Single-Station Sigma Using NGA-West2 Data

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

Oakland, CA

Linda Al Atik

Resource Expert

Sigma Background

GMPEs:

2

ln ( , , , 30 ,...)es es e e es s esY T M F R Vs

Bommer (2010)

Residual Components

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es e esB W

eB : Between-event (inter-event) residual for earthquake e

esW : Within-event (intra-event) residual at station s for earthquake e

2 2

: Between-event standard deviation

: Within-event standard deviation

Strasser et al. (2009)

Single-Station Sigma: Approach

• Given multiple recordings of GM at an individual site, S, allows estimating the systematic site effects, , and removing them from the GM variability: Single-Station Sigma

• represents the systematic deviation of the observed amplification at this site from the median amplification predicted by the model

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2 SS S

2 SS S

Single-Station Sigma: Approach (cont’d)

• : systematic deviation of the observed amplification at this site from the median amplification at this site predicted by the model

• :Single-station within-event standard deviation

• :Single-station standard deviation

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2es es sWS W S S

2 SS S

SS

2 2

SS SS

SS

Application to PSHA

• Removing the site-to-site residual from the GM variability leads to a reduced aleatory variability

• However, the median GM at the SITE needs to be estimated:

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( ) ( , , ,...) 2es es e es s e esln Y T M R T S S B WS

If site-specific knowledge is limited, use of single-station sigma SHOULD be accompanied with an INCREASE in

epistemic uncertainty

Terminology

Ergodic Partially Non-Ergodic

Within-event residual, Single-station within-event residual,

Within-event standard deviation, Single-station within-event standard deviation,

Total standard deviation, Single-station standard deviation,

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esW 2es es sWS W S S

SS

2 2 2 2

SS SS

Al Atik et al. (2010)

Data Needs

• Minimum of 5 recordings per earthquake in order to compute a reliable event term,

• Minimum of 5 recordings per site in order to compute the average site-to-site residual,

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eB

2 sS S

NGA-West2 Dataset

• CA SMM and global LM dataset:

– 21,539 recordings from 600 eqks

– 163 recordings with Sa = -999 eliminated

– 3 recordings missing magnitude eliminated

– 34 recordings missing distance measures eliminated

– 12 recordings missing station info eliminated

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21,327 recordings from 578 eqks at 4,096 stations

NGA-West2 Dataset with Periods

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0

5000

10000

15000

20000

25000

0.01 0.1 1 10

Nb

of

Re

cord

ings

Period (sec)

NGA-West2: Data Distribution

• CA: 15,264 recs

• Taiwan: 1,986 recs

• Japan: 1,946 recs

• China: 1,332 recs

• Italy: 333 recs

• NZ: 217 recs

• Other (Alaska, Iran, Greece, Turkey, …): 249 recs

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3

4

5

6

7

8

0 200 400 600 800 1000 1200 1400 1600

Mag

nit

ud

e

Rrup (km)

California Japan China Italy New Zealand Taiwan

21,327 recordings from 578 eqks of 2.99 ≤ M ≤ 7.9

NGA-West2: Data Distribution (cont’d)

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Total number of earthquakes: 578 408 earthquakes with 5 or more recordings

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8 9 10 > 10

Fre

qu

en

cy

Nb. of Recordings per Eqk

NGA-West2: Data Distribution (cont’d)

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For events with minimum of 5 recordings: Total number of stations: 4,012 838 stations have 5 recordings or more 399 stations have 10 recordings or more

0

200

400

600

800

1000

1200

1400

1600

1800

1 2 3 4 5 6 7 8 9 10 > 10

Fre

qu

en

cy

Nb. of Recordings per Station

NGA-West2: Data Distribution (cont’d)

Minimum of 5 recs per eqk and per station:

15,592 recs from 364 eqks at 838 stations

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3

4

5

6

7

8

0 200 400 600 800 1000 1200 1400 1600

Mag

nit

ud

e

Rrup (km)

California Taiwan China Italy

Region Nrecs CA 13,162

Taiwan 1,339

China 1,076

Italy 15

NGA-West2: Data Distribution (cont’d)

Minimum of 5 recs per eqk and per station:

15,592 recs from 364 eqks at 838 stations

15

0

1000

2000

3000

4000

5000

6000

7000

50 150 250 500 700 900 1100 > 1200

Fre

qu

en

cy o

f R

ecs

Vs30 (m/sec)

Preliminary PhiSS Results: NGA-West2

Using preliminary AS13 within-event residuals:

– Minimum of 3 recs per eqk

– 15,619 recs from 326 eqks at 3,164 stations

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Region Nrecs CA 12,025

Japan 1,700

Taiwan 1,535

Italy 175

New Zealand 72

China 48

Iran + Turkey 43

Others 21 3

4

5

6

7

8

0 50 100 150 200 250 300 350 400

Mag

nit

ud

e

Rrup (km)

CA Japan Taiwan Other

AS13 Dataset at PGA

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0

200

400

600

800

1000

1200

1400

1 2 3 4 5 6 7 8 9 10 >10

Fre

qu

en

cy

Nb. of Recordings per Station

Total number of stations: 3,164 675 stations have 5 recordings or more 322 stations have 10 recordings or more

AS13 Dataset at PGA (cont’d)

Minimum of 5 recs per station: 11,188 recs

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Region Nrecs CA 10,123

Taiwan 1,049

Italy 16

3

4

5

6

7

8

0 50 100 150 200 250 300 350 400

Mag

nit

ud

e

Rrup (km)

CA Taiwan Italy

AS13 Dataset at PGA (cont’d)

Minimum of 5 recs per station: 11,188 recs

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0

500

1000

1500

2000

2500

3000

3500

4000

4500

50 150 250 500 700 900 1100 > 1200

Freq

uen

cy o

f Rec

s

Vs30 (m/sec)

Preliminary Results

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0.3

0.4

0.5

0.6

0.7

0.8

0.01 0.1 1 10

Stan

dar

d D

evi

atio

n

Period (sec)

Phi PhiSS

0.3

0.4

0.5

0.6

0.7

0.8

0.01 0.1 1 10

Stan

dar

d D

evi

atio

n

Period (sec)

PhiSS All PhiSS-CA PhiSS-Taiwan

CA PhiSS Preliminary Results

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80

Ph

iSS s

Nb of Recordings

PGA

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50 60 70 80

Ph

iSS s

Nb of Recordings

T 1 sec

Magnitude Dependence: CA

22

0

0.1

0.2

0.3

0.4

0.5

0.6

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

Ph

iSS

Mag

PGA

0

0.1

0.2

0.3

0.4

0.5

0.6

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5

Ph

iSS

Mag

T 1.0 sec

Distance Dependence: CA

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 50 100 150 200 250

Ph

iSS

Rrup (km)

PGA

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 50 100 150 200 250

Ph

iSS

Rrup (km)

T 1.0 sec

M-R Dependence: CA

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0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250

Ph

iSS

Rrup (km)

PGA

M 3 to 5 M 5 to 6 M 6 to 8

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250

Ph

iSS

Rrup (km)

T 1.0 sec

M 3 to 5 M 5 to 6 M 6 to 8

VS30 Dependence: CA

25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

100 300 500 700 900 1100 1300

Ph

iSS

Vs30 (m/sec)

PGA

0

0.1

0.2

0.3

0.4

0.5

0.6

100 300 500 700 900 1100 1300

Ph

iSS

Vs30 (m/sec)

T 1.0 sec

References (I)

• Al Atik, L., N. Abrahamson, J. Bommer, F. Scherbaum, F. Cotton, N., Kuehn (2010). The variability of ground-motion prediction models and its components, Seism. Res. Let., 81(5), 794-801.

• Bommer, J. J. (2010). Sigma: What it is, why it matters and what we can do with it, NGA-East workshop presentation, February 10, 2010.

• Strasser, F.O., N.A. Abrahamson and J.J. Bommer (2009). Sigma: Issues, insights and challenges, Seism. Res. Let., 80(1), 40-54.

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