Spatial correlations of ground motion for non‐ergodic seismic hazard analysis

Abstract

Traditional probabilistic seismic hazard analysis (PSHA) uses ground-motion models that are based on the ergodic assumption, which means that the distribution of ground motions over time at a given site is the same as their spatial distribution over different sites. Evaluations of ground-motion data sets with multiple measurements at a given site and multiple earthquakes in a given region have shown that the ergodic assumption is not appropriate as there are strong systematic region-specific source terms and site-specific path and site terms that are spatially correlated. We model these correlations using a spatial Gaussian process model. Different correlations functions are employed, both stationary and nonstationary, and the results are compared in terms of their predictive power. Spatial correlations of residuals are investigated on a Taiwanese strong-motion data set, and ground motions are collected at the ANZA, CA array. Source effects are spatially correlated, but provide a much stronger benefit in terms of prediction for the ANZA data set than for the Taiwanese data set. We find that systematic path effects are best modeled by a non-stationary covariance function that is dependent on source-to-site distance and magnitude. The correlation structure estimated from Californian data can be transferred to Taiwan if one carefully accounts for differences in magnitudes. About 50% of aleatory variance can be explained by accounting for spatial correlation.

Comparison of Bayesian Varying Coefficient Models for the Development of Nonergodic Ground-Motion Models

“…Equations ( 8) and ( 25)). There is evidence that spatial correlations of ground-motion within-event are better modeled with a non-stationary or anisotropic correlation function (Kuehn and Abrahamson, 2020;Abbasnejadfard et al, 2020), and one would expect this to be true for spatially varying coefficients as well. INLA models have been developed to account for spatial non-stationarity (Ingebrigtsen et al, 2014(Ingebrigtsen et al, , 2015Bakka et al, 2019); it should be investigated whether incorporating non-stationarity into the nonergodic models leads to improved performance.…”

“…The general approach to performing nonergodic PSHA is outlined in e.g. Abrahamson et al (2019); Villani and Abrahamson (2015); Kuehn and Abrahamson (2020). The key difference between an nonergodic and an ergodic ground-motion model is that the nonergodic GMM explicitly takes into account repeatable, systematic source, path and site effects.…”

“…Different methods have been proposed to further relax the ergodic assumption with respect to path effects (Sung and Lee, 2016;Anderson and Uchiyama, 2011;Kuehn and Abrahamson, 2020). Dawood and Rodriguez-Marek (2013) proposed to model source-to-site specific path effects as the sum of atteuation over small cells, which was extended by Kuehn et al (2019) using Bayesian inference to account for the uncertainties associated with the cell-specific attenuation coefficients.…”

Empirical nonergodic shaking scenarios based on spatial correlation models: An application to central Italy

“…However, a limited number of studies in the literature considers fully nonergodic models and spatial correlation of the repeatable terms to generate ground motion fields. These few studies concern applications on well-sampled areas in California [18][19][20][21] and Europe. 8,[22][23][24] In this paper, we propose a methodology for generating data-driven shaking maps of acceleration spectral ordinates, based on the predictions of a nonergodic and region-specific GMM, in which the systematic contributions of variability are decomposed into event-, source-, site-, and path-effects.…”

“…However, a limited number of studies in the literature considers fully nonergodic models and spatial correlation of the repeatable terms to generate ground motion fields. These few studies concern applications on well‐sampled areas in California 18–21 and Europe 8,22–24 …”