Abstract
The US Geological Survey National Seismic Hazard Models (NSHMs) are used to calculate earthquake ground-shaking intensities for design and rehabilitation of structures in the United States. The most recent 2014 and 2018 versions of the NSHM for the conterminous United States included major updates to ground-motion models (GMMs) for active and stable crustal tectonic settings; however, the subduction zone GMMs were largely unchanged. With the recent development of the next generation attenuation-subduction (NGA-Sub) GMMs, and recent progress in the utilization of “M9” Cascadia earthquake simulations, we now have access to improved models of ground shaking in the US subduction zones and the Seattle basin. The new NGA-Sub GMMs support multi-period response spectra calculations. They provide global models and regional terms specific to Cascadia and terms that account for deep-basin effects. This article focuses on the updates to subduction GMMs for implementation in the 2023 NSHM and compares them to the GMMs of previous NSHMs. Individual subduction GMMs, their weighted averages, and their impact on the estimated mean hazard relative to the 2018 NSHM are discussed. The updated logic trees include three of the new NGA-Sub GMMs and retain two older models to represent epistemic uncertainty in both the median and standard deviation of ground-shaking intensities at all periods of interest. Epistemic uncertainty is further represented by a three-point logic tree for the NGA-Sub median models. Finally, in the Seattle region, basin amplification factors are adjusted at long periods based on the state-of-the-art M9 Cascadia earthquake simulations. The new models increase the estimated mean hazard values at short periods and short source-to-site distances for interface earthquakes, but decrease them otherwise, relative to the 2018 NSHM. On softer soils, the new models cause decreases to the estimated mean hazard for long periods in the Puget Lowlands basin but increases within the deep Seattle portion of this basin for short periods relative to the 2018 NSHM.
Keywords
Introduction
The National Seismic Hazard Models (NSHMs), developed by the US Geological Survey (USGS) for the United States and its territories, have been used to compute design ground motions for the National Earthquake Hazard Reduction Program (NEHRP) Recommended Seismic Provisions for New Buildings and Other Structures (NEHRP Provisions, e.g. Building Seismic Safety Council (BSSC), 2020) since 1996 (i.e. Frankel et al., 1996, adopted by the 1997 NEHRP Provisions). These models combine information from earthquake source models, which estimate the rates of occurrence of earthquakes, and ground-motion models (GMMs), which estimate the distribution of ground-shaking intensity for a given earthquake occurrence, to perform probabilistic seismic hazard analyses (PSHAs). The previous two updates, the 2014 USGS NSHM (Petersen et al., 2015) and the 2018 USGS NSHM (Petersen et al., 2020), resulted in major changes to the GMMs in the western United States (WUS) and the central and eastern United States (CEUS). In the 2014 NSHM, the next generation attenuation (NGA) models for shallow crustal earthquakes in the WUS (NGA-West2) were adopted; see Bozorgnia et al. (2014) for an overview of the models and Rezaeian et al. (2015) for their implementation in the 2014 NSHM. In the 2018 NSHM, the NGA models for stable continental earthquakes in the CEUS (NGA-East) were adopted; see Goulet et al. (2021) for an overview of the models and Rezaeian et al. (2021) for their implementation in the 2018 NSHM. The 2018 USGS NSHM update also introduced multi-period response spectra (MPRS) for adoption into the 2020 NEHRP Provisions (BSSC, 2020), which required GMMs to be applicable for a wide range of spectral periods and site classes categorized by their V S30 values (the time-averaged shear-wave velocity of the top 30 m of the crust).
In the 2014 and 2018 updates, the newly implemented NGA-West2 and NGA-East GMMs were applicable for 22 periods (peak ground acceleration (PGA) and 21 response spectral periods from 0.01 to 10 s) and 8 site classes (identified by V S30 values ranging from 1500 for hard rock to 150 m/s for very loose sand or soft clay). However, the relatively outdated GMMs were used for the Pacific Northwest’s (PNW’s) Cascadia subduction zone suffered from a limited applicability range. As a result, the MPRS requirement necessitated adjustments to these GMMs in the 2018 NSHM. These adjustments are described in the work by Powers et al. (2021) and were meant to produce reasonable ground-motion estimates for all periods and site classes. They included the addition of basin amplification factors (BAFs) based on the crustal model of Campbell and Bozorgnia (2014) to avoid underestimation of design forces at long periods and soft site classes.
The most recent update of the USGS NSHM (Petersen et al., 2023) uses new subduction zone ground-motion data and models that have been published by the NGA-Subduction project (NGA-Sub; Bozorgnia et al., 2022), which are intended to provide better estimates of ground-shaking intensities for Cascadia subduction zone events in the PNW. Furthermore, basin amplifications based on the “M9 Project” Cascadia interface earthquake simulations in the Seattle basin (Frankel et al., 2018; Wirth et al., 2018b) provide more insight into ground-shaking estimates, particularly at relatively large magnitudes and long periods where empirical datasets are lacking (Wirth et al., 2018a).
NGA-Subduction project
The NGA-Subduction project (Bozorgnia et al., 2022) was a large multidisciplinary international project aimed at compiling a uniformly processed database of globally recorded subduction zone events and the development of empirical GMMs. The ground-motion database, described in detail by Mazzoni et al. (2022), consists of over 71,000 three-component recordings from 1880 subduction interface, intraslab, and outer-rise events, recorded at over 6500 stations across seven global regions (Alaska, Cascadia, Central America and Mexico, Japan, New Zealand, South America, and Taiwan). Raw ground-motion time series were processed with the Pacific Earthquake Engineering Research Center (PEER) methods most recently described in the work by Goulet et al. (2021). Computed ground-motion intensity measures (IMs) include PGA and peak ground velocity (PGV) and pseudo-spectral accelerations (SAs) at 111 oscillator periods ranging from 0.01 to 20 s. Multiple earthquake source metrics, including moment-tensor and finite-fault parameters, and distance metrics, including distance to the rupture plane (R RUP ) and depth to the hypocenter and the top-of-rupture (Z HYP and Z TOR ), were compiled as described in the work by Contreras et al. (2022). Recording-station metadata were compiled as described in the work by Ahdi et al. (2022), including measured and proxy-based V S30 values and depths to shear-wave velocity isosurfaces (Z X ), where X = 1.0 and 2.5 km/s. The basin-depth parameters Z1.0 and Z2.5 are often used to characterize deep-basin effects in modern GMMs. Events and stations were also flagged as falling within forearc or backarc regions for each subduction zone, as appropriate. This database was used by four different modeling groups to develop subduction GMMs (Bozorgnia et al., 2022). Many modelers did not consider backarc terms or data when developing the global subduction GMMs. It is unknown whether the Cascadia subduction zone exhibits significant backarc effects to require modifications to NGA-Sub GMMs similar to what was done for the New Zealand NSHM (Bradley et al., 2023); however, the lack of such modifications could lead to a systematic overprediction of hazard. The 2023 NSHM did not investigate such potential backarc effects and a decision was made to not consider these terms in this update.
Of the four groups, three developed global GMMs and regionalized GMMs relevant to the US NSHMs using the above-described NGA-Sub ground-motion database: Abrahamson and Gülerce (2022, hereafter AG20), Kuehn et al. (2020, hereafter KBCG20), and Parker et al. (2022, hereafter PSBAH20). The acronyms for these models refer to the original year of their release as PEER reports (Abrahamson and Gülerce, 2020; Kuehn et al., 2020; Parker et al., 2020); however, the latest versions of their published models were used in the 2023 NSHM (Abrahamson and Gülerce, 2022; Parker et al., 2022). Each modeling team selected a different subset of the NGA-Sub dataset as described in their respective publications, reflecting epistemic uncertainty in data selection by different modeling groups. Furthermore, each GMM provides a global version and a variety of regionalization terms that include Cascadia. A fourth GMM, Si et al. (2022), was developed for Japan only and was not considered for the 2023 NSHM because the other three global GMMs also included the Japanese data. Gregor et al. (2022) present a study comparing the salient features of each GMM, including their functional forms, model parameterization, ranges of applicability, relative response spectral predictions for scenario-specific magnitude scaling, distance attenuation, and basin amplification, and models of epistemic uncertainty on median, aleatory variability, and PSHA-based hazard curves for two sites in the state of Washington.
The key difficulty in developing regionalized models by the GMM developers for the Cascadia subduction zone was the lack of ground-motion data from interface earthquakes and the limited set of recordings from intraslab earthquakes in this region. Worldwide, there are only two recorded earthquakes greater than magnitude (M) 8.6 (the 2010 Maule, Chile, and 2011 Tohoku, Japan, earthquakes) that have empirical data to help constrain the large magnitude portions of subduction zone models; as a result, the empirical interface GMMs may not be robust, as they are being driven at M9 by only two global events. In general, the sparse available data from Cascadia intraslab events show much lower short-period ground motions than the global models. Figure 1 shows the mean residuals of available intraslab recordings in Cascadia with respect to global intraslab models (AG20-GL, KBCG20-GL, PSBAH20-GL from NGA-Sub; ZHAO06 from 2018 NSHM; all reviewed in the following sections) and one regional Cascadia model (AG20-CAS as will be summarized in the following sections). The data used are from the NGA-Subduction database (Mazzoni et al., 2022) and consist of 322 recordings from seven earthquakes with a magnitude range from 5.0 to 6.8 and rupture distances from 26 to 792 km. Observe that the global models overestimate (negative residuals) the Cascadia regional data at short periods. Despite these observations, it is unclear if these short-period lower ground motions are reliable indicators of lower ground motions in future intraslab events and whether they also imply lower ground motions from interface events in this region. As a result, different modeling groups made different modeling choices to address this gap in data as they developed their Cascadia regional terms. The AG20, KBCG20, and PSBAH20 modelers used different subsets of the database and modeling assumptions to adjust their global GMMs for the Cascadia region.
Bias of global subduction GMMs (AG20, KBCG20, PSBAH20, and ZHAO06; refer to Table 2 for abbreviations) and a Cascadia regional GMM (AG20) for intraslab Cascadia events with M > 5. The bias is calculated for the natural logarithm of spectral acceleration (g).
M9 simulations for deep sedimentary basin effects
Deep sedimentary basins can be more than double ground motions at long periods and soft soil sites relative to reference site conditions (e.g. Frankel et al., 2002; Hartzell et al., 1997) due to the reflecting, refracting, and focusing of seismic waves in basin structures. The 2018 NSHM therefore incorporated spatially varying basin-depth data (parameterized by Z1.0 and Z2.5) to better estimate basin effects for long-period ground motions in regions having sufficient information on the shear-wave velocity structure. The 2018 NSHM considered basin depths when computing hazard at periods greater than 0.5 s (i.e. 50% weight at 0.75 s and 100% at 1 s and greater) in the vicinity of Los Angeles, San Francisco, Salt Lake City, and Seattle. Whereas crustal GMMs (e.g. NGA-West2) included basin-effect terms, subduction GMMs at that time did not and were adjusted using BAFs, as described in the work by Powers et al. (2021). The new NGA-Sub GMMs include basin-effect terms; however, their Cascadia regional basin terms are based on limited Cascadia intraslab data and tend to underestimate basin effects in the Seattle region of the Cascadia subduction zone. To address this, we also consider Seattle BAFs computed from simulations of M9 Cascadia earthquakes in the development of the 2023 NSHM.
Initiated in 2013, the “M9 Project” was a large multidisciplinary effort to perform kinematic rupture simulations of Cascadia megathrust earthquake scenarios to address the lack of recorded data from such events in this region. Given the hazard of potentially large events and the associated risk to the built environment in the PNW, simulated ground motions from M9 Cascadia earthquakes filled a knowledge gap for seismic design of buildings and infrastructure, especially at longer periods. As part of the M9 Project, 30 M9 Cascadia earthquake scenarios were developed considering different slip distributions, hypocenter locations, down-dip rupture limits, and locations of high stress-drop subevents (Frankel et al., 2018). The simulated ground motions from these scenarios were produced using a hybrid approach, where long-period deterministic seismograms (≤ 1 Hz) from numerical simulations using the three-dimensional (3D) Cascadia seismic velocity model of Stephenson et al. (2017) were combined with stochastic synthetics for high frequencies (> 1 Hz) to produce broadband (0–10 Hz) seismograms. A primary point of interest was constraining the amplification of long-period seismic waves in the Seattle basin, which is quite deep (Z2.5 ≥ 6 km) and has been shown to exhibit significant ground-motion amplification at long periods (Frankel et al., 2009; Rekoske et al., 2022; Thompson et al., 2020). Both simulated and recorded data in the PNW have highlighted that BAFs derived from GMMs based on crustal earthquakes in California (e.g. Campbell and Bozorgnia, 2014; Chiou and Youngs, 2014) underestimate ground-motion amplification in the Seattle basin (Wirth et al., 2018a). In 2018, the city of Seattle issued a Director’s Rule, requiring the use of simulation-based ground-motion amplification factors for Cascadia subduction zone earthquakes for the design of tall buildings in the Seattle basin (Wirth et al., 2018a).
This article focuses on recent advances in ground-motion modeling in subduction zones and presents options for implementing the best available subduction data, science, and GMMs in the Cascadia subduction zone in the 2023 USGS NSHM. In the following, we first review and discuss the limitations of subduction GMMs used in the 2018 and previous NSHMs. We then review newly available models from the NGA-Subduction project and compare them to previous GMMs in terms of their medians and aleatory variabilities. The changes in representation of epistemic uncertainty and the resulting ground-motion space are also discussed in detail and alternative logic-tree weights and weighted averages of medians and aleatory variabilities are explored. M9 Cascadia earthquake simulations are used to enhance the estimates of ground motions by modifying the BAFs of two NGA-Sub GMMs and the older retained GMMs in the Seattle basin. Finally, we discuss the influence of subduction GMM changes on maps of uniform hazard spectral values from the 2018 to the 2023 NSHM and recommend future research regarding subduction ground-motion modeling to better represent uncertainties in future updates of the NSHM. Throughout this article, the term mean hazard refers to the mean of the annual rate of exceedance, calculated as the weighted average of the rates of exceedance from the sampling of the logic tree. For the presentation of the results, the term hazard refers to the ground-motion level for a given return period computed from the mean hazard curve (uniform hazard spectral values). The terms hazard ratio and hazard difference refer to the ratio and difference in the ground-motion values at a given return period.
Subduction GMMs in previous NSHMs
The geology, tectonics, and earthquake potential represented in the WUS are diverse, ranging from shallow crustal earthquakes to offshore interface and deep intraslab subduction zone earthquakes. The WUS subduction zone GMMs are developed for two different domains: (1) interface earthquakes on the Cascadia subduction zone and faults, and (2) intraslab earthquakes occurring in the subducting plate beneath the PNW. For each domain, the USGS selects the most appropriate set of GMMs for use in each NSHM update based on all available published GMMs, following the selection criteria formally introduced in the 2014 NSHM (Petersen et al., 2014; Rezaeian et al., 2015). This set of 16 GMM selection criteria was designed to vet available published GMMs and select the most appropriate for use in the NSHM. The criteria were intended to be general and flexible to accommodate the continued growth and evolution of GMMs and consisted of four categories: (1) general requirements, (2) database scope, (3) parameters and applicability range, and (4) functional form and modeling procedure. These criteria were updated in the work by Rezaeian et al. (2021) to support the development of MPRS in the 2018 NSHM update. The list of interface and intraslab subduction GMMs in previous NSHMs, along with their references, acronyms, and logic-tree weights, is given in Table 1. The applicability ranges with respect to period and V
S30
are provided in the work by Powers et al. (2021). For the 2018 NSHM update, the lack of basin terms in the GMMs (i.e. BCHydro12, AM09, and Zhao06) was corrected using BAFs based on the work by Campbell and Bozorgnia (2014) crustal GMM. The BAF corrections were necessary to achieve reasonable ground-motion values up to a spectral period of 10 s for all eight site classes of interest as required for MPRS development and as specified by the 10th USGS GMM selection criterion, stated as follows (in Rezaeian et al., 2021): 10. Site Condition Requirement—The GMM must include a term for VS30 or be accompanied by one or more site-effect models that adjust the GMM to, at a minimum, the eight VS30 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 VS30 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.
Subduction GMMs and their weights used in previous NSHMs
Figure 2 shows the GMMs in Table 1 with colored lines indicating 2018 NSHM GMMs and gray lines representing older models. Two scenarios are shown in this figure that roughly correspond to the largest hazard contributors in the Seattle region. Figure 2a represents ground motions from an interface earthquake of magnitude 9 at a distance of 100 km, and Figure 2b represents ground motions from an intraslab earthquake of magnitude 7 at a distance of 50 km. Both scenarios assume a site condition with V S30 = 760 m/s, representing the reference soft rock site condition in NSHMs prior to 2018.
Median ground motions used in the 2018 (in color) and previous (in gray) NSHMs versus period at a soft rock site (
In USGS NSHMs, uncertainties in ground motions are represented by aleatory variabilities (random scatter) and epistemic uncertainties (modeling choices). For the aleatory variabilities, Figure 3 shows standard deviations of the subduction GMMs in Table 1 for the same scenarios as in Figure 2. Epistemic uncertainties include differences in modeling approaches, such as different developer groups using different database subsets, modeling philosophies, and functional forms. These uncertainties are represented by logic-tree weights, such as those shown in Table 1 for past NSHMs, capturing differences in modeling choices and denoting our confidence in each model. In contrast, aleatory variability is directly included in the hazard integral.
GMM selection and weights
In current USGS NSHMs, logic-tree weights are assigned using expert judgment and follow a consensus-building process, which is a subjective method but the most practical and widely accepted method in the United States at this time. Other quantitative and more objective methodologies, such as the Sammon’s mapping procedure (Sammon, 1969; Scherbaum et al., 2010) used by the NGA-East project, have been discussed but are not available for all tectonic regions considered in the NSHMs at this time. We generally consider equal weights across model types and categories and split weights between multiple models developed by a single modeling team who make different assumptions and use different parameters than other teams. Assigning equal group weights rather than equal weights to each GMM considers similarities between new and prior versions of models from the same developer team due to similar formulations and assumptions. These weights are first discussed with the GMM developers and the NSHM Project Steering Committee. They are then presented to the public, and feedback from the community and experts is considered in revisions, if needed.
An important discussion in every NSHM update cycle is what to do with older GMMs as newer models become available. In Table 1, note that the USGS tends to gradually phase out an existing GMM over multiple update cycles by lowering their weights instead of eliminating them immediately by assigning zero weights to them (e.g. Geomatrix, AB03). This approach serves two purposes: (1) due to the current consensus-building nature of our process, when a model is eliminated from the NSHM completely, it is unlikely to be brought back in the next cycle; as such, a smaller weight on an older model is preferred over zero weight until more recent models become widely accepted; and (2) the USGS prefers to gain more confidence in new models through their use by outside researchers and practitioners, in addition to its own assessment of the models, before giving them full weights. As science and data evolve continuously, new models are used and tested, and the above measures are aimed at acknowledging that new models do not always supplant existing ones (like NGA-West2 supplanted NGA-West1).
The 2018 NSHM update did not consider new subduction GMMs in comparison to the previous 2014 NSHM; instead we only modified weights to remove two versions of a GMM by Atkinson and Boore (2003) that were considered outdated at the time. Although new subduction zone models were available for inclusion in the 2018 NSHM (e.g. Abrahamson et al., 2018; Zhao et al., 2016a, 2016b), the NSHM project decided to forego updating the subduction GMMs in the 2018 update in anticipation of the 2020 NGA-Sub GMMs (Bozorgnia et al., 2022). Additional reasons for not including new subduction GMMs in 2018 NSHM were as follows: (1) the two models by Abrahamson et al. (2018) and Zhao et al. (2016a, 2016b) were both represented by their previous versions; (2) Abrahamson et al. (2018) used the same formulation as BCHydro12 but was fitted to a subset of the NGA-Sub database and it was expected to be superseded by a new NGA-Sub GMM in 2023; and (3) Zhao et al. (2016a, 2016b) were based on Japanese data similar to Zhao et al. (2006), but difficulties existed with its implementation, including a continued lack of facilitating MPRS development and nonlinear soil effects; whereas the previous Zhao06 was already implemented, verified, and adjusted/extrapolated to satisfy the USGS selection criteria, the new 2016 version did not accommodate the third USGS selection criterion established in the work by Petersen et al. (2014) and stated as follows: 3. Implementation—GMM modelers are required to provide source codes …, verification tables, or validation plots to the USGS NSHMP team members, and be available to discuss and provide guidance on the implementation of their models.
Subduction GMMs for the 2023 NSHM
The USGS announced a deadline of December 2020 for publication of any new models from outside of USGS to be considered for implementation in the 2023 NSHM (https://www.usgs.gov/programs/earthquake-hazards/science/request-hazard-modeling-contributions, last accessed 4/28/2023). Three relevant NGA-Sub GMMs were available by this deadline as reviewed in the “Introduction.” USGS then formed a working group that met periodically to assess the performance and validity of these new GMMs. This working group held two virtual public workshops in July 2021 and July 2022 to share their assessment of these models with the public and experts in the field. Alternative weighting schemes were presented and discussed at these workshops; a summary of these discussions and the consensus conclusions (not unanimous decisions) are presented in this section.
Available and selected GMMs
Table 2 lists all considered GMMs for the 2023 NSHM that were published in time and presented at the two workshops mentioned above. Zhao06, AM09, and BCHydro12 are GMMs used in the previous NSHMs (Table 1); some weighting alternatives retained these models, and some removed them to understand their effects. BCHydro18-NGA is the updated version of the BCHydro12 that used a subset of the new NGA-Sub dataset, and Zhao16 is the updated version of the Zhao06 model that was discussed in the previous section. Although included in Table 2 for completeness, alternatives that gave weights to these two GMMs are not discussed in this article (and weights are not listed in Table 2) because these models are not used in the 2023 NSHM for the same reasons they were not used in the 2018 NSHM, as described in the previous section.
Subduction GMMs for consideration in the 2023 NSHM
And its variations (i.e. 5th and 95th percentiles).
Three groups of GMMs from different teams are listed in Table 2. AG20 model has a global version (AG20-GL), a Cascadia regional version (AG20-CAS), and a Cascadia regional version adjusted to be closer to the global version (AG20-CAS-ADJ), as the developers acknowledge the sparseness of data in Cascadia. It is worth noting that AG20-CAS is based on not only data from Cascadia but also various scaling relations that comprise this GMM and reflect expectations of the modelers on how scaling relations would behave in this region. Per the modelers’ recommendation, both AG20-CAS and AG20-CAS-ADJ were used to represent epistemic uncertainty, with more weight on AG20-CAS-ADJ (double compared to AG20-CAS). However, for interface earthquakes, the USGS working group reached a consensus to only use the AG20-CAS-ADJ version of the model, due to very little information on large magnitude earthquakes in this region. It is noteworthy that an updated version of AG20 model was later published that included an epistemic uncertainty model for the median, similar to the other two NGA-Sub GMMs described in the following paragraph. Even though this revision had missed USGS’s deadline by a significant time, USGS was able to implement, verify, and validate this AG20 update and proceeded with its three-point representation in the logic tree. Similar to AG20, KBCG20, and PSBAH20, GMMs have global versions (KBCG20-GL and PSBAH20-GL) and Cascadia regional versions (KBCG20-CAS and PSBAH20-CAS).
An advanced modeling feature present in the three NGA-Sub GMMs mentioned above is that they have developed region-dependent epistemic uncertainty,
Discussion: USGS GMM selection criteria update
In the 2023 update, the USGS did not update its GMM selection criteria; although updating was discussed during public workshops, it was rejected based on expert recommendations. Criterion number 10 was enforced to ensure the minimum seismic design requirements for site conditions. During the two subduction GMM workshops, it was discussed in detail whether this criterion should be expanded to require GMM developers to include deep-basin amplifications. This is an important topic that should be re-visited with every NSHM update cycle, as ground-motion amplifications in deep basins can be significant for long periods. However, it was argued and collectively decided that, at this time, the GMM selection criteria should not be changed and that an additional requirement to include basin effects in a GMM would be too restrictive. Furthermore, it was argued that there is no reason to not allow basin adjustment factors that are separate from GMMs. As a result, the two older GMMs (AM09 and Zhao06) that were modified in the 2018 NSHM to reasonably extrapolate to deep basins should be considered, as they satisfy the current selection criteria.
Discussion: uniform weights across periods and site classes
Another important discussion topic during the two subduction GMM workshops was whether USGS should consider different logic-tree weights for the GMMs at different periods or site classes. For the 2023 update, it was recommended to keep the weights uniform across all periods to preserve the shapes of the response spectra. It was also recommended to keep the weights uniform across all site classes at this time to conserve the existing correlations within each model. Another question that was raised, after the two workshops, was whether the weights should be different for GMM medians and standard deviations; this should be discussed in future updates of NSHMs. Under the current GMM selection criteria (number one), published GMMs should provide median and standard deviation models and USGS currently assumes the same confidence levels (i.e. same weights) on the median and standard deviation models, since they are based on the same dataset and modeler assumptions. However, it was discussed that some GMMs may have a better model for their median or standard deviation components compared to other models, which may warrant more weight on one component than the other, especially when making regional models. Notwithstanding, for the 2023 NSHM, the PSHA continues to apply equal weights on various components of subduction GMMs.
Logic-tree weights and considered alternatives
Many different alternative weights were considered by the working group; some are shown in Table 2. The final recommended weights in the last column of Table 2 are shown in the logic trees of Figure 4. For the 2023 NSHM, similar to the previous updates, we follow a consensus-building process, recommend gradually phasing out still-valid existing GMMs, and pay special attention to representing epistemic uncertainties, as we knew they were underrepresented in previous NSHMs due to a paucity of subduction GMMs. As discussed below, the older models AM09 and Zhao06 still meet the USGS selection criteria and have very different modeling approaches worth preserving for a wider range of epistemic uncertainty that cannot be rejected at this time, particularly at longer periods (above 2 s). Global versions of the NGA-Sub GMMs were deemed unnecessary as they fell within the epistemic uncertainty ranges of other available models and were not preferred by the developers for Cascadia, as also discussed below.
Logic trees showing the grouping and weights of subduction (a) interface and (b) intraslab GMMs in the 2023 NSHM.
In Table 2, alternative 1 (Alt 1) only considers the Cascadia regional versions of the three new NGA-Sub GMMs, following the philosophy that newer models should replace the older ones and per recommendations of model developers that the regional versions of their models should be used. This alternative does not model the epistemic uncertainty on each median GMM as this feature was not available for the first workshop. Alternative 2 (Alt 2) considers older and newer GMMs with equal 20% weights on each group of model developers. This alternative also gives equal weight to the global and regional versions of the NGA-Sub GMMs, despite the regional preference of model developers, considering that the regional data are limited and reflecting less confidence in regional Cascadia models. Alternative 3 (Alt 3) also retains the older GMMs, but with a weight of 0.25 on them as a group, while the three new NGA-Sub groups also get a 0.25 weight for each group. Within the older GMMs group, AM09 gets a relatively lower weight compared to Zhao06 because some expressed concerns with the stochastic simulation nature of this model and its magnitude-scaling relation, as will be discussed later in the “Magnitude Scaling” section. In Alt 3, epistemic uncertainties on the median of each NGA-Sub GMM are also included.
The last column of Table 2 presents the final recommended weights for subduction GMMs in the Cascadia region, which are also shown in the logic trees of Figure 4. This weighting approach mainly considers similarities and differences between models at the reference BC Site Class without deep-basin conditions for all 22 periods, as discussed in the following section. Note that in previous NSHM cycles, the GMM weights were distributed based on their behaviors only at PGA, 0.2, and 1 s at BC Site Class; the 2018 NSHM considered all site classes in selection (0 or nonzero weights) of GMMs. For the 2023 NSHM, we did not add additional constraints to our selection criteria based on similar site/basin terms used in the GMMs. However, this could be a good topic for future research and NSHM updates.
Median GMM comparisons
One of the requirements for a GMM to be selected for use in USGS NSHMs is modeling the median and aleatory variability of ground-shaking intensity. USGS assesses the median and standard deviation models separately by comparing them to other models and available data, and together by considering their combined effects on the PSHA results. Based on these assessments, one single weight is assigned to the GMM, considering the validity and performance in the PSHA procedure of both the median and standard deviation components. In this section, we summarize the characteristics of the median GMMs shown in Table 2 for a reference site condition of V
S30
= 760 m/s; standard deviations of the models are discussed in the next section. Basic requirements have been established in the USGS selection criteria numbers 6, 7, 11, 12, 13, and 14 regarding magnitude and distance scaling of the median GMM, which are assessed by the USGS for various earthquake scenarios (copied from p. 109–110 of Petersen et al., 2014): 6. Magnitude—The GMM must have magnitude dependence (also see items 11–13 on functional form). The magnitude applied must be based on moment magnitude. …. The GMMs for subduction earthquakes should be applicable or reasonably extrapolated to a magnitude range of 5.0 to 8.0 for intraslab and 8.0 to 9.3 for interface earthquakes. 7. Distance—The GMM must have distance dependence (also see items 12–13 on functional form). Distance should be measured from the rupture source or from the surface projection of the rupture source. The GMM should be applicable or reasonably extrapolated to a distance of 300 km for shallow crustal and intraslab subduction earthquakes, and 1,000 km for stable continental and interface subduction earthquakes. 11. The GMM should have nonlinear magnitude dependence and a source corner frequency or source spectral shape that is magnitude dependent. 12. The GMM should include magnitude saturation for close distances through the use of an appropriate finite-fault distance measure or fictitious depth term or both. The GMM should have a magnitude-dependent distance decay to reasonably extrapolate across the magnitude and distance range of interest. 13. The GMM should include an exponential decay with distance term to account for frequency dependent attenuation (that is, Q). 14. GMMs should balance model complexity and either data constraints or constraints based on ground motion simulation as decided by the NSHMP team and Steering Committee.
Response spectra
Figure 5 shows the response spectra for median GMMs in Table 2 with colored lines indicating the new NGA-Sub GMM variations, black lines representing models retained from the 2018 NSHM, and a gray line showing a variation of AG20-CAS that was considered in alternative weightings but not recommended in the final logic tree (last column of Table 2). The scenarios shown in this figure are the same as those in Figure 2, roughly corresponding to the largest hazard contributors in the Seattle region, but assuming a reference site condition with V S30 = 760 m/s to exclude the local site effects and basin amplifications that will be discussed later. The dashed lines for KBCG20-CAS and PSBAH20-CAS models are the three-point representations of epistemic uncertainty on their medians, considered a significant improvement in GMM modeling and providing a better representation of the ground-motion space.
Spectral accelerations for medians (heavy solid lines) and 5th and 95th percentile ground motions (dashed lines) for an (a) interface scenario with M = 9, R RUP = 100 km, V S30 = 760 m/s, Z2.5 (and Z 1 ) = default, Z TOR = 10 km and (b) intraslab scenario with M = 7, R RUP = 50 km, V S30 = 760 m/s, Z2.5 (& Z 1 ) = default, Z TOR = 40 km.
In Figure 5a for the interface earthquake scenario, observe that the three NGA-Sub median GMMs are very similar, practically converging to one point around 2 s, and are lower than retained GMMs for long periods. The global versions of these three models were also considered; however, they fall within the epistemic uncertainty range of the other models (i.e. in a vertical cross-section, the -GL versions fall within the 5th and 95th percentiles of the other models; see Appendix Figure 20). For this reason, the global versions of GMMs were not considered in the final recommended weights. Although not a direct deciding factor, it is worthy to note that the model developers also did not recommend the use of their -GL versions in the Cascadia subduction zone. On the contrary, the two retained GMMs of AM09 and Zhao06 fall outside of the epistemic uncertainty range represented by the other models for long periods. These two models are retained in our final weight recommendations because (1) a part of the ground-motion space will not be represented if they are removed; (2) they represent different types of models (AM09 is simulation-based and per USGS selection, criterion 14 adds a different perspective to the NSHM that otherwise would not be represented) or different modeling groups (Zhao06 developers were not a part of NGA-Sub project); (3) they have already been adjusted in the 2018 NSHM to accommodate for the selection criterion number 10; (4) M9 simulations support higher ground motions at longer periods compared to BCHydro12 and closer to AM09 and Zhao06 (Frankel et al., 2018); and (5) the empirical interface GMMs may not be empirically robust because they are being driven at M9 by only two global events (from Chile and Japan). During the public review process for the NSHM, we also received feedback that there are benefits to retaining these older models in the 2023 NSHM for the reasons listed above. Note that variability is large across different modeling approaches; PSBAH20 has a different long-period spectral shape that suggests a faster drop in ground-motion intensity with respect to period, not unlike Zhao06, while AM09 has the slowest attenuation rate with periods, somewhat similar to AG20. The AG20-CAS that was not selected is very different from others at short periods.
For the intraslab scenario in Figure 5b, only Zhao06 is retained from previous NSHMs. Similar conclusions are drawn for the global versions of the NGA-Sub models, which are not selected in the final recommended weights because they fall within the epistemic uncertainty range of other models (see Appendix Figure 20b). Overall, there is less model-to-model variation at long periods compared to interface earthquakes, but all GMMs tend to converge as period increases; however, it is unclear if this is a representation of reality, is due to the lack of alternate models, or is due to similar assumptions being made regarding scaling and spectral shapes. In general, the empirical data from intraslab events in different regions are more similar at long periods compared to short periods, suggesting that large differences at short periods are likely due to the regional differences in the shallow site velocity profiles for a given V S30 that controls the short-period amplification.
Magnitude scaling
An important characteristic of GMMs is the magnitude-scaling terms. Requirements were listed above in the USGS NSHM selection criteria. Figure 6 shows how median GMMs vary with magnitude at 0.2- and 1-s spectral periods for an interface earthquake at 100 km and an intraslab earthquake at 50 km. Similar to previous figures, reference site conditions and default basin terms are selected here. Observe the magnitude break where the slope of median with magnitude changes is about M8 for the interface models and M7.25 for the intraslab models. The breakpoint magnitude, Mbreak, can be an important parameter in subduction GMMs, as these events can become very large and therefore Mbreak can control the large magnitude ground-motion intensities. However, most current models do not explicitly use Mbreak as a parameter and instead use default values. Some parameter variations have been suggested and were explored by the USGS, as described below. Although they were not implemented in the 2023 NSHM, the parameter variations were recommended for future NSHM development by the NSHM Project Steering Committee.
Subduction GMM medians versus magnitude for an (a) interface event at 100 km with Z TOR = 10 km, and (b) intraslab event at 50 km with Z TOR = 40 km (assumption for all magnitudes) at 0.2-s period. (c) and (d) are the same as (a) and (b), respectively but at 1-s period. All plots are for a reference site condition with V S30 = 760 m/s and default basin depths.
Magnitude breakpoint
Subduction zone GMMs lack sufficient empirical recordings from large magnitude events to constrain the scaling of ground motion with magnitude, or the magnitude-scaling rate (MSR). Thus, the NGA-Sub GMMs considered here have assumed aspects of the behavior of ground-motion amplitudes for both interface and intraslab events, typically by enforcing a break in slope above a threshold magnitude, referred as the breakpoint magnitude, Mbreak. As Mbreak influences the amplitude of ground-motion spectra at large magnitudes, it is important to understand the significance of the choice of Mbreak and how it affects the variation in spectra among the models. Here, we seek to evaluate whether the range of epistemic uncertainty is captured using the chosen Mbreak values in the considered NGA-Sub GMMs.
The concept of magnitude breakpoint scaling is not unique to subduction events. The phenomenon has been observed for shallow crustal events—data have shown that as the down-dip width of ruptures reaches a threshold, near 15 km, the slope of the ground motion above this magnitude is reduced. For example, Hanks and Bakun (2014) found a break in magnitude scaling at M6.7, while Baltay and Hanks (2014) observed no scaling with magnitude above M6.7 for shallow crustal events. Similar behavior is hypothesized to hold true for subduction zone faulting. Simulations of intraslab events (Ji and Archuleta, 2018) support this, demonstrating that the magnitude scaling saturates once a certain magnitude is reached. Evidence suggests that this break of MSR with source dimension varies both regionally and across interface and intraslab events. This concept of a change in scaling has been around implicitly for much longer, as many older GMMs used a quadratic scaling in magnitude that is functionally equivalent to a break point in magnitude scaling, but with a smoother and more subtle transition.
Campbell (2020) recently compiled and analyzed 79 subduction zones, comparing the source dimensions and scaling relations using the Slab1.0 model of Hayes et al. (2012) for down-dip estimates of locking widths. He computed the mean and standard deviation of these values, finding that the global average of rupture width for interface events was 156 km, with a much lower value for the Cascadia rupture zone. Due to the reduced width, intraslab events typically have about a 0.5 lower Mbreak than that documented within the work by Ji and Archuleta (2018).
Discussion: implementation of Mbreak for consideration in future NSHMs
Each of the NGA-Sub GMMs use a slightly different approach to incorporate magnitude scaling. Most models have Mbreak as a model parameter, allowing a direct adjustment of the Mbreak value, while some models (e.g. AG20) require an additional constant shift to account for the change in scaling at the breakpoint magnitude. Each model selected a different Mbreak for the Cascadia rupture zone; two GMMs used values suggested in the work by Campbell (2020) for interface and intraslab events. For example, PSBAH20 used the mean value, while KBCG20 chose the mean-plus-one-sigma value, accounting for the increased depth in the Puget sound area. AG20 used results from Ji and Archuleta (2018) to guide the choice of Mbreak for intraslab, while for interface events using an empirically based value from the 2011 M9 Tōhoku and 2010 M8.8 Maule ruptures. These default values are compiled in Table 3.
Magnitude breakpoint values and ranges used in Figure 7 (listed for a reference period of 1 s), with the default values chosen by subduction zone modelers presented in bold
To understand the epistemic uncertainty from the lower and upper bounds of Mbreak, Figure 7 plots the magnitude scaling from the default magnitude breakpoint values, and the bounds compiled in the work by Campbell (2020) for the Cascadia subduction zone (roughly corresponding to the 5% and 95% confidence levels, as tabulated in Table 3). A rupture distance of 50 km is used to minimize differences in attenuation among the models. The range in ground-motion amplitude above the magnitude breakpoint varies considerably, overlapping that from the default Mbreak used for the Cascadia rupture zone. The one exception is that Mbreak is not a critical factor in the implementation of the PSBAH20 GMM for interface events, as the model formulation does not result in strong variations in ground-motion amplitude (Figure 7a). Moreover, AM09 does not use a breakpoint because this model is only intended for large magnitude (M ≥ 7.5) interface events.
Variation in median as a function of the magnitude breakpoint (Mbreak) for (a) interface and (b) intraslab subduction GMMs. The default Mbreak selected is plotted as a solid line for each model with dashed lines indicating the additional range from Campbell (2020) for the Cascadia rupture zone, as tabulated in Table 3. Note: we consider the useable range for AM09 as not extending below M7.5 for interface events, and as constrained to below M8.5 for intraslab events. Plots use V S30 = 760 m/s, with R RUP = 100 km and Z TOR = 10 km for the interface, and R RUP = 50 km, Z TOR = 40 km for the intraslab event.
The range of ground motions plotted in Figure 7 informs the significance of using only a default Mbreak, displaying the plausible range in the ground-motion space from various magnitude breakpoint values for the Cascadia rupture zone. This range may be important to consider in future NSHM updates to capture the epistemic uncertainty present among the models. In addition, understanding how ground motions are affected by variations in magnitude-correlated predictor variables will be useful to guide parameter selections going forward. For example, the downdip width, from which Mbreak is derived (in the work by Campbell, 2020), is known to vary along the Cascadia subduction zone, and thus Mbreak may vary depending on where an event originates within the subduction zone. Regions such as the Puget sound, which has a larger seismogenic zone along strike (compared to the average width assumed by Campbell, 2020 of 68 km), could be evaluated with a different Mbreak than other regions.
Moving forward, simulations performed with varying magnitudes may help constrain the behavior related to the aspect ratio (length/width of the fault) used by Campbell (2020) to derive the estimates of Mbreak. As it is unlikely that the aspect ratios will be fully constrained empirically, these could be incorporated into a logic tree. Finally, the break in scaling is thought to exist at all periods. Campbell (2020) only analyzed PGA, but there is likely a period dependence that may affect the value of Mbreak. It is assumed constant with period in some models, but varies somewhat in the AG20 model, where longer periods have smaller Mbreak values, such that the scaling saturates at lower magnitudes.
Weighted averages of median GMMs
Figures 8 and 9 show the attenuation with distance of weighted-average median ground motions for 0.2- and 1-s periods, and for 2- and 5-s periods, respectively. As in previous figure, the interface M9 and intraslab M7 scenarios and the 760 m/s site condition are used. The weighted-average combinations of GMMs from previous NSHMs (2008, 2014, and 2018) from Table 1 are presented and compared to the recommended weighted-average combination for the 2023 NSHM to understand the changes in the median ground motions given our choices of logic-tree weights. The alternative 2023 weights suggested in Table 2 are also shown for comparison.
Weighted averages of median response spectra from GMMs at 0.2 and 1 s based on Table 2 for an (a) interface scenario with M = 9, R RUP = 100 km, V S30 = 760 m/s, Z2.5 (and Z 1 ) = default, Z TOR = 10 km, and (b) intraslab scenario with M = 7, R RUP = 50 km, V S30 = 760 m/s, Z2.5 (and Z 1 ) = default, Z TOR = 40 km.
Weighted averages of median response spectra from GMMs at 2 and 5 s based on Table 2 for an (a) interface scenario with M = 9, R RUP = 100 km, V S30 = 760 m/s, Z2.5 (and Z 1 ) = default, Z TOR = 10 km and (b) intraslab scenario with M = 7, R RUP = 50 km, V S30 = 760 m/s, Z2.5 (and Z 1 ) = default, Z TOR = 40 km.
For the interface event (Figures 8a and 9a), we observe that the median ground motions tend to be lower than those of the 2018 NSHM (compare black lines to red lines) in almost all cases, except for 0.2 s at shorter distances where we observe an increase. Alternative 1, which represents removing the older GMMs (Zhao06 and AM09) and only using the Cascadia versions of the NGA-Sub GMMs, would result in even lower ground motions at longer periods, most notably at 2 s (Figure 9a). Alternative 2, which represents a combination of the global and Cascadia versions of the NGA-Sub GMMs, is not very different from the final recommended combination, reflecting our previous understanding that the global versions of the models are within the range of epistemic uncertainty from other models. This alternative tends to result in slightly higher median ground motions at longer periods of 2 and 5 s, and it was not recommended by the model developers for use in the Cascadia subduction zone because they felt that the regional versions of their models are more suitable there. Alternative 3, which represents slightly different weights than the final recommended set and was shown to the public in the last workshop makes little difference to the median ground motions. The blue dashed lines in Figures 8a and 9a are very close to the red solid lines for almost all periods and distances; one exception is at 5 s where this alternative tends to give slightly lower median ground motions because of the smaller weight on AM09 compared to Zhao06. AM09 is a stochastic simulation-based model and may not be as reliable at long periods, so in this alternative, it was given lower weight; moreover, this model is quite dated. However, its inclusion is a practical way to enhance the otherwise limited epistemic uncertainty at long periods. Meanwhile, the Zhao06 model was extrapolated at long periods (7.5 and 10 s) based on the BCHydro12 model (a version of which is represented in the final set through the use of AG20 variations) for intraslab earthquakes and based on both BCHydro12 and AM09 for interface earthquakes; therefore, we proposed equal weights between the two models for the 2023 NSHM to ensure that potentially large ground motions at long periods are represented in the ground-motion space. The validity of these two models cannot be further verified until more long-period data and simulations are available in this region.
For the intraslab event (Figures 8b and 9b), we observe that the median ground motions are noticeably lower at 0.2 s, but slightly higher at 2 s compared to those of the 2018 NSHM. There are only two alternatives since Zhao06 is the only GMM that is retained from 2018. Alternative 1, which represents removing the older GMMs and only using the Cascadia versions of the NGA-Sub GMMs, results in lower ground motions, particularly at shorter distances. Since this noticeable decrease happens at the reference site condition, it is not related to the extrapolations that were applied to Zhao06 in the 2018 NSHM and could be due to its different modeling choices, including but also beyond data selection. Therefore, retaining this model better represents epistemic uncertainties. Alternative 2, which represents a combination of the global and Cascadia versions of the NGA-Sub GMMs, is very similar in median ground motions to the final recommended combination, reflecting our previous understanding that the global versions of the models are within the range of epistemic uncertainty from other models.
Aleatory variability
Aleatory variability (GMM standard deviation) accounts for the random variability that is naturally present in ground shaking given a model formulation with magnitude, distance, site condition, and other relatively simple parameters. In the current update, individual subduction GMM standard deviations are used and given the same weights as their medians in the PSHA procedure. We recognize that some GMMs may have better regional models for their medians and others for their standard deviations; however, the expert community was divided on assigning the same or different weights to median-standard deviation pairs at the time of development of the 2023 NSHM. The current assignment of weights is consistent with what has been done in past NSHM cycles. One exception was in the 2018 NSHM, where all 31 CEUS GMMs were assigned the same standard deviation model developed by a working group; this was done because not every model had developed an aleatory variability model, mainly due to the complicated nature of the Sammon’s mapping procedure (Sammon, 1969; Scherbaum et al., 2010). Although this approach has some advantages, it can have disadvantages, such as not accounting for potential correlations and dependencies between the components (e.g. ATC, 2023). Furthermore, unlike the Senior Seismic Hazard Analysis Committee (SSHAC)-level NGA-East project, the NGA-Sub project did not focus on modeling the full ground-motion space and USGS developing a single standard deviation model for the Cascadia subduction zone is out of the scope for the 2023 NSHM development.
The standard deviations for the final set of subduction GMMs are shown in Figures 10 and 11 for the interface and intraslab earthquake scenarios discussed in previous figures. Figures 10a and 11a show the individual GMMs, while Figures 10b and 11b show their square root of the sum of the squares (SRSS) of the models using the weights in Tables 1 and 2. The SRSS figures are only reflective of whether the total effect of standard deviation changes would be generally larger or smaller than another combination.
Note that, except AG20, the Cascadia versions of standard deviations are the same as their global versions; also, they are identical for interface and intraslab events, as the data were combined for both types of events to develop these models. These standard deviations are period-dependent. The peak values near 0.1 s for the PSBAH20 and KBCG20 GMMs are similar to the peak in the Zhao06 GMM, which was developed using only Japanese data. This comparison suggests that the Japanese data could be the cause for this peak at 0.1 s. Whereas the standard deviation models of PSBAH20 and KBCG20 are mainly controlled by global data, the standard deviation of AG20-CAS-ADJ and AG20-CAS is regionalized for the Cascadia subduction zone. In addition to data differences, different standard deviation modeling approaches were used by the different GMM developers. For example, KBCG20 used a distance-independent model, while PSBAH20 and AG20 used distance-dependent models.
Observe that, in general, standard deviations will be slightly higher than they were in 2018 NSHM, except at longer periods above 7 s, as all the new individual standard deviations decrease with period. Also observe that Alternative 1, that is, excluding the smaller standard deviations of AM09, would have increased aleatory variabilities, whereas Alternative 2, that is, including global versions of the models, would have decreased aleatory variabilities. Alternative 3 for interface events is very similar to the final proposed option.
Epistemic uncertainty
Epistemic uncertainty accounts for modeling uncertainty due to the lack of knowledge and is represented by logic-tree branches and weights associated with different models, which includes variations of a GMM. In the 2018 NSHM, we were aware that epistemic uncertainties were underrepresented by the subduction GMMs in comparison to the CEUS GMMs and even the crustal GMMs in the WUS (Powers et al., 2021), but we were limited by the available models at the time. In the 2023 NSHM, since epistemic uncertainty, ϵ, models are available for the median ground motion,
Figure 12 illustrates the increased epistemic uncertainty in the 2023 NSHM from subduction GMMs by showing the range of median ground-motion values and their assigned weights for the 11 and 13 variations of the 2023 subduction interface and intraslab GMMs, respectively, compared to the previous 3 and 2 GMMs. Note that the vertical scale is logarithmic in these figures, and the range of the vertical axes, while different, is an order of magnitude in all subplots for easy comparison. The dotted lines show weighted averages of median ground motions. The solid lines along the vertical axes in Figure 12 are the same as the vertical cross-sections in Figure 5 and indicate the range of ground-motion values from GMMs. These ranges are good representations of epistemic uncertainty (i.e. larger range equals larger uncertainty), but the distribution of assigned weights, shown in Figure 12 as stem plots, is also important. These figures show that the ground-motion values cover a broad epistemic uncertainty range: about a factor of 3–10 depending on the period and scenario. Compare this to a factor of 2 and 10, respectively, for the CEUS Updated Seeds and NGA-East GMMs in the work by Rezaeian et al. (2021). Notably, within-model epistemic uncertainties are not available for the two models AM09 and Zhao06; however, due to the improved representation of epistemic uncertainty as illustrated in Figure 12 compared to the previous NSHM, we expect little relative changes, likely slight increases in the estimated mean hazard, if such uncertainties were added.
Basin amplifications
For the 2018 NSHM, consideration of deep-basin effects at long periods necessitated application of BAFs because none of the subduction GMMs at the time included an explicit basin-depth term. These factors were developed based on the basin-effect term of the Campbell and Bozorgnia (2014) crustal GMM because this was the only model based on Z2.5, which was considered the better parameter for characterization of the deep basins in the Cascadia subduction zone. As a result, all subduction GMMs in the 2018 NSHM were reasonably extrapolated up to a spectral period of 10 s for all eight site classes of interest (Powers et al., 2021). In the 2023 NSHM, BAFs are still applied, within the basin boundaries shown in Figure 13. The outer boundary is that of the Puget Lowlands (corresponding to the Z2.5 = 6 km contour), an approximation of which was used in the 2018 NSHM. The inner boundary shown within the Puget Lowlands by a dashed line is the deep Seattle basin (Z2.5≥ 6 km), for which additional regional models are available and amplifications are treated differently, as explained below.
Basin boundaries, defining sites inside and outside of the Seattle basin in Table 4.
For the development of the 2023 NSHM, all the GMMs were assessed based on available empirical data from the NGA-Subduction database (Mazzoni et al., 2022), which is very limited in the Cascadia region, and the M9 simulations in the Seattle basin, which have recently been accepted by the engineering community in the city of Seattle (Wirth et al., 2018a). Residual analyses were undertaken in these assessments to determine the bias of GMMs at long periods, as the USGS GMM selection criterion number 15 states: 15. GMMs should not display any substantial biases or trends in the between-event (inter-event) or within-event (intra-event) residuals with respect to distance, magnitude, soil conditions such as VS30, and other parameters included in the model.
Overall, consistent bias was observed with respect to available data and simulations for interface events in all considered GMMs except some AG20 variations; however, it is recognized that the data and simulations are limited and not a comprehensive representation of the ground-motion space in this region. As a result, the USGS elected to give 50% weight to an adjusted version of the considered GMMs using an M9-based BAF if the location of interest is within the Seattle basin of the Cascadia subduction zone. The GMM weights, when basin effects exist, within and outside of the Seattle basin, are presented in Table 4; the simulation-based basin effects only occur within the deep parts (
Various basin versions of the subduction GMMs for consideration in the 2023 NSHM Cascadia subduction zone, both within and outside of the Seattle basin
Adjustment factors in Seattle basin for interface events
In evaluating the performance of the NGA-Sub basin-effect terms, we are restricted to data from moderate intraslab earthquakes in Cascadia. The bias relative to the Cascadia GMMs was shown in Figure 1 and suggests that an adjustment to the basin term is not required because the residuals at longer periods (1–10 s) are about zero for intraslab earthquakes. The NGA-Sub dataset does not feature usable Cascadia interface recordings, but it does include interface events from other subduction zones, such as Japan and Chile. Since the NGA-Sub models were adjusted to global amplitudes, the relative over-prediction in Cascadia, which exhibit lower ground motions than average, is expected. Figure 14 shows the bias based on a subset of global events from the NGA-Subduction database with M > 7.5 and R RUP < 300 km. The bias suggests that the NGA-Sub GMMs predict smaller ground motions at longer spectral periods compared to AM09. It is hypothesized that interface earthquakes may generate stronger basin amplifications because of their shallower incidence angle relative to deeper intraslab earthquakes (Wirth et al., 2019). The larger bias of AM09 supports retaining this model in the recommended logic tree to account for such epistemic uncertainty in basin effects at longer periods.
Bias of subduction GMMs for interface global events with M > 7.5. This figure does not use the “BASIN” versions of GMMs when comparing to global events. The bias is calculated for the natural logarithm of spectral acceleration (g).
M9-based factor-of-two basin adjustments for 2023 NSHM
There is a bias when comparing the amplification in the Seattle basin from the M9 simulations to the NGA-Sub GMM basin-effect terms. This motivates the inclusion of an additional BAF for interface earthquakes that adjusts ground motions to be more consistent with the M9 simulations. In the 2023 NSHM, we use the following modified equation to predict the median ground motion for sites on deep sedimentary basins in Seattle (
where
Subduction GMMs with BAFs compared to (a) the M9-based factor-of-two BAFs in Equation 1 and their relevant adjustments (AG20 does not need to be adjusted), and (b) the recent M9-CSIM adjustment suggested by AG20.
Discussion: M9-based GMM constant adjustments for consideration in future NSHMs
In comparing the M9 median ground motions with the NGA-Sub models, we observe that empirical GMMs underestimate the simulations even after using the M9-based factor-of-two BAFs discussed above. To fit M9-simulations, one could center GMMs to the simulated amplitudes by adding a constant term CSIM, calculated by averaging the difference between the simulations and the GMMs where basin effects are not present. Such a CSIM adjustment term has been recommended in a recent publication that was not considered for the development of the 2023 NSHM (Sung and Abrahamson, 2022) and was not implemented by other GMM developers. The effects of this adjustment at T ≥ 2 s are shown in Figure 15b, where the response spectrum for an M9 interface event at a rupture distance of 100 km is adjusted relative to AG20. Note that outside of the period range of 2–3 s, AM09 shows the largest median prediction. We conclude that the CSIM-adjusted AG20 model supports retaining AM09 at this time.
Figure 16 shows the medians of subduction GMMs in Table 4 with basin effects on a soft site condition with V S30 = 185 m/s, Site Class DE according to the 2020 NEHRP Provisions, and a deeper than default basin depth of Z2.5 = 6.709 km, typical of Seattle. The effect of applying the M9-based factor-of-two BAF at long periods for interface earthquakes is demonstrated in Figure 16a for all GMMs except for AG20.
Median spectral accelerations for GMMs in Table 4 for a soft site class DE, categorized with V S30 = 185 m/s, on a deep basin with Z2.5 = 6.709 km for an (a) interface scenario with M = 9, R RUP = 100 km, and Z TOR = 10 km, and (b) intraslab scenario with M = 7, R RUP = 50 km, and Z TOR = 40 km.
Impact of subduction GMM modifications on hazard maps
This section shows the effects of changes in interface and intraslab subduction GMMs from the 2018 NSHM to the 2023 NSHM on uniform hazard maps for a hypothetical site condition with V S30 = 500 m/s. Default basin depth and amplifications are used unless basins are deeper than the V S30 -based default values, in which case the 50% weights from Table 4 are applied. The effects on the maps reflect the changes in the medians, standard deviations, and epistemic uncertainties of subduction GMMs, including the assignments of logic-tree weights discussed in previous sections. Figures 17 to 19 show the difference and ratio maps for a 2% probability of exceedance in 50 years at four response spectral periods of 0.2, 1, 3, and 5 s. To develop these difference and ratio maps, the earthquake source model of the 2018 NSHM is used, but different GMMs (2018 versus 2023 sets) are applied. Figure 17 only uses interface events, demonstrating the effects of the changes to interface GMMs. Observe that the calculated mean hazard only increases at close distances, by the coast, for short periods; everywhere else and at other periods, the calculated mean hazard decreases. A closer look at the Seattle basin is provided in the Appendix in Figure 21. Similar figures for V S30 = 760 and 185 m/s are shown in the Appendix Figures 24 and 30, respectively, with a closer look at the Seattle basin in Figures 27 and 33.
Differences and ratios in calculated hazard in the PNW, calculated using the 2018 and 2023 NSHM subduction interface GMMs (both using the 2018 subduction interface source model) at 0.2, 1, 3, and 5 s for a hypothetical site with V S30 = 500 m/s. A closeup of the Seattle basin is provided in the Appendix Figure 21.
Differences and ratios in calculated hazard in the PNW, calculated using the 2018 and 2023 NSHM subduction intraslab GMMs (both using the 2018 subduction intraslab source model) at 0.2, 1, 3, and 5 s for a hypothetical site with V S30 = 500 m/s. A closeup of the Seattle basin is provided in the Appendix Figure 22.
Differences and ratios in calculated hazard in the PNW, calculated using the 2018 and 2023 NSHM subduction interface, intraslab, and crustal GMMs (both using the 2018 earthquake source models) at 0.2, 1, 3, and 5 s for a hypothetical site with V S30 = 500 m/s. A closeup of the Seattle basin is provided in the Appendix Figure 23.
Figure 18 only uses intraslab events from the 2018 NSHM, demonstrating the effects of the changes to intraslab GMMs. Observe that the calculated mean hazard increases in the Seattle basin, more at 1 and 3 s, less at 0.2 and 5 s. The calculated mean hazard in general increases for 1 and 3 s. It decreases at longer distances for 0.2 and 5 s. A closer look at the Seattle basin is provided in the Appendix in Figure 22. Similar figures for V S30 = 760 and 185 m/s are shown in the Appendix Figures 25 and 31, respectively, with a closer look at the Seattle basin in Figures 28 and 34.
Finally, Figure 19 demonstrates the effects of all GMM changes in the PNW region, including the changes shown in Figures 17 and 18 but also changes due to crustal GMMs. There are minor effects from the crustal GMMs, as the 2023 NSHM introduced long-period basin effects for the Portland–Tualatin basin and the California Great Valley (Ahdi et al., 2023). The earthquake sources are those of the 2018 NSHM. Observe that overall the calculated mean hazard increases in the Seattle basin only for shorter periods (0.2 and 1 s), and it decreases for longer periods (3 and 5 s) and at longer distances from subduction sources. A closer look at the Seattle basin is provided in the Appendix in Figure 23. Similar figures for V S30 = 760 and 185 m/s are shown in the Appendix Figures 26 and 32, respectively, with a closer look at the Seattle basin in Figures 29 and 35.
Summary
The USGS NSHMs are used in building design and many other applications. They combine information from earthquake source models and GMMs to perform PSHA. In the 2014 NSHM update, USGS established a set of 16 GMM selection criteria that included applicability ranges, including three spectral periods and one reference site condition. In the 2018 NSHM update, USGS expanded these criteria to support the MPRS product that requires GMMs to be applicable for 22 spectral periods and 8 site classes. While GMMs in the crustal regions of the WUS and the stable continental regions of the CEUS were updated in 2014 and 2018 for the MPRS requirement and improved representation of epistemic uncertainties, subduction zone GMMs were not updated. This article summarized recent advances in subduction ground-motion modeling and presented a combination of new models and others retained from the 2018 NSHM for the next 2023 NSHM update. It is proposed to retain two of the models from the 2018 NSHM, AM09 and Zhao06, at reduced weights, and to combine them with variations of three NGA-Sub GMMs. Different weighting combinations are suggested for interface and intraslab events. Weighted combinations of medians and standard deviations were shown and compared to the previous cycles to understand the combined effect of the GMM changes. Epistemic uncertainty is represented by the logic-tree weights, retaining AM09 and Zhao06, and representing the new GMMs as three-point distributions of medians and 5th and 95th percentiles. We believe that the representation of epistemic uncertainties for subduction GMMs has improved significantly compared to previous cycles. However, we acknowledge that future studies may better quantify the logic-tree weights and estimate epistemic uncertainties in an even more complete manner.
For deep-basin effects in the Seattle basin of the PNW, the M9 simulations were used to modify the ground-motion estimates at longer periods. These BAFs were suggested in the form of factor-of-two amplifications for interface events only for AM09, Zhao06, PSBAH20, and KBCG20. Finally, the total effect of subduction GMM changes was discussed in the form of difference and ratio maps of uniform hazard ground motions. The subduction GMMs in the Seattle region were further discussed in the Appendix, with logic-tree weights and figures provided.
Additional topics that can be considered in future NSHM cycles include (1) variations in the magnitude-scaling break point parameter, Mbreak; (2) consideration of additional epistemic uncertainty using the method used for crustal GMMs in the WUS (Rezaeian et al., 2015), or the Sammon’s mapping method used in the CEUS (Rezaeian et al., 2021), or other approaches such as developing backbone models for individual GMMs or adding within-model epistemic uncertainties to AM09 and Zhao06; and (3) assignment of non-uniform logic-tree weights to GMMs across periods, site conditions, or median-standard deviation pairs.
Footnotes
Appendix
Acknowledgements
The authors thank the next generation attenuation-subduction (NGA-Sub) model developers (including but not limited to Yousef Bozorgnia, Norm Abrahamson, Jonathan Stewart, Gail Atkinson, Grace Parker, Nicolas Kuehn, and Ken Campbell) for their invaluable participation and continued interactions, the US Geological Survey National Seismic Hazard Model (NSHM) steering committee, participants of the two virtual public workshops held on NGA-Subduction, and the ground-motion review panel for the 2023 NSHM. The detailed reviews from Gail Atkinson, Norman Abrahamson, Brendon Bradley, and Grace Parker are appreciated. The Generic Mapping Tools (GMTs) was used in the creation of the hazard comparison maps (Wessel et al., 2019, 
). Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
ORCID iDs
Data and code availability
The computer codes (nshmp-haz; Powers et al., 2022), data, and models (nshm-conus; Powers and Altekruse, 2022) used in this article are available publicly on GitLab at doi: 10.5066/P9STF5GK and doi: 10.5066/P9J1OVR6, respectively (last accessed March 2024).