ML23257A200

Ground Motion and Seismic Hazard in Central and Eastern United States

ML23257A200
Person / Time
Issue date:	09/14/2023
From:	Rasool Anooshehpoor, Boyd O, Engler D, Ferragut G, Moschetti M, Powers P, Rezaeian S, Thompson E, Worden B NRC/RES/DE/SGSEB, US Dept of Interior, Geological Survey (USGS)
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Rasool Anooshehpoor 301-415-2396
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Download: ML23257A200 (77)

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Ground Motion and Seismic Hazard in Central and Eastern United States Date Published: September 2023 Prepared by:

Morgan P. Moschetti Eric M. Thompson Oliver S. Boyd Davis Engler Bruce Worden Gabriel Ferragut Sanaz Rezaeian Peter M. Powers U.S. Geological Survey Geologic Hazards Science Center 1711 Illinois St.

Golden, CO 80401 Rasool Anooshehpoor, NRC Project Manager Technical Letter Report U.S. Geological Survey, Geologic Hazards

DISCLAIMER The development of this Technical Letter Report was sponsored by the U.S. Nuclear Regulatory Commission (NRC). The views and conclusions contained in the document are those of the authors and should not be interpreted as necessarily representing the official policies of the U.S.

Government.

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ABSTRACT This report describes work carried out under the U.S. Nuclear Regulatory Commission (NRC)

Interagency Agreement to the U.S. Geological Survey (USGS) Research to Support NRCs Seismic Hazard Analyses for Task 3, Seismic Hazard and Ground Motion Models. The focus of this work has been on evaluation of the Next Generation Attenuation (NGA)-East ground-motion models (GMMs) with available ground-motion data and evaluation of alternative methods for characterizing epistemic uncertainty for probabilistic seismic hazard analysis (PSHA).

When the Interagency Agreement commenced, the USGSs National Seismic Hazard Model (NSHM) was being updated, and a significant part of the update for the 2018 NSHM included the introduction of new GMMs for the central and eastern United States (CEUS) (Petersen et al., 2020). In addition to the implementation of the then-recently developed NGA-East GMMs (Goulet et al., 2018), the ground-motion characterization for the CEUS in the 2018 NSHM also included a logic-tree branch with weights applied to the updated adjusted seed models that were developed as part of the NGA-East process and in updates by the GMM developers.

The Statement of Work for Task 3 of the NRC Interagency Agreement to the USGS included the following parts: (1) Describe technically acceptable approaches in combining GMMs for use in PSHA calculations; (2) Evaluate the effect of using different sets of GMMs (NGA-East SSHAC versus NGA-East USGS) on PSHA calculations; (3) Describe the results of the GMM testing against recorded data, and provide a recommendation on the GMMs application for use in the PSHA; (4) Evaluate the impacts of recently updated individual GMMs on the published NGA-East models; and (5) Submit a final Technical Letter Report documenting results of this task.

We present results from this work in two sections: (Chapter 1) Updated Central and Eastern United States Ground Motions and Ground-Motion Analyses; and (Chapter 2) Approaches to Combining Ground-Motion Models for Probabilistic Seismic Hazard Analysis in the Central and Eastern United States.

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FOREWORD For the past five years, the U.S. Geological Survey (USGS) has been conducting research to support the U.S. Nuclear Regulatory Commissions seismic hazard analysis, specifically relating to evaluation of ground-motion models with seismic data in central and eastern North America and to the modeling of epistemic uncertainty in ground-motion models. This document serves to report the findings by the USGS.

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TABLE OF CONTENTS DISCLAIMER ............................................................................................................................... iii ABSTRACT .................................................................................................................................. v FOREWORD ............................................................................................................................... vii LIST OF FIGURES ...................................................................................................................... xi LIST OF TABLES ....................................................................................................................... xv EXECUTIVE

SUMMARY

.......................................................................................................... xvii ACKNOWLEDGEMENTS ......................................................................................................... xix ABBREVIATIONS AND ACRONYMS ...................................................................................... xxi 1 Updated Central and Eastern United States Ground Motions and Ground-Motion AnalyseS .............................................................................................................................. 1-1 1.1 Previous Comparisons to Ground-Motion Data in CENA ............................................... 1-1 1.2 Updated CEUS Ground Motion Dataset ........................................................................ 1-2 1.3 Ground-Motion Analysis ................................................................................................. 1-8 1.3.1 Comparison of USGS Seed Models and NGA-East for Residuals .................. 1-8 2 Approaches to Combining Ground-Motion Models for Probabilistic Seismic Hazard Analysis in CEUS ................................................................................................... 2-1 2.1 Summary of the USGS Approach to Combining GMMs in the CEUS for the 2018 U.S. NSHM ................................................................................................................ 2-1 2.1.1 Multi-Period Response Spectra (MPRS) Influencing the CEUS GMM Selection............................................................................................... 2-2 2.1.2 Updates to the GMM Selection Criteria in the 2018 NSHM ............................. 2-2 2.1.3 Older GMMs and Weights ................................................................................ 2-3 2.1.4 CEUS GMMs in the 208 NSHM for Very Hard Rock Conditions...................... 2-5 2.1.5 Weighted Average of Medians ....................................................................... 2-11 2.1.6 Epistemic Uncertainty of Medians .................................................................. 2-14 2.1.7 Aleatory Variability ......................................................................................... 2-17 2.1.8 Implications of GMM Changes on Hazard ..................................................... 2-17 2.2 Verification and Evaluation of NGA-East Procedure .................................................... 2-19 2.2.1 Summary of NGA-East Procedure ................................................................. 2-19 2.2.2 Remaining Steps to Reproduce NGA-East Procedure .................................. 2-29 2.2.3 Comparisons of USGS and NGA-East Epistemic Uncertainty Through Sammons Maps................................................................................. 2-29 3 Conclusions and Path Forward ......................................................................................... 3-1 4 Data and Software Availability ........................................................................................... 4-1 5 References ........................................................................................................................... 5-2 ix

LIST OF FIGURES Figure 1-1: Workflow for automated processing with the USGS gmprocess code.

Figure from https://ghsc.code-pages.usgs.gov/esi/groundmotion-processing/contents/overview/index.html which makes use of the ObsPy (obspy) Python package for seismic waveform processing and produces metrics for use with USGS Shakemap (Worden et al., 2020), ground-motion prediction (GMPE) or GMM evaluations, and for distribution via CESMD. ............................................................................................................. 1-4 Figure 1-2: Example output from gmprocess workflow for an M4.8 earthquake that occurred May 5, 2011, near Sparks, OK. ........................................................... 1-5 Figure 1-3: Locations of (a) earthquake epicenters and (b) stations providing records for the updated ground-motion data set. ............................................................ 1-6 Figure 1-4: Initial spectral accelerations (SA ( = . )) ground motions plotted as a function of distance with colors depicting (a) earthquake magnitude and (b) the flagged values (i.e., True, False) denoting anomalous ground motions. Evaluation of ground motions as a function of earthquake magnitudes reveals anomalous ground motions at multiple distances and magnitudes that are used to specify the Flagging value in the data set. ......... 1-7 Figure 1-5: Summary figures for the contents of the ground-motion data set.

Presented are (a) the estimated moment magnitudes for events as a function of time; (b) depiction of processed records as a function of moment magnitude ( and closest rupture distance; and (c) numbers of records as a function of oscillator period from multiple distance thresholds. .......................................................................................................... 1-7 Figure 1-6: Total ground-motion residuals plotted as a function of distance using the Thompson et al. (2023) CENA data set.............................................................. 1-9 Figure 1-7: Total ground-motion residuals plotted as a function of distance using the Thompson et al. (2023) CENA data set and limited to events occurring within the Oklahoma-Kansas zone of potentially induced seismicity.................. 1-9 Figure 1-8: Total ground-motion residuals plotted as a function of distance using the Thompson et al. (2023) CENA data set and limited to events occurring outside of the Oklahoma-Kansas zone of potentially induced seismicity (events are predominantly of tectonic origin).................................................... 1-10 Figure 1-9: Between-event terms plotted as a function of magnitude for oscillator periods of (a) 0.1 s, (b) 0.2 s, (c) 0.5 s, (d) 1.0 s, (e) 2.0 s, and (c) 5.0 s. ........ 1-11 Figure 1-10: Within-event terms plotted as a function of rupture distance for oscillator periods of (a) 0.1 s, (b) 0.2 s, (c) 0.5 s, (d) 1.0 s, (e) 2.0 s, and (c) 5.0 s. ........ 1-12 Figure 1-11: Bias terms plotted as a function of oscillator period (T) comparing results from ground-motion residuals computed for = m/s and ground-motion residuals computed for values at station locations (Allen and Wald, 2009). ..................................................................................................... 1-13 Figure 1-12: Comparison of bias terms from tectonic (Tectonic) and potentially induced (IndSeis) earthquakes as a function of period (T) from the Thompson et xi

al. (2023) CENA data set. Plots also depict the effect of including and excluding records from sites within the Atlantic and Gulf Coastal Plains (CP) on the computed bias. .............................................................................. 1-14 Figure 1-13: Sediment thicknesses in the Atlantic and Gulf Coastal Plains. Figure from Boyd et al. (in press). ....................................................................................... 1-14 Figure 1-14: Ground-motion residuals, SA (T=0.4 s), within Coastal Plain and distribution of sediment-thicknesses among USGS and NGA-East data sets. Figures from Boyd et al. (in press). The legend in panel (b) also applies to panel (a). Data sets include the USGS data set (Thompson et al., 2023), the NGA-East data set (Goulet et al., 2021b), and the data set of Chapman and Guo (2021). ........................................................................... 1-15 Figure 2-1: (Figure 1 of Rezaeian et al., 2021): The nine 2014 NSHM GMMs in the CEUS for a magnitude 7 event on a very hard rock site: (a) median ground motions versus period at a distance of 50 km, and (b) median ground motions versus distance at a 0.2 s spectral period. Model abbreviations and logic tree weights used to compute the weighted average are given in Table 2-1. .......................................................................... 2-4 Figure 2-2: (Figure 2 of Rezaeian et al., 2021): Standard deviations of the nine 2014 NSHM GMMs in the CEUS for a magnitude 7 event on a very hard rock site versus spectral period. Model abbreviations are given in Table 2-2. ........... 2-5 Figure 2-3: (Figure 3 of Rezaeian et al. (2021). A logic tree showing the grouping of updated seed GMMs by geometric spreading and model type, as well as the weights assigned to all CEUS GMMs in the 2018 NSHM. Relative weights for each group or model are given in parentheses. ............................... 2-9 Figure 2-4: (Figure 4 of Rezaeian et al., 2021): The 14 updated seed CEUS GMMs in the 2018 NSHM for a magnitude 7 event on a very hard rock site: (a) medians versus period at a distance of 50 km, and (b) medians versus distance at 0.2 s spectral period, superimposed on the 9 CEUS GMMs from the 2014 NSHM of Figure 2-1. Model abbreviations and weights defined in Table 2-2 and Figure 2-3. ................................................................ 2-10 Figure 2-5: (Figure 5 of Rezaeian et al., 2021) Medians of the 17 NGA-East GMMs in the 2018 NSHM for a magnitude 7 event on a very hard rock site: (a) medians versus period at a distance of 50 km, and (b) medians versus distance at 0.2 s spectral period, superimposed on the 9 CEUS GMMs from the 2014 NSHM in Figure 2-1. Vertical bars and arrows indicate the range of ground motions at different spectral periods and distances for the two groups of GMMs and are referenced in Figure 2-10. ........................... 2-11 Figure 2-6: (Figure 7 of Rezaeian et al., 2021) Weighted averages of CEUS GMM medians from the 2018 NSHM, 2014 NSHM (RLME, distances below 500 km), and 2008 NSHM (RLME) versus period for magnitude 5.5 and 7.5 events at 10, 50, and 300 km distances for hard rock representing the original site conditions of the models (about 2000 m/s in 2008 and 2014 NSHMs, 3000 m/s in 2018 NSHM). .................................................................. 2-13 Figure 2-7: (Figure 8 of Rezaeian et al., 2021) Weighted combinations of CEUS GMM medians from the 2018, 2014 (RLME, distances below 500 km), and 2008 NSHM (RLME) versus distance for magnitude 5.5 and 7.5 events at (a) xii

0.2 s and (b) 1 s. These plots are made for hard rock representing the site conditions of the original models (2000 m/s in the 2008 and 2014 NSHMs, 3000 m/s in the 2018 NSHM). .......................................................................... 2-14 Figure 2-8: (Figure 9 of Rezaeian et al., 2021) Epistemic uncertainty of NGA-East GMMs represented by the range and distribution of ground motion medians at vertical cross sections of Figure 2-5, for a magnitude 7 event on hard rock (i.e., = 3000 m/s) at (a) a 50 km distance and three periods, PGA, 0.2, and 1 s; and (b) two distances, 10 and 100 km, at 0.2 s period. ............................................................................................................ 2-15 Figure 2-9: (Figure 10 of Rezaeian et al.) Epistemic uncertainty of updated seed GMMs represented by the range and distribution of ground motion medians at vertical cross sections of Figure 2-4, for a magnitude 7 event on hard rock (i.e., = 3000 m/s) at (a) a 50 km distance and three periods, PGA, 0.2, and 1 s; and (b) two distances, 10 and 100 km, at 0.2 s period. ............................................................................................................ 2-16 Figure 2-10: (Figure 11 of Rezaeian et al., 2021) The two CEUS aleatory variability models (2018 Updated EPRI and 2018 Working Group), used for all 31 GMMs in the 2018 NSHM, and their SRSS combination (2018 NSHM),

superimposed on standard deviation models of the nine 2014 GMMs for a magnitude 7 event on hard rock ( = 2000 or 3000 m/s). ............................ 2-17 Figure 2-11: (Figure 15 of Rezaeian et al., 2021) Differences and ratios in ground motions with 2% probability of exceedance in 50 years hazard level, using the 2014 and 2018 CEUS GMMs (both using the 2014 NSHM source model). Maps are provided for 0.2 and 1 s spectral periods on a uniform hard rock site condition. ................................................................................... 2-18 Figure 2-12: Sample variances from the sample covariance matrices, NGA-East seed models. Scale bar and contours depict variance values. ................................. 2-21 Figure 2-13: Sample variances from the sample covariance matrices, NGA-East seed models with frequency restrictions. Scale bar and contours depict variance values. ............................................................................................... 2-22 Figure 2-14: Reproduction of Goulet et al. (2018) Figure 8-18. Modeled correlation coefficients for f = 1 Hz, plotted against M and . Left; M = 5,

=1000 km, Center: M = 6, =100 km, Right: M= 8, =20 km. ...... 2-23 Figure 2-15: Sammons mapping of 1 Hz GMMs plotted together with the scaled reference models (i.e., scaled by constant factors const-scaled; scaled by magnitude mag-scaled; and scaled by distance dist-scaled). Black circles depict the locations of the seed models, with labels for the abbreviated seed names. ................................................................................. 2-24 Figure 2-16: Summary of weights applied to 18 seed models for the case of 1 Hz gridding. ............................................................................................................ 2-25 Figure 2-17: Example of 10,000 draws from the underlying (epistemic) ground-motion distribution in the Sammons space for 1 Hz ground motions. Seed models are plotted with dark blue symbols. The reference models (constant, magnitude, and distance scaling) are plotted with black, yellow, and red symbols, respectively, with the same legend as in Figure 2-15. ......... 2-26 xiii

Figure 2-18: Number of realizations associated with each seed model. The plotted example corresponds to 1000 total realizations at 1 Hz. .................................. 2-27 Figure 2-19: Clustering of GMM realizations within the 17 sectors of the projected ground motion space. GMMs within each sector are color-coded.................... 2-28 Figure 2-20: GMMs from the realizations of the mixture model of MVN distributions. .......... 2-28 Figure 2-21: Comparison of the weights used in sampling NGA-East seed models with branch weights of USGS updated seed models for SA (T=1 Hz). .................... 2-30 xiv

LIST OF TABLES Table 2-1: (Table 1 of Rezaeian et al.,2021): Minimum requirements for spectral periods and site classes. .................................................................................... 2-3 Table 2-2: (Table 3 of Rezaeian et al., 2021): CEUS ground motion models in the 2018 NSHM. ....................................................................................................... 2-7 xv

EXECUTIVE

SUMMARY

We present results from two separate investigations towards understanding and modeling earthquake ground motions for seismic hazards applications in the central and eastern United States (CEUS).

The first investigation focuses on evaluation of the Next Generation Attenuation (NGA)-East ground-motion models (GMMs) with available data in central and eastern North America (CENA). We compile and process ground motions from earthquakes occurring in CENA from 2010-2020. This data set contains events up to moment magnitude ( ) 5.8 for induced events and 5.7 for tectonic events. We carry out ground-motion analyses with the U.S. Geological Surveys ground-motion logic tree for the CEUS (Petersen et al., 2020; Rezaeian et al., 2021) and investigate the effects of further regionalization (induced earthquakes in the Oklahoma-Kansas region and tectonic events outside of this region) on ground-motion residuals. We find a period-dependent bias that emerges for the CEUS GMMs and the ground-motion data in this region, with an overprediction at short periods (T<1 s) and underprediction at long periods (T>1 s); the cross-over period of the misfit appears to vary based on treatment of site effects and for different subsets of the data. Bias results for both the hard-rock ( = 3000 m/s) conditions of NGA-East and when using assigned values for the locations. Use of recently developed site response models for the CEUS (Stewart et al., 2020) exacerbate the misfit but cannot be the cause due to similar misfits from hard-rock reference conditions. The bias values vary between the induced and tectonic events but show similar gross dependence on period. Trends in the ground-motion residuals with distance also manifest and suggest that there may be further regionalization of path attenuation terms within the CEUS.

The second set of investigations relate to approaches to combining GMMs for probabilistic seismic hazard analysis in the CEUS. Rezaeian et al. (2021) summarize the logic tree for CEUS GMMs that was developed for the 2018 U.S. National Seismic Hazard Model (NSHM) (Petersen et al., 2020). The 2018 NSHM logic tree combines the NGA-East logic tree and a logic tree comprising updated NGA-East seed models. Rezaeian et al. (2021) document the motivation and choices in developing this logic tree and compares epistemic uncertainty in ground motions and aleatory variability for this model. We also carry out work to reproduce the NGA-East Procedure for developing the GMMs and logic tree weights from the set of NGA-East (adjusted) seed models. This section contains a summary of the steps for reproducing NGA-East GMMs, including various verification steps and some additional outputs that make the procedure more transparent. We conclude with future steps that might be addressed to enable a complete implementation of the NGA-East Procedure.

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ACKNOWLEDGEMENTS The authors greatly benefitted from interaction and feedback with NRC staff (R. Anooshehpoor, T. Weaver, S. Stovall, V. Graizer) and appreciate their time and feedback during the course of this work. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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ABBREVIATIONS AND ACRONYMS CENA Central and Eastern North America CESMD Center for Engineering Strong Motion Data CEUS Central and Eastern United States CEUS-SSC Central and Eastern United States Seismic Source Characterization for Nuclear Facilities ComCat Advanced National Seismic System Comprehensive Catalog CP Coastal Plains dB Decible; logarithm of the ratio of the signal to a standard FDSN International Federation of Digital Seismograph Networks GMM Ground-motion model GMPE Ground-motion prediction equation Hz Hertz; unit of frequency IMT(s) Intensity measure type(s)

M Magnitude MW Moment magnitude MPRS Multi-period Response Spectra MVN Multivariate normal NGA Next Generation Attenuation NRC Nuclear Regulatory Commission NSHM National Seismic Hazard Model ObsPy Open-source Python toolbox for processing seismological data OK-KS Oklahoma-Kansas Region PEER Pacific Earthquake Engineering Research Center PGA Peak Ground Acceleration PGV Peak Ground Velocity PSA Pseudo-spectral Acceleration (5% damped)

PSHA Probabilistic Seismic Hazard Analysis QA Quality Assurance R Closest distance to causative fault RotD50 Median horizontal intensity measure SA Spectral accleration SSHAC Senior Seismic Hazard Analysis Committee SWUS Southwestern United States Project T Period USGS U.S. Geological Survey VS30 Time-averaged shear-wave velocity to 30 m depth WUS Western United States xxi

1 UPDATED CENTRAL AND EASTERN UNITED STATES GROUND MOTIONS AND GROUND-MOTION ANALYSES Work on central and eastern United States (CEUS) earthquake ground motions comprises the collection and processing of an updated ground-motion data set for the CEUS and for the broader central and eastern North America (CENA) region, including recent earthquakes and including information from recent work to characterize deep-sediment depths in the Atlantic and Gulf Coastal Plains and initial analyses of the ground-motion data set with the Next Generation Attenuation (NGA)-East ground motion models (GMMs).

1.1 Previous Comparisons to Ground-Motion Data in CENA Evaluation of NGA-East GMMs with CENA ground-motion data has been limited due the recency of publication of the GMMs (Goulet et al., 2018; Goulet et al., 2021a) and due to the relatively lower seismicity ratesand therefore sparser ground-motion datain CENA compared to the western United States (WUS). Development of CENA-specific site-amplification models by Parker et al. (2019) and Stewart et al. (2020) have enabled evaluation of the NGA-East GMMs, which were developed for hard-rock ( = 3000 m/s) site conditions, with recordings made at sites with much slower time-averaged shear-wave velocity to 30 m depth ( ) values. Previously, including during the development of the NGA-East GMMs, WUS-specific site-amplification models were used to adjust site conditions. The data comparisons of Goulet et al. (2018), which were used for partial weighting of the NGA-East GMMs, used the site-amplification models of Boore et al. (2014) for converting to =

760 m/s and then evaluated several models for converting from = 760 m/s to =

3000 m/s. These data comparisons for mean bias are published in the NGA-East Pacific Earthquake Engineering Research Center (PEER) report (Goulet et al., 2018) and include multiple GMMs with a characteristic bias showing shorter-period overprediction and longer-period underprediction; GMMs with this characteristic bias include B_ab95, B_bca10d, B_bs11, 1CCSP, 1CVSP, 2CCSP, 2CVSP, YA15, PZCT15_M1SS, PZCT15_M2ES, Graizer, though the bias analyses are predominantly limited to period bands 0.1-1 s. Differences in bias result from the four models used for converting from = 760 m/s to = 3000 m/s.

Earlier evaluations of the NGA-East GMMs by U.S. Geological Survey (USGS) researchers focused on ground motions from induced earthquakes and evaluations of the ground-motion data published with the NGA-East Project. Rennolet et al. (2018) compiled ground motions (pseudo-spectral accelerations; PSA) from induced earthquakes in Oklahoma and Kansas occurring 2009-2016. Moschetti et al. (2019) evaluated data misfit from the Rennolet et al.

(2018) data set using GMMs from NGA-West-2 (Bozorgnia et al., 2014), the seed models from the NGA-East Project (Goulet et al., 2018), and the CEUS GMMs from the 2014 National Seismic Hazard Model (NSHM; Petersen et al., 2015). Because CEUS site-amplification models were not available at the time of these analyses, Moschetti et al. (2019) used the Boore and Campbell (2017) factors for adjusting = 3000 m/s to = 760 m/s and considered the use of two values of the high-frequency site attenuation parameter, kappa, = 0.01, 0.03 .

They found uniform underprediction of broadband ground motions by the NGA-West-2 GMMs, and a consistent period-dependent misfit from the NGA-East seed models and from the CEUS GMMs of the 2014 NSHM, with short-period ( < 1 s) overprediction and long-period ( > 1 s) underprediction. Furthermore, they identified a distance-dependent misfit trend in the within-event residuals whereby the observed ground motions attenuate with distance more rapidly than the predictions within < 20 km and attenuate more slowly with distance for 20 < < 100 km.

These observations are consistent across the three sets of GMMs.

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McNamara et al. (2019) used ground-motion data sets from induced and tectonic earthquakes (Goulet et al., 2021b; Rennolet et al., 2018) to evaluate 50 GMMs for the CEUS. They used probabilistic scoring metrics to evaluate data misfits in multiple distance ranges and to investigate differences in ground-motion characteristics from induced and tectonic events.

McNamara et al. (2019) found that the NGA-East GMMs scored better than older CEUS GMMs; they identified several GMMs that scored most highly for induced earthquakes, but they concluded that there were insufficient data from tectonic events to distinguish between logic trees comprising NGA-East GMMs and NGA-East seed models. They also observed a distance dependence to the misfit from induced earthquakes, finding that the NGA-East GMMs give higher ground motions than are indicated by the data in a distance range of 10-40 km for induced earthquakes in Oklahoma and Kansas.

More recently, analyses of the NGA-East data by Ramos-Sepulveda et al. (2022) identified period-dependent misfits. Ramos-Sepulveda et al. (2022) evaluated misfit to the NGA-East data using the Stewart et al. (2020) site-amplification for converting from site to = 760 m/s conditions and using two different modelsrepresenting a smooth gradient and a strong impedance contrast in the seismic velocity profilesfor converting from = 760 m/s to

= 3000 m/s conditions. They found similar bias curves, with overpredictions by about a factor of two near oscillator period, = 0.2 s and underpredictions that peaked at oscillator periods near = 7.5 s.

1.2 Updated CEUS Ground Motion Dataset We initiate the update of the CEUS ground-motion data set by defining event and search parameters. We define the event set for earthquakes occurring in the CEUS from the start of 2010 through the end of 2020. The updated data set therefore partially overlaps with records and earthquakes in the NGA-East data set (Goulet et al., 2014; Goulet et al., 2021b), though our primary goal was to process events since the NGA-East data set was completed. Throughout most of central and eastern North America, we compile data for earthquakes 3.5; within the NSHM zone of potentially induced seismicity for Oklahoma, Kansas, and north Texas, the minimum magnitude for earthquakes is increased to 4 because of the prevalence of induced earthquakes during this time period and our desire to not have the ground-motion data set be predominately from induced earthquakes. The USGS Advanced National Seismic System Comprehensive Catalog (ComCat) preferred magnitude is used to construct the event set, and later steps are taken to convert magnitudes to uniform moment magnitude estimates for use in the ground-motion analyses. We collect data from earthquakes with magnitude below the minimum magnitude of the NGA-East GMMs ( 4) to increase the spatial coverage of events for potential future applications. The USGS ShakeMap products have implemented an extrapolation of magnitude scaling for the NGA-East GMMs that may be of use in investigating site response and regionalization; however, we do not make use of this extrapolation to <4 ground motions without further evaluation of this model feature.

Collection of seismic waveforms and processing use the USGS gmprocess automated ground-motion processing tool (Hearne et al., 2019). An overview of the gmprocess workflow is given in Figure 1-1. An example output for one seismic record is depicted in Figure 1-2. We collect available seismic time series from the International Federation of Digital Seismograph Networks (FDSN) and the Center for Engineering Strong Motion Data (CESMD) web services for all available broadband and strong-motion instruments within a fixed search radius from the earthquake epicenter (Figure 1-3). The search radius is set to 5 degrees, but we expand the radius to 9 degrees in the Atlantic and Gulf Coastal Plains to provide additional records in this 1-2

area where we have complementary ongoing work. Ground-motion processing steps largely follow the guidelines from NGA-East (Goulet et al., 2014) and comprise removing the instrument response, pre-processing baseline correction, windowing, calculation of high- and low-pass corner frequencies from signal-to-noise levels of the Fourier spectra, band-pass filtering, and measurement of ground motions. The code makes use of multiple algorithms for detecting waveform clipping in the broadband seismic records (Kleckner et al., 2022). Measured ground motions include peak ground acceleration (PGA) and velocity (PGV), as well as 5-percent-damped pseudo-spectral accelerations at 21 oscillator periods (0.01-10 s). For this data set, ground-motion measurements are made on the horizontal components only, and correspond to the median horizontal intensity (RotD50) metrics (Boore, 2010). Velocity records from broadband seismographs make up an important part of the ground-motion data set in CENA due to the lower seismicity rates and fewer observations of earthquakes. The gmprocess procedure for processing broadband data uses the instrument-response-correction tools of ObsPy (Krischer et al., 2015) with pre-filtering high-pass corners of (0.001 and 0.005 Hz) and low-pass corners defined by the Nyquist frequency, (0.5 and Hz) and a 60 dB water level. Following instrument response correction (and output as velocity record), gmprocess differentiates the records (in the frequency domain) to acceleration units, and the ground-motion timeseries are then assembled with accelerometer into a single file. The code relies on various quality assurance (QA) checks to screen records based on signal-to-noise and other criterion.

We assign necessary source and site metadata to enable ground-motion analyses, including assigning moment magnitudes for all events and assigning information about shallow site conditions and sediment-depth information to all sites. Because modern GMMs use moment magnitudes as predictor variables, we estimate moment magnitudes for all earthquakes for which this magnitude type is not available. The preferred magnitudes in ComCat can reflect choices by the regional networks about the types of magnitudes used to describe each event.

While moment magnitudes are largely preferred for larger-magnitude events, the availability of measured moment magnitudes for smaller earthquakes depends on the methods used in each region, and various other magnitude types are typically assigned for smaller-magnitude ( 4) earthquakes (e.g., , ).

We use regional magnitude-conversion relations from Central and Eastern United States Seismic Source Characterization for Nuclear Facilities (U.S. Nuclear Regulatory Commission (CEUS-SSC), 2012) to estimate moment magnitude, where moment magnitudes are not available. Unlike the CEUS-SSC procedure, we do not combine multiple magnitude types to estimate moment magnitude but instead use only the preferred ComCat magnitude. Our magnitude-conversion differs from the CEUS-SSC procedure because it permits consistency with the earthquake catalogs used for seismic hazard (Mueller, 2019). Moment magnitudes from each event are computed from the expected magnitudes [ ] of CEUS-SSC as:

1

= [ ]+ [ l ]

2 where = ln(10) and we assume a Gutenberg-Richter value of = 1 and [ l ] is the standard deviation of normally distributed error in observed magnitudes. Of the 269 events in our dataset, 105 do not have measured moment magnitude. The converted moment magnitudes range 0-0.6 magnitude units less than the measured magnitudes. Average differences are about 0.25 units less. Errors in the magnitude-estimation process have been identified (Shelly et al., 2022) but have not been incorporated here because they have not become standard practice for seismic hazards applications.

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Site metadata include shallow site conditions from the and sediment thicknesses in the Atlantic and Gulf Coastal Plains. The values are derived from the topography-based-proxy method of Allen and Wald (2009). The shortcomings of proxy-based methods for are well documented, and alternative CEUS-wide estimates are available (e.g., Castellaro et al.,

2008; Heath et al., 2020); however, we chose the use of proxy-based because the values are uniformly available at all sites and the data set does not exhibit artifacts due to the underlying contributed data sources (e.g., discontinuities at state boundaries). The NGA-East approach used topo-based methods combined with local geologic information that were not available for all sites, and these assignments were beyond the scope of this work. Deep-sediment effects (i.e., thick sediment and sedimentary-rock deposits) are known to have significant effects on ground motions in the CEUS (Bodin and Horton, 1999; Boyd et al., in press; Guo and Chapman, 2019). We assign sediment thicknesses, where available, to the resulting CEUS data set. Mills et al. (2020) have developed maps of sediment thicknesses in the Atlantic and Gulf Coastal Plains. Using the mean sediment-thickness map, we assign sediment thickness values to sites in the ground-motion data set. Depths of sediment thicknesses across much of the CEUSeverywhere outside of the Coastal Plainsare not characterized, and the absence of sediment-thickness estimates should not be interpreted as meaning that sediment depths are shallow or absent.

Figure 1-1: Workflow for automated processing with the USGS gmprocess code. Figure from https://ghsc.code-pages.usgs.gov/esi/groundmotion-processing/contents/overview/index.html which makes use of the ObsPy (obspy) Python package for seismic waveform processing and produces metrics for use with USGS Shakemap (Worden et al., 2020), ground-motion prediction (GMPE) or GMM evaluations, and for distribution via CESMD.

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Figure 1-2: Example output from gmprocess workflow for an M4.8 earthquake that occurred May 5, 2011, near Sparks, OK.

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Automated processing for ground-motion records facilitates the use of large data sets but also requires care for QA of the results. Visual inspection may highlight discrepancies between amplification in records of similar magnitudes. In past studies, we have made use of such plots to identify issues with instrument response metadata and other common instrumental issues causing incorrect amplitudes. To quality assure the updated CEUS ground-motion data set we compared processed ground motions with the NGA-East GMM predictions and flagged anomalous ground motions (Figure 1-4). Evaluation of ground motions as a function of earthquake magnitudes reveals anomalous ground motions at multiple distances and magnitudes that are used to specify the Flagging value in the data set. We furthermore examined anomalous records to determine whether there was a problem with the station, if there was a problem with the station at certain times (for example, due to changed equipment without updating instrument response metadata), or if there was noise in the data that contributed to anomalous estimates at high or low frequency. Because we cannot definitively reject seemingly anomalous records, we do not remove them from the data set, but rather we add a column to the data set to flag questionable records. Flagged records account for less than 10 percent of the data set.

Figure 1-3: Locations of (a) earthquake epicenters and (b) stations providing records for the updated ground-motion data set.

Excluding flagged records, the resulting data set comprises more than 20,000 records from earthquakes with moment magnitude 3.9. The numbers of records at periods greater than about 1 s and less than about 0.1 s are reduced compared to numbers in the intermediate period band (~0.1-1 s). Depiction of the data set is provided in Figure 1-5. Maximum earthquake magnitudes are 5.8, and two of the three largest events in the data set occurred in Oklahoma and are likely induced events. Records are sparse at magnitudes greater than 4.5 and at rupture distances less than 50 km. Data is available from Thompson et al. (2023).

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Figure 1-4: Initial spectral accelerations (SA ( = . )) ground motions plotted as a function of distance with colors depicting (a) earthquake magnitude and (b) the flagged values (i.e., True, False) denoting anomalous ground motions.

Evaluation of ground motions as a function of earthquake magnitudes reveals anomalous ground motions at multiple distances and magnitudes that are used to specify the Flagging value in the data set.

Figure 1-5: Summary figures for the contents of the ground-motion data set. Presented are (a) the estimated moment magnitudes for events as a function of time; (b) depiction of processed records as a function of moment magnitude ( and closest rupture distance; and (c) numbers of records as a function of oscillator period from multiple distance thresholds.

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1.3 Ground-Motion Analysis We carry out a ground-motion analysis with the updated CEUS ground-motion data set to evaluate trends with respect to the NGA-East GMMs. The analysis proceeds by computing ground-motion residuals relative to the NGA-East GMMs. For the residual calculations, we use the weighted USGS logic tree for CEUS GMMs ( ), which combines the NGA-East model with a logic tree of updated seed models (see Rezaeian et al., 2021). Residuals are computed for uniform site conditions ( = 3000 m/s) from the NGA-East GMMs and for the site conditions of Allen and Wald (2009).

= ln( ) ( = 3000 m/s)

The uniform-condition residuals provide information on differences between the recorded ground motions and predictions from the averaged, hard-rock predictions of the CEUS GMMs from the USGS. These residuals do not include a site correction, and the residuals should contain site response and other repeatable and scenario-dependent features. Moreover, because the Stewart et al. (2020) site-amplification models predict amplification for all periods for < 3000 m/s, we expect ground-motion residuals from the uniform-condition calculations to be positive, > 0.

= ln( ) ( )

The -corrected residuals, , provide information on the differences between the recorded ground motions and predictions from the -corrected ground motion predictions of the CEUS GMMs from the USGS, ( ). The -corrected ground motion predictions are given by the hard-rock GMM predictions and the CEUS ergodic site-amplification model (Rezaeian et al., 2021; Stewart et al., 2020):

( )= ( = 3000 m/s) + ( )

If the GMM, site-response model, and site assignments are accurate, we do not expect to see average site-response effects in these residuals.

1.3.1 Comparison of USGS Seed Models and NGA-East for Residuals Initial evaluations use the total ground-motion residuals ( ) to highlight features that may be minimized in the evaluations of between- and within-event residuals. In particular, we focus on the distance dependence of the total residuals. A characteristic distance dependence was noted for induced earthquakes by Moschetti et al. (2019), and we evaluate all residuals, as well as subsets of induced and tectonic events. Figure 1-6 depicts total residuals at multiple periods (T=0.1, 0.2, 0.5, 1.0, 2.0, 5.0 s) for all events within a 300 km distance range. Figure 1-7 depicts total residuals at multiple periods within a 300 km distance range for events occurring within the Oklahoma-Kansas (OK-KS) zone of potentially induced seismicity. Figure 1-8 depicts total residuals at multiple periods within a 300 km distance range for events occurring outside the OK-KS zone of potentially induced seismicity; this data set may include recordings from induced earthquakes outside of OK-KS, but we restrict this analysis to the OK-KS region because previous work has identified distinct path-attenuation features from earthquakes in this region, and these effects may not be common to other induced earthquakes.

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Figure 1-6: Total ground-motion residuals plotted as a function of distance using the Thompson et al. (2023) CENA data set.

Figure 1-7: Total ground-motion residuals plotted as a function of distance using the Thompson et al. (2023) CENA data set and limited to events occurring within the Oklahoma-Kansas zone of potentially induced seismicity.

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Figure 1-8: Total ground-motion residuals plotted as a function of distance using the Thompson et al. (2023) CENA data set and limited to events occurring outside of the Oklahoma-Kansas zone of potentially induced seismicity (events are predominantly of tectonic origin).

We find that all subsets of the total ground motion residuals indicate evidence of distance dependence (Figure 1-6, Figure 1-7, Figure 1-8). This feature was observed in a previous data set of induced earthquakes in Oklahoma and Kansas (Moschetti et al., 2019; Rennolet et al.,

2018) and was therefore expected for the subset of earthquakes in Oklahoma and Kansas from the CEUS-wide data set. For the CEUS-wide data set, the distance-dependent feature may be explained because the OK-KS region makes up a large part of the records in the CEUS data set; however, the distance-dependence evident in the non-OK-KS data set suggests that the incorporation of events east and southeast of those included in the NGA-East data set may show different distance attenuation features.

We partition total ground-motion residuals into bias ( ), between-event residuals ( ), and within-event residuals ( ) using linear mixed-effects regressions with a grouping on event IDs (Seabold and Perktold, 2010; Skipper Seabold et al., 2017):

= + +

We evaluate the results from the mixed-effects regressions to determine if there are trends with magnitude, distance, or period. Plots of between-event residuals plotted as a function of magnitude indicate that there are no significant trends (Figure 1-9). Although individual events (event terms) deviate from zero, the average (binned) values support the magnitude scaling of the NGA-East GMMs. Notably, moderate- to large-magnitude earthquakes are missing from the NGA-East data set, and magnitude-scaling of these eventswhich are most significant for seismic hazardremains largely unconstrained.

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Figure 1-9: Between-event terms plotted as a function of magnitude for oscillator periods of (a) 0.1 s, (b) 0.2 s, (c) 0.5 s, (d) 1.0 s, (e) 2.0 s, and (c) 5.0 s.

Distance scaling of the within-event residuals likewise shows an average agreement with the NGA-East predictions (Figure 1-10). Distance-binned within-event terms are near zero between 10 and 500 km, indicating that the path terms in NGA-East GMMs largely match the observations in the region. The large variance in within-event residuals at large distances ( >

100 km) can likely be attributed to regional variations in anelastic attenuation (e.g., Levandowski et al., 2021). The NGA-East GMMs and the NGA-East seed GMMs embody significant variability that is not represented in ground-motion analyses with logic-tree-averaged GMMs because the residual calculations do not explicitly consider the epistemic uncertainties of the GMMs. Further comparisons with variance models, such as the Southwestern U.S. (SWUS)

Project for the Diablo Canyon Nuclear Power Plant (GeoPentech, 2015), Al Atik and Youngs (2014), or Rezaeian et al. (2015), could be instructive.

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Figure 1-10: Within-event terms plotted as a function of rupture distance for oscillator periods of (a) 0.1 s, (b) 0.2 s, (c) 0.5 s, (d) 1.0 s, (e) 2.0 s, and (c) 5.0 s.

Bias terms from the updated CEUS ground motion data set reveal a period-dependent trend, with an on-average overprediction of short-period ( 1 s) and under-prediction of long-period

( 2 s) ground motions (Figure 1-11). Ground-motion residuals computed for hard-rock ( =

3000 m/s) site conditions and computed from the topography-based proxy for and the CEUS site-amplification model (Rezaeian et al., 2021; Stewart et al., 2020) show similar trends, with greater short-period overprediction and lesser long-period underprediction from the use of the site-amplification model. The misfit at short periods from the use of = 3000 m/s site conditions is particularly enigmatic because it suggests a deamplification of the surface motions for average site conditions in the CEUS relative to NGA-East ground-motion levels. Errors in the characterization of by the proxy-based method are likely, and these errors may be improved by using methods previously used in the CEUS (e.g., Goulet et al., 2021) or by applying novel methods; however, the errors in assignments cannot drive the misfit patterns. Because average site conditions in the CEUS are less than 3000 m/s, and current site-amplification models (Stewart et al., 2020; Rezaeian et al., 2021) indicate linear amplifications for sites with < 3000 m/s, relative to the ground motions at = 3000 m/s, these results suggest that: (1) the average short-period ground motion levels of the NGA-East GMMs are too high, (2) that the average linear site response to short-period ground motions is one of deamplification, rather than amplificationas is typically assumed, or (3) a combination of these effects. The causes of this discrepancy were not investigated in the scope of this study, but potential areas of future inquiry may include evaluation of for the hard-rock reference condition of the NGA-East GMMs and investigating the ergodic site-amplification models used in correcting observed ground motions to hard-rock conditions during the NGA-East project. For example, if the reference value of for the hard-rock condition of the GMMs is too low for average conditions in CEUS, the seed models (and resulting GMMs from the NGA-East Procedure) are likely to produce too-high short period ground motions at all conditions.

Spatial variations in or in the attenuation of high-frequency seismic waves at surface 1-12

conditions may also play a factor. At the time of the development of the NGA-East GMMs, CEUS-specific site-amplification models were not available. Such models are now available and should be considered in future updates (e.g., Stewart et al., 2020).

The effects of deep sediments on ground motions in the CEUS have been documented by numerous researchers. During the course of this project, Mills et al. (2020) compiled geologic information on the depths of sediments in the Atlantic and Gulf Coastal Plains. We use this data compilation to identify stations with known sediment thicknesses and evaluate the effect of these sites on the bias from the updated CEUS data set. Removing sites with more than 100 m of sediment in the Coastal Plains (CP) and re-computing bias results in decreased bias, with reduced short-period overprediction and reduced long-period underprediction (Figure 1-11, Figure 1-12, Figure 1-13). However, period-dependent misfit remains after accounting for sites that may include deep-sediment amplification/de-amplification.

Work is ongoing to understand the differences in the bias values from subsets of the ground-motion data set, but initial results suggest that some of the differences may arise due to variations in regional ground motions that manifest due to different spatial sampling. We have compared measured ground motions from the USGS data set (Thompson et al., 2023) with alternative data sets (Chapman and Guo, 2021; Goulet et al., 2021b) and compared metadata (magnitudes, ) to confirm that differences in data and metadata do not explain the differences in bias values. Error! Reference source not found. depicts total residuals for sites within the Coastal Plains of the CEUS. Sites with thin sediment depths have positive residuals, and sites with deep sediment depths have negative residuals. Furthermore, the USGS dataset contains a greater proportion of sites with thin (1000-3000 m) sediment depths than does the NGA-East data set (Error! Reference source not found.), suggesting that the spatial sampling of stations within the CEUS may have a substantial effect on the bias that arises from the data sets.

Figure 1-11: Bias terms plotted as a function of oscillator period (T) comparing results from ground-motion residuals computed for = m/s and ground-motion residuals computed for values at station locations (Allen and Wald, 2009).

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Figure 1-12: Comparison of bias terms from tectonic (Tectonic) and potentially induced (IndSeis) earthquakes as a function of period (T) from the Thompson et al.

(2023) CENA data set. Plots also depict the effect of including and excluding records from sites within the Atlantic and Gulf Coastal Plains (CP) on the computed bias.

Figure 1-13: Sediment thicknesses in the Atlantic and Gulf Coastal Plains. Figure from Boyd et al. (in press).

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Figure 1-14: Ground-motion residuals, SA (T=0.4 s), within Coastal Plain and distribution of sediment-thicknesses among USGS and NGA-East data sets. Figures from Boyd et al. (in press). The legend in panel (b) also applies to panel (a). Data sets include the USGS data set (Thompson et al., 2023), the NGA-East data set (Goulet et al., 2021b), and the data set of Chapman and Guo (2021).

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2 APPROACHES TO COMBINING GROUND-MOTION MODELS FOR PROBABILISTIC SEISMIC HAZARD ANALYSIS IN CEUS This chapter summarizes two separate approaches to combining GMMs for probabilistic seismic hazard analysis (PSHA) in the CEUS that were performed under the Nuclear Regulatory Commissions (NRC) Interagency Agreement. (1) The first subsection describes work done to implement NGA-East and other CEUS GMMs into the U.S. NSHM for the 2018 update (Petersen et al., 2020; Rezaeian et al., 2021). This work has been published as an open-access journal article in Earthquake Spectra (Rezaeian et al., 2021). The first section describes the currently acceptable approaches in combining CEUS GMMs for use in USGS PSHA calculations, summarizes the effects of using different sets of CEUS GMMs (updated seed GMMs, and the final NGA-East GMMs which were an update to the NGA-East for USGS GMMs and aligned with the NGA-East for SSHAC) on PSHA calculations, and provides recommendation on the GMMs application for use in the PSHA based on results of the GMMs testing against recorded data. The subsection also provides information regarding epistemic uncertainties in GMMs and the use of a CEUS-specific site effects model for use in the USGS PSHA. (2) The second subsection summarizes work to implement, verify, and evaluate the NGA-East Procedure.

2.1 Summary of the USGS Approach to Combining GMMs in the CEUS for the 2018 U.S. NSHM In support of this Task, Rezaeian and others published an open-access paper in the journal, Earthquake Spectra (Rezaeian et al., 2021) on the USGSs approach to developing a logic tree of CEUS ground motion models for the 2018 NSHM:

Rezaeian S, Powers PM, Shumway AM, Petersen MD, Luco N, Frankel AD, Moschetti MP, Thompson EM, and McNamara DE (2021). The 2018 update of the US National Seismic Hazard Model: Ground motion models in the central and eastern US. Earthquake Spectra, CENA Special Issue. Online First, March 2021. doi:10.1177/8755293021993837 This subsection (Error! Reference source not found.) summarizes the findings of Rezaeian et al. (2021).

The CEUS GMM updates in the 2018 NSHM consist of (1) 31 new GMMs, including the state-of-the-art NGA-East GMMs (Goulet et al., 2017, 2018, 2021a,b; PEER, 2015), (2) an associated model of aleatory variability (based on Al Atik, 2015; Goulet et al., 2017; Stewart et al., 2019),

and (3) a new site-effect model (for amplification or de-amplification) specific to the CEUS (Hashash et al., 2020; Stewart et al., 2020). The first two items are directly aligned with the objectives of Task 3. We discuss the individual GMMs in terms of their medians, assigned weights, weighted averages, attenuations with distance, and epistemic uncertainty. We also elaborate on the aleatory variability and site-effect models and provide details on their implementation in the 2018 NSHM. Whenever possible, we compare each of these GMM components to those considered in prior NSHMs, specifically, the 2008 and 2014 NSHMs (Rezaeian et al., 2015), both of which are still in use for various engineering and risk assessment applications. Finally, we discuss the impact of the 2018 GMM updates on hazard relative to previous NSHMs for an assumed earthquake source model in the CEUS.

The changes to the CEUS GMMs in the 2018 NSHM were partly motivated by the new multi-period response spectra requirements of seismic design regulations that use hazard results for 22 spectral periods and 8 site classes. As the previous CEUS GMMs were outdated and limited in their periods and site classes, the 2018 NSHM incorporated 31 new GMMs for hard-rock site 2-1

conditions ( = 3000 m/s), including the final NGA-East GMMs. New aleatory variability and site-effect models, both specific to the CEUS, are applied to all median hard-rock GMMs.

Rezaeian et al. (2021) documents the changes to the USGS GMM selection criteria and provides details on the new CEUS GMMs used in the 2018 NSHM update. The median GMMs, their weights, epistemic uncertainty, and aleatory variability are compared to those considered in prior NSHMs. The paper further provides implementation details on the CEUS site-effect model, which allows conversion of hard-rock ground motions to other site conditions in the CEUS for the first time in NSHMs. Compared to the 2014 NSHM hard-rock ground motions, the weighted average of median GMMs increases for large magnitude events at middle to large distance range, epistemic uncertainty increases in almost all situations, but aleatory variability is not significantly different. Finally, the total effect on hazard is demonstrated for an assumed earthquake source model in the CEUS, which shows an increased ring of ground motions in the vicinity of the New Madrid seismic zone and decreased ground motions near the Eastern Tennessee seismic zone.

2.1.1 Multi-Period Response Spectra (MPRS) Influencing the CEUS GMM Selection Selection of GMMs for the 2018 NSHM was not only influenced by the best available scientific modeling and seismic data, but also by the interests of earthquake engineers to move towards multi-period response spectra (MPRS). Prior to the current update, the design ground motion maps of the NEHRP Provisions only required mean hazard values at three spectral periods (i.e.,

0, 0.2, and 1 s) and one reference site condition (i.e., soft rock with = 760 m/s). The USGS therefore developed prior NSHMs primarily to permit computation of mean-hazard ground motions at the reference site condition for the peak ground acceleration (PGA) and pseudo spectral accelerations (SAs) at periods of 0.2 s and 1 s for the average horizontal component (i.e., geometric mean or an approximate equivalent) at a 5% damping ratio. As a result, the USGS GMM selection criteria were limited to the performance of models at the three mentioned periods and one reference site condition; other periods and site classes were also available in reports and at the USGS website over the past several cycles of updates; however, these were not considered in the NEHRP provisions. Project 17, a joint committee of BSSC-organized engineers and USGS researchers, was formed as part of the 2020 NEHRP Provisions update cycle to improve the procedures for development of the next generation of seismic design values. One of the recommendations of Project 17 was to incorporate multi-period and multi-response spectral values (collectively referred to as multi-period response spectra, MPRS) and make use of USGS hazard results at more periods and site conditions. This recommendation was made to improve the design response spectrum of the NEHRP Provisions and avoid potentially dangerous underestimation of design forces for long period structures on soft site conditions. As a result, for the 2018 NSHM update, only GMMs that are applicable for (or can be reasonably extrapolated to) all periods and site conditions of interest are selected.

Updates to the USGS GMM selection criteria that stem from the recommendation of Project 17 to use MPRS are presented in Rezaeian et al. (2021), which is the only 2018 NSHM publication where these updates are formally documented.

2.1.2 Updates to the GMM Selection Criteria in the 2018 NSHM Given the recommendation of Project 17 to use MPRS, the USGS selected 22 periods and 8 values that represent the centers of site classes defined for the 2020 NEHRP Provisions.

These periods and site classes are described in Shumway et al. (2020) and shown in Table 2-1.

They span PGA, a range of periods from 0.01 to 10 s, and a range of site classes from hard rock (site class A) to very loose sand or soft clay (site class E). The 2018 NSHM provides hazard results for all these periods and site classes, and because future NSHMs are also 2-2

expected to do the same, items 1 and 10 in the USGS GMM selection criteria have been updated as follows:

1. Basic Requirement (2018)The GMM must provide, as a minimum, equations for the median and aleatory variability of the horizontal component for peak ground acceleration (PGA) and spectral accelerations at periods from 0.01 to 10 seconds, specifically the 21 periods 0.01, 0.02, 0.03, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 7.5, and 10 seconds. If equations are not provided for all 22 periods (including 0 seconds for PGA), the GMM must be reasonably extrapolated or interpolated to them. The GMM must be applicable to one of the tectonic regions relevant to the United States and its territories.

10. Site Condition Requirement (2018)The GMM must include a term for or be accompanied by one or more site-effect models that adjust the GMM to, at a minimum, the eight values of 1500, 1080, 760, 530, 365, 260, 185, and 150 meters per second (m/s),

representing NEHRP Site Classes A, B, BC, C, CD, D, DE, and E, respectively. If the GMM does not include all eight values, it must be reasonably extrapolated or interpolated to them. For use in softer soil hazard models, the GMM should account for nonlinear soil effects.

While it would be possible to select different suites of GMMs for different periods and site classes, our updated selection criteria above for the 2018 NSHM are designed to result in the same set of GMMs for all periods, in order to achieve a smooth spectral shape that has no discontinuities with respect to period. Furthermore, the selection criteria also maintain GMM consistency across all site classes. However, future research or observations may reveal that a GMM is not acceptable at a particular site class (for example, site class E), but is necessary to represent epistemic uncertainty at other site classes. If such variation across periods and/or site classes is allowed in a future version of the NSHM, USGS GMM selection criteria would require revision.

Table 2-1: (Table 1 of Rezaeian et al.,2021): Minimum requirements for spectral periods and site classes.

2014 NSHM and prior: 2018 and 2023 NSHM*:

Periods, s 0 (PGA), 0.2, 1 0 (PGA), 0.01, 0.02, 0.03, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 7.5, 10

, m/s 760 (BC-soft rock) 1500 (A-hard rock)

(site-class 1080 (B-medium hard rock) description) 760 (BC-soft rock) 530 (C-very dense soil or hard clay) 365 (CD-dense sand or very stiff clay) 260 (D-medium dense sand or stiff clay) 185 (DE-loose sand or medium stiff clay) 150 (E-very loose sand or soft clay)

• See Shumway et al. (2019) for more details on the selection of the given periods and site classes.

2.1.3 Older GMMs and Weights In the 2014 NSHM, the nine CEUS GMMs in Figure 2-1 were used to represent epistemic uncertainty in GMMs, logic tree weights were assigned based on model type (i.e., single-corner models, dynamic-corner models, hybrid models, reference-empirical models, and full-waveform 2-3

simulation-based models) and categorization of near-source geometric spreading (i.e., ,

, or otherwise). The logic tree weights were assigned to avoid redundancy by grouping similar models and to give more weight to models in which experts have greater confidence.

Although this approach is well established, it is subjective. The standard deviations are shown in Figure 2-2 as functions of period; unlike the median models, the standard deviation models do not depend on distance.

The 2014 NSHM GMMs in the CEUS are not applicable or adjustable through reasonable extrapolations for all periods and site conditions of interest in the 2018 NSHM. Most of these GMMs are not available for spectral periods beyond 4 s and very few are available for site classes softer than BC. New and updated GMMs have recently become available via NGA-East Project (Goulet et al., 2021) and other modelers (e.g., Stewart et al., 2020), and therefore all nine CEUS GMMs are replaced in the 2018 NSHM with new models that not only satisfy the MPRS requirements of extended periods and site classes but also better represent the epistemic uncertainty, as described in the following sections.

Figure 2-1: (Figure 1 of Rezaeian et al., 2021): The nine 2014 NSHM GMMs in the CEUS for a magnitude 7 event on a very hard rock site: (a) median ground motions versus period at a distance of 50 km, and (b) median ground motions versus distance at a 0.2 s spectral period. Model abbreviations and logic tree weights used to compute the weighted average are given in Table 2-1.

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2014 CEUS GMM Standard Deviations 1.2 1 F96 T02 S02 0.8 C03 TP05 AB06 Prime 0.6 P11 A08 Prime 0.4 S01 0.2 0

0.01 0.1 1 Spectral Period (s)

Figure 2-2: (Figure 2 of Rezaeian et al., 2021): Standard deviations of the nine 2014 NSHM GMMs in the CEUS for a magnitude 7 event on a very hard rock site versus spectral period. Model abbreviations are given in Table 2-2.

2.1.4 CEUS GMMs in the 208 NSHM for Very Hard Rock Conditions The 2018 NSHM update uses two suites of CEUS GMM medians: (1) 14 updated seed GMMs with a collective weight of 0.333, which are an updated subset of the NGA-East adjusted seed models as described in the next section, and (2) the 17 NGA-East GMMs with a collective weight of 0.667. These group weights, like all USGS NSHM logic trees, are based on a consensus-building process that assigns weights to a range of expert opinions. Figure 2-3 shows these two main logic tree branches and their collective weights. The decision to update to NGA-East GMMs over the 2014 GMMs is also supported by the residual analysis of McNamara et al. (2019), which showed that the NGA-East GMMs provide a more accurate representation of the distribution (both median and standard deviation) of the observed instrumental ground motion data in stable tectonic environments than GMMs used in the 2014 NSHM. All the models in Figure 2-3 are applicable to the 22 periods, but they are only valid for very hard rock site conditions corresponding to = 3000 m/s and = 0.006 s (see Hashash et al., 2014; Campbell, 2009 for the definition of , a term that reflects site attenuation, and more information on site conditions). A site-effect model was developed and applied to these GMMs for conversion to different site conditions.

Although the final NGA-East GMMs and associated weights are intended to represent the entire epistemic uncertainty by quantifying the center, body, and range of the underlying distribution in an objective way, in the 2018 NSHM update we also include a logic tree branch for the updated seed GMMs. This decision was made because some participating experts at the 2018 NSHM workshop made the case that incorporating both suites of GMMs is necessary to accurately represent the epistemic uncertainty. They argued that seed GMMs are more informed by physics, as opposed to the outcome of the Sammons mapping process in the NGA-East approach that results in models which are not interrogated by individual modelers in same the way that has been customary for GMM development. Therefore, seed GMMs should be incorporated directly in the NSHM to capture any physical features that may not be represented by GMMs derived via Sammons mapping. An example of such a physical feature is a strong 2-5

reflection of seismic waves from the Mohorovii discontinuity, the boundary between the crust and the mantle in the Earth that can change the velocity and composition of seismic waves, (hereafter referred to as the Moho reflection) that is seen in the attenuation of most seed GMMs with distance around 60 to 100 km but is somewhat subtle in the final NGA-East GMMs.

Another example is the higher correlations seen between the NGA-East GMMs, with respect to distance, compared to the seed GMMs, which may not affect the mean hazard substantially at an individual site, but is suspected to influence uncertainty analyses and applications that aggregate the hazard, e.g., portfolio risk assessments. Both examples are discussed in detail in this paper. Given that the current primary output of the USGS NSHM is the mean hazard at individual sites, and to reflect the confidence of most workshop participants in the Sammons mapping process, the set of final NGA-East GMMs is assigned double the weight (0.667) of the updated seed GMMs (0.333).

The weighted medians calculated separately for the updated seed and the NGA-East GMMs, assuming hypothetical group weights of 1 for each suite, were compared to each other in Petersen et al. (2020, their Figure 3). In general, the NGA-East GMMs result in larger weighted medians compared to the updated seed GMMs for large magnitude events. Hypothetical hazard maps, also assuming group weights of 1 for each suite of GMMs, are compared in Petersen et al. (2021) to understand the sensitivity of hazard values to each suite of models. In the following, we first present the two suites of 14 updated seed and 17 NGA-East median GMMs.

We discuss the behavior of each suite in terms of attenuation with distance and representation of epistemic uncertainty. We then compare the combined weighted median of the two GMM suites, using their final group weights of 0.333 and 0.667, to the weighted medians from prior NSHM cycles.

2.1.4.1 14 Updated Seed GMMs and Weights For the 2018 NSHM update, we performed our own review of the 19 NGA-East adjusted seed GMMs (PEER, 2015) and selected 13 models based on our GMM selection criteria. We replaced two of the adjusted seed models with three updated versions from Graizer (2016, 2017) and Shahjouei and Pezeshk (2016), which were published after the NGA-East report on adjusted seed models was completed. We refer to these final selected 14 seed models as the updated seed GMMs. All adjusted seed models are listed in Table 2-2 with their assigned weights. If an adjusted seed model was not selected or was replaced in the set of 14 updated seed GMMs, its assigned weight is zero.

Logic tree weights are assigned to the updated seed GMMs using the same method as in the 2014 NSHM. The CEUS GMM logic tree and final weights are illustrated in Figure 2-3. We generally consider equal weights across different geometric spreading categories and model types and split weights between multiple models developed by a single team who assumed alternative input parameters. In the end, the individual model weights are low and are very similar to one another. These weights were discussed with the NGA-East team and the National Seismic Hazard Model Project Steering Committee and found to be reasonable. Other weighting methodologies could be chosen that would also lead to reasonable assessments of mean hazard. During an early sensitivity analysis, two alternative weighting methodologies were considered, which resulted in at most 10% difference in the total mean hazard, with smaller differences at shorter periods, and larger differences at longer periods.

As shown in Error! Reference source not found., the updated seed GMMs are separated into three categories based on their geometric spreading: (1) models, (2) models, and (3) other models, with each group receiving almost equal weight (0.33, 0.33, and 0.34, 2-6

respectively). The models are then grouped by model type, which are different from those used in the 2014 NSHM due to improvements made to previous models and new modeling approaches. Within each branch for a given model type, weights are distributed based on a number of considerations that consist of expert opinions (including those of the modelers when multiple models are available from the same developer team), residual studies, magnitude and distance scaling of the models, and examination of their spectral shapes, Table 2-2: (Table 3 of Rezaeian et al., 2021): CEUS ground motion models in the 2018 NSHM.

Authorship Weight CEUS GMMs (Acronyms) 14 Updated Seed GMMs (used by USGS in 2018 NSHM) 0.333 B-bca10d Boore 0.02209 B-ab95 Boore 0.00736 B-bs11 Boore 0.00736 2CCSP Darragh-Abrahamson-Silva-Gregor 0.01841 2CVSP Darragh-Abrahamson-Silva-Gregor 0.01841 Graizer16 Graizer 0.01813 Graizer17 Graizer 0.01813 PZCT15-M1SS Pezeshk-Zandieh-Campbell-Tavakoli 0.01813 PZCT15-M2ES Pezeshk-Zandieh-Campbell-Tavakoli 0.01813 SP16 Shahjouei-Pezeshk 0.03626 YA15 Yenier-Atkinson 0.03736 HA15 Hassani-Atkinson 0.03736 Frankel15 Frankel 0.03737 PEER-GP Hollenback-Kuehn-Goulet-Abrahamson 0.03850 Other NGA-East Adjusted Seed GMMs (not used by USGS in 2018 NSHM) 0 B-a04 Boore 0 B-ab14 Boore 0 B-sgd02 Boore 0 1CCSP Darragh-Abrahamson-Silva-Gregor 0 1CVSP Darragh-Abrahamson-Silva-Gregor 0 SP15 (replaced with SP16 by USGS) Shahjouei-Pezeshk 0 Graizer (replaced with Graizer16 & 0 Graizer Graizer17 by USGS)

PEER-EX Hollenback-Kuehn-Goulet-Abrahamson 0 ANC15 (see footnote 4) Al Noman-Cramer 0 17 NGA-East GMMs (used by USGS in 2018 NSHM) 0.667 Period-Models 1 to 17 NGA-East Project dependent*

The models are grouped into two types: (1) point-source models (B_bca10d, B_ab95, B_bs11, 2CCSP, and 2CVSP) with a group weight of 0.67, and (2) empirical-factor models 2-7

(Graizer16 and Graizer17) with a group weight of 0.33. More weight is given to the first group because more models of this type are available from two independent developer teams and because this type of model has been used and tested for a longer time in the NSHMs. These models are individually described in Rezaeian et al. (2021).

The models are categorized into three types: (1) hybrid empirical (PZCT15_M1SS and PZCT15_M2ES), (2) hybrid empirical and broadband (SP16), and (3) stochastic equivalent point source (YA15). Each of these three groups is assigned equal weights. These models are also individually described in Rezaeian et al. (2021).

There are three models (HA15, Frankel15, and PEER_GP) with geometric spreading other than or . Each are assigned almost equal weight and further summarized in Rezaeian et al.

(2021).

The 14 updated seed models described above are shown in Error! Reference source not found. for a magnitude 7 event on a very hard rock site condition ( = 3000 m/s), along with the 9 CEUS GMMs of the 2014 NSHM (but with = 2000 m/s as they are not available for 3000 m/s). Note that although the 2014 and 2018 GMMs consider different values for very hard rock, the differences in predicted ground motion values are typically very small for the two site conditions. The updated seed GMMs show complexity in distance scaling (Figure 2-4). The flat segment in Error! Reference source not found.b, around 60 to 100 km, is prominent in many of the seed GMMs. This flattening is likely due to the Moho reflection and is typically seen in physics-informed GMMs (e.g., Frankel15). Furthermore, the updated seed GMMs have varying distance-scaling slopes, with little to no correlation between models with respect to distance (models cross each other in Figure 2-4b).

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Figure 2-3: (Figure 3 of Rezaeian et al. (2021). A logic tree showing the grouping of updated seed GMMs by geometric spreading and model type, as well as the weights assigned to all CEUS GMMs in the 2018 NSHM. Relative weights for each group or model are given in parentheses.

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Figure 2-4: (Figure 4 of Rezaeian et al., 2021): The 14 updated seed CEUS GMMs in the 2018 NSHM for a magnitude 7 event on a very hard rock site: (a) medians versus period at a distance of 50 km, and (b) medians versus distance at 0.2 s spectral period, superimposed on the 9 CEUS GMMs from the 2014 NSHM of Figure 2-1.

Model abbreviations and weights defined in Table 2-2 and Figure 2-3.

2.1.4.2 17 NGA-East GMMs and Weights The NGA-East project team adjusted the seed models, developed by individual modelers, and used them as inputs to a Sammons mapping procedure (Scherbaum et al., 2010). The procedure then resamples the ground-motion space to select an evenly distributed set of GMMs and weights that better represent the underlying continuous distribution (or epistemic uncertainty) than the set of input seed GMMs. The evenly distributed set avoids redundant GMMs and fills out the predicted space of possible GMMs. The resulting NGA-East GMMs are tabulated values (i.e., not equations) for given magnitudes, distances, and spectral periods.

Three early versions of the NGA-East models based on Sammons mapping were considered for use in the 2018 NSHM update: (1) a suite of 29 GMMs; (2) a suite of 13 GMMs; and (3) a suite of 17 GMMs (referred to as NGA-East for USGS, Goulet et al., 2017, with an addendum, referenced in Petersen et al., 2020a). After each version, the USGS provided feedback to the NGA-East modelers for improving the final set, but the overall variation in mean hazard was minor, reflecting robustness of the Sammons mapping process regardless of sampling density.

After the completion of 2018 NSHM, the suite of 17 GMMs was republished by NGA-East for assessing seismic safety of nuclear facilities and was called the NGA-East final suite (Goulet et al., 2018). Hence, the 2018 NSHM uses the NGA-East final suite of GMMs by incorporating the Goulet et al. (2017) report with the addendum.

The final 17 NGA-East GMMs are shown in Error! Reference source not found. for a magnitude 7 event on very hard rock site conditions ( = 3000 m/s), with the 9 CEUS GMMs of the 2014 NSHM for comparison. In this figure, the line type is different for GMMs with less (dotted lines) and more (dashed lines) than about 5% weight to show which GMMs have more weight in the ground motion space. As shown in Error! Reference source not found., the weights are period dependent. To make Figure 2-5a, weights are approximated by taking the average of the weights across all periods. The 17 NGA-East GMMs show less complexity in 2-10

distance scaling compared to both the 2014 NSHM (Figure 2-5b) and the 14 updated seed (Figure 2-4b) GMMs. The Moho reflection resulting in the flat segment around 60 to 100 km is very subtle in NGA-East GMMs (Figure 2-5b). The lack of this strong flattening feature in the NGA-East GMMs is an important consideration in giving the updated seed GMMs some weight in the 2018 NSHM. Furthermore, the NGA-East GMMs exhibit higher correlations between models with respect to distance and are almost subparallel compared to the updated seed GMMs (Figure 2-4b and Figure 2-5b). Error! Reference source not found.b also suggests that the NGA-East GMMs exhibit a geometric spreading with slower attenuation that is better associated with models and higher stress drops. This could be an unintentional result of Sammons mapping or due to more representation of such models in the input seed GMMs (recall that our updated seed GMMs exclude/replace some input seed GMMs, Table 2-2); more studies are required to understand this feature.

Figure 2-5: (Figure 5 of Rezaeian et al., 2021) Medians of the 17 NGA-East GMMs in the 2018 NSHM for a magnitude 7 event on a very hard rock site: (a) medians versus period at a distance of 50 km, and (b) medians versus distance at 0.2 s spectral period, superimposed on the 9 CEUS GMMs from the 2014 NSHM in Error! Reference source not found.. Vertical bars and arrows indicate the range of ground motions at different spectral periods and distances for the two groups of GMMs and are referenced in Figure 2-10.

Additional figures that directly compare the two suites of updated seed GMMs and NGA-East GMMs (without the 2014 GMMs) and additional figures and discussions on the assigned weights are provided in Rezaeian et al. (2021).

2.1.5 Weighted Average of Medians Figure 2-6 and Figure 2-7 show the weighted averages of CEUS GMM medians as functions of spectral period and distance, respectively, for two magnitude scenarios: 5.5, typical of areas with high background or gridded seismicity rate (e.g., the East Tennessee seismic zone), and 7.5, typical of fault-based or RLME sources (e.g., the New Madrid seismic zone). Both figures include the weighted combinations of medians from the 2014 and 2008 NSHMs. Although not exact representations of changes in the final hazard, these weighted averages of GMM medians 2-11

are a good proxy for what happens to the final estimated mean hazard when they are combined with uncertainties discussed in the following sections.

Figure 2-6 shows the ground motions at three distances of 10, 50, and 300 km. The median 2018 GMMs at 0.2 and 1 s periods are slightly lower than the median 2014 GMMs for small magnitude events (e.g., around East Tennessee), but are noticeably larger than the median 2014 GMMs for large magnitude events (e.g., around New Madrid) at larger distances. At short distances, the differences are negligible. The increase for large magnitudes at larger distances could be due to the higher weight that is given to the NGA-East GMMs and their larger values due to their slower attenuation with distance beyond 60 km compared to the updated seed and the 2014 GMMs. This causes a ring of increased ground motion values around, but not in the immediate vicinity of, the New Madrid seismic zone. In Error! Reference source not found.,

median 2008 GMMs are also shown, which also used physics-informed GMMs, but with more weight on models (GMMs with slower attenuation) compared to the 2014 GMMs. The 2008 GMM median is closer to the 2018 GMM median for large magnitude events and middle to large distances. In most cases, the changes in GMM medians from 2014 to 2018 are more significant compared to the previous cycle (from 2008 to 2014), stemming from the use of an entirely new set of GMMs in the 2018 cycle.

Figure 2-7 shows the attenuation of 0.2 and 1 s ground motions with distance, plotted in the linear distance scale unlike Figure 2-4b and Figure 2-5b to show a different perspective and to be comparable to similar figures in previous NSHM publications. Observe that the medians for hard rock slightly decrease from the 2014 to the 2018 cycle for small magnitude events but increase for large magnitude events. Note that for large magnitudes, the increase from 2014 to 2018 accelerates around 60 to 80 km (where Moho reflection happens), and is relatively constant beyond about 80 km. The 2008 GMM medians are also shown in Figure 2-7. Note that, for large magnitude events, the 2018 GMMs are closer to the 2008 GMMs than the 2014 GMMs at middle to large distances.

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Figure 2-6: (Figure 7 of Rezaeian et al., 2021) Weighted averages of CEUS GMM medians from the 2018 NSHM, 2014 NSHM (RLME, distances below 500 km), and 2008 NSHM (RLME) versus period for magnitude 5.5 and 7.5 events at 10, 50, and 300 km distances for hard rock representing the original site conditions of the models (about 2000 m/s in 2008 and 2014 NSHMs, 3000 m/s in 2018 NSHM).

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Figure 2-7: (Figure 8 of Rezaeian et al., 2021) Weighted combinations of CEUS GMM medians from the 2018, 2014 (RLME, distances below 500 km), and 2008 NSHM (RLME) versus distance for magnitude 5.5 and 7.5 events at (a) 0.2 s and (b) 1 s.

These plots are made for hard rock representing the site conditions of the original models (2000 m/s in the 2008 and 2014 NSHMs, 3000 m/s in the 2018 NSHM).

2.1.6 Epistemic Uncertainty of Medians Epistemic uncertainty accounts for variability due to lack of knowledge and modeling choices and is represented by logic tree branches and weights associated with different models.

Replacing the 9 2014 CEUS GMMs with the 31 2018 CEUS GMMs increases the epistemic uncertainty significantly. Figure 2-8 demonstrates the increase of epistemic uncertainty in NGA-East GMMs by showing the range of median ground motion values and their assigned weights for the 17 NGA-East relative to the 9 2014 GMMs. Figure 2-9 makes the same comparison for the 14 updated seed and the 9 2014 GMMs. Both figures show values at three periods for a distance of 50 km, and at two distances for a 0.2 s period for a magnitude 7 event on hard rock site conditions. Note that the vertical scale is logarithmic in these figures and the range of vertical axes, while different, is similar in the order of magnitude in all subplots for easy comparison. The dashed lines show weighted averages of median ground motions. The solid lines on the vertical axes in Figure 2-9 are the same as the vertical cross sections in Figure 2-5 and indicate the range of ground motion values in each suite of GMMs. These ranges are a good representation of epistemic uncertainty (larger range = larger uncertainty), but the distribution of assigned weights, shown in Figure 2-8 and Figure 2-9 as stem plots, is also important. These figures show that the ground motion values for all three suites of models (2014 GMMs, 2018 NGA-East GMMs, 2018 updated seed GMMs) cover a broad epistemic uncertainty range: about a factor of 2 for the 2014 and the updated seed GMMs, and about a factor of 10 for the NGA-East GMMs, for a magnitude 7 event with variations depending on distances and periods.

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Figure 2-8: (Figure 9 of Rezaeian et al., 2021) Epistemic uncertainty of NGA-East GMMs represented by the range and distribution of ground motion medians at vertical cross sections of Figure 2-5, for a magnitude 7 event on hard rock (i.e., =

3000 m/s) at (a) a 50 km distance and three periods, PGA, 0.2, and 1 s; and (b) two distances, 10 and 100 km, at 0.2 s period.

Figure 2-8 and Figure 2-9 illustrate that the NGA-East GMM weights more closely resemble a normal distribution with higher weights in the middle and lower weights at the highest and lowest ground motion values. The peripheral, lower-weighted models are commonly those in the outer rings of the Sammons maps. In contrast, the weights of the 2014 GMMs and the updated seed GMMs are random and asymmetric reflecting the inherent subjectivity of the underlying GMM selection and weighting procedures. Although the NGA-East process may expand the range of GMMs and provide a more complete representation of the ground motion space, it may also have shortcomings that require further studies. For example, in Figure 2-8 and Figure 2-9, note that at 0.2 s and 100 km, where the physics-informed seed GMMs show less variability compared to 10 km, possibly due to the flattening effect of Moho reflections discussed earlier (Figure 2-4b and Figure 2-5b), the NGA-East GMMs show much more variability that is similar in the order of magnitude to that of 10 km. It is also worth noting that the weighted average of the NGA-East GMMs is at the upper end of the 2014 and the updated seed GMM values.

Without observed data for large magnitude events in the CEUS, it is difficult to make a 2-15

conclusion about the accuracy of the two sets of models. However, these considerations are reflected in the collective weights of 0.333 and 0.667, given respectively to the updated seed and NGA-East GMMs, based on a range of expert opinions and their confidence in each suite of models.

Figure 2-9: (Figure 10 of Rezaeian et al.) Epistemic uncertainty of updated seed GMMs represented by the range and distribution of ground motion medians at vertical cross sections of Figure 2-4, for a magnitude 7 event on hard rock (i.e., =

3000 m/s) at (a) a 50 km distance and three periods, PGA, 0.2, and 1 s; and (b) two distances, 10 and 100 km, at 0.2 s period.

Whereas USGS NSHMs have historically focused on mean hazard, or the center, with underlying logic trees of GMMs representing the body, the NGA-East GMMs expand on prior model distributions to represent broader range of possible ground motions. This feature will prove important as the USGS moves toward complementing mean hazard results with estimates of uncertainty in future NSHMs.

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2.1.7 Aleatory Variability Aleatory variability (GMM standard deviation) accounts for the random variability that is naturally present in ground shaking for a given magnitude, distance, and site condition. Unlike the 2008 and 2014 NSHMs, for which each GMM was assigned a different independently developed standard deviation, the 2018 NSHM uses the same standard deviation model for all GMMs.

Details of aleatory variability models from NGA-East and other seed GMMs are provided in Rezaeian et al. (2021).

The final standard deviation model incorporated in the 2018 NSHM consists of a logic tree of the NGA-East recommended model with 0.8 weight (Goulet et al., 2017, denoted 2018 Updated EPRI in Figure 2-10), and an alternate model that includes the working group site-to-site variability term, S2S, with 0.2 weight (denoted 2018 Working Group in Error! Reference source not found.). The final USGS implementation of this logic tree computes hazard for all pairings of CEUS median GMMs and the two aleatory variability models. As shown in Figure 2-10, the 2018 Working Group model is higher at short periods and lower at long periods compared to the WUS-based 2018 Updated EPRI model. The main reason for the higher short-period values is the relative preponderance of short-period resonances in the CEUS compared to the WUS sites. Because these effects are observed in available CEUS data but are not taken into account in the -based site-effect model (described in the next section and used in conversion of data to hard rock site conditions), the high dispersion in the site-effect model results in higher standard deviations. The lower values at long periods are supported by the available CEUS data, whereas the 2018 Updated EPRI model is based on WUS data.

Figure 2-10: (Figure 11 of Rezaeian et al., 2021) The two CEUS aleatory variability models (2018 Updated EPRI and 2018 Working Group), used for all 31 GMMs in the 2018 NSHM, and their SRSS combination (2018 NSHM), superimposed on standard deviation models of the nine 2014 GMMs for a magnitude 7 event on hard rock ( = 2000 or 3000 m/s).

There were other major updates to the site effects model and other implementation details that were not outlined under Task 3; these are explained in detail in Rezaeian et al. (2021).

2.1.8 Implications of GMM Changes on Hazard We calculated uniform hazard maps for 2% probability of exceedance in 50 years for the CEUS for 0.2 and 1 s spectral periods using the 2014 NSHM source model. One map uses the 2014 GMMs and the other used the 2018 GMMs. Figure 2-11 shows the difference and ratios 2-17

between these two maps at the two spectral periods. Difference and ratio maps for more common site classes in the CEUS are not presented because such maps were not developed in the 2014 NSHM due to site class limitations of CEUS GMMs in that cycle.

Figure 2-11: (Figure 15 of Rezaeian et al., 2021) Differences and ratios in ground motions with 2% probability of exceedance in 50 years hazard level, using the 2014 and 2018 CEUS GMMs (both using the 2014 NSHM source model). Maps are provided for 0.2 and 1 s spectral periods on a uniform hard rock site condition.

The 2018 NSHM update incorporates significant changes to the median ground motion values (lower for small magnitude events and higher for large magnitude events at middle to large distances; Figure 2-6 and Figure 2-7), epistemic uncertainty (higher in all cases but much greater for large magnitudes and middle to large distances; Figure 2-5b and Figure 2-8), and aleatory variability (not significantly different; Figure 2-10). The overall effects of these changes on hazard are shown in Figure 2-11 for the two periods of 0.2 and 1 s. Ground motions increase in a ring around the New Madrid seismic zone due to the increase in median ground motions 2-18

and epistemic uncertainty at middle to large distances (60 to 100 km), but a negligible change in median ground motion at short distances for large magnitude events. The median increase at middle to large distances is partly due to the updated seed GMMs, but mainly due to the larger NGA-East GMMs as a result of slower attenuations with distance and their subtle representation of Moho reflections (Figure 2-5b and Figure 2-8b). The epistemic uncertainty increases for large magnitude events at all distances, resulting in some increase in mean hazard everywhere; but because this increase is even greater at distances of about 100 km (Figure 2-5b and Figure 2-8b), it further contributes to the ring around the New Madrid seismic zone. The outer boundary of the ring could be a result of the New Madrid source being less dominant at larger distances.

On the other hand, the ground motions in the vicinity of the East Tennessee seismic zone decrease. This is due to the high rate of smaller magnitude events that control the hazard in this region. For smaller magnitudes, the median ground motion is slightly lower than the 2014 NSHM (Figure 2-6 and Figure 2-7), and the epistemic uncertainty does not increase as much as it does for large magnitude events. Likewise, in the areas outside of the New Madrid seismic zone, where background gridded seismicity with lower magnitude events controls the hazard (e.g., Oklahoma, Virginia, New York), ground motion decreases due to the changes in 2018 CEUS GMMs.

Petersen et al. (2021) further evaluated the effects on seismic hazard of the use of the two GMM logic trees in CEUS. Hazard sensitivity in this study used full weights to the NGA-East logic tree and the USGS updated seed models. Median ground motions were combined with the USGS aleatory variability models. NGA-East produced uniformly higher ground motions than the USGS seed models in this study, with SA ( = 0.2 s) differences exceeding 0.4 g and SA

( = 1.0 s) exceeding 0.2 g at sites in the New Madrid Seismic Zone. These values correspond to ratios of 0.25 or more across broad areas of the highest seismic hazard in CEUS.

2.2 Verification and Evaluation of NGA-East Procedure This work focuses on efforts to independently verify and evaluate the NGA-East Procedure. For the purpose of this report, the NGA-East Procedure consists of the development of the NGA-East GMMs by generating realizations from the multivariate normal (MVN) distribution constructed from the NGA-East seed models, with the use of a mixture model for sampling of realizations, and the development of model weights by discretizing the Sammons mapping space (Sammon, 1969) into a ellipse capturing 95 percent of sampled models, with 17 segments that represent the weights applied to GMMs within each segment. The NGA-East Project did not provide the software to reproduce the calculations presented in the final reports and manuscripts (Goulet et al., 2018); therefore, a primary objective of this work was to implement methods described in the NGA-East documentation, to verify steps in the procedure through reproduction of published figures, to evaluate the choices made by the NGA-East Project, and to provide sensitivity of the GMM logic tree to these choices, where possible, or to identify areas for further sensitivity testing.

2.2.1 Summary of NGA-East Procedure Here we briefly summarize the steps required for reproducing the NGA-East Procedure for producing the final logic tree (i.e., GMMs and associated weights). We partially reproduce the NGA-East Procedure and limit our discussions to these points. This work relies heavily on the NGA-East documentation (Goulet et al., 2021a; Goulet et al., 2018), the NRC evaluation of NGA-East (Stovall et al., 2020), and personal communications with NRC staff.

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(1) Step 1: Select seed GMMs. This work assumes that seed GMMs are available for defining the correlation structure of a continuous ground-motion distribution and that the GMMs are available at a consistent set of magnitudes and distances for defining the magnitude-distance dimensions. Variations in the period band of the seed models can be accommodated during later steps. The magnitude-distance pairs for each model, computed for 4-8.2 and 0 1500 km (values provided in Goulet et al., 2021),

define 374 scenarios for the hyperdimensional calculations. A fundamental assumption of the NGA-East Sammons procedure is that, for each frequency, the epistemic uncertainty in (natural logarithm of) ground motion, ln( ), is distributed as a MVN with mean, , and with a covariance matrix, :

ln( )~ ( , )

(2) Step 2: Determine the mean and sample covariance matrix, identify the target variance model, and calculate the correlation matrix for the scenarios, where scenarios in the NGA-East Procedure are defined as the ground motions at a particular magnitude-distance pair. In our case, the intensity measure types (IMTs) are spectral accelerations, though the procedure can be applied to other IMTs. The scenarios can be retrieved through any code base. We make use of the Python-based OpenQuake (Pagani et al.,

2014) and Shakemap (Wald et al., 2022) codes for instantiating NGAEast(). For each frequency, we loop over GMMs, implementing the frequency restrictions of Table 7-14 in Goulet et al. (2018). The frequency restrictions result in differing numbers of GMMs contributing to the covariance/correlation matrices at each frequency, with several restrictions requiring > 1 . The mean of acceptable GMMs is computed (dimension

) along with the (sample) covariances for all scenarios, which are used to construct a (sample) covariance matrix (dimensions x ). The correlation matrix, , is computed from the sample covariance matrix using the relationship for each element, where is the standard deviation of each of the ground motions for each scenario and indices i and j refer to individual scenarios:

=

Examples of the sample variances are plotted in Error! Reference source not found..

and with frequency restrictions in Error! Reference source not found.. The NGA-East Project noted that the sample variances indicated relatively low values at short distances and large magnitudes, where data is sparse and ground-motion uncertainties are inherently high. The Project therefore took the approach to replace the sample variances with target variances guided by principles including: that modeled uncertainty may be due to the development process (for example at large magnitude and short distances), that the epistemic uncertainty in CENA GMMs should exceed that in GMMs from shallow crustal events in active tectonic regions and that the epistemic uncertainty should vary smoothly in magnitude-distance space (Goulet et al., 2018). NGA-East employed a target variance model, , from SWUS, which evaluated model-to-model variance of semi-empirical GMMs from multiple active crustal regions and developed frequency-, magnitude-, and distance-dependent variance values that include values of 0.15 at zero-distance sites, 0.4 at the maximum distances (1500 km),

and values of 0.1 in the range where data is most prevalent (M4-5 and distances 150-400 km). See Goulet et al. (2018) and GeoPentech (2015) for details.

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Figure 2-12: Sample variances from the sample covariance matrices, NGA-East seed models. Scale bar and contours depict variance values.

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Figure 2-13: Sample variances from the sample covariance matrices, NGA-East seed models with frequency restrictions. Scale bar and contours depict variance values.

The NGA-East Project further modified the sample covariances by fitting the sample correlation structure with a model to ensure smoothly varying covariances and a positive definite covariance matrix, which is required for sampling from the MVN distribution. The sample correlation matrix is fit with a covariance function, with correlations then computed as given above, . Examples of the fit correlation matrices, , are given in Error! Reference source not found. and indicate smoother variations of the correlation coefficients with magnitude and distance. The elements of the final covariance matrix,

, combine the target variances with the model-fit correlation matrix elements:

=

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Figure 2-14: Reproduction of Goulet et al. (2018) Figure 8-18. Modeled correlation coefficients for f = 1 Hz, plotted against M and . Left; M = 5, =1000 km, Center: M = 6, =100 km, Right: M= 8, =20 km.

(3) Step 3: Produce Sammons maps of the seed models at each frequency. Sammons mapping (Sammon, 1969) is a dimensional-reduction method to project the ground motions from -space to two dimensions, through the use of the Sammons stress or error function, :

1

=

Sammons mapping maximizes the preservation of the distance-separation of GMMs in the projected space, , compared to their distance in -space, . Application of Sammons mapping to ground motions was introduced by Scherbaum et al. (2010). We use a Python-based package for the Sammons calculations.

Distances between GMMs i and j for the Sammons mapping calculation are computed as the normalized Euclidean distance (in two dimensions for and in dimensions for

):

1

=

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3 SCALED VERSIONS OF THE MEAN MODEL, , ARE USED TO ORIENT AND PROVIDE SOME INTUITION INTO THE MEANING OF THE PROJECTED DIMENSIONS. SCALED REFERENCE MODELS COMPRISE VERSIONS OF THE MEAN MODEL THAT ARE SCALED BY CONSTANT FACTORS (--,-,+,++), AND THAT APPLY DIFFERENT MAGNITUDE (M--,M-,M+,M++) AND DISTANCE SCALINGS (R--,R-

,R+,R++). EXPRESSIONS FOR THE SCALINGS ARE DESCRIBED IN GOULET ET AL. (2018). AN EXAMPLE SAMMONS MAP AT 1 HZ IS PROVIDED IN Abrahamson N, Kuehn N, Walling M, et al. (2019) Probabilistic Seismic Hazard Analysis in California Using Nonergodic Ground Motion Models. Bulletin of the Seismological Society of America 109(4): 1235-1249. DOI: 10.1785/0120190030.

Allen TI and Wald DJ (2009) On the use of high-resolution topographic data as a proxy for seismic site conditions (VS30). Bulletin of the Seismological Society of America 99(2A):

935-943. DOI: 10.1785/0120080255.

Al Atik and Youngs RR (2014) Epistemic Uncertainty for NGA-West2 Models. Earthquake Spectra 30(3): 1301-1318. DOI: 10.1193/062813EQS173M.

Bodin P and Horton S (1999) Broadband microtremor observation of basin resonance in the Mississippi Embayment, central US. Geophysical Research Letters. DOI:

10.1029/1999GL900146.

Boore DM (2010) Orientation-independent, nongeometric-mean measures of seismic intensity from two horizontal components of motion. Bulletin of the Seismological Society of America.

Boore DM and Campbell KW (2017) Adjusting Central and Eastern North America Ground Motion Intensity Measures between Sites with Different ReferenceRock Site Conditions.

Bulletin of the Seismological Society of America 107(1): 132-148. DOI:

10.1785/0120160208.

Boore DM, Stewart JP, Seyhan E, et al. (2014) NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes. Earthquake Spectra 30(3): 1057-1085. DOI: 10.1193/070113EQS184M.

Boyd OS, Churchwell D, Moschetti MP, et al. (2023) Sediment thickness map of Atlantic and Gulf Coastal Plain strata, central and eastern U.S., and their influence on earthquake ground motions. Earthquake Spectra tbd: tbd.

Bozorgnia Y, Abrahamson NA, Atik LA, et al. (2014) NGA-West2 research program. Earthquake Spectra 30(3): 973-987. DOI: 10.1193/072113EQS209M.

Campbell KW (2009) Estimates of shear-wave Q and k0 for unconsolidated and semiconsolidated sediments in eastern North America. Bulletin of the Seismological Society of America 99(4): 2365-2932.

3-24

Castellaro S, Mulargia F and Rossi PL (2008) Vs30: Proxy for Seismic Amplification?

Seismological Research Letters 79(4): 540-543. DOI: 10.1785/gssrl.79.4.540.

Chapman MC and Guo Z (2021) A response spectral ratio model to account for amplification and attenuation effects in the Atlantic and Gulf Coastal Plain. Bulletin of the Seismological Society of America 111(4): 1849-1867. DOI: 10.1785/0120200322.

Goulet CA, Kishida T, Ancheta TD, et al. (2014) PEER NGA-East Database. PEER 2014-17.

Berkeley, Calif.: Pacific Earthquake Engineering Research Center. Available at:

https://peer.berkeley.edu/publications/2014-17 (accessed 27 January 2023).

Goulet CA, Bozorgnia Y, Abrahamson NA, et al. (2018) Central and eastern North America groundmotion characterizationNGA-East final report. PEER 2018-08. Berkeley, Calif.: Pacific Earthquake Engineering Research Center. Available at:

https://peer.berkeley.edu/publications/2018-08.

Goulet CA, Bozorgnia Y, Kuehn N, et al. (2021a) NGA-East ground-motion characterization model part I: Summary of products and model development. Earthquake Spectra 37(1_suppl): 1231-1282. DOI: 10.1177/87552930211018723.

Goulet CA, Kishida T, Ancheta TD, et al. (2021b) PEER NGA-East database. Earthquake Spectra 37(1_suppl): 1331-1353. DOI: 10.1177/87552930211015695.

Guo Z and Chapman MC (2019) An examination of amplification and attenuation effects in the Atlantic and Gulf Coastal Plain using spectral ratios. Bulletin of the Seismological Society of America 109(5): 1855-1877. DOI: 10.1785/0120190071.

Hashash YM, Ilhan O, Harmon JA, Parker GA, Stewart JP, Rathje EM, Campbell KW and Silva WJ (2020) Nonlinear site amplification model for ergodic seismic hazard analysis in central and eastern North America. Earthquake Spectra 36(1): 69-86.

Hashash YM, Kottke AR, Stewart JP, Campbell KW, Kim B, Moss C, Nikolaou S, Rathje E and Silva WJ (2014) Reference rock site condition for central and eastern North America.

Bulletin of the Seismological Society of America 104(2): 684-701.

Hearne M, Thompson EM, Schovanec H, et al. (2019) USGS automated ground motion processing software. U.S. Geological Survey. DOI: 10.5066/P9ANQXN3.

Heath DC, Wald DJ, Worden CB, et al. (2020) A global hybrid V S 30 map with a topographic slope-based default and regional map insets. Earthquake Spectra 36(3): 1570-1584.

DOI: 10.1177/8755293020911137.

Kleckner JK, Withers KB, Thompson EM, et al. (2022) Automated Detection of Clipping in Broadband Earthquake Records. Seismological Research Letters. DOI:

10.1785/0220210028guo.

Krischer L, Megies T, Barsch R, et al. (2015) ObsPy: a bridge for seismology into the scientific Python ecosystem. Computational Science & Discovery 8(1): 014003. DOI:

10.1088/1749-4699/8/1/014003.

3-25

Kwong NS and Jaiswal KS (2023) Uses of epistemic uncertainties in the USGS National Seismic Hazard Models. Earthquake Spectra 39(2): 1058-1087. DOI:

10.1177/87552930231157424.

Levandowski W, Boyd OS, AbdelHameid D, et al. (2021) Crustal Seismic Attenuation of the Central United States and Intermountain West. Journal of Geophysical Research: Solid Earth 126(12). DOI: 10.1029/2021JB022097.

McNamara DE, Petersen MD, Thompson EM, et al. (2019) Evaluation of GroundMotion Models for USGS Seismic Hazard Forecasts: Induced and Tectonic Earthquakes in the Central and Eastern United States. Bulletin of the Seismological Society of America 109(1):

322-335. DOI: 10.1785/0120180106.

Mills SA, Boyd OS and Rukstales KS (2020) Digitized datasets of the structure of Cenozoic and late Cretaceous strata along the Atlantic and Gulf Coastal Plains from Texas to New Jersey. U.S. Geological Survey. DOI: 10.5066/P9YXMZMJ.

Moschetti MP, Thompson EM, Powers PM, et al. (2019) Ground Motions from Induced Earthquakes in Oklahoma and Kansas. Seismological Research Letters 90(1): 160-170.

DOI: 10.1785/0220180200.

Mueller CS (2019) Earthquake catalogs for the USGS National Seismic Hazard Maps.

Seismological Research Letters 90(1): 251-261. DOI: 10.1785/0220170108.

Pagani M, Monelli D, Weatherill G, et al. (2014) OpenQuake Engine: An Open Hazard (and Risk) Software for the Global Earthquake Model. Seismological Research Letters 85(3):

692-702. DOI: 10.1785/0220130087.

Parker GA, Stewart JP, Hashash YMA, et al. (2019) Empirical Linear Seismic Site Amplification in Central and Eastern North America. Earthquake Spectra 35(2): 849-881. DOI:

10.1193/083117EQS170M.

Pacific Earthquake Engineering Research Center (PEER) (2015) NGA-East: Median ground motion models for the central and eastern North America region. PEER report no.

2015/04, pp. 351. Berkeley, CA: Pacific Earthquake Engineering Research.

Petersen MD, Moschetti MP, Powers PM, et al. (2015) The 2014 United States National Seismic Hazard Model. Earthquake Spectra 31(1_suppl): S1-S30. DOI:

10.1193/120814EQS210M.

Petersen MD, Shumway AM, Powers PM, et al. (2020) The 2018 update of the US National Seismic Hazard Model: Overview of model and implications. Earthquake Spectra 36(1):

5-41. DOI: 10.1177/8755293019878199.

Petersen MD, Shumway AM, Powers PM, et al. (2021) The 2018 update of the US National Seismic Hazard Model: Where, why, and how much probabilistic ground motion maps changed. Earthquake Spectra 37(2): 959-987. DOI: 10.1177/8755293020988016.

Ramos-Sepulveda M, Parker G, Li M, et al. (2022) Performance of NGA-East GMMs and Site Amplification Models Relative to CENA Ground Motions. In: Proceedings of the 3-26

12thNational Conference in Earthquake Engineering, Salt Lake City, UT, 2022. Available at: https://escholarship.org/uc/item/4580n511.

Rennolet SB, Moschetti MP, Thompson EM, et al. (2018) A Flatfile of Ground Motion Intensity Measurements from Induced Earthquakes in Oklahoma and Kansas. Earthquake Spectra 34(1): 1-20. DOI: 10.1193/101916EQS175DP.

Rezaeian S, Petersen MD and Moschetti MP (2015) Ground motion models used in the 2014 U.S. National Seismic Hazard Maps. Earthquake Spectra 31(1_suppl): S59-S84. DOI:

10.1193/111714EQS194M.

Rezaeian S, Powers PM, Shumway AM, et al. (2021) The 2018 update of the US National Seismic Hazard Model: Ground motion models in the central and eastern US.

Earthquake Spectra 37(1_suppl): 1354-1390. DOI: 10.1177/8755293021993837.

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1117-1138. DOI: 10.1193/1.3478697.

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10.25080/Majora-92bf1922-011.

Shelly DR, Mayeda K, Barno J, et al. (2022) A Big Problem for Small Earthquakes:

Benchmarking Routine Magnitudes and Conversion Relationships with Coda Envelope-Derived Mw in Southern Kansas and Northern Oklahoma. Bulletin of the Seismological Society of America 112(1): 210-225. DOI: 10.1785/0120210115.

Shumway AM, Clayton BS and Rukstales KS (2019) 2018 update of the U.S National Seismic Hazard Model: Additional period and site class data. 2018-1111, USGS Open-file report.

Reston, VA: U.S. Geological Survey. DOI: 10.5066/P9RQMREV.

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10.1177/8755293019878185.

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doi:10.5066/P9HX7MYG.

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U.S. Nuclear Regulatory Commission (CEUS-SSCn) (2012) Central and Eastern United States seismic source characterization for nuclear facilities. 1-6. Washington, D.C.: U.S.

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Wald DJ, Worden CB, Thompson EM, et al. (2022) ShakeMap operations, policies, and procedures. Earthquake Spectra 38(1): 756-777. DOI: 10.1177/87552930211030298.

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Figure 3-1: Sammons mapping of 1 Hz GMMs plotted together with the scaled reference models (i.e., scaled by constant factors const-scaled; scaled by magnitude 3-28

mag-scaled; and scaled by distance dist-scaled). Black circles depict the locations of the seed models, with labels for the abbreviated seed names.

(4) Step 4: Subdivide the Sammons map into quadrants, which is used to assign weights to the seed GMMs. The gridding forces GMMs that are close within the Sammons space to share weights during the drawing of realizations. Gridding is done with 0.25 ln units spacing, and the impact of alternative gridding approaches (spacing, etc.) was not considered. Based on the gridding, all gridded regions are given the same weight. For the grid sectors with multiple models, individual GMMs receive partial weight based on the number of GMMs within the sector. Weights extracted from the 1 Hz Sammons mapping are depicted in Figure 3-2.

Figure 3-2: Summary of weights applied to 18 seed models for the case of 1 Hz gridding.

(5) Step 5: Draw realizations of GMMs from MVN distributions. Drawing realizations of GMMs from the MVN distributions proceeds by selecting a seed model using the model weights (Figure 3-2) generating a sample whose mean is the seed model mean, , and covariance is the established covariance across all seed models:

ln( )~ ( , )

Note that this treatment expands the assumed distribution from an MVN to a mixture model of MVN distributions that uses the mean model of the seed GMMs and the covariance matrix that is defined by all GMMs. We evaluate each realization across various screening criterion to determine if the sample is physically realistic and reject the realization if it does not meet these criteria. We have ongoing work related to the physicality constraints, and there may be potential to improve upon the constraints published by NGA-East. Draws of realizations are performed until the desired number of simulations has been reached. Examples of the draws are depicted in Figure 3-3. We 3-29

confirm that the generation of realizations employs the grid-based weighting of the seed models by retaining information about the randomized selection of the seed models and plotting the number of realizations associated with each seed model. We plot an example of the numbers of realizations for 1000 total realizations in Figure 3-4.

Figure 3-3: Example of 10,000 draws from the underlying (epistemic) ground-motion distribution in the Sammons space for 1 Hz ground motions. Seed models are plotted with dark blue symbols. The reference models (constant, magnitude, and distance scaling) are plotted with black, yellow, and red symbols, respectively, with the same legend as in Figure 3-1.

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Figure 3-4: Number of realizations associated with each seed model. The plotted example corresponds to 1000 total realizations at 1 Hz.

Representative GMMs for the 17 regions of the Sammons space are computed by projecting an ellipse in the Sammons space, such that the ellipse captures 95 percent of the density of the sampled GMMs, dividing the ellipse into sectors, and grouping sampled GMMs within each sector. The projection of the ellipse follows the NGA-East Procedure: the ellipse is centered on the mean of the sampled models, with the center ring containing 10 percent of the density, the second ring corresponds to the body of the distribution, which captures 75 percent of the density (65 percent of which is within the inner annulus), and the outer ring captures the range of the distribution. Within each annulus, eight sectors aligning with the semi-major and semi-minor axes of the ellipse are defined. An example of the grouping of sampled GMMs within the projected ellipse in Sammons space is given in Figure 3-5. The GMMs within each sector are averaged to produce the reference GMM for the sector. Examples of the reference GMMs, SA ( = 1 s), for multiple magnitudes are plotted as a function of distance from the center, body, and range sectors of the ground-motion space in Figure 3-6.

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Figure 3-5: Clustering of GMM realizations within the 17 sectors of the projected ground motion space. GMMs within each sector are color-coded.

Figure 3-6: GMMs from the realizations of the mixture model of MVN distributions.

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3.1.1 Remaining Steps to Reproduce NGA-East Procedure During the course of the Interagency Agreement, the USGS did not reproduce all steps of the NGA-East Procedure. The following steps have either not been finalized or have not been implemented and would require further work:

Apply physicality constraints to sampled GMMs, potentially expanding upon criteria for accepting realization.

Compute data misfit component of the weights, including the total residual and likelihood values from the reference GMMs.

3.1.2 Comparisons of USGS and NGA-East Epistemic Uncertainty Through Sammons Maps One of the desired goals for the implementation of the NGA-East Procedure was to compare the weights implied by Sammons mapping to the weights assigned by the USGS for the 2018 NSHM. These weight assignments are discussed in Rezaeian et al. (2021) and use a consensus-based process for the weighting scheme that groups similar models, so as to minimize upweighting particular approaches, and also assigns weights reflecting expert input.

The approach to assigning groupings to CEUS GMMs, which was used for the 2014 and 2018 NSHMs, is similar to the sampling strategy used in the NGA-East Procedure for drawing realizations from the seed models. Direct comparison of these weights facilitates evaluations of the two methods. Figure 3-7 depicts the sampling weights applied to the seed models in the NGA-East Procedure and the branch weights assigned to the set of updated seed models in the USGS updated seed logic tree. Comparison of the weights are complicated because the USGS uses a subset of the NGA-East seed models and several updated GMMs, so we cannot directly compare weights from the USGS approach with the weighted sampling in the NGA-East Procedure. Furthermore, the weights cannot be directly compared for seismic hazard purposes because the NGA-East Procedure uses the realizations from the MVN sampling for computing the 17 final GMMs; however, this comparison is instructive in highlighting the differences that arise between model types and expert opinion (used as the basis for the USGS weights) and in the similarity of seed models in the Sammons mapping. The sampling weights of the seed GMMs from the NGA-East Procedure are sensitive to the grid dimensions used in this process.

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Figure 3-7: Comparison of the weights used in sampling NGA-East seed models with branch weights of USGS updated seed models for SA (T=1 Hz).

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4 CONCLUSIONS AND PATH FORWARD Ground-motion data from earthquakes occurring in the central and eastern United States from 2010-2020 provide information about ground-motion effects in the region and about the accuracy of the NGA-East GMMs. The new datacollected since the end of the NGA-East Projectexpands the region of data coverage in the CEUS further to the east and supports ongoing work to examine Coastal Plains effects (e.g., Boyd et al., in press). Calculation of ground-motion residuals indicate a systematic overprediction by the NGA-East GMMs at short periods ( ~0.1 ) and an underprediction at longer periods ( > 3 ). Additional work is needed to determine if the misfit is limited to specific GMMs from NGA-East or if this is a feature that is uniform across all GMMs. The cause of the period-dependent misfit is not currently understood.

The USGS has implemented partial-weight correction factors to its CEUS GMMs for the 2023 NSHM, and future NSHM updates will likely consider alternative ways to incorporate these correction factors.

The USGS approach to implementing NGA-East and the NGA-East updated seed GMMs for the 2018 NSHM provides an alternative way to use the GMMs from the NGA-East Project (Rezaeian et al., 2021). In addition to direct use of the NGA-East GMMs, this approach also weights seed modelsreplacing updated GMMs with newer GMMsusing a weighting scheme to group similar modeling approaches. The resulting GMM logic tree has less epistemic uncertainty than do the NGA-East GMMs. Seismic hazard sensitivity by Petersen et al. (2021) indicates that the NGA-East logic tree produces higher probabilistic ground motions at shorter and longer periods. Differences in hazard may be partially attributed to small to moderate differences in the (logic-tree-weighted) mean values, though there may be effects from the broader epistemic uncertainty of the NGA-East GMMs as well.

We describe progress in our independent implementation of the NGA-East Procedure. We have achieved most of the key steps in the procedure and report intermediate benchmarks that have been compared with results in the NGA-East reports and articles (Goulet et al., 2021a; Goulet et al., 2018). Two outstanding steps remain to finalize the implementation of this procedure finalizing the incorporation of the physicality constraints and the data-likelihood calculations. We report comparisons of the weights from NGA-East Procedure with the USGS weighting scheme for 1 Hz. Comparisons at additional frequencies are needed to identify underlying trends. During the course of implementation, we identified choices made during the NGA-East Project that would be useful to explore through seismic hazard sensitivity calculations. The primary choices with regard to NGA-East relate to the use of the seed models in a mixture model parameterization for sampling of realizations and the use of the target variance values. Further work is needed to better understand the effects of these choices on probabilistic ground motions.

The USGS now uses three different approaches to modeling epistemic uncertainty for earthquakes in active crustal, subduction, and stable continental seismotectonic provinces in the conterminous United States. During the development of the 2023 NSHM, there were discussions about unifying the approach to epistemic uncertainty modeling across these regions, and future updates of NSHM are likely to consider this update. An important consideration that has come forward since the initiation of the NGA-East Project relates to nonergodic ground-motion modeling (e.g., Abrahamson et al., 2019) and the proposed relationship between aleatory variability and epistemic uncertainty. Under a nonergodic framework, development of epistemic uncertainty models may need to be carried out together with development of models of aleatory variability. As the USGS moves to producing and 4-1

publishing uncertainties associated with its probabilistic seismic hazard analyses (e.g., Kwong and Jaiswal, 2023), there will be further interest in the range of possible ground motions that are allowed by the epistemic uncertainties in GMMs.

4-2

5 DATA AND SOFTWARE AVAILABILITY The gmprocess ground motion processing code is available at https://code.usgs.gov/ghsc/esi/groundmotion-processing (last accessed July 14, 2023). The data described in this report is publicly available (Thompson et al., 2023). The Sammons Mapping package is available at https://github.com/tompollard/sammon (last accessed July 14, 2023).

5-1

6 REFERENCES Abrahamson N, Kuehn N, Walling M, et al. (2019) Probabilistic Seismic Hazard Analysis in California Using Nonergodic Ground Motion Models. Bulletin of the Seismological Society of America 109(4): 1235-1249. DOI: 10.1785/0120190030.

Allen TI and Wald DJ (2009) On the use of high-resolution topographic data as a proxy for seismic site conditions (VS30). Bulletin of the Seismological Society of America 99(2A):

935-943. DOI: 10.1785/0120080255.

Al Atik and Youngs RR (2014) Epistemic Uncertainty for NGA-West2 Models. Earthquake Spectra 30(3): 1301-1318. DOI: 10.1193/062813EQS173M.

Bodin P and Horton S (1999) Broadband microtremor observation of basin resonance in the Mississippi Embayment, central US. Geophysical Research Letters. DOI:

10.1029/1999GL900146.

Boore DM (2010) Orientation-independent, nongeometric-mean measures of seismic intensity from two horizontal components of motion. Bulletin of the Seismological Society of America.

Boore DM and Campbell KW (2017) Adjusting Central and Eastern North America Ground Motion Intensity Measures between Sites with Different ReferenceRock Site Conditions.

Bulletin of the Seismological Society of America 107(1): 132-148. DOI:

10.1785/0120160208.

Boore DM, Stewart JP, Seyhan E, et al. (2014) NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes. Earthquake Spectra 30(3): 1057-1085. DOI: 10.1193/070113EQS184M.

Boyd OS, Churchwell D, Moschetti MP, et al. (2023) Sediment thickness map of Atlantic and Gulf Coastal Plain strata, central and eastern U.S., and their influence on earthquake ground motions. Earthquake Spectra tbd: tbd.

Bozorgnia Y, Abrahamson NA, Atik LA, et al. (2014) NGA-West2 research program. Earthquake Spectra 30(3): 973-987. DOI: 10.1193/072113EQS209M.

Campbell KW (2009) Estimates of shear-wave Q and k0 for unconsolidated and semiconsolidated sediments in eastern North America. Bulletin of the Seismological Society of America 99(4): 2365-2932.

Castellaro S, Mulargia F and Rossi PL (2008) Vs30: Proxy for Seismic Amplification?

Seismological Research Letters 79(4): 540-543. DOI: 10.1785/gssrl.79.4.540.

Chapman MC and Guo Z (2021) A response spectral ratio model to account for amplification and attenuation effects in the Atlantic and Gulf Coastal Plain. Bulletin of the Seismological Society of America 111(4): 1849-1867. DOI: 10.1785/0120200322.

6-2

Goulet CA, Kishida T, Ancheta TD, et al. (2014) PEER NGA-East Database. PEER 2014-17.

Berkeley, Calif.: Pacific Earthquake Engineering Research Center. Available at:

https://peer.berkeley.edu/publications/2014-17 (accessed 27 January 2023).

Goulet CA, Bozorgnia Y, Abrahamson NA, et al. (2018) Central and eastern North America groundmotion characterizationNGA-East final report. PEER 2018-08. Berkeley, Calif.: Pacific Earthquake Engineering Research Center. Available at:

https://peer.berkeley.edu/publications/2018-08.

Goulet CA, Bozorgnia Y, Kuehn N, et al. (2021a) NGA-East ground-motion characterization model part I: Summary of products and model development. Earthquake Spectra 37(1_suppl): 1231-1282. DOI: 10.1177/87552930211018723.

Goulet CA, Kishida T, Ancheta TD, et al. (2021b) PEER NGA-East database. Earthquake Spectra 37(1_suppl): 1331-1353. DOI: 10.1177/87552930211015695.

Guo Z and Chapman MC (2019) An examination of amplification and attenuation effects in the Atlantic and Gulf Coastal Plain using spectral ratios. Bulletin of the Seismological Society of America 109(5): 1855-1877. DOI: 10.1785/0120190071.

Hashash YM, Ilhan O, Harmon JA, Parker GA, Stewart JP, Rathje EM, Campbell KW and Silva WJ (2020) Nonlinear site amplification model for ergodic seismic hazard analysis in central and eastern North America. Earthquake Spectra 36(1): 69-86.

Hashash YM, Kottke AR, Stewart JP, Campbell KW, Kim B, Moss C, Nikolaou S, Rathje E and Silva WJ (2014) Reference rock site condition for central and eastern North America.

Bulletin of the Seismological Society of America 104(2): 684-701.

Hearne M, Thompson EM, Schovanec H, et al. (2019) USGS automated ground motion processing software. U.S. Geological Survey. DOI: 10.5066/P9ANQXN3.

Heath DC, Wald DJ, Worden CB, et al. (2020) A global hybrid V S 30 map with a topographic slope-based default and regional map insets. Earthquake Spectra 36(3): 1570-1584.

DOI: 10.1177/8755293020911137.

Kleckner JK, Withers KB, Thompson EM, et al. (2022) Automated Detection of Clipping in Broadband Earthquake Records. Seismological Research Letters. DOI:

10.1785/0220210028guo.

Krischer L, Megies T, Barsch R, et al. (2015) ObsPy: a bridge for seismology into the scientific Python ecosystem. Computational Science & Discovery 8(1): 014003. DOI:

10.1088/1749-4699/8/1/014003.

Kwong NS and Jaiswal KS (2023) Uses of epistemic uncertainties in the USGS National Seismic Hazard Models. Earthquake Spectra 39(2): 1058-1087. DOI:

10.1177/87552930231157424.

Levandowski W, Boyd OS, AbdelHameid D, et al. (2021) Crustal Seismic Attenuation of the Central United States and Intermountain West. Journal of Geophysical Research: Solid Earth 126(12). DOI: 10.1029/2021JB022097.

6-3

McNamara DE, Petersen MD, Thompson EM, et al. (2019) Evaluation of GroundMotion Models for USGS Seismic Hazard Forecasts: Induced and Tectonic Earthquakes in the Central and Eastern United States. Bulletin of the Seismological Society of America 109(1):

322-335. DOI: 10.1785/0120180106.

Mills SA, Boyd OS and Rukstales KS (2020) Digitized datasets of the structure of Cenozoic and late Cretaceous strata along the Atlantic and Gulf Coastal Plains from Texas to New Jersey. U.S. Geological Survey. DOI: 10.5066/P9YXMZMJ.

Moschetti MP, Thompson EM, Powers PM, et al. (2019) Ground Motions from Induced Earthquakes in Oklahoma and Kansas. Seismological Research Letters 90(1): 160-170.

DOI: 10.1785/0220180200.

Mueller CS (2019) Earthquake catalogs for the USGS National Seismic Hazard Maps.

Seismological Research Letters 90(1): 251-261. DOI: 10.1785/0220170108.

Pagani M, Monelli D, Weatherill G, et al. (2014) OpenQuake Engine: An Open Hazard (and Risk) Software for the Global Earthquake Model. Seismological Research Letters 85(3):

692-702. DOI: 10.1785/0220130087.

Parker GA, Stewart JP, Hashash YMA, et al. (2019) Empirical Linear Seismic Site Amplification in Central and Eastern North America. Earthquake Spectra 35(2): 849-881. DOI:

10.1193/083117EQS170M.

Pacific Earthquake Engineering Research Center (PEER) (2015) NGA-East: Median ground motion models for the central and eastern North America region. PEER report no.

2015/04, pp. 351. Berkeley, CA: Pacific Earthquake Engineering Research.

Petersen MD, Moschetti MP, Powers PM, et al. (2015) The 2014 United States National Seismic Hazard Model. Earthquake Spectra 31(1_suppl): S1-S30. DOI:

10.1193/120814EQS210M.

Petersen MD, Shumway AM, Powers PM, et al. (2020) The 2018 update of the US National Seismic Hazard Model: Overview of model and implications. Earthquake Spectra 36(1):

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