelastic attenuation. Two non-ergodic PSa GMMs are developed using the ASK14 (Abrahamson et al., 2014) and CY14 (Chiou and Youngs, 2014) ergodic GMMs as backbone models, respectively. The PSa non-ergodic effects are expressed as ergodic to non-ergodic PSa ratios, which is the adjustment that needs to be applied to an ergodic PSa GMM to incorporate the non-ergodic effects. To calculate these ratios, first both the ergodic and non-ergodic EAS are calculated for a scenario of interest (M, Rrup, VS30, x_eq, x_site, etc.) and then, with RVT, the equivalent PSa values are computed. It is the second step that introduces the magnitude dependence in the non-ergodic PSa terms. This approach leads to a 30 to 35% reduction in the total aleatory standard deviation compared to the corresponding ergodic GMMs. The epistemic uncertainty associated with the PSa ratios is small in areas close to stations and past events; in areas with sparse data, the mean of the non-ergodic ratios goes to zero implying ergodic scaling and the epistemic uncertainty increases.

The site amplification in most GMMs is quantified by the time-average shear-wave velocity of the top 30m (VS30).However, VS30 is not a fundamental physical property that controls site amplification. It works as predictor variable for site amplification due to its correlation with the site velocity profile (VS(z)), which depends on the empirical data set used to develop each GMM. The VS30 scaling of the NGAWest2 and subduction GMMs may not be applicable to Seattle, as the geological environment in Seattle is different to the geological environments in California and Japan, where most of the data in NGAWest2 and subduction GMMs were recorded, respectively. GMM-to-site scale factors are developed to adjust the NGAWest2 and subduction GMM to the site conditions in Pacific North West. The amplification ratios between the VS(z) profiles implied by the GMMs and VS(z) profiles representative for Seattle are estimated with 1D site response analyses.

A model in the wavenumber domain is developed to describe the surface fault displacements for use in probabilistic fault rupture hazard analysis (PFDHA).The advantages of this method are that it avoids the surface-rupture length normalization and that it considers the along strike correlation of displacements. A regularized Fourier Transform (RFT) is used to compute the Fourier spectra from unevenly sampled surface-slip data which could be potentially biased towards the peaks. The amplitude spectrum is based on the Somerville et al. (1999) model used for the generation of slip distributions in kinematic simulations, and the phase-derivative model is defined as a logistic distribution. Compared to previous models, the wavenumber-spectrum method leads to narrower tails of the slip distribution which is important for PFDHA at long return periods. Near the center of the rupture, the wavenumber-spectrum method gives slip distributions that are consistent with the distributions from the empirical data, but at the ends of the rupture, the wavenumber-spectrum method underestimates the range of the slip. This discrepancy may reflect limitations of the current data sets in terms of mapping the slip near the ends of the ruptures. Improved surface rupture data sets that are currently being compiled will provide improved constrains at the ends of the ruptures.