A fundamental problem for site‐specific ground‐motion prediction, commonly required in seismic‐hazard assessment, lies in the fact that ground‐motion observations over long enough time periods are unavailable at the vast majority of sites. For this reason, most of the ground‐motion prediction equations have been derived using observed data from multiple stations and seismic sources, and the standard deviation (sigma) is related to the statistics of the spatial variability of ground motion instead of temporal variability at a single site (ergodic assumption). In this paper, we explore the variability at single sites, decomposing sigma into different parts so that the various contributions to the variability can be identified and the standard deviation for empirical ground‐motion prediction models quantified by removing the ergodic assumption. The analysis was conducted using three different data sets.
Sigma obtained for Italy using the ergodic assumption is about 0.35log10 units (Bindi, Pacor, et al., 2011) and decreases to about 0.3 when single stations are considered (15% reduction). The values of single‐station sigma obtained in this study for multiple‐source data sets are rather stable, in the range 0.18–0.2log10 units, comparable to the findings of previous studies. The reduction of the epistemic uncertainty achieved through the restriction of the analysis to a particular seismic source leads to a sigma of about 0.25log10 units when the ergodic assumption is removed, suggesting that sigma at a particular site, due to a particular earthquake source, may reduce the sigma obtained for the Italian territory by Bindi, Pacor, et al. (2011) by about 30%.
Online Material: Tables of ground‐motion prediction equation coefficients, site terms, and event‐corrected single‐station standard deviations.