Improvement of the Quantification of Epistemic Uncertainty Using Single‐Station Ground‐Motion Prediction Equations

Abstract 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 (σS) can be ignored. We use 20,006 records of 497 crustal earthquakes with moment magnitudes (Mw) 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 (σT), the single‐station sigma of the regional GMPE as estimated by the variance decomposition method (σSS), and the sigma of single‐station GMPEs (σSS,S), for different periods. For most stations (70%), the σSS,S is about 20%–50% smaller than the σT. Furthermore, we adopt the epistemic‐residual diagram to separate the σSS,S into the epistemic uncertainty (σEP,S) and the remaining unexplained variability (σSP,S) for each station. The results show that in most areas, the σSP,S for the PGA is about 50%–80% smaller than the σT. 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.