The seismic risk assessment of urban areas or critical infrastructures can be biased because the ground-motion models (GMM) implemented in a probabilistic seismic hazard analysis (PSHA) rely on the ergodic assumption due to the lack of local strong ground-motion (GM) data even though local small-magnitude GM databases have become available in the last decades for many regions worldwide. To overcome this issue, a methodology for developing a non-ergodic GMM for a site-specific PSHA using a local small-magnitude GM database of limited size is introduced. The proposed methodology involves three main phases, which are presented along with their application to the southeast region in Slovenia. In the first phase, the local small-magnitude GM database is established. For the analyzed region in Slovenia, the database consists of 1078 GM recordings on the reference rock sites from 130 earthquakes with a moment magnitude range between 2.3 and 5.3. In the second phase, the non-ergodic GMM for effective amplitude spectrum (EAS) is modelled using Bayesian Gaussian process regression in connection with the Markov chain Monte Carlo algorithm. The non-ergodic EAS GMM is defined by the mean regional difference from the ergodic backbone EAS GMM (the BA19 GMM) and the coefficients of the non-ergodic source, site and path adjustment terms. In the third phase, the samples of the net EAS GMM adjustments are realized for selected coordinates and frequencies to capture the effect of epistemic uncertainty and then converted to the pseudo-spectral acceleration (PSA) GMM adjustments using a random vibration theory procedure. The PSA adjustments act complementary to the CY14 GMM as the ergodic backbone GMM to form a full non-ergodic PSA GMM. A non-ergodic aleatory variability model is also developed for both EAS and PSA, considering that the aleatory standard deviation is magnitude-dependent. The developed non-ergodic GMM showed the orientation-dependence of the median GM and reduced aleatory standard deviation in comparison to the ergodic backbone GMM, which is also reflected in the steeper hazard curve for the site of interest.
Babič et al. (Thu,) studied this question.