Ground Motion Model Research Articles

3D Wave Propagation Simulations of Mw 6.5+ Earthquakes on the Tacoma Fault, Washington State, Considering the Effects of Topography, a Geotechnical Gradient, and a Fault Damage Zone

ABSTRACT We simulate shaking in Tacoma, Washington, and surrounding areas from Mw 6.5 and 7.0 earthquakes on the Tacoma fault. Ground motions are directly modeled up to 2.5 Hz using kinematic, finite-fault sources; a 3D seismic velocity model considering regional geology; and a model mesh with 30 m sampling at the ground surface. In addition, we explore how adjustments to the seismic velocity model affect predicted shaking over a range of periods. These adjustments include the addition of a region-specific geotechnical gradient, surface topography, and a fault damage zone. We find that the simulated shaking tends to be near estimates from empirical ground-motion models (GMMs). However, long-period (T = 5.0 s) shaking within the Tacoma basin is typically underpredicted by the GMMs. The fit between simulated and GMM-derived short-period (T = 0.5 s) shaking is significantly improved with the addition of the geotechnical gradient. From comparing different Mw 6.5 earthquake scenarios, we also find that the response of the Tacoma basin is sensitive to the azimuth of incoming seismic waves. In adding surface topography to the simulation, we find that average ground motion is similar to that produced from the nontopography model. However, shaking is often amplified at topographic highs and deamplified at topographic lows, and the wavefield undergoes extensive scattering. Adding a fault damage zone has the effect of amplifying short-period shaking adjacent to the fault, while reducing far-field shaking. Intermediate-period shaking is amplified within the Tacoma basin, likely due to enhanced surface-wave generation attributable to the fault damage zone waveguide. When applied in the same model, the topography and fault damage zone adjustments often enhance or reduce the effects of one another, adding further complexity to the wavefield. These results emphasize the importance of improving near-surface velocity model resolution as waveform simulations progress toward higher frequencies.

The ShakeMap Atlas of Historical Earthquakes in Italy: Configuration and Validation

Abstract Italy has a long tradition of studies on the seismic history of the country and the neighboring areas. Several archives and databases dealing with historical earthquake data—primarily intensity data points—have been published and are constantly updated. Macroseismic fields of significant events are of foremost importance in assessing earthquake effects and for the evaluation of seismic hazards. Here, we adopt the U.S. Geological Survey (USGS)-ShakeMap software to calculate the maps of strong ground shaking (shakemaps) of 79 historical earthquakes with magnitude ≥6 that have occurred in Italy between 1117 and 1968 C.E. We use the macroseismic data published in the Italian Macroseismic Database (DBMI15). The shakemaps have been determined using two different configurations. The first adopts the virtual intensity prediction equations approach (VIPE; i.e., a combination of ground-motion models [GMMs] and ground-motion intensity conversion equations [GMICEs]; Bindi, Pacor, et al., 2011; Oliveti et al., 2022b). The second exploits the intensity prediction equations (IPE; Pasolini, Albarello, et al., 2008; Lolli et al., 2019). The VIPE configuration has been found to provide more accurate results after appraisal through a cross-validation analysis and has been applied for the generation of the ShakeMap Atlas. The resulting maps are published in the Istituto Nazionale di Geofisica e Vulcanologia (INGV) ShakeMap (see Data and Resources; Oliveti et al., 2023), and in the Italian Archive of Historical Earthquake Data (ASMI; see Data and Resources; Rovida et al., 2017) platforms.

Toward multivariate fragility functions for seismic damage and loss estimation of high‐rise buildings

AbstractData‐driven models for seismic damage and loss assessment of buildings have become more common in recent years due to the availability of large repositories of recorded and synthetic ground motions coupled with structural response simulation data. This paper explores the benefits of using bivariate and multivariate fragility functions to estimate earthquake‐induced damage and economic loss in high‐rise buildings. The dataset used in this study encompasses 15,000 simulations of modern high‐rise reinforced concrete shear wall buildings ranging from eight to 24 stories which are subjected to ground motion records at five different intensity levels. The proposed functions are conditioned on average spectral accelerations and ground motion significant duration. The results indicate that bivariate fragility functions improve damage state prediction success (Brier score) by 16%, and multivariate fragility functions by 24% relative to conventional univariate functions (standard of practice). To develop multivariate functions, nominal and ordinal probit regression models are fit to the dataset. While both models yield satisfactory predictive performance, ordinal functions can lead to a 15% reduction in misclassified collapse instances, that is, the minority class. Univariate functions tend to overestimate seismic losses at lower intensity levels while underestimating them at higher intensities. These loss estimates are significantly improved when bivariate or multivariate building fragility functions are used. Given the increase in the use of physics‐based ground motion simulations and/or multi‐variate ground motion models, from which multiple intensity measures can be extracted, a shift toward a more complex representation of fragility functions, for example, multivariate curves, is necessary and inevitable. The proposed functions are used to evaluate the performance of a portfolio of modern high‐rise reinforced concrete shear wall buildings at four sites across the Seattle, Washington metropolitan area under a potential magnitude‐9 Cascadia subduction zone earthquake scenario. The results indicate that the proposed functions can be beneficial in enhancing damage state predictions and loss estimates at a regional scale.

Special issue of the bulletin of earthquake engineering on non-ergodic ground motion models

Special issue of the bulletin of earthquake engineering on non-ergodic ground motion models

A two-stage uncertainty quantification framework for reliability and sensitivity analysis of structures using the probability density evolution method integrated with the Fréchet-derivative-based method

In this work, a novel Fréchet-derivative-based global sensitivity analysis is incorporated into the probability density evolution method for the simultaneous reliability and sensitivity analysis of structures. The two methods are synthesized and realized under a two-stage uncertainty quantification framework. Fundamental and numerical algorithms of the method are described, which is validated by a benchmark problem with theoretical solutions. Then it is applied on studying stochastic seismic responses of a real-world reinforced concrete structure of 288 m high. Results demonstrate that the response characteristics of the structure will be greatly changed when both uncertainties from the ground motions and structural parameters are considered, e.g., the failure probability will be enlarged by 1∼2 orders of magnitude. Besides, contrary to the popular opinion that the uncertainty of structural parameters is trivial compared to that of parameters in the ground-motion model, the importance measures of the structural parameters can be greater than those of the parameters in the ground-motion model by a factor of 2. when the coupling effect of randomness and nonlinearity of structural materials becomes dramatic. Some issues to be further outlined are also discussed.

Constraining earthquake fault sources through the use of intensity data and seismic scenarios: application to the Betic Cordillera (South Spain)

Macroseismic observations can be useful to study pre-instrumental earthquakes when paleoseismological analysis are not viable for various reasons (e.g., erosion or lack of sedimentation). The analysis of the distribution of the macroseismic intensity data points and the reports about geological effects has been shown as a tool that may provide meaningful information to localize the fault source of a historical earthquake. Using this approach, we have studied two earthquakes in the Betic Cordillera (South Spain), the 1804 Dalías and the 1680 Málaga events, and we have used the 2011 Lorca earthquake as a test subject to calibrate the methodologies. During the calibration process, we also find the best performing combination of ground-motion models and ground-motion-to-intensity-conversion equations for generating seismic scenarios in this area. Even though the results for the Málaga earthquake were not conclusive, our methodology successfully identified the most likely source for the Dalías earthquake: a conjunct rupture of the Loma del Viento and Llano del Águila Faults.

Uncertainties in Broadband Determination of the High-Frequency Spectral Decay, Kappa, in Eastern Canada

ABSTRACT Kappa (the high-frequency spectral decay slope at near-source distances; often referred to as κ0) is determined at 25 seismograph stations in Eastern Canada using broadband ground-motion modeling approaches. The database comprises Fourier spectra (effective amplitude spectrum for the horizontal component and the vertical component, 0.8–40 Hz) computed from 3318 earthquakes of moment magnitude M 1.5–5 recorded on stations within 150 km. Average kappa values for bedrock sites, having shear-wave velocities from 850 to 2400 m/s, are highly variable, ranging from −29 to +21 ms (horizontal) and −28 to +11 ms (vertical), but appear on average to be near-zero. The values obtained are sensitive to methodology, especially the necessary adjustments to the spectra to account for site amplification effects. Kappa values do not appear to correlate well with site parameters such as rock shear-wave velocity, average shear-wave velocity in the upper 30 m, primary wave velocity, site class, type and age of rock, or instrument housing. This lack of correlation may reflect the noted sensitivities to methodological factors. We conclude that kappa values in rock environments are not reliably estimated from such proxies and should be determined from recorded ground motions at a given location. On average, there is little evidence of significant high-frequency attenuation on rock sites beyond that already accounted for in ground-motion modeling by the empirical parameterization of regional Q-related path effects.

Performance evaluation of machine learning techniques in predicting cumulative absolute velocity

Cumulative absolute velocity (CAV) is a powerful intensity measure for quantifying potential earthquake damage to structures. Machine learning (ML) methods can provide more accurate and reliable predictions of cumulative absolute velocity due to handling nonlinear relationships, adaptability to changing conditions, automation, efficiency, and the potential for real-time predictions. This study aims to identify machine learning regressions with the highest accuracy for CAV prediction. Several supervised machine learning algorithms were applied and comprehensively compared for performance and accuracy in CAV prediction using the recently compiled Turkish strong-motion database. Support Vector Machine, Linear Regression, Random Forest, Artificial Neural Network, Bayesian Ridge Regression, and Gradient Boosting algorithms were evaluated and compared with traditional Ground Motion Models (GMMs).Two new datasets including 24,667 strong-motion recordings from Turkiye along with global strong-motion recordings are used to build machine learning models. The first dataset contains all recordings of events with 3.5≤MomentMagnitude(Mw)≤7.6, while the second dataset contains only recordings with Mw≥5.5. Moreover, feature selection and outlier detection were performed as preprocessing steps to choose the best of seven CAV estimator parameters in order to boost the ML model performance. To measure the performance of ML methods five evaluation metrics were utilized which are mean square error (MSE), root mean squared error (RMSE), mean absolute error (MAE), mean absolute percent error (MAPE), and correlation coefficient (R).Comparative assessment of the machine learning algorithms suggests that models trained by Mw≥5.5 dataset are quite successful in CAV prediction compared to predictive models trained by the 3.5≤Mw≤7.6 dataset. The result proves that the Gradient Boosting models significantly outperform the other machine learning algorithms in terms of R and RMSE. Machine learning techniques are more successful with user-selected estimators representing the key components that make up earthquake recordings. Finally, the machine learning-based CAV prediction models for Turkiye are compared with available CAV GMMs, and it is observed that the machine learning-based models can predict CAV as successfully as GMMs if there are a sufficient number of recordings for training machine learning algorithms.

Evaluating the effectiveness of ground motion intensity measures through the lens of causal inference

AbstractWhen solving the performance‐based earthquake engineering (PBEE) integral, the engineering demand parameters (EDPs) are assumed to be independent of the “upstream” parameters used in ground motion models (e.g., magnitude and source‐to‐site distance) after conditioning on the intensity measure (IM). This paper formulates a methodology for evaluating this conditional independence assumption through the lens of causal inference (CI). From a causal perspective, the effect of an upstream parameter on the EDP of interest is partially mediated by the IM with the remainder having a direct influence on the EDP. An IM is judged to be desirable (from a conditional independence standpoint) if the mediated effect of the upstream parameter is maximized, which implies that the direct effect is minimized. In the language of causal inference (CI), the IM, EDP and upstream parameters are described as the “treatment”, “outcome” and “confounding” variables, respectively. It then follows that the best performing IM is the one that maximizes the effect on the EDP after controlling for the upstream parameters. A semi‐parametric model that employs double machine learning is used to estimate the causal effect. The methodology is demonstrated through a case study application utilizing the responses from five special steel moment frames analyzed using 240 site‐agnostic ground motions. Compared to sufficiency‐based assessments, the casual inference method produces findings that are more explainable using structural dynamics principles and invariant to the number of ground motions used in the evaluation.

Impact of ground motion directionality (RotDnn) on the coupled and uncoupled inelastic response of RC circular cantilever columns

Directionality in the representation of earthquake demand for structural seismic design has surfaced as a subject of debate in recent years. Design spectra, as defined in building and bridge codes, account for directionality by considering the peak response in all possible orientations of the motion using the RotDnn measure, where “nn” is the percentile of the peak response. Current seismic hazard maps are based on ground motion models that use the RotD50 spectra (median peak response). However, since 2009, building codes have adopted RotD100 spectra (maximum peak response), raising concern among researchers and engineers. The first objective of this study is to evaluate the impact of design spectra definition, RotD50 or RotD100, on the bidirectional inelastic response of azimuth-independent RC systems. Upcoming updates to seismic hazard maps highlight the need of understanding the implication of this choice in bridge design. While previous research focused on the relationship between RotD50 and RotD100, this work assesses the impact of each definition on the inelastic seismic response of RC circular columns designed following the Direct Displacement-Based Design approach and verified through nonlinear time history analyses (NTHA) using ground motions from shallow crustal active and subduction zone regions. The ratios of NTHA to design displacement confirm that RotD100 spectra should be used to design azimuth-independent RC systems and provide the first known verification of DDBD for bidirectional loading (second objective). These ratios are a function of ductility level, tectonic regime, effective period, and coupling (which is the third objective). Overall results show that RC circular cantilever columns designed to RotD100 spectra show less deviation from the expected design displacement than columns designed to RotD50 spectra. This study presents the first step in resolving the ongoing debate over spectra definition and provides recommendations for displacement demand estimations for response spectra-based design approaches.

Lifetime response of a liquefiable soil foundation-embankment system subjected to sequences of mainshocks and aftershocks

During their typical design working life, structures are subjected to multiple sequential earthquakes that are divided into clusters of mainshocks and aftershocks. In consequence, the induced seismic damage accumulates due to these several events in each cluster. On the other hand, the Performance Based Earthquake Engineering (PBEE) methodology presents limitations in accounting for the damage issued from multiple events and the fragility curves represent the failure probability only in one event of a given intensity.For this purpose, this work studies the response of a given structure subjected to sequences of mainshocks–aftershocks during its lifetime. The used time histories (mainshocks) were stochastically generated from a synthetic ground motion model, whereas the aftershocks were generated from the Branching Aftershock Sequence (BASS) model. The cumulative damage measure of the embankment is calculated after the tested sequences. More importantly, its lifetime distribution is estimated and compared with previous results. Finally, to be compatible with the PBEE methodology, the fragility evolution of the embankment over its lifetime was calculated as to emphasize its evolution with the loading history in the soil.

Seismic Hazard in Greece: A Comparative Study for the Region of East Macedonia and Thrace

Greece is located in one of the most seismically active regions in Europe. Many seismic hazard studies have been performed for various sites around Greece, at a regional or local scale. However, the latest national seismic hazard map, currently used for the seismic design of buildings and infrastructure, was published in 2000 and has not been updated since then. In light of recent advances in seismic source and ground motion modeling, the present study focuses on a comparative Probabilistic Seismic Hazard Assessment (PSHA) for the region of East Macedonia and Thrace (EMTH), located in Northern Greece. Various seismic source models are implemented and compared against an updated earthquake catalog to form the necessary source model logic tree. The ground motion logic tree is composed of Ground Motion Prediction Equations (GMPEs), which have been proven suitable for implementation in Greece. PSHA results are presented for the most important cities of East Macedonia and Thrace in a comparative way, which highlights the variability of the seismic hazard among the various seismic source models. An updated seismic hazard map of the study area is proposed, and a comparative disaggregation analysis is performed to estimate the earthquake scenarios with the largest contribution to the seismic hazard.

Ground-Motion Model for Hard-Rock Sites by Correction of Surface Recordings (Part 1): Comparison of Site-Response Estimates at KiK-Net Sites

ABSTRACT Site-specific seismic hazard assessment involves the prior knowledge of (1) the input ground motion at the local bedrock and (2) the site response. In this article and its companion, we address the deconvolution approach to obtain a reference ground-motion model, which consists of removing site effects from surface ground-motion recordings. Laurendeau et al. (2018) applied this approach on the KiK-net network with site response from 1D SH-wave (1DSH) simulations, calculated using the VS profiles available for most sites. Indeed, this approach presents several limitations with 1DSH site response if it is considered to be applied to other networks, especially in the European context. First, the approach requires identification of sites with dominant 1D effects. Second, it needs the presence of accurately measured VS profiles. In this context, we propose to derive deconvolved ground-motion models using site response from generalized inversion techniques () for two main reasons. The first reason is that the GIT delivers empirical site response for all types of sites, conditioned by the presence of sufficient amount of data, and the second is that it reduces the need for VS profiles. We focus on the estimation of site effects from different approaches and present a methodology to obtain reliable site terms from GIT based on the experience from previous studies. We also introduce and detail the difference between absolute and relative site response, which mainly depends on the chosen reference. We estimate and compare site response for the KiK-net stations with different methods, that is, empirical and theoretical 1DSH. We also conclude a list of 1D sites based on comparisons between theoretical and empirical estimates of site response. The results obtained in this article will be the primary input for the deconvolution approach applied in the companion article.

Ground-Motion Model for Hard-Rock Sites by Correction of Surface Recordings (Part 2): Correction, Mixed-Effects Regressions, and Results

ABSTRACT In the framework of site-specific seismic hazard assessment, the definition of reference motion is a crucial step. Reference motion is generally associated with hard-rock conditions, characterized by S-wave velocity exceeding 1500 m/s. However, ground motion recorded at sites with such conditions is poorly represented in existing strong-motion databases. Thus, the validity domains of most empirical ground-motion prediction equations (GMPEs) are not representative of reference rock conditions. To overcome this limitation and assess ground motion at reference conditions, the so-called “deconvolution approach” was proposed by Laurendeau et al. (2018) to correct surface recordings from theoretical 1DSH site response before GMPE developments. With the same purpose, in this article, we propose to apply the deconvolution approach using empirical site-response estimates as an alternative to theoretical ones. Using the Kiban–Kyoshin network (KiK-net) data, we estimate empirical site responses at KiK-net stations using generalized inversion techniques in addition to those from 1DSH numerical simulations, as presented in the companion article. Finally, a reference ground-motion model (RGMM) is determined based on empirically deconvolved ground motions. The advantage of using empirical rather than 1DSH site responses in the deconvolution approach is that in the former case the RGMM can be built based on records from an extensive set of sites, whereas the latter case is restricted to well-characterized sites with dominant 1D behavior. This makes the proposed approach easily exportable to different regions of the world, where precise site characterizations are not systematically available, and the knowledge of site behavior is limited.

An Empirical Spectral Ground-Motion Model for Iran Using Truncated Iranian Strong-Motion Database Enriched by Near-Field Records

ABSTRACT An updated strong-motion database of the Iranian earthquakes has been used to propose empirical equations for the prediction of peak ground velocity (PGV), peak ground acceleration (PGA), and 5%-damped Spectral Accelerations (SA) up to0.0 s for geometric mean of horizontal components. Some records from the NGA-West2 are added to the database to enrich it at near source distances for large magnitude events. Lack of data in the near source distances causes less accuracy in previous Iranian Ground Motion Models (GMMs) in comparison with the current study. In this work, the regression analyses have been performed on a truncated database which causes to obtain unbiased results. We used 3015 acceleration time series from 594 earthquakes after truncation of data to develop a new GMM. The provided model is valid for Joyner-Boore distances ranging from 0 km to80 km and magnitudes ranging from 4 to 7.9 and Vs30 ranging from50 m/s to500 m/s.

Uncertainties in Intensity-Based Earthquake Magnitude Estimates

Abstract Estimating the magnitude of historical earthquakes is crucial for assessing seismic hazard. Magnitudes of early-instrumental earthquakes can be inferred using a combination of instrumental records, field observations, and the observed distribution of shaking intensity determined from macroseismic observations. For earthquakes before 1900, shaking intensity distributions often provide the only information to constrain earthquake magnitude. Considerable effort has been made to develop methods to estimate the magnitude of moderate-to-large historical earthquakes using shaking intensities derived from macroseismic data. In this study, we consider earthquakes in California with known instrumental magnitudes to explore uncertainties in estimating the magnitude of historical earthquakes from intensity information alone. We use three California-specific intensity prediction equations (IPEs) and an IPE based on a global ground-motion model (GMM) to determine optimum intensity-based magnitudes for 33 moderate-to-large California earthquakes between 1979 and 2021. Intensity-based magnitudes are close to instrumental magnitudes on average. However, intensity-based magnitudes for individual events differ by as much as 2.2 magnitude units from instrumental magnitudes. This result reflects the weak dependence of ground motions and shaking intensities on moment magnitude and their strong dependence on stress drop. Considering the intensity distributions of the 1906 San Francisco and 1989 Loma Prieta earthquakes, we show that information that could constrain rupture length is discarded when considering only the 2D decay of intensity with distance. We also show that ground-motion intensity conversion equations used in a GMM-based approach may cause a systematic overestimation of large historical earthquake magnitudes. This study underscores both the reducible and potentially irreducible uncertainties associated with using intensity data to estimate magnitudes of historical earthquakes using IPEs and highlights the value of using additional information to constrain rupture dimensions. Using intensity observations alone, moment magnitude uncertainties are typically on the order of a full unit.

Characterization and modeling of ground motion at depth in soft sedimentary rocks: Application to the Swiss Molasse Basin

The level of earthquake motion observed on the ground surface differs from the shaking at locations buried at a depth. Characterization of the underground shaking is important for the local seismic hazard assessment at depth which is an insufficiently investigated topic so far. Advancements in the prediction of the ground motion at depth are especially important for the design of deep geological disposals of nuclear waste, buildings with deep foundations, or studies focused on soil-structure interactions. In this paper, we analyze site-specific transfer functions that relate ground motions on the surface to that at a depth at sites located within soft sedimentary rocks of the Swiss Molasse Basin. We first evaluate empirical surface-to-borehole amplification functions at six borehole sites, compare them with predictions by a theoretical model, and characterize the high-frequency surface-to-borehole amplification. Next, we perform full-waveform prediction of ground motion at depth from surface recordings of seven significant regional earthquakes with ML > 4. The comparison of predicted and observed acceleration waveforms shows a high level of similarity in a broad frequency range and well-predicted values of PGA, PGV, and response spectra. Finally, we model a scenario earthquake for 9975 years return period at a test site, and we predict associated broadband waveforms at depth. By the latter, we demonstrate that our method to predict ground motions at depth can be used as a basis for the site-specific seismic hazard of deep geological disposals of nuclear waste.

A ground motion model for orientation-independent inelastic spectral displacements from shallow crustal earthquakes

The peak inelastic displacement of a single-degree-of-freedom (SDOF) system is an efficient ground motion (GM) intensity measure (IM) for estimating seismic demands in structures and infrastructures. Most ground motion models (GMMs) that predict this IM are developed to estimate the arbitrary or geometric mean of the horizontal GM components obtained from the two as-recorded orientations. In this study, the median and maximum directional inelastic spectral displacements, denoted as Sdi,RotD50and Sdi,RotD100, respectively, were considered as IMs to develop GMMs. These orientation-independent measures of horizontal motion were calculated by rotating the GMs through all non-redundant rotation angles and have the advantage of removing the sensor orientation as a contributor to overall uncertainty. To do this, several SDOF systems were considered using a subset of the NGA-West2 database to fit GMMs for these IMs. A set of functional forms was developed using a mixed-effects regression approach. The predictor variables were the elastic period, T, the strength ratio, R, and a set of seismological GM causal parameters (i.e. magnitude, distance, soil condition, and so on). Comparison with existing GMMs that consider either inelastic spectral displacement or directionality is provided to highlight key differences and developments. In addition, the response directionality, defined as the ratio Sdi,RotD100/ Sdi,RotD50, was observed to be notably impacted by the strength ratio and elastic period, which has not been discussed in the literature to date. Overall, this GMM has the advantage of quantifying ground motion intensity via an efficient IM in Sdi, which can better highlight some fundamental issues surrounding the directionality of GMs and allow for more informative risk estimates.

Methodology for Including Path Effects Due to 3D Velocity Structure in Nonergodic Ground-Motion Models

ABSTRACT 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.

Ground-motion model for Housner’s spectrum intensity based on a novel hybrid-scenario approach

We use a novel hybrid-scenario approach to develop a ground-motion model (GMM) for Housner’s spectrum intensity ( SI) using estimates of pseudo-spectral acceleration ( PSA) from the authors existing GMMs based on a scenario approach proposed in the literature and predictor variables from the same database used to develop the PSA GMMs. These estimates of SI are used together with the predictor variables to develop a hybrid-scenario GMM using mixed-effects regression analysis. Because the GMM is based on predicted values of PSA, the aleatory variability from the regression is not indicative of the actual variability of observed values of SI. Instead, a hybrid-scenario model for magnitude-dependent between-event, within-event, and total aleatory standard deviations is derived from the PSA GMMs using the scenario approach. The predicted values of SI and its standard deviations from the hybrid-scenario model are found to be relatively consistent with the residuals between these predictions and estimates of SI from the database (i.e. the observations). However, the values of SI predicted from a purely empirical GMM developed directly from the observations are different than those from the hybrid-scenario model by up to a few tens of percent. These differences are the result of an insufficient number of observations resulting from bandwidth limitations of the database that lead to a bias in the empirical results. The near-source standard deviations from the hybrid-scenario GMM are found to be generally consistent with both those from the empirical model and those from the residuals between the hybrid-scenario model and the observations. However, the far-source standard deviations of the hybrid-scenario model are smaller than those from these other methods.