GROUND MOTION PREDICTION EQUATIONS FOR THE

CENTRAL AND EASTERN NORTH AMERICA

Vladimir Graizer U. S. Nuclear Regulatory Commission

16th World Conference on Earthquake Engineering Santiago, Chile

January 12, 2017 1

Introduction and Dataset Used

• Two ground motion prediction equations (GMPEs) for the Central and Eastern North America (CENA) have been recently developed: G-16 and G-16v2.

• 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). – Database for GMPEs uses subset of 5026 data points with M≥3.75 and

fault distances R≤1000 km was used. – 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.

2

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.

PGA Attenuation Model • 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-16v2 is an alternative to the G-16 model.

• In contrast to the G-16 model, the G-16v2 model has bilinear attenuation

slope.

4

PGA CENA model

5

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 new 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 the data 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.

6

Near-Fault Magnitude and PGA Scaling

7

Constraining GMPE coefficients 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

8

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

9

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. 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)

10

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

11

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

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

Comparison of G-16v2 Model with G-16 and Individual CENA Models Used by USGS (2014)

13

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

Residuals (in Natural Log Units)

14

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)

Standard Deviations of G-16v2 and G-16 Models

15

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:

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 450<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.

• The G-16 model is published in Bulletin of the Seismological Society of America Vol. 106, No.4, and the G-16v2 model is scheduled for publication in April 2017, Vol. 107, No.2.

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