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

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 non-stationary, 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.