ML24309A090

Technical Letter Report Global GS24 Ground Motion Models for Active Crustal Regions Based on Non-Traditional Modeling Approach

ML24309A090
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Issue date:	09/09/2024
From:	Bauer L, Vladimir Graizer, Scott Stovall NRC/RES/DE/SGSEB
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TLR-RES-DE-SGSEB-2024-01
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Technical Letter Report

[TLR-RES-DE-SGSEB-2024-01]

Global GS24 Ground Motion Models for Active Crustal Regions based on Non-Traditional Modeling Approach Date:

September 9, 2024 Prepared by NRC staff:

Vladimir Graizer Scott Stovall Laurel Bauer Structural, Geotechnical, and Seismic Engineering Branch Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001

DISCLAIMER This report was prepared as an account of work sponsored by an agency of the U.S. Government.

Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party's use, or the results of such use, of any information, apparatus, product, or process disclosed in this publication, or represents that its use by such third party complies with applicable law.

This report does not contain or imply legally binding requirements. Nor does this report establish or modify any regulatory guidance or positions of the U.S. Nuclear Regulatory Commission and is not binding on the Commission.

EXECUTIVE

SUMMARY

Ground motion models (GMMs) also called ground motion prediction equations (GMPEs), and attenuation relations, use datasets of recorded ground motion parameters at multiple seismic stations during different earthquakes and in various seismic source regions to generate equations.

These equations are later used to estimate site-specific ground motions that may shake a site if an earthquake of a certain magnitude occurs at a nearby location. These models describe the distribution of ground motion in terms of a median and a logarithmic standard deviation and are crucial in assessing seismic hazard, thereby providing estimates of the loading that a structure may undergo during a future earthquake. An expanded Pacific Earthquake Engineering Research (PEER) Center Next Generation Attenuation Phase 2 (NGA-West2) ground motion database compiled from shallow crustal earthquakes in active crustal regions (ACR) is used to develop GS24b and GS24 ground motion models (GMM) for the average (RotD50) horizontal components of peak ground acceleration (), peak ground velocity () and 5% damped elastic pseudo-absolute acceleration response spectral ordinates () at 21 oscillator periods (T) ranging from 0.01 to 10 s. The NGA-West2 dataset was expanded with recordings from the three 2023 Turkish earthquakes with moment magnitudes of 6.3, 7.5 and 7.8 (Buckreis et al.,

2023a, 2023b). We developed the backbone GS24b model that uses the closed form approximation of the spectral acceleration as a multiplication of the and spectral shape (normalized spectral acceleration spectrum) functions and the global GS24 model representing the backbone GS24b GMM adjusted for residuals from multiple ACR regions. The new GS24b and GS24 models are developed using a non-traditional approach to ground motion modeling developed by Graizer and Kalkan (2007 and 2009). These models are applicable to earthquakes with moment magnitudes 4.0 8.5, at rupture distances of 0 400 km, at sites having time-averaged shear wave velocity in the upper 30 meters of the profile 30 in the range from 150 m/sec to 1500 m/sec, and for periods (T) ranging from 0.01 to 10 sec. As compared to the GK17 GMM (Graizer, 2018) the new model includes sediment thickness 2.5 depth (basin effect) correction and calculations.

ACKNOWLEDGEMENTS We are grateful to Jonathan Stewart and Tristan Buckreis from the University of California Los Angeles for providing access to the flatfiles of processed Turkey-Syria ground motion data.

Previous joint work with Erol Kalkan from the U.S. Geological Survey resulted in development of the original GK15 model serving the basis for creating updated GK17, GS24b and GS24 models.

ACRONYMS ACR Active Crustal Region EQL Equivalent-linear Method GMM Ground Motion Models GMPE Ground Motion Prediction Equations GK17 Graizer - Kalkan 2017 GMM GS24 Graizer - Stovall 2024 GMM GS24b Graizer - Stovall 2024 Backbone GMM Earthquake Moment Magnitude NGA-West2 Next Generation Attenuation Phase 2 PEER Pacific Earthquake Engineering Research Center PDF Probability Density Function Peak Ground Acceleration Peak Ground Velocity Pseudo-absolute Spectral Acceleration response spectral ordinates Q0 Seismological quality factor at a frequency of 1 Hz apparent attenuation factor of 5% damped spectral acceleration.

RotD50 50th percentile or median response Closest Distance to the earthquake fault rupture in km RVT Random Vibration Theory Spectral Acceleration SCR Stable Continental Region SDF Single-degree-of-freedom oscillator function SHAKE 1-D EQL Programs 30 Time-averaged shear wave velocity in the upper 30 meters of the profile Total standard deviation (sigma)

Within-event standard deviation Between-event standard deviation 1.0 Depth to the shear wave velocity horizon of 1 km/s 1.5 Depth to the shear wave velocity horizon of 1.5 km/s 2.5 Depth to the shear wave velocity horizon of 2.5 km/s

TABLE OF CONTENTS EXECUTIVE

SUMMARY

................................................................................................. 4 ACKNOWLEDGEMENTS............................................................................................... 5 ACRONYMS................................................................................................................... 6 1

INTRODUCTION...................................................................................................... 8 2

DATASETS.............................................................................................................. 9 3

GS24 GROUND MOTION MODELS...................................................................... 11 3.1 PGA SCALING.................................................................................................... 11 3.2 SPECTRAL SHAPE MODEL................................................................................... 12 4

GS24B BACKBONE MODEL................................................................................ 13 4.1 SITE RESPONSE TERM........................................................................................ 13 4.2 APPARENT ATTENUATION OF SPECTRAL ACCELERATIONS...................................... 14 4.3 EXAMPLES OF BACKBONE MODEL......................................................................... 16 5

GS24 GROUND MOTION MODEL........................................................................ 16 5.1 FAULT STYLE SCALING........................................................................................ 16 5.2 SEDIMENT THICKNESS. SCALING.................................................................. 17 5.3 EXAMPLES OF THE GS24 MODEL APPLICATIONS.................................................... 20 6

RESULTS............................................................................................................... 21 7

DATA AND RESOURCES..................................................................................... 22 8

TABLES................................................................................................................. 23 9

FIGURES................................................................................................................ 25 10 REFERENCES.................................................................................................... 42

1 INTRODUCTION Ground motion models (GMMs) also called ground motion prediction equations (GMPEs), or attenuation relations, use datasets of recorded ground motion parameters at multiple seismic stations during different earthquakes and in various seismic source regions to generate equations.

These equations are later used to estimate site-specific ground motions that may shake a site if an earthquake of a certain magnitude occurs at a nearby location. These models describe the distribution of ground motion in terms of a median and a logarithmic standard deviation and are crucial in assessing seismic hazard, thereby providing estimates of the loading that a structure may undergo during a future earthquake.

Ground Motion Models are typically developed from an empirical regression of observed amplitudes against an available set of predictor variables. Joyner and Boore (1993, 1994) proposed performing analyses of data using the two-stage regression based on the Brillinger and Preisler (1984, 1985) algorithm for applying the random effects model to regression analyses.

Abrahamson and Youngs (1992) presented an alternative mixed-effects algorithm that is more stable according to the authors although less efficient. In these approaches, coefficients were obtained separately for each period resulting in response spectra that demonstrate jaggedness and consequently requiring smoothing (e.g., Abrahamson et al., 2014; Boore et al., 2014; Campbell and Bozorgnia, 2014; Chiou and Youngs, 2014).

In contrast to the above-described traditional approaches, we are using the non-traditional approach first introduced by Graizer and Kalkan (2007, 2009, 2011) and later expanded by Graizer (2017, 2018). In this method at the first stage the closed form expression of the two functions ( and spectral shape ) composition is developed separately for the active crustal and stable continental regions (ACR and SCR) approximating ground motion attenuation. This type of modeling was originally based on the expanded NGA-West1 dataset and is developed using the Nelder-Mead method of nonlinear minimization (Wilson et al., 2003). However, this closed form approximation is not flexible enough to describe variations of response spectral attenuation and to produce lower standard error. This is why we incorporated the second stage when previously developed closed form model is adjusted based on residuals for each period.

In Graizer (2024) the new set of strong motion data from the two strongest 2023 earthquakes in Turkey were used to test the ergodic GK17 (Graizer, 2018) GMM. The GK17 model developed using the NGA-West2 database (Ancheta et al., 2014) for the active crustal regions was applied to the dataset of recordings from the two largest moment magnitude () 7.8 and 7.5 earthquakes in Turkey (Buckreis et al., 2023a, 2023b). The GK17 model demonstrates acceptable performance while mostly underpredicting spectral accelerations at near fault up to ~100 km and far-field more than ~400 km rupture distances for periods < 1 sec. The GK17 model was modified by applying additional distance and 30 residuals corrections creating an updated GK non-ergodic model tuned for Turkey and called the GK_T model. Turkey specific GK_T partially non-ergodic model shows better agreement with recorded data than the ergodic GK17 model, especially at short periods and short rupture distances.

In this report we present two newly developed GMMs:

1. The global backbone GS24b model that uses the closed form approximation of the spectral acceleration as a multiplication of the and spectral shape (normalized spectral acceleration spectrum) functions. This model can be later used for adjusting to the specific ACR region (e.g., Southern and Northern California) creating partially non-ergodic models.

2. The ergodic GS24 model representing the backbone GS24b GMM adjusted for the moment magnitude, time-averaged shear wave velocity in the upper 30 meters 30 and closest distance to the fault rupture residuals.

We also tested previously developed GK17 GMM (Graizer, 2018) against the NGA-West2 dataset expanded with recordings from the three 2023 Turkish earthquakes.

2 DATASETS The new GS24b and GS24 models are based on Pacific Earthquake Engineering Research (PEER) Center Next Generation Attenuation Phase 2 (NGA-West2) expanded with recordings from the three 2023 Turkish earthquakes with moment magnitudes of 6.3, 7.5 and 7.8 (Buckreis et al., 2023a, 2023b) ground motion database compiled from shallow crustal earthquakes in active crustal regions to develop a GMM for the average RotD50 (50th percentile or median response, Boore, 2010) horizontal components of peak ground acceleration (), peak ground velocity

() and 5% damped elastic pseudo-absolute acceleration response spectral ordinates ()

at 21 oscillator periods (T) ranging from 0.01 to 10 sec (Ancheta et al., 2014). The specific spectral periods are 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 sec. The number of predictors used in the current model is limited to a few measurable parameters: moment magnitude (), closest distance to the fault rupture plane (), time-averaged shear wave velocity in the upper 30 m of the geological profile (30), depth to the shear wave velocity horizon of 2.5 km/s (2.5), style of faulting () and apparent (intrinsic and scattering) attenuation factor ((, )) of 5% damped spectral acceleration.

The dataset is created based on the NGA-West2 flat file previously used for developing GK17 model (Graizer, 2018) enhanced by the recordings from the three 2023 Turkish earthquakes with moment magnitudes of 6.3, 7.5 and 7.8 (Buckreis et al., 2023a). The currently used dataset consists of the subset of the NGA-West2 dataset with 13,241 recordings with the addition of 685 Turkish recordings with the total number of 401 earthquakes in the combined dataset. Figure 1 demonstrates the distribution of chosen recordings with respect to moment magnitude and closest distance to the rupture (upper panel), and with respect to and 30 (middle panel). NGA-West2 data are shown with open circles and additional Turkish data with red circles in Figure 1. We limited the dataset by earthquakes with 4.0 7.9 and rupture distances 400 km. The GS24b and GS24 models are based on a dataset combining recordings from California, Alaska (crustal events), Taiwan, Turkey, Italy, Greece, New Zealand and Northwest China ACRs. It did not include data from Japan because most of the sites in Japan are characterized by a subsurface geology significantly different from the site conditions in other ACRs. Like our previous GMMs GS24b and GS24 should be considered to be global models since they include recordings from multiple ACRs.

Aftershock records can be treated differently than data from main shocks because of some concern that the median ground motions from aftershocks are systematically lower than those

from the mainshocks. Existing literature demonstrates conflicting findings, in some cases finding different magnitude scaling for aftershocks relative to main shocks (e.g., Boore and Atkinson, 1989), while in other cases finding similar motions for similar magnitudes (Douglas and Halldórsson, 2010). As a result, some GMM developers exclude aftershock data from regressions (Boore et al., 2014), exclude aftershocks closest to the mainshock (Campbell and Bozorgnia, 2014; Chiou and Youngs, 2014), include a separate coefficient for the attenuation term for the aftershocks data used (e.g., Abrahamson, Silva and Kamai, 2014), or simply include all well recorded aftershocks (Idriss, 2013; Graizer, 2018). Following our previous approach, we are including all well recorded aftershocks in the datasets.

The record processing procedures applied to all records in the NGA-West2 flatfile include the selection of record-specific corner frequencies to optimize the usable frequency range. The most important filter applied to the data is the low-cut filter, which removes low frequency noise. For each record, the maximum usable period applied in our analysis was taken as the inverse of the lowest usable frequency given in the NGA-West2 flatfile. The lowest usable frequency is usually equals 1.25 of the high-pass (equivalent to low-cut) corner frequencies used in the processing of the two horizontal components. Figure 1 (lower panel) demonstrates the number of data points used in our models for different periods with decreasing amount of data for longer periods.

The current versions of the GS24b and GS24 include testing that use the following three datasets:

The 1st dataset of 4 7.9 and distances 400 km that includes 13,926 (Figure 1, lower panel, and Figure 2) called M4_R400.

The 2nd dataset (subset of the 1st dataset) includes 5,063 data points for 5.0 and 150 km (M5_150), and the final dataset:

The 3rd dataset (also subset of the 1st dataset) includes 6,046 data points covering the range of 4 7.9 and 250 km (M4_R250).

The 1st dataset consists of the same NGA-West2 dataset (Ancheta et al., 2014) as used in the development of GK17 (Graizer, 2018) model (total of 13241 data points) enhanced by the data from the three recent 2023 Turkish earthquakes with 6.3, 7.5 and 7.8 (Buckreis et al., 2023a, 2023b). The 2nd dataset is a subset of the 1st dataset limited by magnitude and rupture distance.

The 3rd dataset is also a subset of the 1st group. This dataset was created based on the recordings of earthquakes that can potentially produce structural damage. It consists of the seven half-magnitude bins with varying distance thresholds depending upon magnitude:

1. 4.0 < 4.5 and 25 km

2. 4.5 < 5.0 and 50 km

3. 5.0 < 5.5 and 75 km

4. 5.5 < 6.0 and 100 km

5. 6.0 < 7.0 and 150 km

6. 7.0 < 7.5 and 200 km

7. 7.5 7.9 and 250 km We consider the 3rd dataset to be the most important from the engineering application point of

view.

As shown in Figure 2, the first dataset is heavily dominated by the relatively low magnitude (4

5) earthquakes less likely to produce damage, while the effect of lower magnitude earthquakes is absent in the second dataset. The 3rd dataset is the most magnitude-distance balanced and consequently most important from the engineering/seismic hazard assessment point of view, practically limiting data to the number of events that can potentially produce any damaging effects. This dataset is also much more uniform in terms of magnitude distribution, and mostly limited to more uniform accelerographs recordings (Figure 2).

3 GS24 GROUND MOTION MODELS Model development included multiple steps, like those described in Graizer (2018). As a first step exploratory analyses using the first largest dataset were performed and demonstrated the demand to modify some of the previously developed GK17 relations. However, all formulations described in Graizer (2018) remain valid.

3.1 PGA Scaling We started with testing and adjusting the backbone model presented in Graizer (2018) and originally developed by Graizer and Kalkan (2007, 2009, 2011) to the described datasets. As a reminder, spectral acceleration is a closed form combination of the two functions and normalized spectral shape functions:

=

(1) log() = 1() + 2()

(2)

Where 1() is magnitude scaling and 2() is distance scaling. magnitude scaling function has a linear scaling in logarithmic space for small magnitudes and the same style of saturation approximation function as in our previous model for larger magnitudes (Graizer and Kalkan, 2016):

1(, ) =

([21 (22 )]) 4 < 5.0

([1 ( + 2) + 3]) 5.0 (3) where is moment magnitude, are coefficients, is a scaling factor (Figure 3). In the current GS24 models we modified the turning point on scaling from magnitude 5.5 to 5.0 effectively increasing the scaling for < 5.5.

In the current GS24 models, like Graizer (2017, 2018) we are assuming attenuation of ground motion in the near-source region to be associated with the shear-waves geometric spreading of Rrup-1 while at distances larger than about 50 km maximum ground motion to be associated with surface waves attenuating of Rrup-0.5. This transition point was found by fitting NGA-West2 data (Graizer, 2018).

2() =

1 1

2 2

+ 42 2(/2)

, < 50~

1

[1 2 ]2 + 42 2

2

, 50~

1

(4)

=

(1 50 2)2 + 42 250 2

1 50 2

2

+ 42 2(50/2)

Parameter is a scaling factor applied to Equation 4 to avoid step in slope, and R2 is the corner distance in the near-source defining the plateau without significant attenuation of ground motion.

Parameter 2 is directly proportional to the moment magnitude of an earthquake; the larger is,

the wider is the plateau defined by R2. Corner distance is proportional to the moment magnitude with the scaling law previously developed for the active tectonic environment (Graizer and Kalkan, 2007), and also used in previous models (Graizer, 2016, 2018):

2 = 4+ 5 (5)

Equations (4 and 5) imply that for larger magnitudes, the turning point on the attenuation curve occurs at larger distances. It varies from 1.4 km for = 4.0 to 10.4 km for = 8.0. (Graizer and Kalkan, 2007). I assigned parameter 2 = 0.5, which is equivalent to minor bump (increase in amplitude of ground motion at certain distances from the fault also called over saturation) on attenuation with a smooth transition from a plateau to the R-1 or R-0.5 geometrical spreading.

3.2 Spectral Shape Model For modeling spectral shape, we are using the approximation function developed by Graizer and Kalkan (2009). This function is a combination of a single-degree-of-freedom (SDF) oscillator and a modified log-normal probability density function (PDF). The updated spectral shape model

() is a continuous function of spectral period (or frequency) and is formulated as shown in Figure 4.

= 1(30, ) x 2((, )) x 3(, ) x 4(2.5, ) x,0 x (6)

In equation 6, is spectral shape,,0 is a generic spectral shape function (anchored at = 1g), 1,.., are functions of a set of independent parameters representing shallow site conditions, apparent attenuation of spectral acceleration, style of faulting and other parameters affecting the physical process of ground motion distance attenuation with random error term,

which has a mean of zero and a standard deviation. The 1(30, ) is for shallow site amplification, 2((, )) is for apparent (intrinsic and scattering) attenuation correction, 3(, ) is for style of fault effect, and 4(2.5, ) for additional deep sediments (often called basin effect) correction beyond the depth range 0.67 2.5 3.15 km. Parameters of spectral shape functions were originally determined using nonlinear optimization to fit the recorded data.

4 GS24B BACKBONE MODEL We first developed a backbone model which is a combination of the generic spectral shape,,

site amplification and apparent anelastic attenuation functions:

= 1(30,) x 2((, )) x x,0 (7) 4.1 Site Response Term The 1(30, ) item (referred to these items as filters in our previous publications) in equations 6 and 7 is for shallow site amplification due to geological conditions in the upper section of geological profile as characterized by the parameter 30. Site correction was developed in Graizer (2016) based on multiple runs of different representative shear wave velocity profiles through SHAKE-type 1-D equivalent-linear (EQL) programs using time histories and random vibration theory (RVT) approaches (Kottke and Rathje, 2008) and on EQL RVT type code developed by the staff of the U.S. Nuclear Regulatory Commission. Soil profiles were chosen from the set of California profiles collected by the U.S. Geological Survey, California Geological Survey, UC Santa Barbara and other organizations (e.g., Gibbs et al., 1992; De Alba et al., 2004) and the NRC library of appropriate profiles. For the 1(30, ) filter we used same functional form as that used in Graizer (2018) for ACR:

1(30, ) = 1 +

30 1 30

2

+ 1.96 30

(8) 30 = 0.5 ( 30/1100) 180 30 1100 /

30 =

275 120 2.0 180 30 275 /

30 120 2.0 275 30 1100 /

where is frequency. Like in Graizer (2018) we characterized our reference rock (also sometimes called western hard rock) as 30 = 1100 m/s. This value of reference rock is identical to Campbell and Bozorgnia (2014) and close to 30 = 1130 m/s in Chiou and Youngs (2014) and to 30 =

1180 m/s in Abrahamson et al. (2014). Site amplification functions are calculated for different 30 relative to the reference rock of 30 =1100 m/s. The limits of model saturation are 180 30 1100 m/s covering most of the velocity profiles. Figure 5 shows 30 site amplification from

Equation 8 representing 1-D site amplification derived from a collection of S-wave profiles basically demonstrating a semi-empirical approach.

Our approach to implementing nonlinearity is discussed in detail in Graizer (2017 and 2018).

Before implementing nonlinearity in our model, we reviewed current approaches for modeling it in site response (e.g. Kamai et al., 2014; Walling et al., 2008; Campbell and Bozorgnia, 2014) and performed independent analyses. Our assessment showed significant variability in results and approaches. We can speculate that there is no simple nonlinear correlation between site amplification and 30. For example, Laurendeau et al. (2013) and Ktenidou and Abrahamson (2016) demonstrated that the addition of kappa is needed to get reasonable soft rock to hard rock spectral amplification ratios. Based on the analysis of strong motion recordings from the 2014 6.0 South Napa earthquake at Carquinez Bridge geotechnical array Kishida et al. (2018) demonstrated that the apparent S-wave velocity decreased when the was greater than 0.07g, confirming that soil nonlinear behavior was observed due to strong shaking. Another argument about the deficiency in current approaches to nonlinearity is that they are actually capping on the possible level of strong ground motion, contradicting a number of strongest records: e.g., more than 2 g at Parkfield Fault Zone 16 during the 6.0 earthquake (Shakal et al., 2006), 1.9 g Tarzana record from the 6.7 Northridge earthquake or a 2.2 g Heathcote Valley School record from the 6.3 Christchurch, New Zealand earthquake (Graizer, 2012). As a result of the tests and analysis performed, we decided to implement nonlinearity in a simple way by putting cap on site amplification. As can be seen from equation 8 and Figure 5 the coefficient of amplification reaches its maximum at 30 = 180 m/s and is constant for lower velocities. Similarly, coefficient of amplification reaches its minimum at 30 = 1100 m/s and is constant and equal to 1 for higher velocities (Figure 5).

4.2 Apparent Attenuation of Spectral Accelerations We are calling apparent attenuation the combined intrinsic absorption and scattering dissipation representing the beyond (everything else except) geometrical spreading attenuation. We avoid calling it anelastic because part of it is scattering which is elastic.

The 2(,, ) filter adjusts the distance attenuation rate by including the apparent attenuation of the response spectra given as:

2(,, ) = (

(, ))

(9) in which (, ) is a frequency dependent apparent attenuation quality factor of spectral acceleration amplitudes, and is apparent wave velocity. As in Graizer (2017), we want to distinguish between the well-known seismological () usually measured using Fourier spectra of S-, Lg-or coda-waves (e.g., Erickson et al., 2004; Maeda et al., 2005; Malagnini et al., 2007; Ford et al., 2008), and the quality factor of response spectral acceleration amplitudes (, ).

To estimate apparent anelastic attenuation and the corresponding response spectra (, )

quality factor we performed inversions using the same approach as that applied to the Fourier amplitude spectra described in Graizer (2018, 2022). Inversions were performed at 21 frequencies for 7 different averaging distance intervals from 50 to 400 km (Figure 6). An overall power approximation of frequency dependent apparent quality factor based on our inversion results (Graizer, 2018, 2022):

(, ) = 00.96 (10) where 0 = 120 for the ACRs corresponding to the average = 5.25 in the original NGA-West2 dataset of 4 7.9 and distances 400 km used in Graizer (2018). In Graizer (2018, eq.8) we used approximation of (, ) as a combination of three frequency intervals creating minor jaggedness. To avoid this, we approximated (, ) with a smooth equation in the interval 50 400 km:

(, ) = 2 + 41 (11) 1 = 0

= 1 2 Figure 6 shows comparison of the above-described response spectra quality factor with that of the published seismological quality factor () for the Southern and Northern California (Erickson et al., 2004; Malagnini et al., 2007) covering the frequency range 0.25-20 Hz. These comparisons demonstrate the differences in slopes and amplitudes of the seismological and response spectra apparent attenuations. In the meantime, the values of 0 0 (seismological quality factor at frequency of 1 Hz) apparent quality factor of response spectra and seismological are similar at a frequency near 1 Hz. As was shown in Graizer (2018), another important consequence of equation 10 is that apparent attenuation is almost frequency independent at a rupture distance of more than 50 km.

(, ) 01 2(, )

0

> 50 (12)

Figure 6 also demonstrates magnitude dependence of the resulting apparent attenuation factor.

Resulting apparent attenuation of response spectral amplitudes at rupture distances of more than 50 km are practically frequency independent (equation 12), but significantly different from that of the seismological. As mentioned above, it is an empirical result that is only applicable to shallow crustal earthquakes in active tectonic regions and is associated with the geometrical spreading R- 0.5 of surface waves. Most importantly, apparent attenuation of response spectral amplitudes is different from that of the seismological -factor and should be estimated based on actual spectral acceleration data and not transferred from seismological measurements.

We found that magnitude dependent better fit existing data. A reason for this may be that larger earthquake faults generally penetrate deeper in the crust than the smaller ones, and consequently a significant portion of the wave propagation paths are associated with deeper layers and correspondingly higher. In other words, it is not a magnitude, but a path dependence of apparent attenuation.

If (, ) 01 the anelastic attenuation rate () becomes frequency independent, and the exponential factor in equation 12 can be included in the distance-dependent power law R-.

Potentially, instead of R-0.5 apparent geometrical attenuation rate can become of ~R-07.

4.3 Examples of Backbone model Figures 7 shows examples of response spectral accelerations at rupture distances of 10, 50 and 200 km for moment magnitudes varying from = 4.5 to 8 calculated using the backbone model.

As expected, all curves are smooth with maxima shifting toward longer periods and slope decreasing for larger magnitudes. Figure 8 shows examples of different periods attenuation with distance to the fault. As prescribed by equation 4 attenuation rate changes from that of shear to surface waves at = 50 km.

The backbone model GS24b was tested against all three subsets. As expected, standard error is higher for the first largest subset (M4_R400) (Figure 9). If compared to our previous GK17 model, GS24b mostly demonstrates higher sigma except for short periods 0.01-0.1 s for the M4_R250 dataset considered the most important. In the meantime, we did not expect the backbone model to perform as well as the final model adjusted for residuals as well as for style of fault and additional deep sediment (basin) effect. Another important conclusion is that GK17 model demonstrates acceptable performance against all the three datasets confirming results achieved in Graizer (2024) using Turkish data.

The backbone model includes magnitude 1(, ), distance geometrical spreading 2, site response term 1(30, ) and apparent (anelastic) attenuation 2(,, ) scaling. We referred to them as filters in our previous publications. We intentionally did not incorporate style of fault 3(, ) and an additional deep sediment 4(2.5, ) effect correction into GS24b backbone model to allow future adjustments to the specific areas.

5 GS24 GROUND MOTION MODEL 5.1 Fault Style Scaling The need to include style of faulting factors and the estimation of these factors is highly debatable and varies significantly based on recent publications. For example, Bindi et al., (2014) differentiates between normal (N), reverse (R), strike slip (S) and unspecified (U) fault types; Boore et al. (2014), Chiou and Youngs (2014), Campbell and Bozorgnia (2014) differentiate between N-, R-and S-type faults; Idriss (2013) differentiates between R-and S-type faults; while Bindi et al. (2017) found not enough justification for distinguishing between different fault styles.

In the meantime, even the authors differentiating between normal and strike slip faults acknowledge that there is only a small number of normal fault events in the NGA-West2 database (Chiou and Youngs, 2014; Boore et al., 2014). In our dataset (that includes three Turkish earthquakes in addition to NGA-West2 used previously in Graizer, 2018) normal faults represent only 2.9% of data, not providing enough magnitude and distance coverage to constrain the frequency and distance ratio relative to the strike slip faults. Our current dataset consists of 59.8%

strike slip faults, 21.7% of reverse faults and 15.6% of others. Based on the above-mentioned reasons, and like Idriss (2013) and our previous work, we decided to differentiate between reverse faults and all other types, mainly strike slip faults. In this paper we adopted our previously developed style of fault correction (Graizer, 2018).

3(,,, ) = 0(,, )

1 (13)

We found that the style of fault effect is magnitude, distance, and period dependent, which is similar to the models developed by Ambraseys et al. (2005), and Chiou and Youngs (2008 and

2014). Comparisons demonstrated that reverse faults produce higher ground motions for periods up to about 3 to 5 seconds and this effect is more pronounced for larger magnitude events.

Differences in the style of fault effect disappear for magnitudes lower than 4.0. The functional form used to model the style of fault term (,, ) was determined from an analysis of residuals and is shown in equations 14-15.

0,,

1

< 4.0 1 + 0, 1exp(5.5) 5.5 90 1 + [0(, 90) 1] exp(5.5) 4.0 5.5 > 90 0,

> 5.5 90 0(, 90)

> 5.5

> 90 (14) 0(, ) = [1 +

2 1 + (/7)2][3 +

1 1 + (/100)]

(15) where and are coefficients.

Figure 10 demonstrates the smoothed ratios of reverse-to-strike slip spectra for different periods and rupture distances, and shows example comparisons of reverse and strike slip response spectra for 4.0 8.0 at rupture distances of 10 and 50 km.

Style of fault effect is not demonstrated for earthquakes with < 4.0. It is also slowly phasing out for all magnitude events at periods up to 5 sec at rupture distances of more than about 90 km and practically completely disappearing at distances of about 120 km. For periods T >5 s reverse fault events produce slightly lower ground motion than the strike slip events. We can speculate that the reason for this is that reverse fault events are generally shorter in length (more compact and having the same surface) than the strike slip events.

Comparisons of residuals calculated with and without the style of fault effect demonstrate improvement especially at rupture distance closest to the fault, phasing out at larger distances.

Incorporating the style of fault effect also results in modest improvements in sigma.

5.2 Sediment Thickness. Scaling A typical geologic basin consists of alluvial deposits and sedimentary rock that are geologically younger and have a significantly lower shear wave velocity structure than the underlying rocks, creating a strong impedance contrast. The information about basin depth under the strong motion station is rarely available. The current practice in GMM development is to substitute basin depth with the depth to the shear wave velocity horizon of 1 km/s (1.0), 1.5 km/s (1.5) or 2.5 km/s (2.5) as a proxy to the basin effect.

Similar to Choi et al. (2005) and the NGA-West2 developers (e.g., Chiou and Youngs, 2014; Abrahamson et al., 2014; Campbell and Bozorgnia, 2014), we concluded that at most locations in California there is a strong correlation between shallow (30) and deep sediment (1.0, 1.5 or 2.5) site effects with naturally softer soil sites located in a basin (this does not apply to the artificial fill sites). For example, Boore and Atkinson (2008) wrote: It is clear that the softer sites are in basins, and hence basin depth and 30 are strongly correlated (this was found previously by Choi et al. 2005, Figure 7). Therefore, any basin depth effect will tend to have been captured by the

empirically determined site amplification. To try to separate the amplification and the basin depth effects in the data would require use of additional information or assumptions. The 1.0 and 2.5 datasets in the NGA-West2 database are significantly larger than that of 1.5 with 1441 and 1411 data points correspondingly compared to only 386 data points for 1.5. Based on the findings of Frankel et al. (2018) and a relatively high number of data points in the dataset we choose 2.5 measure as a proxy for the basin response term.

Figure 11 demonstrates the 30 2.5 dataset from the NGA-West2 subset used to create GK17 and the current GS24 sediments thickness model. The data shown in Figure 11 are a combination of the 2.5 measurements shown in the columns CW and CZ of the NGA-West2 flatfile representing the two SCEC 3-D velocity models CVM-S4 and CVM-H. The data distribution is sparse with no clear tendency. We tried several approximations: exponential, power, logarithmic and polynomial of 1-3 orders. Figure 11 demonstrates the best two approximations based on the coefficient of determination (R2 - metric, a measure of the goodness of fit of the regression):

exponential (bold double dashed line) and power approximation (blue line). As shown in the Figure 11, R2 is higher for the power approximation corresponding to the following equation:

( 2.5) = 7.521 1.233 ( 30)

(16) where 2.5 is measured in kilometers and 30 is in m/s, which has a R2 value of 0.154 and a standard deviation of 0.813. The green dashed line in Figure 11 demonstrates equation 16 extended to 30 interval of 100 - 2800 m/s, while the thick double green line shows the 30 interval covered by GK17 and GS24 site correction (150 - 1500 m/s). Based on equation 16, one can conclude that the original GK17 and GS24 site correction can be deficient for shallow and deep sediments thicknesses and may require additional site effect correction. Our approach is consistent with the approach of Campbell and Bozorgnia (2014, equation 33) and Choi et al.

(2005, Figure 7) also using power approximation between 30 and 2.5. Equation 16 can be used to estimate 2.5 when only 30 is available. Equation 17 shows CB14 relation between 30 and 2.5 (Equation 33 of CB14):

( 2.5) = 7.089 1.144 ( 30)

(17) which has a R2 value of 0.131 and a standard deviation of 1.026. Figure 11 also compares equation 16 with that of equation 17 from CB14 (red dashed line) demonstrating their similarities.

Since CB14 and GS24 use different subsets of the NGA-West2 database, these equations are considered similar. However, none of the explored approximations demonstrate a good fit to the empirical data. This is most likely due to relatively high level of errors in both 30 and especially 2.5 estimates. Table 1 (updated from Petersen et al., 2019) provides comparisons of the default 30 values with 1.0 and 2.5 depths calculated from the NGA-West2 and the current model. As expected, the 2.5 CB14 and GS24 30 2.5 estimates are similar.

Considering that a significant part of the sediments thickness effect (called basin effect by some researchers) is already incorporated in 30 scaling, the 30 component of the GMM already implicitly includes average sediments thickness effects within each GMMs specified 30 range.

Therefore, it is more appropriate to say that the sediments thickness response -terms in current GMMs represent additional adjustments not incorporated in the average 30 scaling. For example, even though the three NGA-West2 GMMs (ASK14, BSSA14 and CY14) are using the

same 1.0 metrics, they have different sediments thickness correction equations. The reason for this is that each model has different 30 corrections that already account for an average 30 1.0 ratio. In the meantime, all four NGA-West2 models are characterized by the amplification in the adjustment models with increased sediments thickness depth of more than 1 km as well as some deamplification for shallow sediments thickness (typically less than 0.5 km for 1.0 and below 1 km for 2.5 in CB14).

The additional sediments thickness effect adjustment (correction) covers the depth range of less than 0.67 km and higher than 3.15 km depth (Figure 12, middle right panel) with zero additional correction needed in the range of 0.67 2.5 3.15 km. This additional correction is similar in shape and amplitudes to that of Campbell and Bozorgnia (2014, equation 20) (Figure 3, lower panels) requiring zero additional basin effect correction for 1.0 2.5 3 km. As was mentioned before, we dont recommend calling this step sediments thickness or basin effect correction, but rather an additional sediments effect correction not covered by the 30 correction.

Additional sediments thickness response correction amplification factors (also called adjustment factors) 4(2.5) for the GS24 GMM are:

4(2.5) =

1 2.5 < 0 1(0.18)2 0 2.5 0.18 1(2.5)2 0.18 < 2.5 0.67 1

0.67 < 2.5 < 3.15 3(2.5)4 2.5 3.15 (18)

First line in equation 18 corresponds to the case when 2.5 depth is not known (-999 in the NGA-West2 flatfile), and are coefficients determined based on residuals and shown in Table 2.

Adjustments to the base-case model for the effects of sediments thickness depth are made based on residual analysis.

Our site amplification results are consistent with the simulations performed by Day et al. (2008).

Equation (19) demonstrates modification of the GS24b backbone model by applying style of faulting (3(,,, )) and sediment thickness corrections (4(2.5)):

= 3(,,,) x 4(2.5) x (19)

As a next steps magnitude, 30 and rupture distance residual corrections calculated for 16 frequencies were applied to the calculated spectral acceleration (equation 19). To avoid jagedeness in corrected spectral accelerations we did not split residuals into bins but applied correction functions to the whole range of magnitudes 4.0 8.5, distances of 0 < 400 km, and velocities 150 30 1500 ms. Two rounds of magnitude and distance residual corrections were performed to achieve near-zero trends.

Final, 30 and residuals calculated after application of the residual corrections for the six

frequencies of 100, 25, 10, 2, 1 and 0.33 Hz are shown in Figures 13-15.

5.3 Examples of the GS24 model applications As compared to the GS24b backbone model, the final GS24 model includes application of style of faulting (3), sediment thickness corrections (4) and also magnitude M, 30 and rupture distance Rrup residual corrections.

Figures 16 shows examples of response spectral accelerations at rupture distances of 10, 50 and 200 km for moment magnitudes varying from = 4.5 to 8 calculated using the GS24 model. As expected, the curves are not as smooth as in the backbone model (Figures 7, 8). Figure 17 shows examples of different periods attenuation with respect to closest distance to the fault. Similar to the backbone model (Figure 8) attenuation rate changes from that of shear to surface waves at

= 50 km.

Figures 18-20 demonstrate comparisons of the GS24, GS24b and GK17 ground motion models with empirical spectral accelerations data for the three magnitude ranges of 4.77 5.21 with an average = 4.99, 5.7 6.24 with an average = 6.06, and 7.28 7.9 with an average = 7.64.

As discussed before, we are considering the 3rd dataset that includes 6046 data points, covers the range of magnitudes 4 7.9 and rupture distances 250 km (M4_R250) to be the most important from the engineering applications point of view since it was created based on the recordings of earthquakes that can potentially produce damage. Figure 21 demonstrates the natural logarithmic standard deviation sigma () for the final GS24, GS24b and GK17 model predictions for the 3rd dataset. As expected, the newest GS24 model demonstrates the lowest total sigma. However, previously developed GK17 sigma is only in average 1.9 % higher demonstrating acceptable performance. The backbone sigma is in average 4.6% higher than that of the GS24 model.

We also split the total standard deviation () into within-event () and between-event () standard deviations.

= 2 + 2 (20)

The within-event standard error () is calculated by averaging within-event standard errors of earthquakes well represented in the database by more than 10 data points. Between-event standard deviation () is calculated as

= 2 2 (21)

The GK17 models sigma recommended for use in hazard calculations published in Graizer (2018, Table 1) is lower, having been developed using subset of data with > 5.5 and < 140 km following the practice of NGA-West2 GMM developers. For example, Campbell and Bozorgnia (2014) recommended using sigma for the subset of data with > 5.5 and < 80 km. We believe that using the 3rd subset of data shown in Figure 1 and 2 is more appropriate for engineering applications in seismic hazard calculations. Figure 21 also demonstrates sigma shown on the plot beyond the GMM range and connected with dash lines.

6 RESULTS The new GS24b backbone and GS24 models are developed for the average RotD50 horizontal component of ground motion from shallow crustal earthquakes in active crustal regions. The models are derived based on a subset of the same NGA-West2 dataset (Ancheta et al., 2014) as used in the development of the GK17 (Graizer, 2018) model enhanced by the data from the three recent 2023 Turkish earthquakes with moment magnitudes 6.3, 7.5 and 7.8 (Buckreis et al.,

2023a, 2023b) with a total of 13926 data points. We did not use data from earthquakes with magnitudes < 4.0 and we limited the rupture distance range to 400 km. Records from earthquakes in Japan were not used, because most of sites in Japan are characterized by subsurface geology significantly different from site conditions in other ACRs.

We consider the subset of 4 7.9 and 250 km (M4_R250) of 6046 data points to be the most important from the engineering application point of view since it was created based on the recordings of earthquakes and distances that can potentially create structural damage.

Similar to GK17, the new models have a bilinear attenuation slope of Rrup-1 representing geometrical spreading of body waves for the closest 50 km from the fault, and Rrup-0.5 at larger distances representing geometrical spreading of surface waves. The 50 km fault distance shift in the geometrical spreading is supported by the NGA-West2 data.

The number of input predictors in the GS24b and GS24 models are limited to a few measurable parameters: moment magnitude, closest distance to fault rupture plane, time-averaged shear wave velocity in the upper 30 m of the profile 30, style of faulting, apparent anelastic attenuation quality factor (, ), and sediment thickness depth 2.5. We did not include hanging wall and directivity effects since the existing models incorporating these effects are not based on empirical data, and their effects in our GMM are captured through the variability of the empirical data. The GMMs are applicable for earthquakes with 4.0 8.5, at rupture distances from 0 < 400 km, at sites having 30 in the range from 150 ms to 1500 ms, and for spectral periods of 0.01 10 sec.

We created a new GS24b global backbone model that uses the closed form approximation of the spectral acceleration as a multiplication of the and spectral shape functions. This model can be later used for adjusting to the specific active crustal region (e.g., Southern and Northern California and others) creating partially non-ergodic models.

We created a new ergodic GS24 model adjusted to best fit NGA-West2 data combined with the three strong 2023 Turkish earthquakes. As compared to the GS24b backbone model, the final GS24 model includes application of style of faulting (3(,,, )), sediment thickness corrections (4(2.5)) and also magnitude (), average shear wave velocity in the upper 30 meters (30), and rupture distance () residual corrections.

As expected, the GS24 final model performs better than the GS24b and GK17 demonstrating lower standard error and residuals.

The GS24b and GS24 ground motion models for spectral acceleration and peak ground velocity are developed using MATLAB software.

We tested the GK17 model against the same set of data and demonstrated acceptable performance with standard error slightly higher than that of the new GS24 model.

7 DATA AND RESOURCES The newly developed ground motion models discussed in this report are based on the Pacific Earthquake Engineering Research Center Next Generation Attenuation Phase 2 (NGA-West2) database of processed ground motions from shallow crustal earthquakes in active tectonic regimes (http://ngawest2.berkeley.edu/). The NGA-West2 flatfile and the associated website were last accessed in July 2016. Turkish strong motion accelerometer data were retrieved from the Department of Earthquake, Disaster and Emergency Management Authority (AFAD; https://deprem.afad.gov.tr/stations) of Türkiye through the Turkish National Strong Motion Network (DOI: 10.7914/SN/TK), and Kandilli Observatory and Earthquake Engineering Research Institute of Boaziçi University (KOERI, Istanbul; DOI: 10.7914/SN/KO) and processed by Buckreis et al. (2023a, 2023b). Other data used in this study came from the published sources listed in the text or in the references. All data processing was performed offline using a commercial software package (MATLAB R2021a, The MathWorks Inc., Natick, Massachusetts, 2021).

8 TABLES Table 1. Comparisons of site class and the default 30 values with 1.0 and 2.5 depths (km) calculated from the NGA-W2 and GS24.

Site Class VS30 ASK14 (Z1.0)

BSSA14 (Z1.0)

CY14 (Z1.0)

CB14 (Z2.5)

GS24 (Z2.5)

(m/s)

A 2000 0

0 0

0.201 0.157 A/B 1500 0

0.001 0.001 0.279 0.224 B

1080 0.005 0.005 0.005 0.406 0.336 B/C 760 0.048 0.041 0.041 0.607 0.518 C

530 0.213 0.194 0.194 0.917 0.808 C/D 365 0.401 0.397 0.4 1.4 1.28 D

260 0.475 0.486 0.485 2.07 1.94 D/E 185 0.497 0.513 0.513 3.06 2.96 E

150 0.502 0.519 0.519 3.88 3.83 Table 2. Adjustments coefficients to the base-case model for the effects of sediments thickness (equation 18).

T(sec) 0.010 1.0000 0.0000 0.7139 0.2935 0.020 1.0000 0.0000 0.7220 0.2837 0.040 1.0000 0.0000 0.7415 0.2605 0.075 1.0000 0.0000 0.7855 0.2103 0.10 1.0000 0.0000 0.7896 0.2057 0.20 1.0000 0.0000 0.8228 0.1698 0.40 1.0741 0.1764 0.8166 0.1764 0.50 1.0760 0.1806 0.8127 0.1806 0.75 1.1264 0.2935 0.8112 0.1823 1.0 1.1219 0.2837 0.7905 0.2047 2.0 1.1114 0.2605 0.7148 0.2924 3.0 1.0890 0.2103 0.6543 0.3694 4.0 1.0870 0.2057 0.6321 0.3995 5.0 1.0713 0.1698 0.6149 0.4235 8.0 1.0741 0.1764 0.6333 0.3978 10.0 1.0760 0.1806 0.6600 0.3619

Table 3. Model Standard Deviations GS24 M4_250 Standard Deviations

Period, s

Total

()

Within-Event

()

Between-Event ()

0.01 0.716 0.531 0.480 0.02 0.720 0.537 0.480 0.04 0.748 0.551 0.505 0.08 0.789 0.586 0.529 0.10 0.797 0.597 0.528 0.15 0.790 0.599 0.515 0.20 0.778 0.583 0.515 0.40 0.758 0.582 0.485 0.50 0.770 0.590 0.495 0.75 0.788 0.603 0.508 1.00 0.787 0.595 0.515 2.00 0.803 0.609 0.524 3.00 0.776 0.595 0.498 4.00 0.740 0.570 0.472 5.00 0.742 0.550 0.498 8.00 0.769 0.550 0.538 10.00 0.744 0.540 0.511 0.554 0.477 0.281

9 FIGURES Figure 1. Distribution of recordings with respect to moment magnitude and rupture distance (upper panel), peak ground acceleration () and 30 (middle panel), and number of recordings in each subset depending upon maximum period range (lower panel). NGA-West2 data are shown with open circles and additional Turkish data with red circles.

Figure 2. The three datasets used to create GS24 GMMs.

Figure 3. magnitude scaling in GK17 and GS24.

0 1000 2000 3000 4000 5000 6000 7000 M4_400 M5_150 M4_250 Datasets M4_5 M5_6 M6_7 M7_7.9 0.1 1

3.5 4.5 5.5 6.5 7.5 8.5 Mw Magnitude Scaling GS24 MagScale GK17 MagScale

Figure 4. Generic spectral shape,0 model, and its controlling parameters: I(M,Rrup) -

defines the peak spectral intensity, (M,Rrup) and Tsp,0(M,Rrup) define the predominant period of the spectrum, S(M,Rrup) - defines the wideness area under the spectral shape, and - controls the decay of the spectrum at long periods.

Figure 5. G1 filter 30 site amplification from equation 8.

Figure 6. Seismological () and inverted (, ) with approximation by equation 12.

y = 120.25x0.9581 R² = 0.9952 1.0E+01 1.0E+02 1.0E+03 1.0E+04 0.1 1

10 100 QSA Frequency, Hz Western US QSA(f,M)

Average Qsa Malagnini 2007, N. California Erickson 2004, S. California Erickson 2004, N. California M=5 M=6 M=7

Figure 7. Examples of response spectral accelerations at rupture distances of 10, 50 and 200 km for moment magnitudes varying from M=4.5 till 8 calculated using GS24b backbone model.

Figure 8. Examples of different periods attenuation with distance to the fault for GS24b backbone model.

Figure 9. Standard errors of GS24b and GK17 models predictions for the three subsets of data.

0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 0.01 0.1 1

10 Sigma, log-natural units Period, s Sigma GS24b_M5_R150 GS24b_M4_R250 GS24b_M4_R400 GK17_M5_R150 GK17_M4_R250 GK17_M4_R400

Figure 10 (copy of Figure 6 from Graizer (2018)). Developed ratios of reverse-to-strike slip spectra with respect to periods (upper left panel) and with respect to distances (upper right panel).

Example comparisons of reverse and strike slip response spectra for 4.0 M 8.0 at rupture distance of 10 (lower left panel) and 50 km (lower right panel).

Figure 11. Comparison of 30 2.5 approximations by the Equation 16 with NGA-West2 data and the Equation 33 of Campbell and Bozorgnia (2014).

Figure 12. GS24 30site amplification (upper panel), additional deep sediments thickness 2.5 correction (middle panel) and combined 30 and 2.5 site amplification (lower panel).

Figure 13. GS24 residuals versus moment magnitude M for frequencies of 100, 25, 10, 2, 1, and 0.33 Hz.

Figure 14. GS24 residuals versus 30 for frequencies of 100, 25, 10, 2, 1, and 0.33 Hz.

Figure 15. GS24 residuals versus fault rupture distance Rrup for frequencies of 100, 25, 10, 2, 1, and 0.33 Hz.

Figure 16. Examples of response spectral accelerations at rupture distances of 10, 50 and 200 km for moment magnitudes varying from M=4.5 till 8 calculated using GS24 model.

Figure 17. Examples of different periods attenuation with closest distance to the fault for the GS24 model.

Figure 18. Comparison of the recorded spectral accelerations (open circles) from earthquakes in a magnitude range of 4.77 to 5.21 and calculated using the GS24, GS24b and GK17 ground motion models SA fr the average earthquake of M = 4.99 and average 30 = 456 m/s.

Figure 19. Comparison of the recorded spectral accelerations (open circles) from earthquakes in a magnitude range of 5.7 to 6.24 and calculated using the GS24, GS24b and GK17 ground motion models SA for the average earthquake of M = 6.06 and average 30 = 414 m/s.

Figure 20. Comparison of the recorded spectral accelerations (open circles) from earthquakes in a magnitude range of 7.28 to 7.9 and calculated using the GS24, GS24b and GK17 ground motion models SA for the average earthquake of M = 7.64 and average 30 = 451 m/s.

Figure 21. Comparison of the GS24 total (), within-event (), and between-event () log-natural sigma to the GK17 and GS24b (backbone) sigma for the third dataset with 4.0 M 7.9 and rupture distances of 0Rrup250 km. sigma are shown separately beyond 10 s and connected with dash lines.

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.01 0.1 1

10 Sigma, log-natural Period, s Sigma GS24_M4_R250 GS24 Within Event PHI GS24 Between Event TAU GK17_M4_R250 GS24b_M4_R250 PGV GS24 PGV within-event PGV between-event PGV GS24b

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