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The Bucaramanga seismic nest has the highest concentration in volume of intermediate depth seismic events with light and moderate magnitudes (Mb > 4.8) worldwide. Despite the nest depth (Zhypo ≥ 100 km), these events play a crucial role in the seismic hazard assessment for several cities in northern South America (NoSAm), particularly those situated close to their epicenters. Moreover, these earthquakes are widely felt across the country, even hundreds of kilometers away from the nest. This paper assesses the performance of commonly used subduction intraslab Ground Motion Models (GMMs) in predicting the updated nest database gathered and processed by the Colombian Geological Survey. This analysis confirms the necessity of a partially non-ergodic ground motion model for estimating the spectral accelerations produced by Bucaramanga nest earthquakes in northern South America. The GMM presented herein is the first model developed specifically for seismic nests in the region and is conceived as a regionalization of the recent NGA-Sub Abrahamson and Gülerce (Earthq Spectra 38(4):2638−2681, 2022) GMM. Additionally, we provide estimates of the variance components at both the earthquake and station levels and compare the developed GMM with the spectral accelerations recorded for typical earthquakes, for the highest magnitude earthquake in the database, and for a recent Bucaramanga nest earthquake having a moment magnitude over 5. [ABSTRACT FROM AUTHOR]

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 Dawood and Rodriguez-Marek (Bull Seismol Soc Am. 103 (2B): 1360–1372, 2013) and 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 5 Hz seismic hazard for two sites using the non-ergodic EAS GMM. At the 1E-4 annual frequency of exceedance hazard level, there can be a large difference between the ergodic hazard and the non-ergodic hazard if the distance between the chosen site and the available data is smaller than the correlation length of the non-ergodic terms). 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 at the 1E−4 hazard level than will see an increase as a result of using the non-ergodic GMM. [ABSTRACT FROM AUTHOR]

This paper provides an overview and introduction to the development of non-ergodic ground-motion models, GMMs. It is intended for a reader who is familiar with the standard approach for developing ergodic GMMs. It starts with a brief summary of the development of ergodic GMMs and then describes different methods that are used in the development of non-ergodic GMMs with an emphasis on Gaussian process (GP) regression, as that is currently the method preferred by most researchers contributing to this special issue. Non-ergodic modeling requires the definition of locations for the source and site characterizing the systematic source and site effects; the non-ergodic domain is divided into cells for describing the systematic path effects. Modeling the cell-specific anelastic attenuation as a GP, and considerations on constraints for extrapolation of the non-ergodic GMMs are also discussed. An updated unifying notation for non-ergodic GMMs is also presented, which has been adopted by the authors of this issue. [ABSTRACT FROM AUTHOR]

Standard random vibration theory (RVT) methods for estimating the horizontal spectral acceleration (PSA) amplitudes given the Fourier spectral amplitude (FAS) and ground-motion duration leads to a bias in the PSA values of up to 20%. Two models for converting FAS to PSA with reduced bias are developed. The first model replaces the ground-motion duration with an optimized RVT duration while maintain the RVT scaling, similar to the approach used by Bora et al. (Earthq Spectra 35(1):61–93). The second model maintains the ground-motion duration and replaces the scaling in RVT with empirically derived scaling using the conditional ground-motion model approach. The data set used to develop the two models includes strong-motion recordings from active crustal regions in the NGA-W2 Pacific Earthquake Engineering Research database from California earthquakes (M3.0–7.25) and global earthquakes (M5.0–7.9). The ground-motion duration, and the zeroth moment and ratio of the second/zeroth moment of the FAS of the 5%-damped oscillator response are used as known input parameters in the conditional model. Both the RVT-duration model and the conditional GMM are significant improvements over standard RVT using ground-motion based duration. The two models give similar results in the range well constrained by the data, but they extrapolate differently. The RVT-duration model does not extrapolate well to large values of the zeroth moment that can occur in the near-fault region. The conditional model has unbiased scaling with the zeroth moment including for large values of the zeroth moment. These two models are appropriate for use in converting non-ergodic GMMs for the median FAS to non-ergodic GMMs for the median PSA. The aleatory variability, required for seismic hazard applications, should be estimated from comparisons of the converted median PSA GMM and observed PSA values. [ABSTRACT FROM AUTHOR]

A new non-ergodic ground-motion model (GMM) for effective amplitude spectral (EAS) values for California is presented in this study. EAS, which is defined in Goulet et al. (Effective amplitude spectrum (eas) as a metric for ground motion modeling using fourier amplitudes, 2018), is a smoothed rotation-independent Fourier amplitude spectrum of the two horizontal components of an acceleration time history. The main motivation for developing a non-ergodic EAS GMM, rather than a spectral acceleration GMM, is that the scaling of EAS does not depend on spectral shape, and therefore, the more frequent small magnitude events can be used in the estimation of the non-ergodic terms. The model is developed using the California subset of the NGAWest2 dataset (Ancheta in PEER NGA-West2 database. Tech. rep., PEER, Berkeley, CA, 2013). The Bayless and Abrahamson (Bull Seismol Soc Am 109(5): 2088-2105, https://doi.org/10.1785/0120190077, 2019b) (BA18) ergodic EAS GMM was used as backbone to constrain the average source, path, and site scaling. The non-ergodic GMM is formulated as a Bayesian hierarchical model: the non-ergodic source and site terms are modeled as spatially varying coefficients following the approach of Landwehr et al. (Bull Seismol Soc Am 106(6):2574-2583. https://doi.org/10.1785/0120160118, 2016), and the non-ergodic path effects are captured by the cell-specific anelastic attenuation attenuation following the approach of Dawood and Rodriguez-Marek (Bull Seismol Soc Am 103(2B):1360-1372, https://doi.org/10.1785/0120120125, 2013). Close to stations and past events, the mean values of the non-ergodic terms deviate from zero to capture the systematic effects and their epistemic uncertainty is small. In areas with sparse data, the epistemic uncertainty of the non-ergodic terms is large, as the systematic effects cannot be determined. The non-ergodic total aleatory standard deviation is approximately 30 to 40 % smaller than the total aleatory standard deviation of BA18. This reduction in the aleatory variability has a significant impact on hazard calculations at large return periods. The epistemic uncertainty of the ground motion predictions is small in areas close to stations and past events. [ABSTRACT FROM AUTHOR]

Accelerometric data from the well-studied valley EUROSEISTEST are used to investigate ground motion uncertainty and variability. We define a simple local ground motion prediction equation (GMPE) and investigate changes in standard deviation (σ) and its components, the between-event variability (τ) and within-event variability (φ). Improving seismological metadata significantly reduces τ (30-50%), which in turn reduces the total σ. Improving site information reduces the systematic site-to-site variability, φS2S (20-30%), in turn reducing φ, and ultimately, σ. Our values of standard deviations are lower than global values from literature, and closer to path-specific than site-specific values. However, our data have insufficient azimuthal coverage for single-path analysis. Certain stations have higher ground-motion variability, possibly due to topography, basin edge or downgoing wave effects. Sensitivity checks show that 3 recordings per event is a sufficient data selection criterion, however, one of the dataset’s advantages is the large number of recordings per station (9-90) that yields good site term estimates. We examine uncertainty components binning our data with magnitude from 0.01 to 2 s; at smaller magnitudes, τ decreases and φSS increases, possibly due to κ and source-site trade-offs Finally, we investigate the alternative approach of computing φSS using existing GMPEs instead of creating an ad hoc local GMPE. This is important where data are insufficient to create one, or when site-specific PSHA is performed. We show that global GMPEs may still capture φSS, provided that: (1) the magnitude scaling errors are accommodated by the event terms; (2) there are no distance scaling errors (use of a regionally applicable model). Site terms (φS2S) computed by different global GMPEs (using different site-proxies) vary significantly, especially for hard-rock sites. This indicates that GMPEs may be poorly constrained where they are sometimes most needed, i.e., for hard rock. [ABSTRACT FROM AUTHOR]