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The time-averaged shear-wave velocity in the top 30 m, VS30, is used to represent the site condition in many ground-motion models (GMMs). Regionalized GMMs account for regional differences in the in(VS30) scaling by including region-specific coefficients for the site term. For example, recent GMMs developed for subduction zone earthquakes as part of the Next Generation Attenuation-Subduction (NGA-Sub) project include region-specific VS30 scaling for seven regions: South America, Central America, Japan, New Zealand, Taiwan, Cascadia (Pacific Northwest America), and Alaska. Of these seven regions, South America has the largest within-event standard deviation. One cause for the larger within-event standard deviation is a weaker relation between VS30 and the site term in South America compared to other regions. A cause for this weak correlation is that most of the VS30 values for the South American region in the NGA-Sub data set are based on proxies. The relation between VS30 and the site term improves significantly for periods less than 1 s if only stations with measured VS30 are considered, but the correlation is weak for periods greater than 1 s even for stations with measured VS30, indicating that, for the South America region, VS30 is not well correlated with the deeper shear-wave velocity profile that controls the long-period amplification. To improve the site terms for South America, we develop a model based on the horizontal-to-vertical spectral ratio (HVSR) from microtremors, similar to the approach used by Pinilla-Ramos et al. (2022) for California. The data set includes 660 recordings from 51 earthquakes recorded at 274 sites. The site-term model includes the period-dependent HVSR amplitude and the geometric mean of the average HVSR amplitude over the frequency band of 0.25 to 15 Hz. Including these two parameters reduces the standard deviation of site-specific site terms over the period range 0.3-3 s, with the largest reduction in the period range 1-2 s. This site-term model can be incorporated into subduction GMMs and implemented in probabilistic seismic hazard analyses for South America. [ABSTRACT FROM AUTHOR]

We investigate the nonergodic behavior of ground motions from subduction zone earthquakes and crustal earthquakes in Japan using the National Research Institute for Earth Science and Disaster Resilience strong-motion flatfile together with various reference ergodic ground-motion models (GMMs). For the nonergodic path effects, our nonergodic GMM has two path effects terms: a cell-specific linear-distance scaling, denoted as δP2PQ, that mimics the effects of a 3D Q structure, and a source- and site-specific term related to the effects of the 3D velocity structure, denoted δP2PV. The resulting model provides spatially varying nonergodic source, site, and path terms. The GMM smoothly interpolates and extrapolates the nonergodic terms in space so that the GMM can be applied to any combination of source and site locations in the region. In regions where data are sparse, the median nonergodic terms will approach zero but with large epistemic uncertainty. Over the period range of 0-10 s, the ranges of the standard deviations of the nonergodic source, path, and site terms are 0.2-0.65, 0.25-0.40, and 0.15-0.40 natural log units, respectively. The fully nonergodic models lead to a 40%-55% decrease in the aleatory standard deviation compared to the reference ergodic GMMs. This large reduction in the aleatory standard deviation combined with the change in the median given by the nonergodic terms can exert a significant impact on the computed seismic hazard for the Japan region. [ABSTRACT FROM AUTHOR]

A duration ground-motion model for crustal earthquakes based on the normalized Arias intensity (IA) is developed. Two sets of seismological simulations are used to constrain the form and scaling of the duration model. Simulations using a 3D crustal model show that an additive model for the source, path, and site terms captures the physical behavior of duration better than a multiplicative model for the site term. Stochastic finite-fault simulations are used to constrain the saturation of the large-magnitude scaling at short distances. The duration model is developed in two parts: a duration model for the time interval between 5% and 75% of the normalized Arias intensity (D5-75) and a duration model for the ratio of the D5-X/D5-75 duration for X values from 10 to 95. Together, these two models provide a more complete description of the evolution of the seismic energy with time than a single duration metric. A new aspect of the statistical model for duration is the inclusion of a random effect for the path term in addition to random effects for the source and site terms. The source and site random effects are modeled as scale factors on the duration, whereas the path-term random effect is a scale factor on the distance slope. The distribution of the duration residuals has a skewness that is between the skewness of a lognormal distribution and the symmetry of a normal distribution. The final duration aleatory variability is modeled by a power-normal distribution with an exponent of 0.3, which accounts for the amplitude dependence of the aleatory variability of the duration with smaller aleatory variability for large-magnitude events and larger aleatory variability for small-magnitude events as compared to the variability from a lognormal distribution. [ABSTRACT FROM AUTHOR]

A new approach is developed to incorporate the anisotropic path effects in ground motions due to the 3D velocity structure into nonergodic ground-motion models (GMMs) using the varying coefficient model (VCM) in a two-step process. The first step uses the VCM to estimate the spatially varying path term for each site separately with the spatial correlation based on the separation between earthquakes. The model for the correlation length varies as a function of rupture distance to reflect that, for a given separation between events, the path effects are more similar for longer path lengths. The second step uses the step-1 VCM results as the input to estimate path terms for a specific source location for any site location. The final model is a smooth spatially varying nonergodic path term that can be applied to any source-site pair. An example application of the proposed method using a subset of 600 scenarios of the v15.4 CyberShake simulation for T = 3 s response spectral values shows that nonergodic path terms can be significant, ranging from -0.8 to 0.8 ln units, which corresponds to factors of 0.45-2.23 in the median ground motion compared to the ergodic approach. With nonergodic path terms, the single-path aleatory variability for the nonergodic GMM is reduced to 0.34 ln units as compared to 0.52 ln units for single-station sigma without systematic path effects. A comparison of probabilistic hazards shows that the proposed approach leads to a nonergodic GMM that can capture the path effects seen in the CyberShake simulations in terms of both the median and the aleatory standard deviation. The resulting nonergodic GMM extends the applicability of the 3D simulation results to site-source pairs in the region and not limited to the locations of the simulations, making the simulation results more practical to use in seismic hazard studies. [ABSTRACT FROM AUTHOR]

Most ground-motion models (GMMs) parameterize the earthquake source by magnitude, style of faulting, and source depth. GMMs are isotropic in terms of the source scaling for these three parameters. The radiation pattern, which leads to azimuthally varying source effects, is not included in most GMMs. As a result, any systematic radiation-pattern effects are treated as aleatory variability in the path terms in the GMMs, which does not make physical sense. We incorporate the far-field radiation pattern into GMMs for pseudospectral acceleration and Fourier amplitude spectra for the Taiwan region. A key issue is how to combine the radiation pattern from the SH and SV components for predicting the RotD50 amplitudes of ground motions used in GMMs. A suite of point-source simulations was generated for a range of focal mechanisms and site azimuths. Empirical models for the phase differences between the radial and transverse components were developed to constrain the between-component phase differences in simulations. The results show that the vector sum of the SH and SV far-field radiation patterns, FS, has a higher correlation with the RotD50 amplitudes of the ground motion than the arithmetic mean or the geometric mean. The radiation-pattern term is modeled by S0(M)+S1(M)ln(FS+S2), in which S0(M) and S1(M) are linear functions of magnitude between M 4 and 6; they equal 0 for M > 6. The magnitude dependence reflects that, for large magnitudes and short distances, ground motions are more affected by the slip distribution and rupture timing than by the average radiation pattern from the subevents along the rupture, but the radiation pattern has a significant effect on the long-period ground-motion amplitude for small-magnitude events. Including radiation patterns into GMMs will improve estimates of 3D path effects from small-magnitude events by removing radiation-pattern effects from combined radiation-pattern and path terms used in current GMMs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Ground‐motion intensity conversion equations (GMICEs) allow for conversions between ground‐motion amplitude and shaking intensity. The current methods used to develop GMICEs model the dependence of the intensity on the peak ground‐motion (PGM) parameter. For some models, there is a second step that models the magnitude and distance dependence of the residuals from the initial regression. We show that this approach for developing GMICEs works well for estimating the intensity from median ground motions, but for ground‐motion values away from the medians, the intensities estimated by the GMICE can have large bias, with overprediction for positive PGM residuals and underprediction for negative PGM residuals. The bias is due to an implicit assumption in the current approach that there is a direct causal relation between intensity and the ground‐motion parameter and that the residuals of the intensity and ground‐motion parameter are fully correlated. We present two alternative methodologies for developing GMICEs that do not suffer from this bias. The first method includes the magnitude and distance scaling of the GMICE in the initial regression for the scaling with the PGM. The second method excludes the magnitude and distance terms but includes the number of standard deviations of the PGM (ϵ) as an additional parameter in the GMICE. Using a synthetic data set of intensity and peak ground acceleration values, we show that the GMICE developed using the proposed method leads to more accurate estimates of the intensity than current methods. We also discuss implications of using GMICEs based on the proposed methods for the evaluation of probabilistic hazard maps and as input to ShakeAlert estimates. [ABSTRACT FROM AUTHOR]

Crustal earthquakes are some of the main contributors to the seismic hazard in northern South America (NoSAm). There is evidence of historical crustal events with epicenters near populated cities, such as the 1999 MW 6.2 Coffee Region earthquake, whose damages added up to 1.9% of Colombia's gross domestic product and reported about 1200 deaths. Because the global crustal ground-motion models (GMMs) routinely used in seismic hazard assessments of the region are biased with respect to the available ground-motion records, this article presents a regional GMM developed using local data from earthquakes in Colombia, Ecuador, and Venezuela. The filtered database contains 709 triaxial records from 56 earthquakes, recorded at 92 stations between 1994 and 2020 by the Colombian Geological Survey. The moment magnitudes of the events range between 4.5 and 6.8, with hypocentral depths =60 km. The model covers rupture distances =350 km. The model site amplification is based on a categorization approach relying on the predominant site period, identified through the horizontal-to-vertical response ratios of 5%-damped response spectra. The proposed GMM is developed as a regionalization of the global Next Generation Attenuation-West2 Project ASK14 model. Our model corrects the misfit of the ASK14 GMM with respect to the observed ground-motion data in NoSAm for moderate magnitudes and intermediate to large distances while keeping the extrapolation capabilities. The proposed GMM considers the added attenuation for ray paths crossing the volcanic arc. Analysis of the variance components allows approximating plausible reductions of the standard deviation in future nonergodic models. [ABSTRACT FROM AUTHOR]

The horizontal-to-vertical spectral ratios from microtremor (mHVSR) data obtained at 196 seismic stations in California are used to evaluate three alternative microtremor-based proxies for site amplification for use in ground-motion models (GMMs): the site fundamental period (f0), the period-dependent amplitude of the mHVSR(T), and the normalized amplitude of the mHVSR(T). The alternative parameters are evaluated for the sites with and without measurements of VS30. If a VS30 measurement is not available for a site, then f0 has the highest correlation with the site amplification for short periods (T <1 s) and the normalized amplitude of the mHVSR(T) has the highest correlation for long periods (T =1 s). If a measurement of the VS30 is available for a site, then the normalized amplitude of the mHVSR(T) has the highest correlation for the site amplification not explained by VS30 for all periods. For both cases, the correlations are strongest at the longer periods as mHVSR(T) measurements excel at providing valuable information for sites with long-period amplification due to the deeper velocity structure. In particular, for sites with a VS30 measurement, the normalized mHVSR(T) amplitude provides more information about the long-period site terms than the basin depth currently used in GMMs. Empirical models of the median and standard deviation of the site terms based on the normalized mHVSR(T) curves are developed for the two cases. These models can be used directly in the ASK14 GMM to modify the median and aleatory standard deviation or they can be used to estimate the site-specific site term in the context of a partially nonergodic GMM. Including the mHVSR(T) measurement can have a significant effect on estimates of the ground motion at a site: the range 5%-95% on the observed HVSR(T) values corresponds to factors of 0.6-1.6 for the median spectral acceleration for periods between 0.5 and 4 s. [ABSTRACT FROM AUTHOR]

Recently, a number of conditional ground-motion models (CGMMs) have been developed for intensity measures (IMs) other than pseudospectral acceleration (PSA) values that are particularly useful for geotechnical earthquake engineering problems. In a CGMM, a non-PSA IM is conditioned on PSA IMs, and other earthquake parameters (e.g., magnitude Mw rupture distance Rrup) as well as site conditions (e.g., the time-averaged shear-wave velocity in the top 30 m VS30). Even though CGMMs are useful in engineering practice, their interpretation in the context of traditional (non-CGMM) has not been discussed to the authors' best knowledge. In this study, we provide an interpretation of CGMMs in terms of the scaling difference between the spectral and nonspectral IMs used in the formulation of a CGMM and the coefficient of correlation of these spectral and nonspectral IMs. In addition, the interpretation can derive into an alternative procedure for calculating correlation coefficients between PSA IMs and non-PSA IMs, which is illustrated. [ABSTRACT FROM AUTHOR]

The Abrahamson and Gulerce (2020) ground-motion model (GMM), called AG20, is modified to include the nonergodic effects from the suite of 3D numerical simulations of long-period ground motions from M 9 megathrust earthquakes on the Cascadia subduction zone developed by the M 9 project (Frankel et al., 2018). Three modifications are made to the AG20 model. First, the scaling of the basin effects as a function of the depth to a shear-wave velocity of 2.5 km/s (Z2.5) is modified to be consistent with the Z2.5 scaling from the 3D simulations. Second, the spatial distribution of the nonergodic site terms is estimated using the varying coefficient model for the region covered by the 3D velocity model. The change in the median ground motion due to the nonergodic site terms ranges from factors of 0.25 to 5 at a period of 3 s. Third, a reduction in the aleatory variability for single-station sigma is estimated. On average, including the nonergodic site terms reduces the sigma by 15%-25% compared with an ergodic sigma for Cascadia. In addition, a spatially varying single-station sigma model is developed, showing the highest variability for sites near the basin edges. Application of nonergodic GMMs requires an estimate of the epistemic uncertainty in the nonergodic terms. Without simulation results for different 3D velocity models, we assumed that the epistemic uncertainty due to uncertainty in the 3D velocity model is half of the between-site standard deviation from the simulations. As an example, the seismic hazard for interface events using the nonergodic GMM is compared with the hazard using the original AG20 GMM. [ABSTRACT FROM AUTHOR]

Probabilistic seismic hazard analysis (PSHA) is moving from ergodic ground-motion models (GMMs) to nonergodic GMMs that account for site-source-specific source, path, and site effects and which require a much larger number of GMM branches on the logic tree to capture the full epistemic uncertainty. An efficient method for computing PSHA with a large number of GMM branches was developed by Lacour and Abrahamson (2019) using polynomial chaos (PC) expansion with the key assumption that the epistemic uncertainty in the median ground motion is fully correlated. In the current study, we remove the assumption of full correlation using a multivariate PC expansion. The correlation structure of the available median GMMs across scenarios is computed empirically. The median ground motion is modeled as a Gaussian random process with the correlation structure of the GMMs across the range of relevant earthquake scenarios. This Gaussian random process is discretized using the Karhunen-Loeve expansion, which leads to multivariate PC expansions of uncertain hazard curves. The hazard fractiles can be reconstructed during an efficient postprocessing phase that includes the effects of partial correlation between the GMMs. Multivariate PC expansions require significantly more terms than for the fully correlated case, which increases the calculation time by about a factor of 5, but it is still much more efficient than direct sampling of the branches of the GMM logic for a large number of branches. An example hazard calculation shows that the effect of using partial correlation in place of full correlation of the GMMs is small for the Next Generation Attenuation-West2 (NGA-West2) set of GMMs, indicating that the fully correlated assumption may be adequate for many applications. The multivariate PC method can be used to evaluate the effects of the partial correlation of the GMMs for sets of GMMs that are different from the NGA-West2 GMMs. [ABSTRACT FROM AUTHOR]

We document the first use of fragile geologic features (FGFs) to set formal design earthquake motions for a major existing engineered structure. The safety evaluation earthquake (SEE) spectrum for the Clyde Dam, New Zealand (the mean 10,000 yr, ka, return period response spectrum) is developed in accordance with official guidelines and utilizes constraints provided by seven precariously balanced rocks (PBRs) located 2 km from the dam site and the local active Dunstan fault. The PBRs are located in the hanging wall of the fault. Deterministic PBR fragilities are estimated from field measurements of rock geometries and are the dynamic peak ground accelerations (PGAs) required for toppling. PBR fragility ages are modeled from 10Be cosmogenic isotope exposure dating techniques and are in the range of 24-66 ka. The fragility ages are consistent with the PBRs having survived at least two large Dunstan fault earthquakes. We develop a PGA-based fragility distribution from all of the PBRs, which represents the cumulative toppling probability of a theoretical random PBR as a function of PGA. The fragility distribution is then used to eliminate logic-tree branches that produce PGA hazard curves that would topple the random PBR with a greater than 95% probability (i.e., less than 5% survival probability) over a time period of 24 ka (youngest PBR fragility age). The mean 10 ka spectrum of the remaining hazard estimates is then recommended as the SEE spectrum for the dam site. This SEE spectrum has a PGA of 0.55g, which is significantly reduced from the 0.96g obtained for a preliminary version of the SEE spectrum. The reduction is due to the combined effects of the PBR constraints and a substantial update of the probabilistic seismic hazard model. The study serves as an important proof-of-concept for future applications of FGFs in engineering design. [ABSTRACT FROM AUTHOR]

The traditional approach used to incorporate site response into the ground-motion hazard analysis is to compute a design spectrum for a rock-site condition and then propagate the rock motion from the base of the soil model to the surface. The main limitation with this approach is that it can be inconsistent with the ground-motion models (GMMs) used to develop the input rock motion. The VS profile implicit in the GMMs is unlikely to match the site-specific VS profile (value and gradient), because the GMMs were developed for ground motions from different VS profiles over large regions and are unlikely to match the profile of any one site well. This article presents the VS profile correction method for developing surface ground motions as an alternative to the soil-over-rock approach routinely used in earthquake engineering practice. This approach is similar to the standard soil-over-rock analysis, but uses different input motions and involves performing two site response analyses' one for the generic profile associated with the GMM(s) and one for the site-specific profile--then applying the ratio of the two site response analysis results to correct the design spectrum for the reference site condition developed using the GMMs. Two example applications are included to illustrate the VS profile correction methodology as well as some of the challenges that may arise when doing so. [ABSTRACT FROM AUTHOR]

Site response in ground-motion prediction equations (GMPEs) is primarily characterized as a function of the time-averaged shear-wave velocity over the top 30 m of the site profile (VS30). Although the use of VS30 as a main site-response predictor parameter is practical, GMPE site adjustments to different target regions or target site conditions require characterization of the GMPE's rock-site response in terms of host VS profile and host kappa. Regional VS profiles and kappa values have been traditionally used to characterize GMPEs host site conditions. These regional site properties may not reflect the average site response in GMPEs. We present a methodology, based on the quarter-wavelength principles, that allows the derivation of GMPE-compatible host 1D VS profiles and kappa values. This methodology is applied to the Next Generation Attenuation-West2 (NGA-West2) GMPEs to derive GMPE-specific host VS profiles and kappa for western United States (WUS) site conditions with VS30 of 360, 490, 620, 760, and 1100 m/s. This application uses, for input, the GMPEs' site response in Fourier amplitude spectra domain relative to a reference VS30 of 1000 m/s and requires an assigned VS profile for the reference site condition. The impact of the choice of reference VS profile on the results is not large. Comparisons of the derived GMPE-specific VS profiles for VS30 of 760 m/s show differences in the host VS profiles among the NGA-West2 GMPEs for the same site condition in WUS. Differences are also observed when comparing the derived GMPE-compatible VS profiles with the commonly used profiles for WUS for VS30 of 760 m/s. These differences highlight the importance of using GMPE-compatible VS profiles and kappa in GMPE adjustments and in site-response analyses. Limitations of this approach for soft site conditions are discussed. [ABSTRACT FROM AUTHOR]

Ground-motion models (GMMs) are developed for peak ground displacement (PGD) and for bandlimited PGD based on strong-motion data that has been filtered as part of standard processing and the total PGD that includes the tectonic deformation as well as the vibratory ground motion. For the bandlimited PGD, we develop conditional ground-motion models (CGMMs) using subsets of the Pacific Earthquake Engineering Research Center Next Generation Attenuation-West2 Project (NGA-W2) database and the National Center for Research on Earthquake Engineering Taiwan Senior Seismic Hazard Analysis Committee level 3 project database. The CGMM approach includes the observed pseudospectral acceleration (PSA(T)) as an input parameter in addition to magnitude and distance. The period of the PSA(T) is used as an input parameter; it is magnitude dependent and is based on the period for which there is the highest correlation between the ln(PGD) and ln(PSA(T)). Two CGMMs are developed: a global model based on the NGA-W2 data and a region-specific model for Taiwan. The conditional PGD models are combined with traditional GMMs for PSA(T) values to develop GMMs for both the median and standard deviation of PGD without the dependence on PSA. A second set of PGD GMMs are developed to correct for two factors: the effect of the high-pass filtering from standard record processing and the stronger large magnitude (M>6.5) scaling due to tectonic deformation. For magnitudes greater than 7, the PGD values from the total PGD GMMs are 2-5 times larger than the bandlimited PGD values based on the strong-motion data sets, but the increase is at very long periods. The appropriate PGD model to use, bandlimited PGD or total PGD, depends on the period range of interest for the specific engineering application. [ABSTRACT FROM AUTHOR]

The Pacific Earthquake Engineering Research Center Next Generation Attenuation‐West2 database is used to derive a new conditional ground‐motion model (CGMM) and a set of scenario‐based models for estimating cumulative absolute velocity (CAV) for earthquakes in shallow crustal tectonic settings. Random‐effects regressions were performed to develop the conditional model, with random effects across different earthquakes. The estimate of CAV is conditioned on the estimated peak ground acceleration (PGA), the time averaged shear‐wave velocity in the top 30 m (⁠VS30⁠), the earthquake magnitude (⁠Mw⁠), and the rupture distance (⁠Rrup⁠). By combining the conditional CAV model with ground‐motion models (GMM) in shallow crustal earthquake zones for PGA, new scenario‐based models are developed for estimating the median CAV and its standard deviation, directly from an earthquake scenario and site conditions. A scenario‐based CAV model captures inherently the complex ground‐motion scaling effects included in the GMMs for spectral accelerations on which it is based on, such as, sediment‐depth effects, soil nonlinearity effects, and regionalization effects. This approach also ensures consistency between the estimated CAV values and a design spectral acceleration response spectrum. The conditional and scenario‐based models to estimate CAV are presented, and trends of the developed scenario‐based models and previous traditional models for CAV are compared. Interestingly, we found a remarkable consistency between scenario‐based and traditional nonconditional CAV models, when the underlain spectral GMM used in the implementation of the scenario‐based model is properly constrained. Finally, we provide examples for the use of the conditional and scenario‐based models in performance‐based earthquake engineering. [ABSTRACT FROM AUTHOR]

The velocity pulse in near-fault ground motions has been used as a key characteristic of damaging ground motions. Characterization of the velocity pulse involves three parameters: presence of the pulse, period of the pulse, and amplitude of the pulse. The basic concept behind the velocity pulse is that a large amount of seismic energy is packed into a short time, leading to larger demands on the structure. An intensity measure for near-fault ground motions, which is a direct measure of the amount of energy arriving in short time, called instantaneous power (IP (T1)), is defined as the maximum power of the bandpass-filtered velocity time series measured over a time interval of 0.5T1, in which T1 is the fundamental period of the structure. The records are bandpass filtered in the period band (0.2T1-3T1) to remove the frequencies that are not expected to excite the structure. Zengin and Abrahamson (2020) showed that the drift is better correlated with the IP (T1) than with the velocity pulse parameters for records scaled to the same spectral acceleration at T1. A conditional ground-motion model (GMM) for the √IP is developed based on the 5%-damped spectral acceleration at T1, the earthquake magnitude, and the rupture distance. This conditional GMM can be used for record selection for near-fault ground motions that captures the key features of velocity pulses and can lead to a better representation of the median and variability of the maximum interstory drift. The conditional GMM can also be used in a vector hazard analysis for spectral acceleration (T1) and IP (T1) that can be used for more accurate estimation of drift hazard and seismic risk. [ABSTRACT FROM AUTHOR]

We present a summary of the Bayless and Abrahamson (2018b) empirical ground-motion model (GMM) for shallow crustal earthquakes in California based on the Next Generation Attenuation-West2 database (Ancheta et al., 2014). This model is denoted as BA18. Rather than the traditional response spectrum GMM, BA18 is developed for the smoothed effective amplitude spectrum (EAS), as defined by the Pacific Earthquake Engineering Research Center (Goulet et al., 2018). The EAS is the orientation-independent horizontal-component Fourier amplitude spectrum of ground acceleration. The model is developed using a database dominated by California earthquakes but takes advantage of crustal earthquake data worldwide to constrain the magnitude scaling and geometric spreading. The near-fault saturation is guided by finite-fault numerical simulations, and nonlinear site amplification is incorporated using a modified version of Hashash et al. (2018). The model is applicable for rupture distances of 0-300 km, M 3.0-8.0, and over the frequency range 0.1-100 Hz. The model is considered applicable for VS30 in the range 180-1500 m/s, although it is not well constrained for VS30 values >1000 m/s. Models for the median and the aleatory variability of the EAS are developed. Regional models for Japan and Taiwan will be developed in a future update of the model. A MATLAB program that implements the EAS GMM is provided in the supplemental content to this article. [ABSTRACT FROM AUTHOR]

A computationally efficient methodology for propagating the epistemic uncertainty in the median ground motion in probabilistic seismic hazard analysis is developed using the polynomial chaos (PC) approach. For this application, the epistemic uncertainty in the median ground motion for a specific scenario is assumed to be lognormally distributed and fully correlated across earthquake scenarios. In the hazard calculation, a single central ground-motion model (GMM) is used for the median along with the epistemic standard error of the median for each scenario. A set of PC coefficients is computed for each scenario and each test ground-motion level. The additional computation burden in computing these PC coefficients depends on the order of the approximation but is less than computing the median ground motion from one additional GMM. With the PC method, the mean and fractiles of the hazard due to the epistemic uncertainty distribution of the median ground motion are computed as a postprocess that is very fast computationally. For typical values of the standard deviation of epistemic uncertainty in the median ground motion (<0.2 natural log units), the methodology accurately estimates the epistemic uncertainty distribution of the hazard over the 1%-99% range. This full epistemic range is not well modeled with just a small number of GMM branches uses in the traditional logic-tree approach. The PC method provides more accuracy, faster computation, and reduced memory requirements than the traditional approach. For large values of the epistemic uncertainty in the median ground motion, a higher order of the PC expansion may be needed to be included to capture the full range of the epistemic uncertainty. [ABSTRACT FROM AUTHOR]

Conditional ground-motion models (CGMMs) for estimating Arias intensity (IA) for earthquakes in subduction zones are developed. The estimate of IA is conditioned in these models on the estimated peak ground acceleration (PGA), the spectral acceleration at T=1 s (SA1), time-averaged shear-wave velocity in the top 30 m (VS30), and magnitude (Mw). Random-effects regressions are used to develop CGMMs for Japan, Taiwan, South America, and New Zealand. By combining the conditional models of IA with the ground-motion models (GMMs) for PGA and SA1, the conditional models are converted to scenario-based GMMs that can be used to estimate the median IA and its standard deviation directly for a given earthquake scenario and site conditions. The conditional scaling approach ensures the estimated IA values are consistent with a design spectrum that may correspond to above-average spectral values for the controlling scenario. In addition, this approach captures the complex ground-motion scaling effects found in GMMs for spectral acceleration, such as sediment-depth effects, soil nonlinearity effects, and regionalization effects, in the developed scenario-based models for IA. Estimates from the new scenario-based IA models are compared to those from traditional GMMs for IA in subduction zones. [ABSTRACT FROM AUTHOR]

With an increasing number of strong-motion records over the past decade, it has become clear that there are significant differences in ground-motion scaling even within relatively small regions such as California. These differences are not modeled in typical ground-motion models (GMMs) that are based on the ergodic assumption. By including systematic source, path, and site effects in fully nonergodic GMMs, it is possible to reduce the value of the aleatory variability by about 30%-40%; however, to use this reduced aleatory variability, it is important to account for the epistemic uncertainty in the nonergodic terms. We build a nonergodic GMM for California that explicitly accounts for nonergodic source, path, and site effects by combining the results and methods outlined by Dawood and Rodriguez-Marek (2013) and Landwehr et al. (2016). The deviation of the systematic terms form the ergodic mean is constrained by observed ground-motion data. The uncertainty of the systematic terms is tracked and explicitly taken into account. The uncertainty becomes small in the vicinity of observed data and large in regions that lack data. We calculate seismic hazard for three different sites in California using the nonergodic GMM. The results show that the mean hazard can change significantly for sites that have data in the vicinity compared to an ergodic hazard analysis, whereas the epistemic uncertainty associated with hazard results increases for sites with no observed data as compared to the ergodic approach. This presents the first fully nonergodic seismic hazard analysis with the systematic effects based on observed ground-motion and fully including their uncertainty. [ABSTRACT FROM AUTHOR]

An empirical ground-motion model (GMM) is presented for the interfrequency correlation of normalized residuals, epsilon (ε), for smoothed Fourier amplitude spectra (FAS). The interfrequency correlation of ε (ρε) model is developed for the smoothed effective amplitude spectrum (EAS), as defined by Pacific Earthquake Engineering Research Center (PEER; Goulet et al., 2018). The EAS is the orientation-independent horizontal-component FAS of ground acceleration. Ground-motion data are from the PEER Next Generation Attenuation-West2 database (Ancheta et al., 2014), which includes shallow crustal earthquakes in active tectonic regions. The normalized residuals are obtained from the Bayless and Abrahamson (2018b) GMM and are partitioned into between-event, between-site, and within-site components, and a model is developed for the total correlation between frequencies. The total correlation model features a two-term exponential decay with the natural logarithm of frequency. At higher frequencies, the model differs substantially from previously published models, in which the ground-motion smoothing technique used has a large effect on the resulting correlations. The empirical ρε is not found to have statistically significant magnitude, distance, site parameter, or regional dependence, although potential regional variations should be studied further. The model is applicable for crustal earthquakes in active tectonic regions worldwide, for rupture distances of 0-300 km, M 3.0-8.0, and over the frequency range 0.1-24 Hz. Tables for the total correlation model coefficients and covariance matrices are provided in the Ⓔ supplemental content to this article. [ABSTRACT FROM AUTHOR]

A new wavenumber-domain methodology to model surface-slip profiles and generate potential displacement profiles for use in probabilistic fault-rupture hazard analysis is developed. The benefits of this approach are it captures the correlation of the surface-slip variability along a strike, and it avoids the surface-rupture length (SRL) normalization. A regularized Fourier transform (RFT) approach is used to compute the Fourier spectra from uneven and biased sampling, typical of surface-slip data sets. The wavenumber amplitude spectrum for surface displacements is modeled by a functional form based on the shape of the Butterworth filter. The proposed RFT approach is validated using synthetic data sets with known model parameters, which are downsampled to be consistent with the sampling in empirical surface-rupture data sets. Preliminary models for the scaling of the amplitude and phase derivative as a function of the SRL are developed using a subset of the earthquakes compiled by Wesnousky (2008). The analyzed events range from magnitude 6.1 to 7.9 and include both single and multisegment ruptures. Compared with other published models, the wavenumber-spectrum method leads to narrower tails of the slip distribution, which is important for probabilistic fault displacement analyses at long-return periods. Near the center of the rupture, the wavenumber-spectrum method gives slip distributions that are consistent with the distributions from the empirical data, but at the ends of the rupture, the wavenumber-spectrum method underestimates the range of the slip. This discrepancy may reflect limitations of the current data sets in terms of sampling of the slip near the ends of the ruptures. Improved surface-rupture data sets are currently being compiled and will provide improved constraints at the ends of the ruptures. [ABSTRACT FROM AUTHOR]

Typical ground-motion prediction equations (GMPEs) do not account for systematic path effects, which leads to an overestimation of aleatory variability. We provide an update to the Californian GMPE model of Abrahamson et al. (2014) that explicitly accounts for path effects in California by replacing the anelastic attenuation coefficient with a regionally varying one. The updated attenuation model is based on the approach of Dawood and Rodriguez-Marek (2013). Accounting for path effects leads to a smaller value of the aleatory variability, and results in different median predictions, depending on source and site location. The model is cast as a Bayesian hierarchical model, which allows one to capture the epistemic uncertainties in the anelastic attenuation coefficients. We show that it is important to account for the uncertainty in the attenuation coefficients when using the model for prediction. The differences in attenuation decrease with increasing spectral period. The updated attenuation model is developed with respect to the GMPE of Abrahamson et al. (2014) but can be easily extended for other models and other regions as well. [ABSTRACT FROM AUTHOR]

We demonstrate that the interperiod correlation of epsilon (ρε) is an essential component of ground motions for capturing the variability of structural response that is needed in seismic fragility and seismic risk studies. To perform this demonstration, we generate large suites of scenario ground‐motion simulations using the point‐source (PS) stochastic method. Two compatible suites of simulations are developed; one suite without any imposed interperiod correlation, and one with Fourier amplitude ε sampled from a multivariate normal distribution with covariance specified by our empirical model. We illustrate how the effect of ρε propagates through the structural response and into seismic risk calculations. Without the adequate interperiod correlation of ground motions, variability in the structural response may be underestimated. This leads to structural fragilities that are too steep (underestimated dispersion parameter β⁠) and propagates to nonconservative estimates of seismic risk. To assess the current state of multiple existing ground-motion simulation methods, we evaluate their interfrequency correlations and compare with empirical models. None of the six finite-fault simulation methods tested adequately capture the interperiod correlations over the entire frequency range evaluated, although several of the methods show promise, especially at low frequencies. Using the correlation of the Fourier spectra provides the developers of the simulation methods better feedback in terms of how they can modify their methods, which is unclear when using response spectra comparisons. Based on the relative differences in the correlations of the Song (2016) source method, it appears that changes to the rupture generator may be the most promising approach to modifying the long-period interperiod correlations. [ABSTRACT FROM AUTHOR]

Ground-motion prediction equations (GMPEs) are critical elements of probabilistic seismic hazard analysis (PSHA), as well as for other applications of ground motions. To isolate the path component for the purpose of building nonergodic GMPEs, we compute a regional GMPE using a large dataset of peak ground accelerations (PGAs) from small-magnitude earthquakes (0.5=M=4.5 with >10,000 events, yielding ~120,000 recordings) that occurred in 2013 centered around the ANZA seismic network (hypocentral distances =180km) in southern California. We examine two separate methods of obtaining residuals from the observed and predicted ground motions: a pooled ordinary least-squares model and a mixed-effects maximum-likelihood model. Whereas the former is often used by the broader seismological community, the latter is widely used by the ground-motion and engineering seismology community. We confirm that mixed-effects models are the preferred and most statistically robust method to obtain event, path, and site residuals and discuss the reasoning behind this. Our results show that these methods yield different consequences for the uncertainty of the residuals, particularly for the event residuals. Finally, our results show no correlation (correlation coefficient [CC] <0.03) between site residuals and the classic site-characterization term VS30, the time-averaged shear-wave velocity in the top 30 m at a site. We propose that this is due to the relative homogeneity of the site response in the region and perhaps due to shortcomings in the formulation of VS30 and suggest applying the provided PGA site correction terms to future ground-motion studies for increased accuracy. [ABSTRACT FROM AUTHOR]