David M. Boore

For many decades, it has been common practice to overlook the differences between response spectra and pseudo response spectra. This practice stems from analyses indicating that the average difference between response spectra and pseudo response spectra is negligible for a viscous damping ratio of 5%, which is near‐universally adopted. As others have shown, the differences depend strongly on the damping ratio, earthquake magnitude, and oscillator period, with larger differences for larger damping, smaller magnitudes, and longer periods. To quantify the full statistical distribution of the ratio of the absolute acceleration response spectrum (SA) to the pseudo absolute acceleration response spectrum (PSA), we fit empirical ratios with the generalized gamma distribution. Data for magnitudes from 4.0 to 5.5 give 95% prediction intervals for the ratio of 1.00–1.02 at 1 s and 1.01–2.24 at 10 s for 5% damping. For 30% damping, these intervals increase to 1.14–2.01 at 1 s and 1.62–11.8 at 10 s, respectively. Further, we demonstrate how the shape of the ground‐motion Fourier amplitude spectrum interacts with the natural period of the oscillator to control the differences in the response spectra type. Routinely treating the two measures of acceleration response spectra as interchangeable may lead to unacceptable inconsistencies when the response spectra of individual records are important or when larger damping ratios are used, such as in direct displacement‐based design. If one must convert between them, the uncertainty of the conversion should be accounted for during analysis.

An indispensable component of any site‐specific probabilistic seismic hazard analysis (PSHA) is incorporating local site effects through site response analyses, rather than relying on generic amplification factors in ground‐motion models (GMMs). Traditionally, the seismic hazard is calculated at a buried rock horizon and then convolved with amplification factors for the overlying layers, which requires the definition and characterization of the buried rock profile (without which neither the model for rock motions nor the site response analyses can be developed). An alternative approach is to retain the host reference rock profile in the GMM for the hazard calculations and then perform the host‐to‐target site response adjustment for the full profiles in a single step. This approach is illustrated by its application to a site‐specific Senior Seismic Hazard Analysis Committee Level 3 PSHA for Idaho National Laboratory. The site adjustment factors are calculated using a logic‐tree approach that captures the full epistemic uncertainty in these factors. This is not necessarily achieved when the logic tree only captures uncertainty in the near‐surface shear‐wave velocity profile. The application illustrates the use of borehole and noninvasive shear‐wave velocity measurements, in conjunction with local recordings of weak earthquake motions, to constrain the logic‐tree branches and their associated weights.

The square-root-impedance (SRI) method is commonly used to approximate the seismic site amplifications computed using the full-resonance (FR) method for gradient shear-wave velocity (VS) profiles that are smoothly varying with depth. The SRI site amplifications have been observed to systematically underpredict the FR site amplifications by a ratio of FR/SRI amplifications around 1.05 to 1.3 across a wide frequency range (Boore, 2013). Recently, Boore and Abrahamson (2023; hereafter, BA23) related this difference in the SRI and FR methods to differences in the exponent η of the ratio of seismic impedances between the two methods. They proposed the implementation of a modified frequency-dependent η in the SRI method to improve its match to the FR site amplifications. This modified η was derived using only five VS profiles. We investigate the performance of the BA23 η for a wide range of realistic gradient VS profiles with VS30 ranging from 180 to 1500 m/s. These gradient VS profiles are constructed using two power-law functions of depth and are constrained by the assigned VS30 value, the depth and velocity of the half-space, and depths to shear-wave velocity horizons of 1.0 and 2.5 km/s (Z1.0 and Z2.5) based on western United States sites. Despite observing a VS30 dependence of η, we find that the BA23 η generally works reasonably well for the range of VS profiles analyzed. Using the VS30-dependent η derived in this study results in improvements in matching the FR site amplification compared to using the BA23 η. These improvements are more pronounced for the soft-site conditions and become modest to negligible for the stiff site conditions.

Amplifications of seismic waves traveling upward through a continuous, interface-free velocity profile are consistently smaller when computed using the square-root-impedance (SRI) method than when computed using full-resonance (FR) calculations. This was found for a wide range of velocity profiles. For realistic profiles, for which the gradient of velocity decreases with depth, the differences are not large, with the ratio of FR/SRI amplifications ranging from about 1.05 to 1.3. Comparisons of the amplifications from a continuous velocity profile with those from approximations to that profile using a stack of constant-velocity layers give some support to the hypothesis that the difference between FR and SRI amplifications for gradient profiles is because the former is controlled by the ratio of seismic impedances, whereas the latter is based on the square root of the seismic impedance ratios. This implies that gradient profiles will always have FR amplifications greater than SRI amplifications. A model-independent, easy-to-implement modification of the SRI amplifications is proposed that shows promise in bringing the SRI amplifications closer to the FR amplifications.

In this article, ground‐motion models (GMMs) for subduction earthquakes recently developed as part of the Next Generation Attenuation‐Subduction (NGA‐Sub) project are compared. The four models presented in this comparison study are documented in their respective articles submitted along with this article. Each of these four models is based on the analysis of the large NGA‐Sub database. Three of the four current models are developed for a global version as well as separate regionalized models. The fourth model was developed based on earthquakes only from Japan, and as such is applicable only for Japan. As part of this comparison study, a general discussion on the parameterization of the four models and the regionalization of the three models is provided. The specific strengths and or weaknesses or the technical decisions and justifications of any one model are not part of this comparison. A selected suite of deterministic attenuation curves and spectra are presented for the models along with a selected suite of currently used subduction models. A limited number of comparisons are presented in this article with a larger number of comparisons and the digital values provided in the electronic attachment. In addition to these scenario calculation comparisons, the results from a standard probabilistic seismic hazard analysis (PSHA) for two sites located in the Pacific Northwest Region in the state of Washington are presented. These calculations highlight the potential impact of using the new GMMs. Based on the comparisons presented here, a general understanding of these new GMMs can be obtained with the expectation that the implementation of a specific seismic hazard study should incorporate similar and additional comparisons and sensitivity studies pertinent to the site of interest.

The purpose of a median ground-motion logic tree is to capture the center, body, and range of possible ground-motion amplitudes for each earthquake scenario considered in a seismic hazard analysis. For site-specific hazard analyses, the traditional approach of populating the logic tree branches with ground-motion prediction models (GMPMs) selected and weighted on the basis of vaguely defined applicability to the target region is rapidly being abandoned in favor of the backbone GMPM approach. In this approach, the selected backbone model is first adjusted to match the earthquake source and path characteristics of the target region, and then it is separately adjusted to account for the site-specific geotechnical profile. For a GMPM to be amenable to such host-to-target adjustments, the magnitude scaling of response spectral ordinates should be consistent with the theoretical scaling of Fourier amplitude spectra. In addition, the influence of individual source and path parameters should be clearly distinguished in the model to allow the adjustments to be applied individually, and reliable estimates of the source and path parameters from the host region of the GMPM should be available, as should a reference rock profile for the model. The NGA-West2 project GMPM of Chiou and Youngs (2014; hereafter, CY14) has been identified as a very suitable backbone model. Moreover, rather than adopting generic source and path parameters and a rock site profile from the host region for CY14, which is not easily defined because the data from which it was derived came from several geographical locations, recent studies have inverted the model to obtain a CY14-consistent reference rock profile and CY14-compatible source and path parameters. Using these host-region characteristics, this study illustrates the process of building a ground-motion logic tree through the sequential application of multiple host-to-target-region adjustments, each represented by a node on the logic tree to achieve a tractable model for the total epistemic uncertainty.

Stress parameters (Δ σ ) are determined for nine relatively well-recorded earthquakes in eastern North America for ten attenuation models. This is an update of a previous study by Boore et al. (2010). New to this paper are observations from the 2010 Val des Bois earthquake, additional observations for the 1988 Saguenay and 2005 Riviere du Loup earthquakes, and consideration of six attenuation models in addition to the four used in the previous study. As in that study, it is clear that Δ σ depends strongly on the rate of geometrical spreading (as well as other model parameters). The observations necessary to determine conclusively which attenuation model best fits the data are still lacking. At this time, a simple 1/ R model seems to give as good an overall fit to the data as more complex models.