Erratum toRegional Stochastic GMPEs in Low‐Seismicity Areas: Scaling and Aleatory Variability Analysis—Application to the French Alps

Abstract

We generate stochastic ground‐motion prediction equations (GMPEs) for a wide magnitude range ( M w 3–8) that are adapted to the French Alps. Based on inversions of source, path, and site terms from weak‐motion accelerometric data (Drouet et al. , 2010), we build seismological stochastic models to use in conjunction with the simulation program Stochastic‐Method SIMulation (SMSIM) to stochastically simulate ground‐motion response spectral amplitudes. All the input parameters are considered random variables, and the uncertainty is propagated through simulations by random sampling of the corresponding distributions. Constant and magnitude‐dependent stress parameter models are compared with variable large‐magnitude stress levels. Stochastic simulations are performed for periods between 0.01 and 3 s, M w from 3 to 8, epicentral distances from 1 to 250 km, and two site conditions: rock ( V S 30=800 m/s) and hard rock ( V S 30=2000 m/s). These synthetic data are then regressed to produce stochastic GMPEs using an up‐to‐date regression form, the parameterization of which can be defined in terms of different distance metrics (i.e., epicentral, hypocentral, Joyner–Boore, or rupture distance). The impact of the uncertainty on each input parameter on the GMPE standard deviation is determined through sensitivity analysis. The major contributors to the uncertainty are the site model, both V S 30 and κ (the high‐frequency parameter), which affect the within‐event standard deviation, and the uncertainty on the stress parameter, which affects the between‐event term. The GMPEs are compared to real data using statistical analysis of residuals. Two sets of strong‐motion data are considered (the Reference Database for Seismic Ground Motion in Europe [RESORCE] and the worldwide Next Generation Attenuation databases), as well as weak‐motion data recorded in France. The results show that the magnitude‐dependent stress parameter models (for magnitudes below 4.6) fit the French data better, and a large‐magnitude constant stress parameter of 10 MPa gives a better fit to strong‐motion data. Online Material: Tables of ground‐motion prediction equation coefficients.