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G-16 and G-16v2 GROUND MOTION PREDICTION
EQUATIONS FOR THE CENTRAL AND EASTERN NORTH AMERICA
Vladimir Graizer U. S. Nuclear Regulatory Commission
2018 NSHM Update Workshop Newark, CA
March 7, 2018 1
Introduction and Dataset Used
• Two ground motion prediction equations (GMPEs) for the Central and Eastern North America (CENA) have been developed in 2016: G-16 and G-16v2 (published in 2017).
• Both models are based on the Next Generation Attenuation NGA-East database for the horizontal peak ground acceleration (PGA) and 5%-damped pseudo spectral acceleration (PSA) RotD50 component (Goulet et al., 2014). – For the GMPEs development I used subset of 5026 data points with
M≥3.75 and fault distances R≤1000 km. – Data with lower magnitudes and larger distances were not used. – The dataset includes 48 earthquakes from different regions in the
CENA including the Mid-Continent and Gulf Coast regions.
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September 2014 NGA-East Database (M>3.75)
3
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
1 10 100 1000
Mag
nitu
de
Rupture dist, km
Magnitude - Rupture Distance
Earthquake…
Data in the database are sparse and cover mostly a limited range of moment magnitudes M<6.0 with only three data points with M>6 from the 1985 M=6.8 Nahanni earthquakes.
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
100 1000
PGA,
g
Vs30, m/sec
PGA - Vs30
PGA
Effect of non-linearity is not significant since only 2 data points with VS30<300 m/s are ~ 0.1 g.
4
100
1000
10000
0.01 0.1 1 10
Num
ber o
f Dat
a Po
ints
Period, s
Period Dependence of the Number of Recordings in the Dataset
Number of Records
There is a clear deficiency of high-frequency recordings in the NGA-East database and the dataset used.
G-16 and G-16v2 Attenuation Models • Developed GMPEs models are based on the same modular filter based
approach developed for active tectonic environment by Graizer and Kalkan (2007, 2009, and 2011).
• There are a number of simplifications relative to the original model developed for active tectonic environment: – No bump (oversaturation) in the near-field since there are no
empirical data to support it; – No basin effect; and – No distinguishing between different fault styles.
• G-16 model has a uniform attenuation slope.
• G-16v2 is an alternative and not a replacement to the G-16 model.
• In contrast to the G-16 model, the G-16v2 model has bilinear attenuation
slope. 5
PGA CENA model
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1 2 3 4 YPGA G G G G ε= × × × ×
2
1
1
2 22 2 2
2 22 2 2
1 , 701 ( ) 4 ( / )
, 70[1 ] 4
( , )
rup
rup
R
R
rup
rup rup
ruprup rup
R kmR R D R R
w R kmR R D R R
G M R
< ⇒− +
≥ ⇒− +
=
The G-16v2 model has bilinear slope with different attenuation functions:
The G1 filter is for magnitude scaling, G2 is for core attenuation equations, G3 is for apparent (intrinsic and scattering) attenuation correction, and G4 is for shallow site amplification.
Where M is moment magnitude, Rrup is the distance to the fault rupture and R2 is the corner distance defining the plateau without significant attenuation of ground motion.
Constraining Bilinear Slope
• Conducted testing of the slope of attenuation of the response spectra amplitudes at the 9 spectral frequencies between 0.1 and 100 Hz. Average slope of the distance attenuation within the 50-70 km distance from the fault is about -1.0 at 7 out of 9 spectral frequencies. For frequencies of 0.5 and 0.2 Hz the slope is about -1.3.
• Taking into account that total attenuation is a combination of geometrical spreading, intrinsic and scattering attenuation it was concluded that classical body-waves geometrical spreading of R-1 best fit response spectral accelerations at distances up to 70 km.
• Examined the recorded data for estimating where the change of slope occurs varying the distance from 50 to 100 km, and concluded that distance of about 70 km best fits the transition.
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Near-Fault Magnitude and PGA Scaling
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Constraining GMPE coefficients for large magnitudes based on: • Ratios of amplitude of earthquakes
with 3.75<M<6 from the NGA-East database relative to the NGA-West;
• Average stress-drop ratio between CENA and Western US (2-3 times higher); and
• Check against recent ground motion simulations ratios between M=5.0 and higher M (Atkinson and Assatourians, 2015; Graves and Pitarka, 2015; Olsen and Takedatsu, 2015).
0.01
0.1
1
10
3 4 5 6 7 8 9
Spec
tral
Acc
eler
atio
n, g
Magnitude
PGA and 100 Hz Magnitude Scaling at Rrup=0.1 km
PGA
100 Hz G-16v2
100 Hz G-16 orig
VS30 Site Correction
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y = -0.044ln(x) + 0.2701
-4
-3
-2
-1
0
1
2
3
4
100 1000
Resi
dual
s in
ln u
nits
Vs30, m/s
5 Hz Residuals
0-800km
Log. (0-800km)
y = 0.0464ln(x) - 0.241
-4
-3
-2
-1
0
1
2
3
4
100 1000
Resi
dual
s in
ln u
nits
Vs30, m/s
0.5 Hz Residuals
0-800km
Log. (0-800km)
0.8
1
1.2
1.4
1.6
1.8
2
2.2
0.1 1 10 100
Ampl
ifica
tion
Frequency, Hz
Site Amplification Function from Hard Rock
2800
450/2800
760/2800
1100/2800
1500/2800
Frankel 1996
Apparent Attenuation of Spectral Accelerations
10
Introduced is a new parameter: attenuation factor QSA(f) representing apparent (intrinsic and scattering) attenuation of 5% damped spectral accelerations. This parameter is different from the classical seismological Q(f) determined from Fourier spectra of S-, Lg- or coda-waves. To get the QSA(f) factor, inversions were performed for the 15 frequencies between 0.1 to 40 Hz using different distance ranges. Apparent attenuation of SA amplitudes were found to be significantly different from the typical seismological estimates for the CENA.
120<R<800km y = 169.96x1.0003
200<R<800km y = 174.45x0.9903
400<R<800km y = 183.83x1.0102
400<R<1000km y = 192.81x1.0028
10
100
1000
10000
0.1 1 10 100
QSA
-fact
or
Frequency, Hz
QSA - factor
120<R<800 km200<R<800 km400<R<800 km400<R<1000 kmPower (120<R<800 km)Power (200<R<800 km)Power (400<R<800 km)Power (400<R<1000 km)
Comparing QSA(f) with Seismological Q(f)
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y = 186.35x0.9933
10
100
1000
10000
0.1 1 10 100
QSA
-fact
or
Frequency, Hz
QSA - factor
HF 120-800km
HF 200-800km
HF 300-800km
HF 400-800km
HF 400-1000km
MR 120-800km
MR 200-800km
MR 300-800km
MR 400-800km
MR 400-1000km
LF 120-800km
LF 200-800km
LF 300-800km
LF 400-800km
LF 400-1000km
Average
G-16v2 approximation
Q, Pasyanos, 2015
Q, Erickson et al. 2004
Power (Average)
0.99( ) 186SAQ f f=
In a frequency range of 0.1-40 Hz the data can be well represented by the power law with the average dependence of:
QSA(f) should be estimated based on actual response spectral acceleration data, and not transferred from seismological measurements.
Examples SA Functions at R = 1 and 20 km
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In contrast to the WUS, CENA response spectra flatten at much higher frequencies. In G-16 and G-16v2 models response spectra flatten completely at a frequency of 250 Hz and this corresponds to the value of PGA.
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
0.001 0.01 0.1 1 10
SA, g
Period, s
Spectral Acceleration at R=1 km, Vs=2800 m/s
M=4.5 G-16v2
M=5.5 G-16v2
M=6.5 G-16v2
M=7.5 G-16v2
M=4.5 G-16 orig
M=5.5 G-16 orig
M=6.5 G-16 orig
M=7.5 G-16 orig
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
0.001 0.01 0.1 1 10
SA, g
Period, s
Spectral Acceleration at R=20 km, Vs=2800 m/s
M=4.5 G-16v2
M=5.5 G-16v2
M=6.5 G-16v2
M=7.5 G-16v2
M=4.5 G-16 orig
M=5.5 G-16 orig
M=6.5 G-16 orig
M=7.5 G-16 orig
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Magnitude Scaling for Hard Rock Vs=2800 m/s
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
4 5 6 7 8 9
SA, g
Magnitude
Magnitude Scaling 100 Hz
G-16v2, R=2 km
G-16v2, R=20 km
G-16v2, R=50 km
G-16v2, R=200 km
R=2 km G-16 orig
R=20 km G-16 orig
R=50 km G-16 orig
R=200 km G-16 orig
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
4 5 6 7 8 9
SA, g
Magnitude
Magnitude Scaling 1 Hz
G-16v2, R=2 km
G-16v2, R=20 km
G-16v2, R=50 km
G-16v2, R=200 km
R=2 km G-16 orig
R=20 km G-16 orig
R=50 km G-16 orig
R=200 km G-16 orig
Comparisons of the G-16v2 SA functions for CENA with GK15 for WUS
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At fault distances up to about 100 km long period components of response spectra are similar in the East and West. At larger distances eastern data are higher at all periods due to higher Qsa.
Comparison of G-16v2 Model with G-16 and Individual CENA Models Used by USGS (2014)
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0.001
0.01
0.1
1
10
1 10 100 1000
1 H
z SA
(g)
Distance (km)
Median 1 Hz SA: M=7.5
Tav&Pez
Campbell
Somer M7.5
SilvaEA02
ToroEA 97
AtkBoore 140
AtkBoore-200
G-16v2
G-16
0.001
0.01
0.1
1
10
1 10 100 1000
100
Hz
SA (g
)
Distance (km)
Median 100 Hz: M=7.5
Tav&Pez
Campbell
Somer
SilvaEA02
ToroEA 97
AtkBoore 140
AtkBoore-200
G-16v2
G-16
Distance Residuals (in Natural Log Units)
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y = 3.59E-07x + 9.59E-05
-4
-3
-2
-1
0
1
2
3
4
1 10 100 1000
Resi
dual
s in
ln u
nits
Rupture dist, km
25 Hz Residuals
Residuals 800 km
Linear (Residuals 800 km)
y = -1.78E-07x - 2.20E-04
-4
-3
-2
-1
0
1
2
3
4
1 10 100 1000
Resi
dual
s in
ln u
nits
Rupture dist, km
2.5 Hz Residuals
Residuals 800 km
Linear (Residuals 800 km)
y = 4.32E-07x + 3.92E-04
-4
-3
-2
-1
0
1
2
3
4
1 10 100 1000
Resi
dual
s in
ln u
nits
Rupture dist, km
1.0 Hz Residuals
Residuals 800 km
Linear (Residuals 800 km)
y = -1.12E-06x + 1.71E-04
-4
-3
-2
-1
0
1
2
3
4
1 10 100 1000
Resi
dual
s in
ln u
nits
Rupture dist, km
0.5 Hz Residuals
Residuals 800km
Linear (Residuals 800km)
Vs30 Residuals (in Natural Log Units)
17
Comparison of Models Predictions with Data for M4.0 and M5.5
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Standard Deviations of G-16v2 and G-16 Models
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.01 0.1 1 10
Sigm
a (L
n U
nits
)
Period, s
Standard Deviations
G-16v2
G-16v2 Phi
G-16v2 Tau
G-16
G-16 Phi
G-16 Tau
2 2σ φ τ= +
Total (σ) and within-event (ϕ) and between-event (τ) standard deviations:
Bilinear G-16v2 model demonstrates slight improvement in σ for most periods.
Summary of the G-16 and G-16v2 Models • GMPEs Summary:
– CENA stable continental environment – Functional forms work for 4.0<Mw<8.5 – Rupture distances 0<R<1000 km – Period range 0.01 to 10 sec – S-wave velocities of 250<VS30<2800 m/s
• Apparent attenuation of response spectral amplitudes QSA(f) in G-16v2 should be
estimated based on actual response spectral acceleration data, and not transferred from seismological measurements.
• Models are published in: G-16 – Bull. Seismol. Soc. Am. 2016, Vol. 106, No. 4, 1600-1612. G-16v2 - Bull. Seismol. Soc. Am. 2017, Vol. 107, No. 2, 869-886.
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