Prepared in cooperation with the U.S. Nuclear Regulatory Commission

Ground-Motion Predictions for California—Comparisons of 

Three Prediction Equations

Open-File Report 2020–1028

U.S. Department of the Interior

U.S. Geological Survey

Ground-Motion Predictions for California—

Comparisons of Three Prediction Equations

By Erol Kalkan and Vladimir Graizer

Prepared in cooperation with the U.S. Nuclear Regulatory Commission

Open-File Report 2020–1028

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

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Suggested citation:

Kalkan, E., and Graizer, V., 2020, Ground-motion predictions for California—Comparisons of three prediction 

equations: U.S. Geological Survey Open-File Report 2020–1028, 28 p., https://doi.org/10.3133/ofr20201028.

ISSN 2331-1258 (online)
iii

Acknowledgments

The authors would like to thank Emel Seyhan (Risk Management Solutions) and Dan 

McNamara (U.S. Geological Survey [USGS]) for their reviews, which helped improve the 

technical quality and presentation of this study. We also thank Annemarie Baltay (USGS) for 

providing MATLAB functions of the NGA-West2 ground-motion prediction equations.

Contents

Acknowledgments ...............................................................................................................................................iii

Abstract...................................................................................................................................................................1

Introduction............................................................................................................................................................1

Dataset and Model Applicability Range...........................................................................................................2

Functional Forms and Parameters of GMPEs .................................................................................................2

Stage 1: Comparisons of Median Predictions.................................................................................................5

Distance-Scaling Features ........................................................................................................................5

Magnitude-Scaling Features.....................................................................................................................5

Site Effects ....................................................................................................................................................9

Style-of-Faulting Effects...........................................................................................................................10

Response Spectra .....................................................................................................................................10

Standard Deviations..................................................................................................................................12

Stage 2: Comparisons with Earthquake Data................................................................................................12

Stage 3: Comparisons of Residuals Using the NGA-West2 Database.....................................................18

Intra-Event Residuals Analysis of Path, Site, and Basin-Depth Effects .........................................20

Analysis of Source Effects Using Inter-Event Residuals ...................................................................23

Standard Deviations..................................................................................................................................25

Conclusions..........................................................................................................................................................25

Data and Resources ...........................................................................................................................................26

References Cited.................................................................................................................................................26
iv

Figures

1. Plots showing a comparison of distance-scaling features of median estimates of peak 

ground acceleration and spectral accelerations at 0.2, 1.0, and 3.0 seconds predicted by 

the Graizer and Kalkan (2015, 2016) and Abrahamson and others (2014) ground-motion 

prediction equations for strike-slip moment magnitude 5, 6, 7, and 8 earthquakes..................... 6

2. Plots showing a comparison of distance-scaling features of median estimates of peak 

ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds predicted by 

the Graizer and Kalkan (2015, 2016) and Boore and others (2014) ground-motion prediction 

equations for strike-slip moment magnitude 5, 6, 7, and 8 earthquakes......................................... 7

3. Plots showing a comparison of distance-scaling features of median estimates of peak 

ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds predicted by the 

ground-motion prediction equations of Abrahamson and others (2014) and Boore and 

others (2014) for strike-slip moment magnitude 5, 6, 7, and 8 earthquakes ................................... 8

4. Plots showing a comparison of magnitude scaling features of median estimates of peak 

ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds by the groundmotion prediction equations of Graizer and Kalkan (2015, 2016), Abrahamson and others 

(2014), and Boore and others (2014) for 10, 30, and 150 kilometers .................................................. 9

5. Plots showing a comparison of VS30-scaling features of the median estimates of peak 

ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds by the groundmotion prediction equations of Graizer and Kalkan (2015, 2016), Abrahamson and others 

(2014), and Boore and others (2014) for a magnitude 7 strike-slip earthquake at 10 and 50 

kilometers ......................................................................................................................................................10

6. Plots showing a comparison of style-of-faulting ratios versus period between reverse and 

strike-slip events and between normal and strike-slip events at 30 kilometers among the 

Graizer and Kalkan (2015, 2016), Abrahamson and others (2014), and Boore and others 

(2014) ground-motion prediction equations..........................................................................................11

7. Plots showing a comparison of VS30-scaling features of the median estimates of responsespectral shapes and amplitudes versus period among the Graizer and Kalkan (2015, 2016), 

Abrahamson and others (2014), and Boore and others (2014) ground-motion prediction 

equations for a strike-slip magnitude 7 earthquake at 30 kilometers............................................11

8. Plots showing a comparison of the median estimates of response-spectral shapes and 

amplitudes versus period between the Graizer and Kalkan (2015, 2016) and Abrahamson 

and others (2014) ground-motion prediction equations for strike-slip magnitudes 6, 7, and 

8 earthquakes at a rupture distance of 1 and 30 kilometers ............................................................12

9. Plots showing a comparison of the median estimates of response-spectral shapes and 

amplitudes versus period between the Graizer and Kalkan (2015, 2016) and Boore and 

others (2014) ground-motion prediction equations for strike-slip magnitudes 6, 7, and 8 

earthquakes at a rupture distance of 1 and 30 kilometers ...............................................................13

10. Plots showing a comparison of total, inter-event, and intra-event variability versus period 

of the Graizer and Kalkan (2015, 2016), Abrahamson and others (2014), and Boore and 

others (2014) ground-motion prediction equations for a magnitude 5 earthquake....................13

11. Plots showing a comparison of the median estimates of response-spectral shapes 

and amplitudes versus period by the Graizer and Kalkan (2015, 2016), Abrahamson and 

others (2014), and Boore and others (2014) ground-motion prediction equations with 

the observations from select six major Californian earthquakes from the NGA-West2 

database........................................................................................................................................................14
v

12. Plots showing a comparison of the median estimates of response-spectral shapes 

13. Plots showing a comparison of the median estimates of response-spectral shapes

and amplitudes versus period by the Graizer and Kalkan (2015, 2016), Abrahamson and 

others (2014), and Boore and others (2014) ground-motion prediction equations with 

the observations from select six major Californian earthquakes from the NGA-West2 

database........................................................................................................................................................16

14. Plots showing ground-motion attenuation during the 2014 magnitude 6 South Napa

earthquake, California................................................................................................................................17

15. Plots showing the distribution of the NGA-West2 near-source California earthquake 

events with respect to moment magnitude, VS30 and Rrup..................................................................18

16. Plots showing the distribution of intra-event residuals in natural logarithmic units for

peak ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds with 

respect to Rrup ..............................................................................................................................................20

17. Plots showing the distribution of intra-event residuals in natural logarithmic units for

peak ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds with 

respect to VS30 ..............................................................................................................................................21

18. Plots showing the distribution of intra-event residuals in natural logarithmic units for

peak ground acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds with 

respect to Bdepth ...........................................................................................................................................22

19. Plots showing the distribution of event terms in natural logarithmic units for peak ground

acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds with respect to moment 

magnitude......................................................................................................................................................23

20. Plots showing the distribution of event terms in natural logarithmic units for peak ground

acceleration and spectral acceleration at 0.2, 1.0, and 3.0 seconds with respect to style-offaulting parameter F....................................................................................................................................24

Tables

1. Earthquakes used to update the Graizer and Kalkan (GK15) ground-motion prediction

equation........................................................................................................................................................... 3

2. Summary of databases, intensity measures, and applicability ranges of independent

predictors three ground-motion prediction equations........................................................................ 4

3. Event terms for the 2014 magnitude 6.0 South Napa earthquake for three ground-motion

prediction equations...................................................................................................................................16

4. List of California earthquake events in a near-source subset of the NGA-West2 database...19

5. Maximum-likelihood fit to intra-event residuals and distance for three ground-motion

prediction equations...................................................................................................................................22

6. Maximum-likelihood fit to inter-event residuals and moment magnitude for three 

ground-motion prediction equations..................................................................................................25

7. Standard deviations of residuals in natural logarithmic units for three ground-motion

prediction equations for near-source California earthquake events ............................................25
vi

Abbreviations

ASK14 Abrahamson and others (2014)

BSSA14 Boore and others (2014)

g gravitational acceleration

GK15 Graizer and Kalkan (2015, 2016)

GM ground motion

GMPE ground-motion prediction equation

GMRotI50 orientation-independent geometric mean ground motion measure

GMRotD50 orientation-independent but period-dependent geometric mean ground motion 

 measure

km kilometers

km/s kilometers per second

M magnitude

m meters

m/s meters per second

NEHRP National Earthquake Hazards Reduction Program

NGA Next Generation Attenuation project

NM normal faulting

PGA peak ground acceleration

PGV peak ground velocity

REV reverse faulting

s seconds

SOF style of faulting

SA spectral acceleration

SS strike slip faulting

U unspecified faulting mechanism
vii

Notation

a intercept of maximum-likelihood fit

b slope of maximum-likelihood fit

Bdepth basin depth

F style-of-faulting parameter used in Graizer and Kalkan (2015, 2016)

RJB closest distance to horizontal projection of fault rupture plane

Rrup closest distance to fault rupture

Resij residual of jth recording of ith earthquake

Q0 quality factor at 1 hertz

VS30 shear-wave velocity in upper 30 meters of geologic profile

Z1.0 depth to 1.0 km/s shear-wave velocity isosurface

Z1.5 depth to 1.5 km/s shear-wave velocity isosurface

ZTOR depth to top of rupture plane

δz1 depth differential used in BSSA14

σ total standard deviation

ηi event term for event i

εij intra-event residual for recording j in event i

τ standard deviation of event term

φ standard deviation of intra-event term

Ground-Motion Predictions for California—Comparisons 

of Three Prediction Equations

By Erol Kalkan1 and Vladmir Graizer2

Abstract

We systematically evaluate datasets, functional forms, 

independent parameters of estimation, and resulting groundmotion predictions (as median and aleatory variability) of 

the Graizer and Kalkan (2015, 2016) (GK15) ground-motion 

prediction equation (GMPE) with the next generation of 

attenuation project (NGA-West2) models of Abrahamson 

and others (2014) (ASK14) and Boore and others (2014) 

(BSSA14) for application to earthquakes in California. This 

evaluation is performed in three stages: (1) by comparing 

attenuation, magnitude scaling, style-of-faulting effects, site 

response, response-spectral shape and amplitude, and standard 

deviations; (2) by comparing median predictions, standard 

deviations, and analyses of residuals with respect to near-field 

(within 20kilometers [km] of the fault) and intermediate-field

(50 to 70 km from the fault) records from major earthquakes 

in California, and (3) by comparing total, intra-event, and 

inter-event residual distributions among the GMPEs with 

respect to a near-source (within 80 km of the fault) subset of 

the NGA-West2 database covering 975 ground motions from 

73 events in California ranging from moment magnitude 5 to 

7.36. The results reveal that the scaling features of the GK15 

GMPE and the ASK14 and BSSA14 GMPEs are, in general, 

similar in terms of distance attenuation but differ in terms of 

scaling with magnitude, style of faulting, and site effects. The 

original standard deviations of GMPEs are also different. For 

the near-source California subset, the three GMPEs result in 

standard deviations that are similar to each other. The mixedeffect residuals analysis shows that the GK15 GMPE has no 

perceptible trend with respect to the independent predictors.

Introduction

The previous version of the Graizer and Kalkan (2015, 

2016) (herein abbreviated as GK15) ground-motion prediction 

equation (GMPE) was developed using the NGA-West1 database 

(Chiou and others, 2008) along with additional records from 

1

QuakeLogic Inc., Roseville, California.

2

U.S. Nuclear Regulatory Commission.

major events in California and several earthquakes from other 

shallow crustal continental regions (Graizer and Kalkan, 2007, 

2009). The NGA-West2 project (Bozorgnia and others, 2014) and 

recent earthquake data (Baltay and Boatwright, 2015) accentuated 

a need to include regionalization in GMPEs to account for 

differences in far-source (beyond 80 kilometers [km]) distance 

attenuation and soil response. Motivated by this need, we have 

updated our GMPE to include a new anelastic attenuation term as 

a function of the quality factor at 1 hertz (Q0

) to capture regional 

differences in far-source attenuation and a new frequencydependent sedimentary-basin scaling term as a function of depth 

to the 1.5 kilometer per second (km/s) shear-wave velocity 

isosurface to improve ground-motion predictions for sites on deep 

sedimentary basins (the GK15 GMPE does not explicitly consider 

strong basin amplification on shallow basins).

In this report, we systematically compare the datasets, 

functional forms, independent predictor variables, and resulting 

ground-motion estimates (as median and aleatory variability) 

of GK15 with the broadly used next generation of attenuation 

project (NGA-West2) models of Abrahamson and others (2014) 

(herein abbreviated as ASK14) and Boore and others (2014) 

(herein abbreviated as BSSA14) for application to earthquakes in 

California. We do not include three other NGA-West2 models—

Campbell and Bozorgnia (2014), Chiou and Youngs (2014), or 

Idriss (2014)—for brevity and because they compare well with 

the ASK14 and BSSA14 GMPEs (Gregor and others, 2014). The 

evaluation of the GMPEs here is performed in three stages:

1. Compare distance attenuation, magnitude scaling, 

style-of-faulting (SOF) effects, site response, responsespectral shape and amplitude, and standard deviations;

2. Compare median predictions, standard deviations, and 

analyses of total residuals with respect to near-field 

(within 20 km of the fault) and intermediate-field (50 to 

70 km from the fault) records from major earthquakes in 

California; and

3. Compare total, intra-event, and inter-event residuals 

among the GMPEs by using a near-source (within 80 km 

of the fault [Campbell, 2016]) subset of the NGA-West2 

database.

Results of these comparisons are presented in the following 

sections.
2 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Dataset and Model Applicability Range

In development of the GK15 GMPE, a total of 2,583 

ground-motion recordings from 47 shallow crustal continental 

earthquakes with focal depths less than 20 km were used. This 

dataset, summarized in table 1, includes events gathered from the 

Pacific Earthquake Engineering Research Center database created 

under the NGA-West1 project (Chiou and others, 2008) and data 

from several additional events and stations. Specifically, additional 

data from the following California and international earthquakes 

were included: 1994 magnitude (M) 6.7 Northridge, 1999 M7.1 

Hector Mine, 2003 M4.9 Big Bear City, 2003 M6.5 San Simeon, 

2004 M6 Parkfield, 2005 M5.2 Anza and M4.9 Yucaipa, 1976 

M6.8 Gazli (Uzbekistan), 1988 M6.8 Spitak (Armenia), 1991 

M6.2 Racha (Georgia), and 1999 M7.4 Kocaeli and M7.2 Düzce 

(Turkey). The source for additional data was primarily the Center 

for Engineering Strong Motion Data. To avoid bias, the records 

were processed uniformly (that is, the same corner frequencies 

and n-roll value were used for acausal filtering and the filter corner 

frequencies were selected conservatively to accommodate a range 

of signal-to-noise ratio).

A total of 47 earthquakes were selected and can be 

summarized as follows: 32 earthquakes from California; 

6 earthquakes from Turkey; 4 earthquakes from Taiwan and 

Italy; 3 earthquakes from Armenia, Georgia, and Uzbekistan; 

and 2 earthquakes from Alaska and Nevada. Approximately 

70 percent of the earthquakes are from California. This 

dataset, representing mainshocks only, includes data recorded 

within 0.2 to 250 km of the earthquake faults from events in 

the magnitude range of 4.9 to 7.9. GMRotI501 is the intensity 

measure used in the development of the NGA-West1 database 

(Boore and others, 2006).

The NGA-West2 database (using GMRotD502) includes 

21,336 three-component recordings from 600 shallow crustal 

earthquakes in the magnitude range of 3 to 7.9 and a rupture 

distance range of 0.05 to 1,533 km (Ancheta and others, 2014). 

For ASK14, 15,750 recordings from 326 earthquakes were used 

in analyses for peak ground acceleration (PGA); among them 

274 earthquakes with 12,044 recordings are from California. For 

BSSA14, 18,436 recordings from 404 events were used for PGA 

analyses. We did not use the NGA-West2 database for GK15 

because it was not available to us.

Based on the final selected datasets used for the GK15, 

ASK14, and BSSA14 GMPEs, the models’ applicable 

ranges (in terms of magnitude, distance, VS30 [shear-wave 

velocity in upper 30 meters of geologic profile], and spectral 

periods) are listed in table 2. Additional details are provided 

in individual papers that describe the GK15, ASK14, and 

BSSA14 GMPEs (Boore and others, 2014; Abrahamson and 

others, 2014; Graizer and Kalkan, 2015, 2016). It should also 

be noted that GK15 provides the predictions for GMRotI50, 

1

This term refers to the orientation-independent geometric mean groundmotion measure.

2

This term refers to the orientation-independent but period-dependent 

geometric mean ground-motion measure.

a component definition different from that of the NGA-West2 

models. We ignored the difference in definitions of component 

combination because it may be small and does not affect the 

results of comparisons (Mak and others, 2017; Van Houtte and 

others, 2017; Farhadi and others, 2018).

Functional Forms and Parameters of 

GMPEs

The functional forms of the ASK14 and BSSA14 GMPEs 

are significantly different than those of the GK15 GMPE. The 

ASK14 and BSSA14 GMPEs each consist of a single predictive 

equation covering both PGA and spectral acceleration (SA); 

however, the GK15 GMPE is composed of two separate 

predictive equations. The first equation predicts PGA and the 

second equation constructs the spectral shape. The term spectral 

shape refers to the acceleration response spectrum normalized by 

PGA. The final SA response spectrum is obtained by anchoring 

the spectral shape to the PGA. In this model, the SA response 

spectrum is a continuous function of the spectral period, which 

is explained in detail by Graizer and Kalkan (2009). On the 

other hand, the ASK14 and BSSA14 GMPEs use a discrete 

functional form for predicting the response spectral ordinates. 

The concept of a continuous function assumes cross correlation 

of spectral ordinates at different periods (Baker and Cornell, 

2006; Baker and Jayram, 2008) and de facto eliminates the 

difference between period intervals by making period intervals 

infinitesimally short. As a result, spectral ordinates are estimated 

smoothly and a long list of estimator coefficients for a range of 

spectral periods is eliminated (Graizer and Kalkan, 2009).

Although ground-motion distance attenuation is a complex 

process, in our opinion, modeling it should not be very complex. 

According to the principle of parsimony, given a set of possible 

explanations, the simplest competing explanation is the most 

likely to be correct (Thorburn, 1915). In our case, the simplicity 

refers to striking a balance between consistency of a groundmotion prediction model with the observed earthquake data and 

the prior degree of belief in a model (Cairns, 2000). According 

to Jeffreys (1961), the prior degree of belief in a model should be 

inversely related to the number of parameters. In GK15, simplicity 

postulates. This is evident in two ways. First, GK15 has only 31 

estimator coefficients as compared to 1,008 estimator coefficients 

in ASK14 and 2,889 coefficients in BSSA14. Second, GK15 has 

a much simpler mathematical form than the other two GMPEs. 

Vandekerckhove and others (2015) state that “goodness-of-fit must 

be balanced against model complexity to avoid overfitting—that 

is, to avoid building models that well explain the data at hand but 

fail in out-of-sample predictions.” The principle of parsimony 

forces researchers to abandon complex models that are tweaked to 

the observed data in favor of simpler models that can generalize to 

new datasets. To prevent overfitting, we not only avoided complex 

functions but also stopped adding new parameters when we had 

a high degree of belief that the residual errors are random rather 

than containing any further structure. We performed a detailed 
Functional Forms and Parameters of GMPEs 3

Table 1. Earthquakes used to update the Graizer and Kalkan (GK15) ground-motion prediction equation.

[GK15, Graizer and Kalkan (2015, 2016). These events were also used in the development of the GK07-09 model (Graizer and Kalkan, 2007, 2009). Latitude 

and longitude in decimal degrees north and east. Mtn., Mountain; km, kilometers]

No. Event Date Style of faulting Moment 

magnitude

Depth

(km)

Epicenter coordinates No. of 

data

Distance range (km)

Latitude Longitude Min. Max.

1 Adana-Ceyhan (Turkey) 1998 Strike slip 6.3 18.0 36.850 35.550 4 28.0 96.0

2 Anza 2005 Strike slip 5.2 14.2 33.529 −116.573 279 4.8 197.6

3 Big Bear City 2003 Strike slip 4.9 6.3 34.310 −116.848 178 8.6 166.7

4 Bingol (Turkey) 2003 Strike slip 6.4 6.0 38.940 40.510 1 6.1

5 Bishop (Round Valley) 1984 Strike slip 5.8 9.0 37.460 −118.590 1 21.9

6 Borrego Mtn. 1968 Strike slip 6.6 8.0 33.190 −116.142 5 45.7 222.4

7 Chalfant Valley 1986 Strike slip 5.8 6.7 37.577 −118.449 5 6.4 24.5

8 Chi-Chi (Taiwan) 1999 Reverse 7.6 16.0 23.860 120.800 420 0.3 172.2

9 Coalinga-01 1983 Reverse 6.4 4.6 36.233 −120.310 46 8.4 55.8

10 Coalinga-05 1983 Reverse 5.8 7.4 36.241 77.191 11 4.6 16.2

11 Coyote Lake 1979 Strike slip 5.7 9.6 37.085 −121.505 10 3.1 33.8

12 Denali (Alaska) 2002 Strike slip 7.9 4.9 63.538 −147.444 24 2.7 275.9

13 Dinar (Turkey) 1995 Normal 6.4 5.0 38.110 30.050 2 3.0 39.6

14 Düzce (Turkey) 1999 Strike slip 7.2 10.0 40.740 31.210 23 0.2 188.7

15 Erzincan (Turkey) 1992 Strike slip 6.9 9.0 39.720 39.630 2 5.0 65.0

16 Friuli (Italy) 1976 Reverse 6.5 5.1 46.345 13.240 5 15.8 102.2

17 Gazli (Uzbekistan) 1976 Reverse 6.8 10.0 40.381 63.472 1 5.0

18 Racha (Georgia, USSR) 1991 Reverse 6.2 9.0 42.461 44.009 8 37.0 155.0

19 Gulf of California 2001 Strike slip 5.7 10.0 32.037 −114.906 12 76.7 134.1

20 Hector Mine 1999 Strike slip 7.1 5.0 34.574 −116.291 213 10.7 259.3

21 Imperial Valley 1979 Strike slip 6.5 10.0 32.644 −115.309 33 0.1 50.1

22 Kocaeli (Turkey) 1999 Strike slip 7.4 15.0 40.727 29.990 31 3.2 349.6

23 Landers 1992 Strike slip 7.3 7.0 34.200 −116.430 69 2.2 190.1

24 Lazio-Abruzzo (Italy) 1984 Normal 5.8 14.0 41.710 13.902 5 18.9 51.3

25 Little Skull Mtn. (Nevada) 1992 Normal 5.7 12.0 36.720 −116.286 8 16.1 100.2

26 Livermore 1980 Strike slip 5.8 12.0 37.855 −121.816 7 16.7 56.1

27 Loma Prieta 1989 Reverse/strike slip 6.9 17.5 37.041 −121.883 82 3.9 117.1

28 Mammoth Lakes-02 1980 Strike slip 5.7 14.0 37.628 −118.927 3 9.1 16.9

29 Mammoth Lakes-03 1980 Strike slip 5.9 16.0 37.561 −118.831 4 5.9 11.5

30 Mammoth Lakes-04 1980 Strike slip 5.7 5.0 37.625 −118.859 4 2.8 14.2

31 Mammoth Lakes-06 1980 Strike slip 5.9 14.0 37.506 −118.856 5 12.0 46.5

32 Manjil (Iran) 1990 Strike slip 7.4 19.0 36.810 49.353 7 12.6 174.6

33 Morgan Hill 1984 Strike slip 6.2 8.5 37.306 −121.695 28 0.5 70.9

34 Northridge 1994 Reverse 6.7 17.5 34.206 −118.554 174 4.0 78.1

35 North Palm Springs 1986 Strike slip/thrust 6.1 11.0 34.000 −116.612 32 8.6 268.0

36 Parkfield 1966 Strike slip 6.2 10.0 35.955 −120.498 6 6.3 63.3

37 Parkfield 2004 Strike slip 6.0 8.8 35.819 −120.364 94 0.3 169.6

38 San Fernando 1971 Reverse 6.6 13.0 34.440 −118.410 44 1.8 218.8

39 San Simeon 2003 Reverse 6.5 7.1 35.702 −121.108 138 12.4 317.8

40 Santa Barbara 1978 Thrust 5.9 12.7 34.399 −119.681 2 12.2 27.4

41 Sierra Madre 1991 Reverse 5.6 12.0 34.259 −118.001 9 10.4 48.2

42 Spitak (Armenia) 1988 Reverse 6.8 5.0 40.987 44.185 1 25.0

43 Superstition Hills-02 1987 Strike slip 6.5 9.0 33.022 −115.831 11 1.0 27.0

44 Taiwan, Smart(5) 1981 Reverse 5.9 11.1 24.429 121.896 7 28.7 32.0

45 Whittier Narrows 1987 Reverse 6.0 14.6 34.049 −118.081 116 14.5 103.9

46 Yountville 2000 Strike slip 5.0 10.1 38.379 −122.413 25 9.9 95.7

47 Yucaipa 2005 Reverse 4.9 11.6 34.058 −117.011 388 2.6 160.1

 Total 2,583
4 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

mixed-effects residual analysis to demonstrate that our simpler 

functional form and limited number of estimation coefficients 

were sufficient enough to reach unbiased ground-motion estimates 

(Graizer and Kalkan, 2015).

In table 2, we summarize independent parameters of 

estimations for the three GMPEs. The distance metric for 

the GK15 and ASK14 GMPEs is the closest distance to the 

rupture plane, Rrup. The BSSA14 GMPE uses the closest 

distance to the horizontal projection of the rupture plane, RJB. 

ASK14 also uses RJB for its hanging-wall function.

Each GMPE includes a SOF parameter according to its 

own faulting mechanism classification. The SOF parameter is 

dependent on earthquake magnitude for ASK14, whereas the 

SOF parameter of BSSA14 is magnitude independent. In the 

GK15 GMPE, the SOF parameter is adapted from Sadigh and 

others (1997) and is also magnitude independent. The ASK14 

GMPE contains an explicit functional form for hanging-wall 

sites and a rupture depth term. The BSSA14 GMPE indirectly 

accounts for hanging-wall features through the use of RJB

without incorporating a rupture depth term, and locations over 

the fault plane have constant ground-motion values (Gregor 

and others, 2014). GK15 does not include a functional form 

for its hanging-wall effect.

All three GMPEs are defined for a range of VS30 values 

(see table 2). In ASK14, numerical simulations of nonlinear 

site amplification factors by Kamai and others (2014) were 

used to constrain the site response. In BSSA14, a semiempirical nonlinear site response model by Seyhan and 

Stewart (2014) was used; this model is based on empirical 

data and simulations of Kamai and others (2014). For a 

reference site condition, the nonlinear site amplification 

factor is a function of PGA for BSSA14 and of SA for 

ASK14. The GK15 GMPE contains a linear site amplification 

feature based on the more limited VS30 range. In addition to 

Table 2. Summary of databases, intensity measures, and applicability ranges of independent predictors for three ground-motion

prediction equations.

[Ground-motion prediction equations are GK15, Graizer and Kalkan (2015, 2016); ASK14, Abrahamson and others (2014); BSSA14, Boore and others (2014). 

PGA, peak ground acceleration; PGV, peak ground velocity; SA; spectral acceleration; s, seconds; SS, strike slip; REV, reverse; NM, normal; U, unspecified; 

km, kilometers; VS30, shear-wave velocity in upper 30 meters of geologic profile; m/s, meters per second; km/s, kilometers per second]

Item GK15 ASK14 BSSA14

Database Expanded NGA-West1 NGA-West2 NGA-West2

Number of events (for PGA) 47 326 404

Number of recordings (for PGA) 2,583 15,750 18,436

Intensity measures PGA, SA PGA, PGV, SA PGA, PGV, SA

Period range (s) 0.01–5 0.01–10 0.01–10

Period definition (number of periods) Continuous Discrete (21) Discrete (42)

Number of estimation coefficients 31 1,008 2,889

Number of independent predictors 7 7 6

Class 2 event flag Unused Included Unused

Magnitude (style of faulting) 5.0–8.0 (SS, REV) 3.0–8.5 (all) 3.0–8.5 (SS, REV)

7.0–8.0 (NM) 3.3–7.0 (NM)

Style of faulting SS, REV, NM SS, REV, NM SS, REV, NM, U

Dip Unused Used Unused

Down-dip rupture width Unused Used Unused

Closest distance to rupture plane (km) 0–250 0–300 Unused

Joyner-Boore distance (km) Unused Unused 0–400

Horizontal distance to top edge of rupture plane measured 

perpendicular to strike

Unused Used Unused

Horizontal distance to top edge of rupture plane measured 

parallel to strike

Unused Used Unused

VS30 (m/s) 200–1,300 180–1,500 150–1,500

Depth to 1.0 km/s isosurface Unused Used Used

Depth to 1.5 km/s isosurface Used Unused Unused

Depth to basin Used Used Used

Nonlinear site effects Unused Used Used

Quality factor Used Unused Unused

Hanging wall Unused Used Indirectly used

Regional adjustment Used Used Used

Standard deviation (total, intra, inter) Used Used Used
Stage 1: Comparisons of Median Predictions 5

the VS30 parameter, ASK14 and BSSA14 also incorporate 

a parameter that is dependent on the depth to the 1.0 km/s 

shear-wave isosurface (Z1.0) and GK15 uses the depth to the 

1.5 km/s shear-wave isosurface (Z1.5). These extra parameters 

are to capture the difference in site amplification from deep 

sedimentary basins. Furthermore, ASK14 uses the depth to 

the top of rupture (ZTOR), whereas GK15 and BSSA14 found 

a depth parameter to be insignificant for ground-motion 

prediction with their mathematical forms.

The NGA-West2 project (Bozorgnia and others, 2014) and 

recent earthquake data (for example, Baltay and Boatwright, 

2015) signify regionalization when accounting for differences 

in far-source distance attenuation of ground motions and site 

response. Hence, ASK14 and BSSA14 have developed regional 

adjustments for either site response and (or) the long-distance 

anelastic attenuation between various geographic regions. 

BSSA14 incorporated only the regional attenuation adjustment 

feature. GK15 uses Q0

—determined using Lg or coda waves—

as an independent predictor that can be changed to suit the 

region of interest.

Stage 1: Comparisons of Median 

Predictions

In the following sections, we compared the distance-scaling 

features, magnitude-scaling features, SOF effects, site effects, 

response spectra (shape and amplitude), and standard deviations of 

ASK14, BSSA14, and GK15.

Distance-Scaling Features

Figures 1A and 2A show a comparison of the distancescaling features of the median estimates of PGA and SA at 0.2, 

1.0, and 3.0 seconds (s) for horizontal ground motions predicted 

by the three GMPEs for vertically dipping strike-slip earthquake 

scenarios with M5, 6, 7, and 8 as a function of Rrup for ASK14 

and GK15 and as a function of RJB for BSSA14. Note that Rrup

and RJB are the same for vertical strike-slip events with the 

depth to top of the rupture equal to zero (for brevity, we did not 

include a comparison for dip-slip faults). The results are for 

National Earthquake Hazards Reduction Program (NEHRP) 

classes B and C reference site conditions (VS30 = 760 meters 

per second [m/s], in other words, engineering rock). These 

scenarios were chosen because the magnitude range, strike-slip 

faulting mechanism, and B/C reference site conditions are the 

most common for hazard computations in California (Petersen 

and others, 2014). For this comparison, ASK14 is evaluated 

for default values of Z1.0 (0.0481 km) and ZTOR (6 km for M5, 

3 km for M6, 1 km for M7, and 0 km for M8) and BSSA14 

is evaluated for a default value of δz1 (0); these values were 

adapted from Gregor and others (2014). The region parameter 

is set to 1 for ASK14 and 0 for BSSA14 considering California. 

The GK15 GMPE is evaluated for a regional Q0

 of 150, which 

is an average for California (Singh and Herrmann, 1983; 

Mitchell and Hwang, 1987; Erickson and others, 2004).

Figures 1A and 2A also illustrate short-distance saturation as 

a function of magnitude for the three GMPEs. For PGA and SA 

at 0.2 s, GK15 produces similar or slightly lower median results 

compared to ASK14 and BSSA14 at close distances (0–2 km). 

The GK15 GMPE produces higher median predictions because of 

oversaturation of attenuation (bump) between 2 and 15 km. The 

bump phenomenon (also called oversaturation of attenuation) was 

recently demonstrated through modeling geometric spreading and 

relative amplitudes of ground motions in eastern North America. 

The bump was attributed to radiation pattern effects combined 

with wave propagation through a one-dimensional layered earth 

model (Chapman and Godbee, 2012; Baumann and Dalguer, 

2014). In the case of earthquakes, this bump can be the result 

of one or many factors, including the aforementioned radiation 

pattern, directivity and nonlinear behavior of soil near a fault 

source (for example, low-velocity faultzone-guided waves [Li and 

Vidale, 1996]), and by measuring distance as that closest to the 

rupture plane and not from the seismogenic (most energetic) part 

of the fault rupture.

To quantify the differences for a range of magnitudes and 

distances, figure 1B presents the ratio between median predictions 

of GK15 and those of ASK14. The upper and lower bounds of 

the shaded areas indicate a factor of 2 difference. The median 

predictions of GK15 are generally similar to those of ASK14 

within a factor of 1.5 for PGA and SA at 0.2 s within about 30 km 

for M5 events, about 45 km for M6 events, and about 150 km for 

M7 and M8 events. For these intensity measures, the difference 

becomes more than 2 only for M5 events beyond 50 km and M6 

events beyond about 90 km. At 150 km, the difference in PGA is 

less than 2.5 for M6 events and 4 for M5 events. For SA at 0.2 s, 

the difference at 150 km is 3 for M6 events and more than 4 for 

M5 events. For SA at 1.0 and 3.0 s, the difference between the 

GK15 median predictions and those of ASK14 are, in general, 

within a factor of 2.5 except for M5 events beyond about 40 

km for SA at 1.0 s and beyond about 75 km for SA at 3.0 s. At 

150 km, the largest difference for M5 events becomes 3.7 for SA 

at 1.0 s and 2.7 for SA at 3.0 s.

Figure 2B shows the ratios between the GK15 and 

BSSA14 median predictions. For PGA and SA at 0.2 s, the 

difference is within a factor of 1.5 for M6, 7, and 8 events 

within 150 km. For SA at 1.0 and 3.0 s, this difference is within 

a factor of 2. The main difference between the GK15 and 

BSSA14 predictions is for M5 events for SA at 1.0 and 3.0 s, 

which is within a factor of 3.5.

Magnitude-Scaling Features

The effect of magnitude scaling for vertical strike-slip 

earthquakes at distances of 10, 30, and 150 km is shown in 

figure 4 for VS30 = 760 m/s for median predictions of PGA 

and SA at 0.2, 1.0, and 3.0 s by the three GMPEs. ASK14 

and BSSA14 were evaluated for default values, as described 

previously. The magnitude range is from 5 to 8. Note that the 
6 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

5, 6, 7, and 8 earthquakes. Calculations made for National Earthquake Hazards Reduction Program (NEHRP) 

 is the closest 

and spectral 

others (2014) (ASK14) ground-motion 

rup R

, Plots of the ratio of 

, Plots showing a comparison of distance-scaling (attenuation) features of median estimates of peak ground acceleration (PGA) 

 are only used in GK15. Region is California. (

B is depth to basin). depth 

B

depth

is quality factor; 0 Q

B and 0 Q = 0 kilometers (km). depth = 150, and 

B 0 Q = 760 meters per second, 

-wave velocity in the upper 30 meters of the geologic profile; is shear S30 V

S30 V

A Figure 1.

accelerations (SA) at 0.2, 1.0, and 3.0 seconds (s) predicted by the Graizer and Kalkan (2015, 2016) (GK15) and Abrahamson and prediction equations for strike-slip moment magnitude (M)classes B and C with distance to fault rupture; median estimates between GK15 and ASK14; the upper and lower bounds of shaded areas indicate a factor of 2 difference.

0.001

0.01

0.1

1

Acceleration (g)

PGA NEHRP B/C

M=8 (GK15)M=7M=6M=5M=8 (ASK14)M=7M=6M=5

SA at 0.2 s

43210

Ratio (GK15 / ASK14)

PGA M=8

M=7M=6M=5

SA at 0.2 s

0.1 1 10 100

R

rup (km)

0.001

0.01

0.1

1

Acceleration (g)

SA at 1.0 s

0.1 1 10 100

R

rup (km)

SA at 3.0 s

0.1 1 10 100

R

rup (km)

43210

Ratio (GK15 / ASK14)

SA at 1.0 s

0.1 1 10 100

R

rup (km)

SA at 3.0 s

A

B
Stage 1: Comparisons of Median Predictions 7 and spectral acceleration , Plots showing a comparison of distance-scaling (attenuation) features of median estimates of peak ground acceleration (PGA) 14) ground-motion prediction equations -Boore distance, in kilometers (km). of 2 difference. generally in the range of 1.5–2, it is is the Joyner est2 GMPEs (BSSA14 and that of Abrahamson and others [2014] [ASK14]) are generally e also performed similar comparisons in figure 3, which demonstrates the median ances. The differences demonstrated in figures (SA) at 0.2, 1.0, and 3.0 seconds (s) predicted by the Graizer and Kalkan (2015, 2016) (GK15) and Boore and others (2014) (BSSA JB R 6, 7, and 8 earthquakes. All parameters are as defined in figure 1; (GMPEs) for strike-slip moment magnitude (M) 5, , Plots of the ratio of median estimates between GK15 and BSSA14; the upper and lower bounds of shaded areas indicate a factor A 

B Region is California. 

According to Gregor and others (2014), the median ground motions from NGA-Wsimilar—within a factor of about 1.5–2 for 5<M<7 and distances of 10–100 km. Wpredictions between ASK14 and BSSA14 and their ratios. Although this figure elucidates that the difference between the GMPEs isgreater than 2 for M5 for SA at 1.0 and 3.0 s. For M5 and SA at 3.0 s, the difference becomes larger than 3.5 at short dist

 for GK15 are overall in agreement with the range of differences between ASK14 and BSSA14, shown in figure 3.

Figure 2.

B and 2 B1

0.001

0.01

0.1

1

Acceleration (g)

PGA

M=8 (GK15)M=7 NEHRP B/CM=6M=5M=8 (BSSA14)M=7M=6M=5

SA at 0.2 s

43210

Ratio (GK15 / BSSA14)

PGA M=8

M=7M=6M=5

SA at 0.2 s

0.1 1 10 100

R

rup

 or 

RJB (km)

0.001

0.01

0.1

1

Acceleration (g)

SA at 1.0 s

0.1 1 10 100

R

rup

 or 

RJB (km)

SA at 3.0 s

0.1 1 10 100

R

rup

 or 

RJB (km)

43210

Ratio (GK15 / BSSA14)

SA at 1.0 s

0.1 1 10 100

R

rup

 or 

RJB (km)

SA at 3.0 s

A

B
8 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations 0.001 0.01 0.1

1

Acceleration (g)

PGA

M=8 (ASK14)M=7 NEHRP B/CM=6M=5M=8 (BSSA14)M=7M=6M=5

SA at 0.2 s

43210

Ratio (ASK14 / BSSA14)

PGA M=8

M=7M=6M=5

SA at 0.2 s

0.1 1 10 100

R

rup

 or 

RJB (km)

0.001

0.01

0.1

1

Acceleration (g)

SA at 1.0 s

0.1 1 10 100

R

rup

 or 

RJB (km)

SA at 3.0 s

0.1 1 10 100

R

rup

 or 

RJB (km)

43210

Ratio (ASK14 / BSSA14)

SA at 1.0 s

0.1 1 10 100

R

rup

 or 

RJB (km)

SA at 3.0 s

A

B

nd spectral acceleration (SA)

K14) and Boore and others (2014) (BSSA14)

-Boore distance, in kilometers (km). Region is

 of 2 difference.

, Plots showing a comparison of distance-scaling (attenuation) features of median estimates of peak ground acceleration (PGA) a

at 0.2, 1.0, and 3.0 seconds (s) predicted by the ground-motion prediction equations (GMPE) of Abrahamson and others (2014) (AS

 is the Joyner JB R 6, 7, and 8 earthquakes. All parameters are as defined in figure 1; 5,

A

, Plots of the ratio of median estimates between ASK14 and BSSA14; the upper and lower bounds of shaded areas indicate a factor B

 Figure 3.

for strike-slip moment magnitude (M)California. 
Stage 1: Comparisons of Median Predictions 9

0.0001

0.001

0.01

0.1

1

Acceleration (g)

PGA

10 km

30 km

150 km

GK15

ASK14

BSSA14 SA at 0.2 s

5 6 7 8

Moment magnitude, M

0.0001

0.001

0.01

0.1

1

Acceleration (g)

SA at 1.0 s

5 6 7 8

Moment magnitude, M

SA at 3.0 s

Figure 4. Plots showing a

comparison of magnitude (M) 

scaling features of median 

estimates of peak ground 

acceleration (PGA) and spectral 

acceleration (SA) at 0.2, 1.0, and 

3.0 seconds (s) by the groundmotion prediction equations of 

Graizer and Kalkan (2015, 2016) 

(GK15), Abrahamson and others 

(2014) (ASK14), and Boore and 

others (2014) (BSSA14) for 10, 30, 

and 150 kilometers (km). Region is 

California. All parameters are as 

defined in figure 1.

break in the magnitude scaling of GK15 at M5.5 is driven by 

the spectral shape of records used to constrain the magnitudescaling function. The weak scaling of the short-period motion 

at short distances reflects the saturation with magnitude, 

which is common to all three GMPEs. The magnitude-scaling 

features of these GMPEs show similarities and differences 

depending on the intensity measure and magnitude level. For 

instance, the median ground motions are within a factor of 

2 for short periods (PGA and SA at 0.2 s) for M6 events and 

larger. At long periods, the range increases to a factor of 3 at 

M6 events and larger.

The differences between model predictions are greater 

for M5 events, especially at 150 km distance. We attribute 

these dissimilarities to regional variations and data used in 

constraining the GMPEs. In the case of GK15, 97.9 percent 

of small-magnitude (4.9≤M< 6) earthquake data were from 

California (table 1) and the remaining 3.1 percent were 

from Nevada, Italy, and Taiwan. In contrast, the ASK14 

and BSSA14 GMPEs used small-magnitude event data 

from other regions in larger percentages. Recent studies 

have shown that small- to moderate-magnitude events have 

different attenuation trends compared with moderate- to 

large-magnitude events (Chiou and others, 2010; Atkinson 

and Morrison, 2009) and the regional variation is even 

more significant for smaller magnitude events (Zafarani and 

Farhadi, 2017).

Site Effects

All three GMPEs use VS30 for modeling site response 

scaling. A comparison of median spectrum as a function of 

VS30 values is shown in figure 5 for a M7 vertical strike-slip 

earthquake at the closest distances to the rupture plane of 10 

and 50 km. For ASK14, ZTOR is 1 km and for other parameters, 

including Z1.0 and Z2.5, the default values of ASK14 and 

BSSA14 are used. The GK15 GMPE is limited to VS30≥200m/s

and does not contain a nonlinear site amplification term 

because of the large variability in nonlinear site-correction 

models.

For higher VS30 values, ASK14 and BSSA14 saturate 

by predicting constant ground-motion values. For shorter 

distances (<10 km), the nonlinear effects are apparent by the 

observed curvature in the amplification functions for ASK14 

and BSSA14, especially for PGA and SA at 0.2 s. Overall, the 

site amplification results are alike among the three GMPEs; the 

largest difference is 35 percent between GK15 and the other two 

GMPEs at 200 m/s for SA at 0.2 s.
10 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Figure 5. Plots showing a 

comparison of VS30-scaling features 

of the median estimates of peak 

ground acceleration (PGA) and 

spectral acceleration (SA) at 

0.2, 1.0, and 3.0 seconds (s) by 

the ground-motion prediction 

equations of Graizer and Kalkan 

(2015, 2016) (GK15), Abrahamson 

and others (2014) (ASK14), and 

Boore and others (2014) (BSSA14) 

for a magnitude 7 strike-slip 

earthquake at 10 and 50 kilometers 

(km). VS30 is in units of meters per 

second (m/s). Region is California. 

All parameters are as defined 

figure 1.

0.01

0.1

1

Acceleration (g)

PGA

10 km

50 km

GK15

ASK14

BSSA14 SA at 0.2 s

200 1000 1600

VS30 (m/s)

0.01

0.1

1

Acceleration (g)

SA at 1.0 s

200 1000 1600

VS30 (m/s)

SA at 3.0 s

Style-of-Faulting Effects

Figure 6 compares SOF ratios between reverse and 

strike-slip events and between normal and strike-slip events 

for the period range of 0.01 to 5 s at 30 km. These ratios are 

computed for a M7 event. In GK15, the SOF factor is period 

and magnitude independent. In ASK14, a magnitude-dependent 

but period-independent SOF factor was used for reverse and 

normal earthquakes only. In BSSA14, a magnitude-dependent 

SOF factor, which is a function of the period-dependent “hinge 

magnitude,” was used for unspecified, strike-slip, reverse, and 

normal faults. GK15 predicts larger reverse/strike-slip ratios 

than either ASK14 or BSSA14. For reverse/strike-slip ratios, the 

difference between ASK14 and BSSA14 are less than 10 percent, 

except at long periods. For normal/strike-slip ratios, the difference 

between ASK14 and BSSA14 are larger for short periods and 

smaller at long periods. These comparisons suggest that there is a 

noteworthy variation.

Response Spectra

A comparison between the linear site-effect scaling features 

of the GK15 GMPE and the ASK14 and BSSA14 GMPEs is 

shown in figure 7 for a M7 strike-slip event at a distance of 30 km 

for a range of VS30 values representing NEHRP soil classifications 

B (VS30 = 750 to 1,200 m/s), C (VS30 = 450 to 750 m/s), and D 

(VS30 = 250 to 450 m/s). The independent estimation parameters 

used in figure 1 were repeated.

The spectral shapes from the three GMPEs are similar 

between 0.01 and 3.0 s. The GK15 GMPE shows faster decay 

at long periods (3.0 to 5.0 s), as controlled by the decay term 

in the spectral shape prediction model, which is a function of 

basin depth. As compared to the ASK14 and BSSA14 GMPEs, 

variations in site effects owing to different site classes are less 

pronounced in the GK15 GMPE, but the overall spectral shapes 

are analogous.

The median response spectra predicted by GK15 for M6, 

7, and 8 earthquakes at 1 and 30 km from a vertically dipping 

strike-slip fault with VS30 = 760 and 270 m/s are compared 

with those predicted by ASK14 and BSSA14 in figures 8 and 

9, respectively. Again, the default parameters shown in figure 

1 were repeated. There is resemblance (within a factor of 1.5) 

among the three models for the M6–8 cases. The difference 

between GK15 and ASK14 increases to a factor of 2 for the 

M8 case, especially at 1.0 s for VS30 = 760 m/s; this difference 

is much less for VS30 = 270 m/s. The largest relative change in 

the response spectra between GK15 and BSSA14 is for long 
Stage 1: Comparisons of Median Predictions 11

0.01 0.1 1 5

Period (s)

0.4

0.6

0.8

1

1.2

1.4

1.6

SOF ratio

Reverse / Strike slip

GK15

ASK14

BSSA14

0.01 0.1 1 5

Period (s)

Normal / Strike slip

Figure 6. Plots showing a comparison of style-of-faulting (SOF) ratios versus period (in

seconds [s]) between reverse and strike-slip events and between normal and strikeslip events at 30 kilometers (km) among the Graizer and Kalkan (2015, 2016) (GK15), 

Abrahamson and others (2014) (ASK14), and Boore and others (2014) (BSSA14) groundmotion prediction equations.

Figure 7. Plots showing a comparison

of VS30-scaling features of the median 

estimates of response-spectral shapes 

and amplitudes versus period (in seconds 

[s]) among the Graizer and Kalkan (2015, 

2016) (GK15), Abrahamson and others 

(2014) (ASK14), and Boore and others 

(2014) (BSSA14) ground-motion prediction 

equations for a strike-slip magnitude 7 

earthquake at 30 kilometers (km). VS30 is 

in units of meters per second (m/s). All 

parameters are as defined in figure 1.
12 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Figure 8. Plots showing a 

comparison of the median 

estimates of response-spectral 

shapes and amplitudes 

versus period (in seconds 

[s]) between the Graizer and 

Kalkan (2015, 2016) (GK15) 

and Abrahamson and others 

(2014) (ASK14) ground-motion 

prediction equations for 

strike-slip magnitudes 6, 7, 

and 8 earthquakes at a rupture 

distance (Rrup) of 1 and 30 

kilometers (km). Comparisons 

are shown for VS30 equal to 270 

and 760 meters per second (m/s). 

All parameters are as defined 

figure 1.

0.001

0.01

0.1

1

Spectral acceleration (g)

Rrup = 1 km, VS30 = 760 m/s

M=8 (GK15)

M=7

M=6

M=8 (ASK14)

M=7

M=6

Rrup = 1 km, VS30 = 270 m/s

0.01 0.1 1

Period (s)

0.001

0.01

0.1

1

Spectral acceleration (g)

Rrup = 30 km, VS30 = 760 m/s

0.01 0.1 1 5

Period (s)

Rrup = 30 km, VS30 = 270 m/s

periods. For intermediate and short periods, the range in GK15 

predictions is similar to BSSA14. For the M6 case, the response 

spectra predictions are generally similar between the GK15 and 

BSSA14 GMPEs, except for VS30 = 270 m/s at 30 km, where the 

differences are noticeable for a wide range of periods.

Standard Deviations

Figure 10 compares the period dependence of the standard 

deviations among GK15, ASK14, and BSSA14 for a M5 vertical 

strike-slip event at 30 km and VS30 = 760 m/s. All standard 

deviations (σ) are in natural logarithmic units. Only the standard 

deviations of ASK14 are magnitude dependent. GK15 standard 

deviations are generally lower than the other two GMPEs between 

0.01 and 0.7 s. At 1.0 s, σ is similar between the three GMPEs. 

For longer spectral periods (>1.0 s), GK15 has larger σ than the 

other two GMPEs. Differences are greater for intra-event standard 

deviations (φ) than inter-event standard deviations (τ). Large φ

values for ASK14 and BSSA14 suggest potential supplementary 

variability in PGA and SA owing to the additional events included 

in the NGA-West2 database. The ASK14 GMPE shows generally 

flat τ trends with period, whereas the trends of τ for GK15 and 

BSSA14 are similar and fluctuate with period. The GK15 GMPE 

has lower values of φ than the other GMPEs at periods less than 

0.7 s with the overall impact on σ at the lowest values of σ.

Stage 2: Comparisons with Earthquake 

Data

In figures 11–13, SA predictions between 0.01 and 

5 s from the three GMPEs are compared with the response 

spectra for near-field (0 to 20 km) and intermediate-field (50 

to 70 km) ground-motion records of select major earthquakes 

in California from the NGA-West2 database. Specifically, 

the 1966 M6.2 Parkfield, 1979 M6.5 Imperial Valley, 1984 

M6.2 Morgan Hill, 1986 M6.1 North Palm Springs, 1987 

M6.5 Superstition Hills, 1989 M6.9 Loma Prieta, 1992 M7.3 

Landers, 1994 M6.7 Northridge, 2004 M6 Parkfield, and 2010 

M7.2 El-Mayor Cucapah earthquakes are covered. Among 

all the events listed, the M7.2 El-Mayor Cucapah is not in 

the GK15 database. Our objective here is to demonstrate the 

performance of the GMPEs in predicting the ground motions 

from California regardless of whether the particular event was 

used in deriving the GMPE.
Stage 2: Comparisons with Earthquake Data 13

0.001

0.01

0.1

1

Spectral acceleration (g)

R

rup or RJB = 1 km, VS30 = 760 m/s

M=8 (GK15)

M=7

M=6

M=8 (BSSA14)

M=7

M=6

R

rup or RJB = 1 km, VS30 = 270 m/s

0.01 0.1 1

Period (s)

0.001

0.01

0.1

1

Spectral acceleration (g)

R

rup or RJB = 30 km, VS30 = 760 m/s

0.01 0.1 1 5

Period (s)

R

rup or RJB = 30 km, VS30 = 270 m/s

Figure 9. Plots showing a

comparison of the median estimates 

of response-spectral shapes and 

amplitudes versus period (in seconds 

[s]) between the Graizer and Kalkan 

(2015, 2016) (GK15) and Boore and 

others (2014) (BSSA14) ground-motion 

prediction equations for strike-slip 

magnitudes 6, 7, and 8 earthquakes at 

a rupture distance (defined as either 

Rrup or RJB) of 1 and 30 kilometers (km). 

Comparisons are shown for VS30 equal 

to 270 and 760 meters per second 

(m/s). All parameters are as defined in 

figure 1.

0.01 0.1 1 5

0

0.3

0.6

0.9

1.2

Total, 

<

GK15

ASK14

BSSA14

0.01 0.1 1 5

Period (s)

Inter-event, 

=

0.01 0.1 1 5 Intra-event, 

?

Figure 10. Plots showing a comparison of total, inter-event, and intra-event variability versus period (in seconds [s]) of 

the Graizer and Kalkan (2015, 2016) (GK15), Abrahamson and others (2014) (ASK14), and Boore and others (2014) (BSSA14) 

ground-motion prediction equations for a magnitude 5 earthquake.
14 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Figure 11. Plots showing a comparison of the median estimates of response-spectral shapes and amplitudes versus

period (in seconds [s]) by the Graizer and Kalkan (2015, 2016) (GK15), Abrahamson and others (2014) (ASK14), and Boore and 

others (2014) (BSSA14) ground-motion prediction equations (GMPEs) with the observations from select six major Californian 

earthquakes from the NGA-West2 database. Ground-motion data correspond to near-field records (0–20 kilometers [km]) 

within National Earthquake Hazards Reduction Program site class C. Dashed curves indicate the 16th- and 84th-percentile 

predictions by the GK15 GMPE. Style of faulting (SOF), site class, and number of ground motions (GMs) from each 

earthquake are indicated. M, magnitude; SS, strike slip; REV, reverse; REV–OB, reverse oblique; σ, standard deviation. 

In figures 11–13, the ground-motion records correspond 

to NEHRP site class C or D. The number of records satisfying 

the distance and soil condition selection criteria is listed on 

each panel where the average spectra of records are shown 

by thick jagged curves and they are compared with the 

predictions. Individual spectra of records are also shown 

by thin jagged curves to demonstrate the variability. The 

predictions are for the average VS30 of each ground-motion set. 

The 16th- and 84th-percentile predictions of GK15, shown by 

dashed curves, bound most of the SA data. For all near- and 

intermediate-field events, the GK15 GMPE yields predictions 

closer to the average of the observations (that is, the predicted 

and observed trends of the peak [period and amplitude] of the 

response spectra with magnitude and distance match). The 

width of the predicted response spectra is also comparable to 

the observations. Some of the variability is possibly caused by 

the fluctuations of the site condition within the site class. The 

predicted response spectra by GK15 are also close to those 

estimated by the other two GMPEs.

In figure 14, comparisons are shown for the strongmotion data of the 2014 M6 South Napa earthquake—the most 

recent damaging event in California that is not included in the 

NGA-West2 database. Ground-motion data shown uses VS30

adjusted to 760 m/s following Seyhan and Stewart (2014). The 

GMPE predictions are also shown for VS30 = 760 m/s to be able 

to compare observations directly with the attenuation curves. 

The 16th- and 84th-percentile predictions of the GMPEs are 

also shown by dashed curves. The first panel shows amplified 

PGA as a near-field (0 to 10 km) bump—this phenomenon is 

captured by the GK15 GMPE. A more pronounced anelastic 

decay of the attenuation curves at about 90 km for GK15 as 

compared to figure 1A is caused by lower Q0 (50) for the Napa 

region, according to the range suggested by Ford and others 

(2008). As previously mentioned, Q0 = 150 is the average 

for California; it could be lower or higher in certain regions. 

The largest PGA (~1 g) during this earthquake, recorded at 

the Carquinez Bridge, is significantly affected by local site 

amplification (Baltay and Boatwright, 2015). Residual plots 
Stage 2: Comparisons with Earthquake Data 15

Figure 12. Plots showing a comparison of the median estimates of response-spectral shapes and amplitudes versus 

period (in seconds [s]) by the Graizer and Kalkan (2015, 2016) (GK15), Abrahamson and others (2014) (ASK14), and Boore 

and others (2014) (BSSA14) ground-motion prediction equations (GMPEs) with the observations from select nine major 

Californian earthquakes from the NGA-West2 database. Ground-motion data correspond to near-field records (0–20 

kilometers [km]) within National Earthquake Hazards Reduction Program site class D. Dashed curves indicate the 16th- and 

84th-percentile predictions by the GK15 GMPE. Style of faulting (SOF), site class, and number of ground motions (GMs) from 

each earthquake are indicated. M, magnitude; SS, strike slip; REV, reverse; REV–OB, reverse oblique; σ, standard deviation. 

show a logarithmic difference between the observations and 

predictions. Both the ASK14 and BSSA14 GMPEs’ median 

predictions are systematically larger than the observations.

Event term, representing approximately the mean offset 

of the data from predictions by the GMPE median, is used to 

evaluate GMPE performance (Boore and others, 2014). Based 

on the residuals, event terms for each intensity measure and 

each GMPE are listed in table 3. The GK15 GMPE has the 

lowest event terms. Both ASK14 and BSSA14 GMPEs have 

negative event terms, suggesting that the South Napa event is 

an earthquake with probably a much lower stress-drop than the 

NGA-West2 average.
16 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Figure 13. Plots showing a comparison of the median estimates of response-spectral shapes and amplitudes versus

period (in seconds [s]) by the Graizer and Kalkan (2015, 2016) (GK15), Abrahamson and others (2014) (ASK14), and Boore and 

others (2014) (BSSA14) ground-motion prediction equations (GMPEs) with the observations from select six major Californian 

earthquakes from the NGA-West2 database. Ground-motion data correspond to intermediate-field records (50–70 

kilometers [km]) within National Earthquake Hazards Reduction Program site class D. Dashed curves indicate 16th- and 

84th-percentile predictions by the GK15 GMPE. Style of faulting (SOF), site class, and number of ground motions (GMs) from 

each earthquake are indicated. M, magnitude; SS, strike slip; REV, reverse; REV–OB, reverse oblique; σ, standard deviation.

Table 3. Event terms for the 2014 magnitude 6.0 South Napa earthquake for three groundmotion prediction equations.

[Ground-motion prediction equations are GK15, Graizer and Kalkan (2015, 2016); ASK14, Abrahamson and 

others (2014); and BSSA14, Boore and others (2014)]

Event term GK15 ASK14 BSSA14

Peak ground acceleration −0.180 −0.679 −1.185

Spectral acceleration at 0.2 seconds −0.046 −0.703 −1.210

Spectral acceleration at 1.0 seconds 0.124 −0.427 −0.876

Spectral acceleration at 3.0 seconds 0.441 −0.377 −0.594
Stage 2: Comparisons with Earthquake Data 17

0.0001

0.001

0.01

0.1

1

Acceleration (g)

PGA SA at 0.3 s

GK15 ASK14 BSSA14

SA at 1.0 s SA at 3.0 s

1 10 100 200

-3

30

ln (residual)

1 10 100 200

Distance (km)

1 10 100 200 1 10 100 200

ons from the Plots showing ground-motion attenuation during the 2014 magnitude 6 South Napa earthquake, California. Also shown are predicti

ion prediction equations 

 = 760 m/s. Plots show amplified peak 

ions and predictions. 

S30 = 760 meters per second (m/s); GMPE predictions are for V S30 V

-field distances (0 to 10 kilometers [km]); this phenomenon is captured by the GK15 GMPE. Dashed curves 

Figure 14.Graizer and Kalkan (2015, 2016) (GK15), Abrahamson and others (2014) (ASK14), and Boore and others (2014) (BSSA14) ground-mot(GMPEs). Ground-motion data shown is adjusted to ground acceleration (PGA) as a bump at neardenote the 16th- and 84th-percentile predictions of the GMPEs. Residual plots show logarithmic difference between the observatNumber of data points compared is 303.
18 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Stage 3: Comparisons of Residuals 

Using the NGA-West2 Database

We performed mixed-effects residuals analyses in order 

to evaluate how well GK15, ASK14, and BSSA14 predict the 

near-source (within 80 km of the fault) subset of the NGA-West2 

database and to confirm that GK15 is not biased with respect to M, 

Rrup, VS30, depth to basin (Bdepth), or style-of-faulting (F) parameters 

by examining trends of residuals against them. The distribution 

of data, covering 975 ground motions from 73 Californian events 

(listed in table 4) ranging from M5 to 7.36, is displayed in figure 

15 against M, Rrup, and VS30. Histogram bar charts are also shown 

with NEHRP site classifications marked by varying symbols.

The residuals at PGA and SA at 0.2, 1.0, and 3.0 s spectral 

periods are computed as follows:

Resij = ln(Yij) − μij(M, Rrup, VS30, Bdepth, F), (1)

where i is the event,

j is the recording index,

Resij is the residual of the jth recording of the ith

event,

Yij is the intensity measure, such as PGA or SA 

ordinates, from the jth recording of the ith 

event, and

μij is the GMPE’s median estimate in natural 

logarithmic units.

In order to separate inter-event disparities from intra-event 

variations, we performed a mixed-effects analysis with respect 

to independent predictors of M, Rrup (RJB for BSSA14), VS30, and 

Bdepth. We fit an intercept a and slope b to residuals according to the 

following formulation:

Resij = a + bxi +ηi + εij, (2)

where xi is the independent predictor parameter,

ηi is the event term (inter-event residual) for event i, 

and

εij is the intra-event residual for recording j in 

event i.

Event term ηi represents the approximate mean offset of the 

data for event i from the predictions provided by the median of 

the GMPE. Event terms (ηi) are used to evaluate the GMPE’s 

performance relative to source predictor variables. Both event and 

intra-event terms are assumed to be random Gaussian variables 

with zero mean; their standard deviations are indicated by τ and 

φ, respectively. Further details of the analyses performed on the 

residuals here can be found in Joyner and Boore (1993) and 

Spudich and others (1999).

5

5.5

6

6.5

7

7.5

Moment magnitude

0.1 1 10 100

100

500

1000

1500

2000

Rrup (km)

VS30 (m/s)

0 100 200 300 400 500

Counts

SA

SB

SC

SD

0

20

40

60

80

100

Counts

Figure 15. Plots showing 

the distribution of the NGAWest2 near-source California 

earthquake events with respect 

to moment magnitude (M), VS30

(in meters per second [m/s]), 

and Rrup (in kilometers [km]). 

Near source refers to Rrup≤80 

km. Bar charts show histograms 

of data; National Earthquake 

Hazards Reduction Program 

site categories are marked 

by various symbols. For these 

events, M≥5, the number of 

records is 975, and the number 

of events = 73.
Stage 3: Comparisons of Residuals Using the NGA-West2 Database 19

Table 4. List of California earthquake events in a near-source (within 80 kilometers of the fault) subset of the NGA-West2 database.

[No., number; Calif or CA, California; N., North]

No. Year Event name Moment 

magnitude

1 1937 Humbolt Bay 5.80

2 1938 Imperial Valley-01 5.00

3 1938 Northwest Calif-01 5.50

4 1940 Imperial Valley-02 6.95

5 1941 Northern Calif-01 6.40

6 1942 Borrego 6.50

7 1951 Imperial Valley-03 5.60

8 1951 Northwest Calif-03 5.80

9 1952 Kern County 7.36

10 1952 Northern Calif-02 5.20

11 1952 Southern Calif 6.00

12 1953 Imperial Valley-04 5.50

13 1954 Central Calif-01 5.30

14 1954 Northern Calif-03 6.50

15 1955 Imperial Valley-05 5.40

16 1957 San Francisco 5.28

17 1960 Central Calif-02 5.00

18 1960 Northern Calif-04 5.70

19 1961 Hollister-01 5.60

20 1961 Hollister-02 5.50

21 1966 Parkfield 6.19

22 1967 Northern Calif-05 5.60

23 1967 Northern Calif-06 5.20

24 1968 Borrego Mtn 6.63

25 1971 San Fernando 6.61

26 1973 Point Mugu 5.65

27 1974 Hollister-03 5.14

28 1975 Northern Calif-07 5.20

29 1975 Oroville-01 5.89

30 1978 Santa Barbara 5.92

31 1979 Imperial Valley-06 6.53

32 1979 Imperial Valley-07 5.01

33 1979 Imperial Valley-08 5.62

34 1980 Livermore-01 5.80

35 1980 Livermore-02 5.42

36 1980 Anza (Horse Canyon)-01 5.19

37 1980 Mammoth Lakes-01 6.06

No. Year Event name Moment 

magnitude

38 1980 Mammoth Lakes-02 5.69

39 1980 Mammoth Lakes-03 5.91

40 1980 Mammoth Lakes-04 5.70

41 1980 Mammoth Lakes-05 5.70

42 1980 Mammoth Lakes-06 5.94

43 1983 Mammoth Lakes-10 5.34

44 1983 Mammoth Lakes-11 5.31

45 1983 Borah Peak, ID-01 6.88

46 1983 Borah Peak, ID-02 5.10

47 1984 Morgan Hill 6.19

48 1984 Bishop (Round Valley) 5.82

49 1986 Hollister-04 5.45

50 1986 N. Palm Springs 6.06

51 1987 Baja California 5.50

52 1987 Whittier Narrows-01 5.99

53 1987 Whittier Narrows-02 5.27

54 1987 Superstition Hills-01 6.22

55 1987 Superstition Hills-02 6.54

56 1989 Loma Prieta 6.93

57 1992 Cape Mendocino 7.01

58 1992 Landers 7.28

59 1992 Big Bear-01 6.46

60 1994 Northridge-01 6.69

61 1991 Sierra Madre 5.61

62 1992 Joshua Tree, CA 6.10

63 1994 Northridge-02 6.05

64 1994 Northridge-03 5.20

65 1994 Northridge-04 5.93

66 1994 Northridge-05 5.13

67 1994 Northridge-06 5.28

68 1998 San Juan Bautista 5.17

69 2000 Yountville 5.00

70 2001 Gulf of California 5.70

71 2002 CA/Baja Border Area 5.31

72 2003 San Simeon, CA 6.50

73 2004 Parkfield-02, CA 6.00
20 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Intra-Event Residuals Analysis of Path, Site, and 

Basin-Depth Effects

The intra-event residuals (εij) are used to test the GK15 

GMPE with respect to distance, site effects, and basin depth. 

In figure 16, the intra-event residuals are plotted in natural 

logarithmic units for PGA and other intensity measures against 

Rrup (0 to 80 km) with means and standard errors shown 

within bins. The bin sizes were adjusted so that each bin has 

approximately the same number of data points. The maximumlikelihood line is dashed, and its intercept (a) and slope (b) are 

provided on top of each plot in order to check for systematic 

bias with respect to the independent predictors. Although the 

data are slightly overpredicted at 3.0 s for distances between 

50 and 60 km, the results generally show no perceptible trend 

within the body of a predictor, indicating that the path-scaling 

−3

0

3

PGA

dashed line is maximum likelihood fit (y=a+bx): a=0.081 and b=−0.00269

−3

0

3

Intra−event Residual

SA at 0.2 s

a=0.030 and b=−0.00100

−3

0

3

SA at 1.0 s

a=0.039 and b=−0.00129

0 20 40 60 80

−3

0

3

R

rup (km)

SA at 3.0 s

a=0.064 and b=−0.00211

Figure 16. Plots showing the distribution of intra-event residuals in natural logarithmic units for peak ground

acceleration (PGA) and spectral acceleration (SA) at 0.2, 1.0, and 3.0 seconds (s) with respect to Rrup (in kilometers 

[km]). Solid horizontal lines indicate the size of the bins and their mean value, vertical solid lines show their standard 

deviation, dashed lines denote a maximum-likelihood fit to residuals, and different symbols indicate different events. 

Note that a and b are intercept and slope of the maximum-likelihood fit, respectively.
Stage 3: Comparisons of Residuals Using the NGA-West2 Database 21

functions in GK15 reasonably represent the data trends. In 

similar plots in figures 17 and 18 for VS30 and Bdepth, the flatness 

of the trends indicates that our linear site response function 

(applicable for VS30≥200 m/s) is a reasonable average for 

California and there is little dependence (underprediction) on 

Bdepth between 200 and 300 meters (m) at 1.0 and 3.0 s.

In table 5, we compare a and b values of the 

maximum-likelihood fit to intra-event residuals and 

distance for the GK15, ASK14, and BSSA14 GMPEs. 

In general, the GMPEs have similar intercept and slope 

values. Neither GMPE has the lowest a and b values for all 

intensity measures, which emphasizes the need to include 

a variety of GMPEs in seismic hazard analysis in order 

to capture the epistemic uncertainty (Al Atik and Youngs, 

2014; Petersen and others, 2014; Bommer and Scherbaum, 

2008).

−3

0

3

PGA

dashed line is maximum likelihood fit (y=a+bx): a=−0.038 and b=0.00010

−3

0

3

Intra−event Residual

SA at 0.2 s

a=0.008 and b=−0.00002

−3

0

3

SA at 1.0 s

a=0.005 and b=−0.00001

200 400 600 800 1000 1200 1400 1600 1800 2000

−3

0

3

VS30 (m/s)

SA at 3.0 s

a=−0.029 and b=0.00008

Figure 17. Plots showing the distribution of intra-event residuals in natural logarithmic units for peak ground

acceleration (PGA) and spectral acceleration (SA) at 0.2, 1.0, and 3.0 seconds (s) with respect to VS30 (in meters 

per second [m/s]). Solid horizontal lines indicate the size of the bins and their mean value, vertical solid lines show 

their standard deviation, dashed lines denote a maximum-likelihood fit to residuals, and different symbols indicate 

different events. Note that a and b are intercept and slope of the maximum-likelihood fit, respectively.
22 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

Table 5. Maximum-likelihood fit to intra-event residuals and distance for three ground-motion prediction equations.

[Ground-motion prediction equations are GK15, Graizer and Kalkan (2015, 2016); ASK14, Abrahamson and others (2014); and BSSA14, Boore and others (2014). Data 

consist of NGA-West2 California events (Rrup or RJB ≤ 80 kilometers, magnitude ≥ 5). Number of records is 975; number of events is 73. See table 4 for list of events]

Intensity measure Intercept (a) Slope (b)

GK15 ASK14 BSSA14 GK15 ASK14 BSSA14

Peak ground acceleration 0.081 −0.011 0.020 −0.00269 0.00037 0.00073

Spectral acceleration at 0.2 seconds 0.030 −0.046 0.001 −0.00100 0.00154 0.00002

Spectral acceleration at 1.0 seconds 0.039 −0.009 −0.015 −0.00129 0.00030 0.00055

Spectral acceleration at 3.0 seconds 0.064 −0.003 −0.016 0.00211 0.00009 0.00058

−3

0

3

PGA

dashed line is maximum likelihood fit (y=a+bx): a=−0.021 and b=−0.00003

−3

0

3

Intra−event Residual

SA at 0.2 s

a=−0.045 and b=−0.00006

−3

0

3

SA at 1.0 s

a=0.031 and b=0.00004

200 400 600 800 1000 1200 1400

−3

0

3

BDepth (m)

SA at 3.0 s

a=0.014 and b=0.00002

Figure 18. Plots 

showing the distribution 

of intra-event residuals 

in natural logarithmic 

units for peak ground 

acceleration (PGA) and 

spectral acceleration 

(SA) at 0.2, 1.0, and 3.0 

seconds (s) with respect 

to Bdepth (in meters [m]). 

Solid horizontal lines 

indicate the size of the 

bins and their mean 

value, vertical solid lines 

show their standard 

deviation, dashed lines 

denote a maximumlikelihood fit to residuals, 

and different symbols 

indicate different events. 

Note that a and b are 

intercept and slope of 

the maximum-likelihood 

fit, respectively.
Stage 3: Comparisons of Residuals Using the NGA-West2 Database 23

Analysis of Source Effects Using Inter-Event 

Residuals

In figures 19 and 20, event terms (ηi) are plotted respectively 

against magnitude in the range 5≤M≤7.9 and the style of faulting 

parameter (F) considering PGA and SA at 0.2, 1.0, and 3.0 s. The 

GK15 GMPE magnitude-scaling function captures the trends from 

various events as evident by the near-zero intercept and near-zero 

slope for the magnitude of the maximum-likelihood fit, indicating 

that there is no significant trend with this parameter or a notable 

offset from zero. For the style-of-faulting parameter, near-zero 

slope for PGA and SA at 0.2 s indicates negligible dependence 

and no systematic bias in the residuals from GK15. Slope values 

smaller than −1.0 for SA at 1.0 and 3.0 s signify that data are 

slightly overpredicted, which is attributed to the limited number of 

events with reverse faulting mechanisms.

Figure 19. Plots showing the distribution of event terms (ηi) in natural logarithmic units for peak ground 

acceleration (PGA) and spectral acceleration (SA) at 0.2, 1.0, and 3.0 seconds (s) with respect to moment 

magnitude. In each plot, the dashed line indicates a maximum-likelihood fit to all event terms; its slope (a) and 

intercept (b) are provided at the top of each plot. 
24 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

−3

0

3

PGA

number of events =73

dashed line is maximum likelihood fit (y=a+bx): a=0.586 and b=−0.555

−3

0

3

Event timing, 

ηi

SA at 0.2 s

a=0.483 and b=−0.456

−3

0

3

SA at 1.0 s

a=1.312 and b=−1.240

5 5256 5237 −3

0

3

SA at 3.0 s

Style of faulting, F

a=1.823 and b=−1.724

Figure 20. Plots showing the distribution of event terms (ηi) in natural logarithmic units for peak ground 

acceleration (PGA) and spectral acceleration (SA) at 0.2, 1.0, and 3.0 seconds (s) with respect to 

style-of-faulting parameter F. In each plot, the dashed line indicates a maximum-likelihood fit to all event terms; its 

slope (a) and intercept (b) are provided at the top of each plot. 
Conclusions 25

In table 6, we compare a and b values of the maximumlikelihood fit to inter-event residuals and moment magnitude. In 

general, the GMPEs result in similar results. GK15 yields the 

lowest values of a and b for PGA. For SA at 0.2 s, BSSA14 and 

GK15 produce similar a and b, which are smaller than those of 

ASK14. For SA at 1.0 s, the intercept and slope are the smallest for 

ASK14, in between for GK15, and largest for BSSA14. For 3.0 s, 

BSSA14 has the lowest values of a and b.

Standard Deviations

Table 7 compares the standard deviations of residuals 

among three GMPEs. The values are computed for four intensity 

measures considering the near-source California subset of the 

NGA-West2 database (see table 4). All standard deviations are 

in natural logarithmic units. The terms of standard deviations 

including inter event, intra event, and the total are very similar 

among the three GMPEs and their values increase with spectral 

period. These results underline that the GK15 GMPE does not 

always have the lowest standard deviations.

Conclusions

We systematically compared the GMPE of Graizer and 

Kalkan (2015, 2016) (GK15) with the NGA-West2 GMPEs of 

Abrahamson and others (2014) (ASK14) and Boore and others 

(2014) (BSSA14) to evaluate the similarities and differences 

among them. The comparisons were conducted in terms of 

median predictions, standard deviations, and analyses of total 

residuals with respect to near-field (within 20 km of the fault) and 

intermediate-field (50 to 70 km from the fault) ground motions 

from major earthquakes in California. We also used a subset of 

the NGA-West2 database, including 975 ground motions within 

80 km of the fault from 73 Californian events ranging from M5 to 

7.36 in order to compare intra- and inter-event residuals among the 

GMPEs. The key findings of this study are as follows:

1. The GK15, ASK14, and BSSA14 GMPEs demonstrate 

median ground-motion estimates for California generally 

within a factor of 1.5–2 for M5–7 events. The largest 

differences are for very large magnitude events with no 

or sparse data and for small magnitude events at long 

Table 6. Maximum-likelihood fit to inter-event residuals and moment magnitude for three ground-motion prediction equations.

[Ground-motion prediction equations are GK15, Graizer and Kalkan (2015, 2016); ASK14, Abrahamson and others (2014); and BSSA14, Boore and others (2014). Data 

consist of NGA-West2 California events (Rrup or RJB ≤ 80 kilometers, magnitude ≥ 5). Number of records is 975; number of events is 73. See table 4 for list of events]

Intensity measure Intercept (a) Slope (b)

GK15 ASK14 BSSA14 GK15 ASK14 BSSA14

Peak ground acceleration 0.230 −0.505 −0.271 −0.039 0.087 0.047

Spectral acceleration at 0.2 seconds −0.188 −0.992 −0.182 0.032 0.170 0.031

Spectral acceleration at 1.0 seconds 0.650 0.244 1.129 −0.112 −0.042 −0.194

Spectral acceleration at 3.0 seconds −0.923 −0.995 0.276 0.158 0.171 −0.047

Table 7. Standard deviations of residuals in natural logarithmic units for three ground-motion prediction equations for near-source 

California earthquake events.

[Ground-motion prediction equations are GK15, Graizer and Kalkan (2015, 2016); ASK14, Abrahamson and others (2014); and BSSA14, Boore and others (2014). Data 

consist of NGA-West2 California events (Rrup or RJB ≤ 80 kilometers, magnitude ≥ 5). Number of records is 975; number of events is 73. See table 4 for list of events]

Intensity measure Inter event (τ) Intra event (φ) Total (σ)

GK15 ASK14 BSSA14 GK15 ASK14 BSSA14 GK15 ASK14 BSSA14

Peak ground acceleration 0.425 0.420 0.377 0.519 0.546 0.529 0.670 0.688 0.649

Spectral acceleration at 0.2 seconds 0.440 0.465 0.415 0.576 0.599 0.568 0.725 0.758 0.703

Spectral acceleration at 1.0 seconds 0.626 0.807 0.635 0.632 0.706 0.622 0.890 1.072 0.889

Spectral acceleration at 3.0 seconds 0.842 1.091 0.818 0.710 0.908 0.691 1.101 1.419 1.071
26 Ground-Motion Predictions for California—Comparisons of Three Prediction Equations

distances. To account for the variable density of data in 

different magnitude and distance bins, Petersen and others 

(2014) introduced additional epistemic uncertainty terms 

for hazard computations.

2. The GK15 GMPE produces similar or slightly smaller

ground motions at very close distances to the fault (within 

~5 km) and at distances of more than 20 km from the fault 

for earthquakes with magnitude larger than 6. Between 

5 and 20 km from the fault, the GK15 GMPE results 

in higher estimates of ground motion than either the 

ASK14 or BSSA14 GMPE does. The distance scaling of 

the GMPEs shows some differences, which stem from 

different functional forms used for distance scaling and 

the different datasets used for constraining the estimation 

coefficients of each GMPE.

3. An additional difference between the GK15 GMPE and 

the other two GMPEs that was not directly assessed in the 

comparisons, but is essential, is related to the inclusion 

of a quality factor (Q0). The GK15 GMPE’s use of a Q0 

that can be changed to suit the region of interest is an 

improvement over other GMPEs. On the other hand, 

GK15 neither includes nonlinear-site response nor 

hanging-wall effect parameters.

4. The standard deviations of original GMPEs are different. 

At periods less than 0.7 s, the GK15 GMPE offers lower 

standard deviations than the ASK14 and BSSA14 GMPEs 

do. At longer periods (>1.0 s), the standard deviations 

of other GMPEs are smaller than those of the GK15 

GMPE. When the subset of the NGA-West2 database is 

considered, the terms of standard deviations (total, intra 

event, and inter event) among the three GMPEs become 

similar; for instance, total standard deviation for the three 

GMPEs is between 0.65 and 0.69 for PGA, 0.7 and 0.76 

for SA at 0.2 s, 0.89 and 1.07 for SA at 1.0 s, and 1.07 and 

1.42 for SA at 3.0 s.

5. The analysis of mixed-effects residuals based on the subset 

of the NGA-West2 database reveals that the GK15 GMPE 

is generally unbiased with respect to its independent 

predictors, including moment magnitude, closest distance to 

fault, VS30, style of faulting, and basin depth.

Data and Resources

The Graizer and Kalkan (2015, 2016) ground-motion 

prediction equation (GMPE) is available for MATLAB and 

Excel at https://earthquake.usgs.gov/research/software/#gmpe

(last accessed on March 1, 2019). A summary (flat-file) of the 

NGA-West2 database is available as an Excel spreadsheet at 

http://peer.berkeley.edu/ngawest2/databases/ (last accessed 

on March 1, 2019). The additional Californian events used in 

development of the Graizer and Kalkan (2015, 2016) GMPE are 

available at https://www.strongmotioncenter.org/ (last accessed 

on March 1, 2019).

References Cited

Abrahamson, N.A., Silva, W.J. and Kamai, R., 2014, Summary 

of the ASK14 Ground Motion Relation for Active Crustal 

Regions: Earthquake Spectra, v. 30, no. 3, p. 1025–1055.

Al Atik, L., and Youngs, R.R., 2014, Epistemic uncertainty for 

NGA-West2 models: Earthquake Spectra, v. 30, no. 3, 

p. 989–1005.

Ancheta, T.D., Darragh, R.B., Stewart, J.P., Seyhan, E., Silva, W.J., 

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Menlo Park Publishing Service Center, California

Manuscript approved March 13, 2020

Edited by Monica Erdman

Layout by Cory Hurd 
Kalkan and Graizer—Ground-Motion Predictions for California—Comparisons of Three Prediction Equations—Open-File Report 2020–1028

ISSN 2331-1258 (online)

https://doi.org/10.3133/ofr20201028