Improvement of the quantification of epistemic uncertainty using single-station ground-motion prediction equations

The results of probabilistic seismic hazard analysis (PSHA) are sensitive to the standard deviation of the residuals of the ground-motion prediction equations (GMPEs), especially for long-return periods. Recent studies have proven that the epistemic uncertainty should be incorporated into PSHA using a logic-tree method instead of mixing it with the aleatory variability. In this study, we propose using single-station GMPEs with a novel approach (an epistemic-residual diagram) to improve the quantification of epistemic uncertainty per station. The single-station attenuation model is established from the observational recordings of a single station, hence, site-to-site variability (σ_S) can be ignored. We use 20,006 records of 497 crustal earthquakes with moment magnitudes (M_w) greater than 4.0, obtained from the Taiwan Strong Motion Instrumentation Program network, to build the single-station GMPEs for 570 stations showing the peak ground acceleration (PGA) and spectral accelerations. A comparison is made between the total sigma of the regional GMPE (σ_T), the single-station sigma of the regional GMPE as estimated by the variance decomposition method (σ_SS), and the sigma of single-station GMPEs (σ_SS,S), for different periods. For most stations (70%), the σ_SS,S is about 20%–50% smaller than the σ_T. Furthermore, we adopt the epistemic-residual diagram to separate the σ_SS,S into the epistemic uncertainty (σ_EP,S) and the remaining unexplained variability (σ_SP,S) for each station. The results show that in most areas, the σ_SP,S for the PGA is about 50%–80% smaller than the σ_T. Finally, the variations in the various sigma and model coefficients are mapped with the geographical locations of the stations for analysis of different regional characteristics.