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At least 73 records · Page 4Linked to original sources
USGS2021

NGA-East Ground-Motion Characterization model part I: Summary of products and model development

In this article, we present an overview of the research project NGA-East, Next Generation Attenuation for Central and Eastern North America (CENA), and summarize the key methodology and products. The project was tasked with developing a new ground motion characterization (GMC) model for CENA. The final NGA-East GMC model includes a set of 17 median ground motion models (GMMs) for peak ground acceleration and velocity (PGA, PGV) and response spectral ordinates for periods ranging from 0.01 to 10 s. The NGA-East GMMs are applicable to horizontal components of ground motions on very hard rock, for the moment magnitude range of 4.0–8.2, and distances of up to 1500 km. The aleatory standard deviations of GMMs are also provided for site-specific analysis (single-station standard deviation) and for general probabilistic seismic hazard analyses (PSHA) applications (ergodic standard deviation). In addition, adjustment factors are provided for source depth and hanging-wall effects, as well as for hazard computations at sites in the Gulf Coast Region. During the course of the project, several innovative technologies were developed and implemented to increase the transparency and repeatability of the GMC building process. This involved expanding on a set of candidate median GMMs to define and capture an appropriate range of epistemic uncertainty in ground motions. We also developed a new approach for modeling the aleatory variability that was completely independent of the median GMMs. The development made extensive use of the CENA database but also borrowed data from other parts of the world when relevant and led to an integrated suite of models. Through this repeatable process, epistemic uncertainty could be quantified more objectively than before, relying less on expert opinion. The NGA-East project went through a comprehensive Seismic Senior Hazard Analysis Committee (SSHAC) Level 3 peer review process before its release.

Earthquake Spectra↗
USGS2021

Selection of random vibration theory procedures for the NGA-East project and ground-motion modeling

Traditional ground-motion models (GMMs) are used to compute pseudo-spectral acceleration (PSA) from future earthquakes and are generally developed by regression of PSA using a physics-based functional form. PSA is a relatively simple metric that correlates well with the response of several engineering systems and is a metric commonly used in engineering evaluations; however, characteristics of the PSA calculation make application of scaling factors dependent on the frequency content of the input motion, complicating the development and adaptability of GMMs. By comparison, Fourier amplitude spectrum (FAS) represents ground-motion amplitudes that are completely independent from the amplitudes at other frequencies, making them an attractive alternative for GMM development. Random vibration theory (RVT) predicts the peak response of motion in the time domain based on the FAS and a duration, and thus can be used to relate FAS to PSA. Using RVT to compute the expected peak response in the time domain for given FAS therefore presents a significant advantage that is gaining traction in the GMM field. This article provides recommended RVT procedures relevant to GMM development, which were developed for the Next Generation Attenuation (NGA)-East project. In addition, an orientation-independent FAS metric—called the effective amplitude spectrum (EAS)—is developed for use in conjunction with RVT to preserve the mean power of the corresponding two horizontal components considered in traditional PSA-based modeling (i.e., RotD50). The EAS uses a standardized smoothing approach to provide a practical representation of the FAS for ground-motion modeling, while minimizing the impact on the four RVT properties ( zeroth moment, m0 ; bandwidth parameter, δ ; frequency of zero crossings, fz ; and frequency of extrema, fe ). Although the recommendations were originally developed for NGA-East, they and the methodology they are based on can be adapted to become portable to other GMM and engineering problems requiring the computation of PSA from FAS.

Earthquake Spectra↗
USGS2021

A near-real-time model for estimating probability of road obstruction due to earthquake-triggered landslides

Coseismic landslides are a major source of transportation disruption in mountainous areas, but few approaches exist for rapidly estimating impacts to road networks. We develop a model that links the U.S. Geological Survey (USGS) near-real-time earthquake-triggered landslide hazard model with Open Street Map (OSM) road network data to rapidly estimate segment-level obstruction risk following major earthquake activity worldwide. To train and validate the model, we process OSM data for 15 historical earthquakes and calculate the average segment-level landslide hazard from the USGS model for each event. We then fit a multivariate adaptive regression spline model for the probability of road obstruction as a function of road segment length and landslide hazard, using a training and validation dataset derived from the intersections of road networks with earthquake-triggered landslide inventories. The resulting probabilistic model is well calibrated across a range of earthquake events, with estimated obstruction probabilities matching the relative frequency of potential road obstructions. The model runs quickly and is capable of producing road segment-level obstruction estimates within minutes to hours of a major earthquake. However, in near-real-time application, the accuracy of the obstruction estimates will be dependent on the quality of the ShakeMap shaking estimates, which often improves with time as more information becomes available after the earthquake. By providing a rapid first-order translation of landslide hazard into potential infrastructure impacts, this model helps provide emergency responders with tangible information on initial areas of concern.

Earthquake Spectra↗
USGS2021

Spectral damping scaling factors for horizontal components of ground motions from subduction earthquakes using NGA-Subduction data

This article develops global models of damping scaling factors (DSFs) for subduction zone earthquakes that are functions of the damping ratio, spectral period, earthquake magnitude, and distance. The Next Generation Attenuation for subduction earthquakes (NGA-Sub) project has developed the largest uniformly processed database of recorded ground motions to date from seven subduction regions: Alaska, Cascadia, Central America and Mexico, South America, Japan, Taiwan, and New Zealand. NGA-Sub used this database to develop new ground motion models (GMMs) at a reference 5% damping ratio. We worked with the NGA-Sub project team to develop an extended database that includes pseudo-spectral accelerations (PSA) for 11 damping ratios between 0.5% and 30%. We use this database to develop parametric models of DSF for both interface and intraslab subduction earthquakes that can be used to adjust any subduction GMM from a reference 5% damping ratio to other damping ratios. The DSF is strongly influenced by the response spectral shape and the duration of motion; therefore, in addition to the damping ratio, the median DSF model uses spectral period, magnitude, and distance as surrogate predictor variables to capture the effects of the spectral shape and the duration of motion. We also develop parametric models for the standard deviation of DSF. The models presented in this article are for the RotD50 horizontal component of PSA and are compared with the models for shallow crustal earthquakes in active tectonic regions. Some noticeable differences arise from the considerably longer duration of interface records for very large magnitude events and the enriched high-frequency content of intraslab records, compared with shallow crustal earthquakes. Regional differences are discussed by comparing the proposed global models with the data from each subduction region along with recommendations on the applicability of the models.

Earthquake Spectra↗
USGS2021

ShakeMap operations, policies, and procedures

The US Geological Survey’s ShakeMap is used domestically and globally for post-earthquake emergency management and response, engineering analyses, financial instruments, and other decision-making activities. Recent developments in the insurance, reinsurance, and catastrophe bond sectors link payouts of potentially hundreds of millions of dollars to ShakeMap products. Similarly, building codes, post-earthquake building damage forensic evaluations, and geotechnical evaluations often rely on estimated peak response-spectral values for site-specific evaluations that may lead to costly analyses, retrofits, or other expenditures. Given such activities, financial, engineering, and other technical users demand processing specifications and a metadata trail for actuarial, escrow, and forensic purposes for each significant earthquake. Recent inquiries include how and why maps change with time, how to interpret metadata, and how to obtain the creation and update history of various map layers. Similarly, the collection of ShakeMap scenarios and historical ShakeMaps—either created in earlier versions or rerun as part of the latest version of the ShakeMap Atlas—warrant a full explanation of the inputs, processing, and archiving given their contribution to fragility curve development and loss model calibration. For these reasons, in addition to event-specific ShakeMap metadata and a comprehensive online ShakeMap Manual, we have crafted this practice paper to answer several of the most frequently asked technical questions. We also describe an application programming interface (API) for accessing site-specific shaking metrics and their uncertainties for earthquake forensic purposes in a consistent fashion. In all, we describe the advantages of employing ShakeMaps for these critical purposes as well as describe their limitations and uncertainties, offering an extensive set of instructions and disclaimers that can be referenced by ShakeMap users.

California↗
USGS2021

The US Geological Survey ground failure product: Near-real-time estimates of earthquake-triggered landslides and liquefaction

Since late 2018, the US Geological Survey (USGS) ground failure (GF) earthquake product has provided publicly available spatial estimates of earthquake-triggered landslide and liquefaction hazards, along with the qualitative hazard and population exposure-based alerts for M > 6 earthquakes worldwide and in near real time (within ∼30 min). Earthquake losses are oftentimes greatly aggravated by the impacts due to ground failure, yet those particular events with dramatic additional losses have not, heretofore, been rapidly identifiable. The GF product now provides situational awareness about the potential extent and severity of ground failure in the crucial time period before direct observations are available. We describe our implementation of the GF product and the lessons learned from the earthquakes that have occurred since the GF product was released. We describe the product design process, the underlying GF models, the methods we have developed for modeling uncertainty, and the development of the alert levels. The GF product has been produced in near real time for 320 events over the 2-year period since its public implementation in late 2018 through early 2021. The majority of these events yielded the lowest level (green) alerts for all ground-failure types, with 25 resulting in elevated hazard or exposure to landslides and 47 for liquefaction. In a qualitative comparison between the GF product alerts and GF occurrence information, we found that the product succeeds at assigning appropriate alert levels in the majority of cases. Based on our experience with the product, we have identified the following priorities for future improvements: (1) refinements of the underlying probabilistic models to incorporate severity and explicitly model the type of landslide/liquefaction; (2) development of models for fatalities and economic losses due to ground failure; and (3) estimation of the impacts of ground failure on infrastructure.

Earthquake Spectra↗
USGS2021

NGA-subduction global ground motion models with regional adjustment factors

We develop semi-empirical ground motion models (GMMs) for peak ground acceleration, peak ground velocity, and 5%-damped pseudo-spectral accelerations for periods from 0.01 to 10 s, for the median orientation-independent horizontal component of subduction earthquake ground motion. The GMMs are applicable to interface and intraslab subduction earthquakes in Japan, Taiwan, Mexico, Central America, South America, Alaska, the Aleutian Islands, and Cascadia. The GMMs are developed using a combination of data inspection, data regression with respect to physics-informed functions, ground-motion simulations, and geometrical constraints for certain model components. The GMMs capture observed differences in source and path effects for interface and intraslab events, conditioned on moment magnitude, rupture distance, and hypocentral depth. Site effect and aleatory variability models are shared between event types. Regionalized GMM components include the model constant (that controls ground motion amplitude), anelastic attenuation, magnitude-scaling break point, linear site response, and sediment depth terms. We develop models for the aleatory between-event variability ( τ ) "> ( τ ) , within-event variability ( ϕ ) "> ( ϕ ) , single-station within-event variability ( ϕ SS ) "> ( ϕ SS ) , and site-to-site variability ( ϕ S 2 S ) "> ( ϕ S 2 S ) . Ergodic analyses should use the median GMM and aleatory variability computed using the between-event and within-event variability models. An analysis incorporating non-ergodic site response should use the median GMM at the reference shear-wave velocity condition, a site-specific site response model, and aleatory variability computed using the between-event and single-station within-event variability models. Epistemic uncertainty in the median model is represented by standard deviations on the regional model constants, which facilitates scaled-backbone representations of model uncertainty in hazard analyses.

Earthquake Spectra↗
USGS2021

Hazard characterization for alternative intensity measures using the total probability theorem

Since their inception in the 1980s, simplified procedures for the analysis of liquefaction hazards have typically characterized seismic loading using a combination of peak ground acceleration and earthquake magnitude. However, more recent studies suggest that certain evolutionary intensity measures (IMs) such as Arias intensity or cumulative absolute velocity may be more efficient and sufficient predictors of liquefaction triggering and its consequences. Despite this advantage, widespread hazard characterizations for evolutionary IMs are not yet feasible due to a relatively incomplete representation of the ground motion models (GMMs) needed for probabilistic seismic hazard analysis (PSHA). Without widely available hazard curves for evolutionary IMs, current design codes often rely on spectral targets for ground motion selection and scaling, which are shown in this study to indirectly result in low precision of evolutionary IMs often associated with liquefaction hazards. This study presents a method to calculate hazard curves for arbitrary intensity measures, such as evolutionary IMs for liquefaction hazard analyses, without requiring an existing GMM. The method involves the conversion of a known IM hazard curve into an alternative IM hazard curve using the total probability theorem. The effectiveness of the method is illustrated by comparing hazard curves calculated using the total probability theorem to the results of a PSHA to demonstrate that the proposed method does not result in additional uncertainty under idealized conditions and provides a range of possible hazard values under most practical conditions. The total probability theorem method can be utilized by practitioners and researchers to select ground motion time series that target alternative IMs for liquefaction hazard analyses or other geotechnical applications. This method also allows researchers to investigate the efficiency, sufficiency, and predictability of new, alternative IMs without necessarily requiring GMMs.

Earthquake Spectra↗
USGS2021

2021 U.S. National Seismic Hazard Model for the State of Hawaii

The 2021 U.S. National Seismic Hazard Model (NSHM) for the State of Hawaii updates the two-decades-old former model by incorporating new data and modeling techniques to improve the underlying ground shaking forecasts of tectonic-fault, tectonic-flexure, volcanic, and caldera collapse earthquakes. Two earthquake ground shaking hazard models (public policy and research) are produced that differ in how they account for declustered catalogs. The earthquake source model is based on (1) declustered earthquake catalogs smoothed with adaptive smoothing methods, (2) earthquake rate forecasts based on three temporally varying 60-year time periods, (3) maximum magnitude models that extend to larger earthquakes than previously considered, (4) a separate Kīlauea-specific seismogenic caldera collapse model which accounts for clustered event behavior observed during the 2018 eruption, and (5) fault ruptures that consider historic seismicity, GPS-based strain rates, and a new Quaternary fault database. Two new Hawaii-specific ground motion models (GMMs) and five additional global models consistent with Hawaii shaking data are used to forecast ground shaking at 23 spectral periods and peak parameters. Site effects are modeled using western U.S. and Hawaii specific empirical equations and provide shaking forecasts for eight site classes. For most sites the new model results in similar spectral accelerations as those in the 2001 NSHM, with a few exceptions caused mostly by GMM changes. Ground motions are highest in the southern portion of the Island of Hawai‘i due to high rates of forecasted earthquakes on décollement faults. Shaking decays to the northwest where lower earthquake rates result from flexure of the tectonic plate. Large epistemic uncertainties in source characterizations and GMMs lead to an overall high uncertainty (more than a factor of 3) in ground shaking at Honolulu and Hilo. The new shaking model indicates significant chances of slight or greater damaging ground motions across most of the island chain.

Hawai'i↗
USGS2021

NGA-Subduction research program

This article summarizes the Next Generation Attenuation (NGA) Subduction (NGA-Sub) project, a major research program to develop a database and ground motion models (GMMs) for subduction regions. A comprehensive database of subduction earthquakes recorded worldwide was developed. The database includes a total of 214,020 individual records from 1,880 subduction events, which is by far the largest database of all the NGA programs. As part of the NGA-Sub program, four GMMs were developed. Three of them are global subduction GMMs with adjustment factors for up to seven worldwide regions: Alaska, Cascadia, Central America and Mexico, Japan, New Zealand, South America, and Taiwan. The fourth GMM is a new Japan-specific model. The GMMs provide median predictions, and the associated aleatory variability, of RotD50 horizontal components of peak ground acceleration, peak ground velocity, and 5%-damped pseudo-spectral acceleration (PSA) at oscillator periods ranging from 0.01 to 10 s. Three GMMs also quantified “within-model” epistemic uncertainty of the median prediction, which is important in regions with sparse ground motion data, such as Cascadia. In addition, a damping scaling model was developed to scale the predicted 5%-damped PSA of horizontal components to other damping ratios ranging from 0.5% to 30%. The NGA-Sub flatfile, which was used for the development of the NGA-Sub GMMs, and the NGA-Sub GMMs coded on various software platforms, have been posted for public use.

Earthquake Spectra↗
USGS2021

Ergodic site response model for subduction zone regions

We present an ergodic site response model with regional adjustments for use with subduction zone ground-motion models. The model predicts site amplification of peak ground acceleration, peak ground velocity, and 5% damped pseudo-spectral accelerations of the orientation-independent horizonal component for oscillator periods from 0.01 to 10 s. The model depends on the time-averaged shear-wave velocity in the upper 30 m ( V S 30 ), basin depth, and region and is independent of subduction earthquake type. It has three components: a linear site-amplification term in the form of V S 30 -scaling, a nonlinear term that depends on V S 30 and shaking intensity parameterized by peak ground acceleration at the reference-rock velocity condition of 760 m/s, and a basin sediment-depth term for Japan and Cascadia conditioned on the depth to the 2.5 km/s shear-wave velocity isosurface ( Z 2.5 ). A global V S 30 -scaling model is provided along with regional adjustments for Japan, Taiwan, South America, Alaska, and Cascadia. The nonlinear model is global, with a functional form that has often been used to fit nonlinear responses inferred from simulations, but here we calibrate it empirically. Relative to a prior model for shallow earthquakes in active tectonic regions, our subduction zone global V S 30 -scaling is comparable at short periods (<1.0 s) but weaker at long periods, while the nonlinear site response is generally less pronounced but extends to lower levels of shaking. Basin depth models are conditioned on the difference of the actual Z 2.5 and a V S 30 -conditioned mean Z 2.5 . Sites with positive differential depths have increased long-period site responses and decreased short-period responses, with the opposite occurring for negative differential depths.

Earthquake Spectra↗
USGS2022

Validating predicted site response in sedimentary basins from 3D ground motion simulations

We introduce procedures to validate site response in sedimentary basins as predicted using ground motion simulations. These procedures aim to isolate contributions of site response to computed intensity measures relative to those from seismic source and path effects. In one of the validation procedures, simulated motions are analyzed in the same manner as earthquake recordings to derive non-ergodic site terms. This procedure compares the scaling with sediment isosurface depth of simulated versus empirical site terms (the latter having been derived in a separate study). A second validation procedure utilizes two sets of simulations, one that considers three-dimensional (3D) basin structure and a second that utilizes a one-dimensional (1D) representation of the crustal structure. Identical sources are used in both procedures, and after correcting for variable path effects, differences in ground motions are used to estimate site amplification in 3D basins. Such site responses are compared to those derived empirically to validate both the absolute levels and the depth scaling of site response from 3D simulations. We apply both procedures to southern California in a manner that is consistent between the simulated and empirical data (i.e. by using similar event locations and magnitudes). The results show that the 3D simulations overpredict the depth-scaling and absolute levels of site amplification in basins. However, overall patterns of site amplification with depth are similar, suggesting that future calibration may be able to remove observed biases.

Earthquake Spectra↗
USGS2022

Hybrid broadband ground-motion simulation validation of small magnitude active shallow crustal earthquakes in New Zealand

This article presents a comprehensive validation of the hybrid broadband ground-motion simulation approach (via the commonly used Graves and Pitarka method) in a New Zealand context with small magnitude point source ruptures using an extensive set of 5218 ground motions recorded at 212 sites from 479 active shallow crustal earthquakes across the country. Modifications to the simulation method inferred from a previous New Zealand validation are implemented, and the improvements are explicitly quantified. Empirical ground-motion models are also considered to provide a benchmark for simulation prediction accuracy and precision. Examination of intensity measure residuals identifies that the simulation method modifications lead to reduced model prediction bias and within-event variability and provides evidence toward the use of spatially varying coefficient models for simulation parameters, such as the high-frequency Brune stress parameter. Additional biases identified include, among others, underprediction of significant durations at soft soil sites and overprediction of short-period pseudo-spectral accelerations at stiff alluvial gravel and rock sites due to low-estimated 30 m time-averaged shear-wave velocity values.

Earthquake Spectra↗
USGS2022

Development of a companion questionnaire for “Did You Feel It?”: Assessing response in earthquakes where an earthquake early warning may have been received

Earthquake early warning (EEW) systems are relatively new technologies having first emerged as regional systems in the 1990s. Japan was the first nation to develop and implement a nationwide system in October 2007, and in the United States, ShakeAlert ® became available on the entire length of the US West Coast in May 2021. Assessing how EEW is perceived and utilized by alert recipients is considered essential. Such assessments are necessary to evaluate whether alert recipients are taking advantage of alert messages to initiate protective actions upon receipt of an alert, how they regard the usefulness of alerts, desirable thresholds for issuing alerts, and other aspects of these systems. Having information from users will also facilitate assessments of the success of earthquake preparedness educational programs such as the ShakeOut and whether annual drills which include information on EEW systems are resulting in behavioral response consistent with the content of these programs. Finally, information on EEW utilization will provide data useful to social scientists who study hazards to advance our understanding of behavioral response to warnings. Survey research in the aftermath of a significant earthquake in which an EEW has been issued is one obvious method of achieving these objectives and there already exist a number of survey instruments for this purpose. A related strategy and the goal of the present research is to develop a brief questionnaire, consistent with those already developed, as a supplement to the United States Geological Survey’s “Did You Feel It?” questionnaire that has provided earthquake intensities and information on behavioral response in earthquakes, both domestic and international, since 2004. Having the intensity level at each respondent’s location is essential for relating their perspectives and actions to the shaking they experienced.

Earthquake Spectra↗
USGS2023

Uses of epistemic uncertainties in the USGS National Seismic Hazard Models

The need for US Geological Survey (USGS) National Seismic Hazard Models (NSHMs) to report estimates of epistemic uncertainties in the hazard (e.g. fractile hazard curves) in all forthcoming releases is increasing. With fractile hazard curves as potential new outputs from the USGS 2023 NSHM, a simultaneous need is to help end-users better understand these epistemic uncertainties and clarify their potential uses. In this article, we address the latter need by (1) characterizing epistemic uncertainties in two updates of the USGS NSHM (2014 for California and 2021 for Hawaii), (2) illustrating a variety of downstream applications of fractile hazard curves in both hazard and risk contexts, and (3) discussing implications from the various types of uncertainties. We found that the epistemic uncertainty in hazard is generally larger for Hawaii than for California, the epistemic uncertainty in hazard can be reasonably approximated with a lognormal distribution for most of the cases considered, and the correlation between epistemic uncertainty in hazard at two different intensity measure levels generally varies with both location and type of intensity measure. Furthermore, we developed models for readily generating approximate fractile hazard curves in California and Hawaii. Finally, given the complexities involved in the hazard modeling process, we developed an open-source interactive tool to enable a broad range of users to independently examine and potentially start using such epistemic uncertainties for their respective applications.

Earthquake Spectra↗
USGS2023

Sediment thickness map of United States Atlantic and Gulf Coastal Plain Strata, and their influence on earthquake ground motions

With the recent successful accounting of basin depth ground-motion adjustments in seismic hazard analyses for select areas of the western United States, we move toward implementing similar adjustments in the Atlantic and Gulf Coastal Plains by constructing a sediment thickness model and evaluating multiple relevant site amplification models for central and eastern United States seismic hazard analyses. We digitize and combine existing sediment thickness data sets into a composite surface that delineates the base of Cretaceous sediments under the Atlantic Coastal Plain and the base of Mesozoic sediments under the Gulf Coastal Plain. Amplification models dependent on sediment thickness, site natural period, and source-to-site path length are compared with data sets of observed ground motions to evaluate the ability of the new models to improve ground motion estimates. We find that the amplification models can account for observed trends in sediment-thickness and period-dependent residuals, but some tuning is required. For example, the model of Chapman and Guo requires a reference V S 30 , the time-averaged shear-wave velocity within 30 m of the Earth’s surface, for non-Coastal Plain sites, which we estimate to be between about 1 and 2 km/s. Along with our sediment thickness model, we estimate a velocity profile for application to the Harmon et al. site-natural-period-based model in order to best match the Chapman and Guo period dependence for a broad range of sediment thicknesses. The Next Generation of Attenuation models for the eastern United States Gulf Coast path-based adjustment models can also account for seismic attenuation in the Coastal Plain sediments and reduce the standard deviation of total residuals. If enacted in the U.S. Geological Survey National Seismic Hazard Model, these amplification models will reduce predicted short-period (<1 s) and increase predicted long-period (>1 s) ground motions in the Coastal Plains appreciably.

Earthquake Spectra↗
USGS2023

Least cost path analysis as an objective and automatic method to define the main fault trace for probabilistic fault displacement hazard analyses

A main goal of probabilistic fault displacement hazard analysis (PFDHA) is to quantify displacement along and across an identified active fault that poses a hazard to nearby infrastructure such as roads, bridges, pipelines, and telecommunications. PFDHA relies on empirical models developed using data sets of displacement measurements and mapped surface rupture traces compiled from past global surface rupturing earthquakes by field surveys or remote sensing. However, current approaches to determine the location of the main rupture trace are subjective and lack repeatability due to different geological interpretations of the often complex network of mapped rupture traces. This subjectivity makes it difficult to compile and analyze displacement measurements and ruptures from multiple events in a consistent manner. This study provides an objective and repeatable approach to define a main rupture trace that can be applied to either field or remote sensing data. The new approach defined here can be used in developing rupture trace connectivity and geometry for use in displacement model developments and for use in objectively defining the input fault trace for assessing fault displacement hazard.

Earthquake Spectra↗