A Non-Ergodic Ground-Motion Model of Fourier Amplitude Spectra for France

Abstract

We used an ergodic ground-motion model (GMM) of California of Bayless and Abrahamson (Bull Seismol Soc Am 109(5):2088–2105, 2019) as a backbone model and incorporated the varying-coefficient model (VCM), with a modification for anisotropic path effects, to develop a new non-ergodic GMM for France based on the French RESIF data set (1996-2016). Most of the earthquakes in this database have small-to-moderate magnitudes (M2.0 – M5.2). We developed the GMM for the smoothed effective amplitude spectrum (EAS) rather than for elastic spectral acceleration because it allows the use of small magnitude data to constrain linear effects of the path and site without the complication of the scaling being affected by differences in the response spectral shape. For the VCM, the coefficients of GMM can vary by geographical location and they are estimated using Gaussian-process regression. There is a separate set of coefficients for each source and site coordinate, including both the mean coefficients and the epistemic uncertainty in the coefficients. We further modify the anelastic attenuation term of a GMM by the cell-specific approach of Kuehn et al. (Bull Seismol Soc Am 109 (2): 575–585, 2019) to allow for azimuth-dependent attenuation for each source which reduces the standard deviation of the residuals at long distances. As an example, we compute the 5Hz seismic hazard for two sites using the non-ergodic EAS GMM. At the 1 10-4 annual frequency of exceedance hazard level, there can be a large difference between the ergodic hazard and the non-ergodic hazard if the site is close to the available data. The combination of the non-ergodic median ground motion and the reduced aleatory variability can have large implications for seismic-hazard estimation for long return periods. For some sites, the estimated hazard will increase and for other sites the estimated hazard will decrease compared to the traditional ergodic GMM approach. Due to the skewed distribution of the epistemic uncertainty of the hazard, more of the sites will see a decrease in the mean hazard mean hazard at the 1 10-4 hazard level than will see an increase as a result of using the non-ergodic GMM.

Lessons learned from applying varying coefficient model to controlled simulation datasets

“…Therefore, it is unlikely to run into the same problem of large correlation lengths. For example, the source effects obtained by VCM for California and France datasets do not exhibit such behaviors (Lavrentiadis et al 2021;Sung et al 2021). However, if an empirical dataset exclusively consists of one earthquake sequence or swarm, in which all the events have similar stress drop and are located densely along one fault, the VCM will likely yield large correlation lengths of and unreasonable predictions at locations without data.…”

Fully Data-driven non-ergodic ground-motion prediction models for low to moderate seismicity areas: using RESIF-RAP, ESM, RESORCE and NGA-West 2 data.

“…Consequently, the GMAV will decrease by transmitting the reproducible systematic effects of source, wave propagation and site into epistemic uncertainties so that the ground motion prediction is spatially independent. FNE-GMPMs achieve a 60% to 70% reduction in GMAV compared to ergodic GMPMs (Lin et al 2011;Landwehr et al 2016;Abrahamson et al 2019) This reduction in GMAV has a great impact on improving the probabilistic seismic hazard assessment PSHA (Sung et al 2021).…”

“…These variabilities represent systematic effects that can be removed from GMAV if we have multiple paths (Villani and Abrahamson 2015;Baltay et al 2017;Abrahamson et al 2019;Kotha et al 2020 andSung et al 2021). Under the fully non-ergodic assumption, the δS2S, δP2P and δL2L variabilities are therefore epistemic uncertainties.…”

Regional physics-based simulation of ground motion within the Rhȏne Valley, France, during the MW 4.9 2019 Le Teil earthquake

“…However, because of their ergodic nature, classical GMMs do not provide quantitative estimates of the region-and site-specific features of earthquake ground motion, unless empirical non-ergodic adjustments are considered (e.g., Biro and Renault, 2012;Ameri et al 2017) or fully non-ergodic models are implemented in the considered region (e.g. Landwehr et al, 2016;Sung et al, 2022).…”