Kappa for Candidate GMPEs

Linda Al Atik Resource Expert

SSHAC Level 3 Southwestern U.S. Ground Motion Characterization WS-1, March 21, 2013

Oakland, CA

Overview

• Kappa controls the high-frequency spectral decay of FAS modeled as:

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Anderson & Hough (1984)

• It is important because: - Significant impact on the results of PSHA for nuclear

PP sensitive to high-frequency GM - Difficult to constrain empirically - Kappa scaling not explicitly captured in the median

prediction of GMPEs

Overview (cont’d)

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Kappa Adjustments

• Applied to adjust empirical GMPEs from one region (host) to use in another region (target) to account for differences in kappa between host and target regions. Usually Vs-k adjustments are needed.

• The process generally involves: – Developing k models for host region GMPEs

– Developing k models for target region

– Selecting k adjustment methods

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Estimating Target Kappa

1. Ground motion recordings in target region: – Requires GM recorded to high frequencies

– Log-linear slope above corner frequency while addressing the path attenuation (ex., Anderson & Hough 1984)

– Full inversion or model fitting to observed acceleration response spectra or Fourier amplitude spectra

– Use of small mag data (M<1) to measure kappa on the low-frequency part of the Fourier disp spectra (Biasi & Smith 2001)

2. Vs30 - kappa relationships: – Chandler et al. (2006), Van Houtte et al. (2011), Silva et al.

(1998), Edwards et al. (2011)

– Few sites with high Vs30; May require extrapolation.

5 See Ktenidou et al. (2013) for more detailed review

Estimating Host GMPE Kappa

Determination of k from GMPE response spectra is a challenge.

1. Inversion of GMPE response spectra to obtain equivalent set of stochastic parameters (Silva ?, Scherbaum et al. 2006)

- Separates source, path and site effects

- Careful choice of parameters to avoid trade-offs; e.g. stress drop, Q, and kappa trade-offs

- Results sensitive to magnitude and distance ranges

6 Scherbaum (2010)

Estimating Host GMPE Kappa (cont’d)

2. Visual comparison of the high-frequency slope of PGA-normalized response spectra with master curves obtained from stochastic simulation for different kappa values (Silva & Darragh 1995, Scherbaum 2010)

- Some parameter trade-offs cancel out when normalizing by PGA

- Still relies on developing stochastic background models for GMPEs

7 Scherbaum (2010)

Estimating Host GMPE Kappa (cont’d)

3. Published Vs30-k relationships

- Rough estimates with a lot of scatter

- Data come from different regions

- Different methods for estimating

kappa

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0.001

0.01

0.1

100 1000

Kap

pa

(se

c)

Vs30 (m/sec)

Chandler et al. 2006 - Worldwide

Douglas et al. 2010 - France

Drouet et al. 2010 - France

Edwards et al. 2011 - Switzerland

Silva et al. 1998 - CA

Van Houtte et al. 2011 - Japan

Van Houtte et al. 2011 - NGA

Chandler et al. 2006 - Model

Silva et al. 1998 - Model

Van Houtte et al. 2011 - Model

Edwards et al. 2011 - Model (LIN-LIN)

Estimating Host GMPE Kappa (cont’d)

4. K-famp relationships (Al Atik 2011)

- Relationships developed from response spectra generated using stochastic simulations with a range of kappa values

- Different definitions for famp; e.g. highest frequency that corresponds to Sa = logarithmic average of PGA and peak Sa

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0.01

0.1

1

1 10

Kap

pa

(se

c)

famp(Hz)

Coastal CA Model

WUS Profile-620m/s WUS Profile-800m/s WUS Profile-100m/s

Estimating Host GMPE Kappa (cont’d)

4. K-famp relationships (Al Atik 2011) – cont’d

– Not very robust. Different famp definitions lead to different kappa values

– Generally leads to very high kappa values

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GMPE VS30 (m/s) Kappa (s) famp

AbSi08 800

0.0495 Geometric mean of the 2 frequencies corresponding to 5% spectral

acceleration below the peak of the acceleration response spectrum and on

both sides of the peak spectral acceleration.

0.0671 Highest frequency that corresponds to a spectral acceleration value equal to

double the peak ground acceleration.

0.0606 Highest frequency that corresponds to Sa = logarithmic average of PGA and peak Sa

Estimating Host GMPE Kappa (cont’d)

5. Slope of IRVT-derived equivalent FAS (Al Atik et al. 2013)

- STRATA is used to derive FAS that are compatible with GMPE response spectra

- High frequency slope of FAS is used to estimate kappa based on the Anderson & Hough (1984) kappa scaling function

- Use scenarios with magnitude 5, 6, 7 and distances of 5, 10 and 20km to estimate average kappa for a relatively high VS30

- Q effect is considered to be negligible

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IRVT Approach – CB08

IRVT

0

0.1

0.2

0.3

0.4

0.5

0.1 1 10 100

PSA

(g)

Frequency (hz)

M6 - Rjb 10km - Vs 620m/sec

Sa GMPE

0

0.1

0.2

0.3

0.4

0.5

0.1 1 10 100

PSA

(g)

Frequency (hz)

M6 - Rjb 10km - Vs 620m/sec

Sa GMPE Sa RVT-Calc

0.0001

0.001

0.01

0.1

0 20 40 60 80 100

FA (

g-s)

Frequency (hz)

M6 - Rjb 10km - Vs 620m/sec

FAS RVT-Calc

0.0001

0.001

0.01

0.1

0 20 40 60 80 100

FA (

g-s)

Frequency (hz)

M6 - Rjb 10km - Vs 620m/sec

FAS RVT-Calc Kappa Scaling

Average host kappa = 0.041 sec, stdev = 0.0015

IRVT Approach – PRP Results

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GMPE VS30 (m/s) Kappa Ave StDev

AbSi08

620 0.0412 0.0005

800 0.0407 0.0004

1000 0.0394 0.0009

BoAt08

620 0.0404 0.0010

800 0.0402 0.0010

1000 0.0400 0.0011

CaBo08

620 0.0405 0.0016

800 0.0398 0.0015

1000 0.0385 0.0017

ChYo08

620 0.0379 0.0007

800 0.0353 0.0007

1000 0.0339 0.0007

Zhao06

500 0.0425 0.0013

700 0.0376 0.0017

900 0.0376 0.0017

AkBo10

600 0.0424 0.0027

800 0.0367 0.0021

1000 0.0367 0.0021

AtBo06

2000 0.0051 0.0021

2200 0.0051 0.0021

2800 0.0051 0.0021

Toro02 2800 0.0081 0.0009

AkCa10

800 0.0445 0.0023

950 0.0442 0.0024

1100 0.0440 0.0024

Bi11 800 0.0445 0.0069

950 0.0413 0.0055

Available Approaches for k Adjustments

1. Hybrid Empirical Approach (Campbell 2003, 2004)

– Applied and considered for site adjustments on several projects (Europe, PEGASOS Refin. Project, South Africa PSHA Project…)

2. IRVT Approach (Al Atik et al. 2012)

– Developed for site adjustments for the PEGASOS Refin. Project

– Considered on other projects (South Africa PSHA Project, Blue Castle Project)

3. Empirical Approach (Al Atik & Abrahamson 2012)

– Developed for site adjustments for the PEGASOS Refin. Project

– Considered on other projects (South Africa PSHA Project, Blue Castle Poject) 14

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References (I)

• Al Atik, L. (2011). Summary of updated kappa-fpeak relationships. Report submitted to PRP.

• Al Atik, L. and N. Abrahamson (2012). Kappa scaling using empirical ground motion data. Report prepared for the PEGASOS Refinement Project.

• Al Atik, L., A. Kottke, N. Abrahamson, and J. Hollenback (2013). Kappa scaling of ground motion prediction equations using IRVT approach. Paper submitted to BSSA.

• Abrahamson, N., and W. Silva (2008). Summary of the Abrahamson & Silva NGA ground-motion Relations, Earthquake Spectra, 24(1), 67-97.

• Akkar, S. , and J. J. Bommer (2010). Empirical equations for the prediction of spectral accelerations in Europe, the Mediterranean and the Middle East, Seismological Research Letters, 81(2), 195-206.

• Akkar, S. and Cagnan, Z., 2010. A local ground-motion predictive model for Turkey and its comparison with other regional and global ground-motion models, Bulletin of the Seismological Society of America, 100, 2978-2995.

• Anderson, J. G., and S. E. Hough (1984). A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencie, Bulletin of the Seismological Society of America, 74(5), 1969–1993.

• Atkinson, G. M. , and D. M. Boore (2006). Earthquake ground-motion prediction equations for eastern north America, Bulletin of the Seismological Society of America, 97(3), 2181- 2205.

• Biasi, G.P., and K.D. Smith (2001). Site effects for seismic monitoring stations in the vicinity of Yucca Mountain, Nevada, MOL20011204.0045, a report prepared for the US DOE/University and Community College System of Nevada (UCCSN) Cooperative Agreement.

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References (II)

• Bindi, D., Pacor, F., Luzi, L., Puglia, R., Massa, M., Ameri, G., and R. Paolucci, (2011): Ground motion prediction equations derived from the Italian strong motion database. Bulletin of Earthquake Engineering, 9, 6, 1899-1920.

• Boore, D. M., and G. M. Atkinson (2008). Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s, Earthquake Spectra, 24(1), 99-138.

• Campbell, K.W. (2003). Prediction of strong ground motion using the hybrid empirical method and its use in the development of ground-motion (attenuation) relations in eastern North America. Bull. Seism. Soc. Am., 93, 1012–1033.

• Campbell, K.W. (2004). Erratum to Prediction of strong ground motion using the hybrid empirical method and its use in the development of ground-motion (attenuation) relations in Eastern North America, Bulletin of the Seismological Society of America, 94(6), 2418.

• Campbell, K. W. , and Y. Bozorgnia (2008). NGA ground motion model for the geometric mean horizontal component of PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01 to 10 s, Earthquake Spectra, 24(1), 139-171.

• Chandler, A.M., N.T.K. Lam, and H.H. Tsang (2006). Near-surface attenuation modeling based on rock shear-wave velocity profile. Soil Dyn. Earthq. Eng., 26, 1004–1014.

• Chiou, B. S. J. , and R. R. Youngs (2008). An NGA model for the average horizontal component of peak ground motion and response spectra, Earthquake Spectra, 24(1), 173-215.

• Douglas, J., P. Gehl, L.F. Bonilla, and C. Gelis (2010). A kappa model for mainland France. Pure Appl. Geophys., 167, 1303–1315.

References (III)

• Edwards, B., D. Faeh, and D. Giardini (2011). Attenuation of seismic shear wave energy in Switzerland. Geophys. J. Int., 185, 967–984.

• Ktenidou, O-J, F. Cotton, N. Abrahamson, and J. Anderson (2013). Don’t call it kappa: Add a subscript, Seism. Res. Letters (in press).

• Silva, W.J. and R. Darragh (1995). Engineering characterization of earthquake strong ground motion recorded at rock sites. Palo Alto, Electric Power Research Institute, TR-102261.

• Silva, W., R.B. Darragh, N. Gregor, G. Martin, N. Abrahamson, and C. Kircher (1998). Reassessment of site coefficients and near-fault factors for building code provisions. Technical Report Program Element II: 98-HQ-GR-1010, Pacific Engineering and Analysis, El Cerrito, USA.

• Scherbaum F., F. Cotton, and H. Staedtke (2006). The estimation of minimum-misfit stochastic models from empirical ground-motion prediction equations, Bulletin of the Seismological Society of America, 96, 427–445.

• Scherbaum F. (2010). Determination of Vs-k correction factors, Report for PEGASUS Refinement Project (PRP), TP2-TB-1036.

• Toro, G. R. (2002). Modification of the Toro et al. (1997) attenuation equations for large magnitudes and short distances, Technical Report, Risk Engineering.

• Van Houtte, C., S. Drouet, and F. Cotton (2011). Analysis of the origins of κ (kappa) to compute hard rock to rock adjustment factors for GMPEs, Bulletin of the Seismological Society of America 91, in press.

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References (IV)

• Zhao, J. X., K. Irikura, J. Zhang, Y. Fukushima, Paul G. Somerville, Akihiro Asano, Yuki Ohno, Taishi Oouchi, Toshimasa Takahashi, and Hiroshi Ogawa (2006). An empirical site-classification method for strong-motion stations in Japan using H/V response spectral ratio, Bulletin of the Seismological Society of America, 96(3), 914-925.

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