[PPT] - F OR P ROBABILISTIC S EISMIC H AZARD A NALYSIS : C ASE S TUDY OF T PowerPoint Presentation

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5th IASPEI / IAEE International Symposium

Effects of Surface Geology on Seismic Motion

NTU

SELECTION OF GROUND-MOTION PREDICTION EQUATIONS FOR PROBABILISTIC SEISMIC HAZARD ANALYSIS : CASE STUDY OF TAIWAN

Phung-Van Bang, Chin-Hsiung Loh, Norman Abrahamson Department of Civil Engineering University of California, Berkeley National Taiwan University USA Taipei, TAIWAN August 15-17, 2016 Taipei, TAIWAN

UC-Berkeley

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National Taiwan University Department of Civil Engineering

In 2015-June National Center for Research on Earthquake Engineering (NCREE), supported by Tai-Power Company (to response the request of NTTF 2.1 Seismic Reevaluation), launched NUREG/CR– 6372 researches (SSHAC), in understanding and documenting lessons learned from recent PSHAs conducted at the higher SSHAC Levels. (follow the experiences of research on Diablo Canyon Nuclear Power plant)

Background

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Content

◆ Introduction ◆ Selection of candidate GMPEs for PSHA ◆ Visualization technique for GMPE selection ◆ Selection of GMPE common form ◆ Visualization of model space ◆ Calculate GMPE weighting ◆ Conclusion

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National Taiwan University Department of Civil Engineering

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Peak Ground Acceleration (PGA) Attenuation

Hazard Curve

Introduction

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Selection of appropriate GMPEs for PSHA

1. Need best estimate of GMPE
2. Consider range of alternative models to

characterize the uncertainty in the GMPEs Type of uncertainty in GMPEs

1. Aleatory uncertainty:

expressing random variability of amplitude about a median prediction equation,  can be handled in a PSHA by integrating over the distribution

f ground-motion amplitude about the median,
2. Espistemic uncertainty:

expressing uncertainty concerning the correct value of the median,  can be handled by considering alternative GMPEs in a logic tree format (must capture uncertainties in form & amplitude),

Introduction

Sensitivity analysis of the proposed weights for GMPEs on the seismic hazard.

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GMPE GMPE Acronym Regions Magnitude Interval Primary distance Style of faulting Site effect Component Number of records and events (Abrahamson, N. A., Silva, W. J., and Kamai, R., 2014)

ASK14 Global

Mw (3.0-8.5) Rrup (<300km) SS,NML,REV Vs30 PGA,PGV,PSA in GMRotI50 15750 and 326 (Boore, D. M., Stewart, J. P ., Seyhan, E., and Atkinson, G. M., 2014)

BSSA14 Global

Mw (3.0-8.5) Rjb(<300km) U,SS,NML,REV Vs30 PGA,PGV,PSA in GMRotI50 ~16000 and ~400 (Campbell, K. W., and Bozorgnia, Y., 2014)

CB14 Global

Mw (3.3-8.5) Rrup (<300km) SS,NML,REV Vs30 PGA,PGV,PSA in GMRotI50 15521 and 322 (Chiou, B. S-J., and Youngs, R. R., 2014)

CY14 Global

Mw (3.5-8.5) Rrup (<300km) SS,NML,REV Vs30 PGA,PGV,PSA in GMRotI50 12444 and 300 (Idriss, 2014)

Id14 Global

Mw (5-8.5) Rrup (<150km) SS,NML,REV Vs30 PGA,PGV,PSA in GMRotI50 7135 and 160 (Akkar, S., Sandikkaya, M. A., and Bommer, J. J., 2014)

ASB14 EU and ME

Mw (4-7.5) Rjb (<200km) SS,NML,REV Vs30 PGA,PGV,PSA in GM 1041 and 221 (Bindi D., Massa M., Luzi L., Ameri G., Pacor F., Puglia R., and Augliera, P., 2014)

Bi14 EU and ME

Mw(4-7.6) Rjb (<300km) U,SS,NML,REV Vs30 PGA,PGV,PSA in GM 2126 and 365 (Graizer, V., and Kalkan, E., 2015)

GK15 Global

Mw(5.0-8.0) Rrup (<250Km) SS,NML,REV Vs30 PGA,PGV,PSA in GM 2583 and 47 Zhao et al. 2016

Zhao16 Japan

Mw(5.0-7.3) Rrup(<300km ) FN,SS Dummy variable PGA, PSA in GM 6482 and 76 (cr), 47(mum) Özkan Kale, Sinan Akkar, Anooshiravan Ansari, and Hossein Hamzehloo

Ka15 Turkey and Iran

Mw(4.0-8.0) Rjb(<200km) U,SS,NML,RE V Vs30 PGA, PGV, PSA in GM 670(Tur),528(Ir) Lin , P.S et al. 2011

Lin11 Taiwan

Mw(5.0-7.6) Rrup(<240km)

no

PGA,PSA in GM 5268 and 52 (Cauzzi, C., Faccioli, E., Vanini, M., and Bianchini, A., 2014)

Ca14 Global

Mw(4.5-7.9) Rrup (<150km) U,SS,NML,REV Vs30 PGA,PGV,PSA in GM 1880 and 98

General Feature of Candidate GMPEs

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Selected GMPEs: ASK14, BSSA14, CB14, CY14, Id14, GK15,

ASB14, Bi14, Ca14 Lin11, KAAH15-Turkey, KAAH15-Iran, Zhao16 (total of 13 models)

2 10 100 200 10

3

10

2

10

1

10

RRUP,km PSA(T=0.01s),g M=6; Vs30=760 m/s Sof=0

ASK14 BSSA14 CB14 CY14 Id14 ASB14 Bi14 Ca14 GK15 LLCS11 KAAH15-Turkey KAAH15-Iran Zhao16

5 5.5 6 6.5 7 7.5 8 10

2

10

1

10

RJB=10km; Vs30=760 m/s M=6; Sof=0 PSA(T=0.01s),g M

(strike slip fault)

Selection of candidate GMPE

Use of multiple models with alternative functional forms is required to properly capture uncertainties in forms as well as in amplitude.

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Selected GMPEs: ASK14, BSSA14, CB14, CY14, Id14, ASB14, Bi14, Ca14,

GK15, Lin11, KAAH15-Turkey, KAAH15-Iran, Zhao16 (total of 13 models)

The scenarios for generate synthetic data:
M = 5.0, 5.2, 5.4, 5.5, 5.6, 5.8, 6.0, 6.2, 6.4, 6.5, 6.6, 6.8, 7.0, 7.2, 7.4, 7.5, 7.6, 7.8,

8.0 for strike slip and reserve faulting.

M = 5.0, 5.2, 5.4, 5.5, 5.6, 5.8, 6.0, 6.2, 6.4, 6.5, 6.6, 6.8, 7.0 for normal faulting.
Rx=-200,-150,-100,-85,-70,-65,-60,-55,-50,-45,-40,-35,-30,-28,-26,-24,-22,-20,-

18,-16,-15,-14,-12,-10,-8,-6,-5,-4,-2. (foot wall)

From fault geometry, Rrup, and Rjb can be calculated.
Vs30 = 760 m/s.
Dip =90o for strike slip, and dip = 45o for normal and reverse faulting events.
Other parameters are set to default (Ztor, W,...)

Develop Mix Model from scenatios of candidate GMPEs

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 

1

, ,

N i i i

Mix wGMPE M R 



 

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 Add the reference to the set of 13GMPEs:

 Mix Model (average of all models) :  Up-Down Scaled models :  Magnitude Scaled models :  Distance Scaled models:

 

1

, ,

N i i i

Mix wGMPE M R 





log , with = 0.67, 0.8, 1.25, 1.5 S--, S-,S+,S++ Mix   

 

6.5 , with = -0.4, -0.2, 0.2, 0.4 M--, M-, M+, M++ Mix M    

 

70 , with = -0.01, -0.005, 0.005, 0.01 R--, R-, R+, R++ Mix R    

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Reference to the set of 13GMPEs

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 Add the reference to the set of 13GMPEs:

 Mix Model (average of all models) :  Up-Down Scaled models :  Magnitude Scaled models :  Distance Scaled models:

 

1

, ,

N i i i

Mix wGMPE M R 





log , with = 0.67, 0.8, 1.25, 1.5 S--, S-,S+,S++ Mix   

 

6.5 , with = -0.4, -0.2, 0.2, 0.4 M--, M-, M+, M++ Mix M    

 

70 , with = -0.01, -0.005, 0.005, 0.01 R--, R-, R+, R++ Mix R    

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Reference to the set of 13GMPEs

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1

10

2

10

3

10

2

10

1

10

RJB,km,km lnPSA(T=0.01)

M=6.5, sof=0, Vs30=760m/s

Mix S-- S- S+ S++ 10

1

10

2

10

3

10

2

10

1

10

RJB,km lnPSA(T=0.01)

M=6.5, sof=0, Vs30=760m/s

5.5 6 6.5 7 7.5 8 10

3

10

2

10

1

10

M lnPSA(T=0.01)

RJB=70km, sof=0, Vs30=760m/s

Reference to the set of 13GMPEs

Up-Down Scaled models Magnitude Scaled models Distance Scaled models

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Generate Sammon Map

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The simplest technique for dimensionality reduction is a straightforward linear projection, for example, as in PCA — principal component analysis. (PCA simply maximizes variance) Non-linear projections may therefore be desirable when analyzing such data.

Sammon Mapping: To minimize the differences between corresponding inter-point distances in the dimension space

(13 Candidate GMPEs) + (13 Reference models: mix & scale models) GMPEi = f(M, R)

M = 5.0, 5.2, …, 7.8, 8.0 (for SS & NF) Rx=-200,-150, …., -4,-2. (foot wall)

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Visualization technique-GMPEs Calculation

 

xN xN

R M Lin R M CY R M BSSA R M ASK

13 13

) , ( 11 ) , ( 14 ) , ( 14 ) , ( 14                  

GMPE

μ

xN xN xN xN xN xN scales

R M S Mix

13 4 4 4 1 13

] [ ] [ ] [ ] [              μ

     

      

xN Scaled xN GMPE xN

X

13 13 26

μ μ

 Combined the embedded GMPEs Es and the Mix Model l & Scaled led Models ls into the [X] matrix considered to be N-dimensional space

   

1 2 2

~ , 1

T pca D pca

XX X N  



             

              

 26 2 1 26 2 1 2

] [ y y y x x x X

PCA D

 

Construct the initial PCA-based map

2D visualization (preliminary)

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Visualization technique-GMPEs Calculation

Min. Determine : to construct the Sammon map

Map PCA



 

 

 

j i ij map ij ij j i ij

E    

2

) ( 1

 

2 26x map Sammon

X



 To construct the 



2 26x map Sammon

X



 

26 26 2 26 1 26 26 2 1 2 26 1 2 1 26 26 } [ x X X X X X X x X

             

     

            

  



N X X

N k jk ik ij

/ ) ) ( (

2 1

 

  

     

      

xN Scaled xN GMPE xN

X

13 13 26

μ μ

Using and define to construct

 

 

2 1 2 , , ,

) (

p p Xj p Xi j Xi

x x 

 

26 26 2 , 26 1 , 26 26 , 2 1 , 2 26 , 1 2 , 1 26 26 x X X X X X X x Map PCA

               



            

Define Calculate inter-point distance

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Visualization technique-GMPEs Calculation

 

2 N GMPE ij k ik jk k

w GMPE GMPE   



  



N GMPE GMPE

N k jk ik ij

/ ) ) ( (

2 1

 

  

 

26 26 2 26 1 26 26 2 1 2 26 1 2 1 26 26 } [ x X X X X X X x X

             

     

            

 

1 0.5 ,

k k k

w DEAGG M R NS        

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 Visualization of models in 2-Ddimension

0.6
0.4
0.2

0.2 0.4 0.6

0.6
0.4
0.2

0.2 0.4 0.6

Average S-- S- S+ S++ M-- M- M+ M++ R-- R- R+ R++ ASK14 BSSA14 CB14 CY14 Id14 ASB14 Bi14 Ca14 GK15 Lin11 KAAH15-Turkey KAAH15-Iran Zhao16

Candidate GMPEs Distribution T001

ln (units) ln (units)

GMPE Distribution

The considered GMPE models are not adequate to fully capture the range

f epistemic uncertainty because of the existing gaps among models.

              

 26 2 1 26 2 1

] [ y y y x x x X

Map Sammon

 

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 

  



 

2 2 1 5 6 7 2 2

2 2 8 9 11 10 3

5 ln 5.5 + 5.5 6.5

exp( ) exp( ) M M M-5.5

Rrup based rup tor REV rup

NML

SA R Z F M R for M for M

F

         

 



         

  

   

2

3 4

6.5

M M-5.5 6.5

for M

M  



       

 

  



   

2 2 1 5 6 7 2 2 2

2 8 11 10 3 3

5 ln 5.5 + 5.5 6.5

exp( ) exp( ) M M M-5.5 M M-5.5

Rjb based jb REV jb

NML

SA R F M R for M for M

F

        

  



        

    

 

4

6.5

for M

M 



     

(Behave differently on the hanging wall side)

Model A - based on rupture distance, RRUP Model B - based on rupture distance, RJB

Selection of candidate GMPE common form

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GMPE Distribution

Develop common funtional form for each candidate GMPE

   

ln , , ,... y f M R   

For each GMPE i, estimate the set of coefficients i (using senthetic data)

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Select common form to fit the synthetic data

5 5.5 6 6.5 7 7.5 8 10

2

10

1

10

RJB=10km; Vs30=760 m/s M=6; Sof=0 PSA(T=0.01s),g M

2 10 100 200 10

3

10

2

10

1

10

RRUP,km PSA(T=0.01s),g M=6; Vs30=760 m/s Sof=0

ASK14 BSSA14 CB14 CY14 Id14 ASB14 Bi14 Ca14 GK15 LLCS11 KAAH15-Turkey KAAH15-Iran Zhao16

(Sof=0) : strike slip fault Comparison between the common form GMPE with respect to the candidate GMPE

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2 10 100 200 0.001 0.01 0.1 0.5 Rrup,km PSA[g] ASK14 T001 M=5 M=6 M=7 M=8 Original 5 6 7 8

0.4
0.2

0.2 0.4 ASK14 T001 Residual M 2 10 100 200

0.4
0.2

0.2 0.4 ASK14 T001 RRUP 2 10 100 200 0.001 0.01 0.1 0.5 Rrup,km PSA[g] BSSA14 T001 M=5 M=6 M=7 M=8 Original 5 6 7 8

0.4
0.2

0.2 0.4 BSSA14 T001 Residual M 2 10 100 200

0.4
0.2

0.2 0.4 BSSA14 T001 RRUP 2 10 100 200 0.001 0.01 0.1 0.5 Rrup,km PSA[g] CB14 T001 M=5 M=6 M=7 M=8 Original 5 6 7 8

0.4
0.2

0.2 0.4 CB14 T001 Residual M 2 10 100 200

0.4
0.2

0.2 0.4 CB14 T001 RRUP

Example : Fit common form to synthetic data. RRUP-based

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Example: Fit common form to synthetic data. RJB-based

2 10 100 200 0.001 0.01 0.1 0.5 Rrup,km PSA[g] ASK14 T001 M=5 M=6 M=7 M=8 Original 5 6 7 8

0.4
0.2

0.2 0.4 ASK14 T001 Residual M 2 10 100 200

0.4
0.2

0.2 0.4 ASK14 T001 RRUP 2 10 100 200 0.001 0.01 0.1 0.5 Rrup,km PSA[g] BSSA14 T001 M=5 M=6 M=7 M=8 Original 5 6 7 8

0.4
0.2

0.2 0.4 BSSA14 T001 Residual M 2 10 100 200

0.4
0.2

0.2 0.4 BSSA14 T001 RRUP 2 10 100 200 0.001 0.01 0.1 0.5 Rrup,km PSA[g] CB14 T001 M=5 M=6 M=7 M=8 Original 5 6 7 8

0.4
0.2

0.2 0.4 CB14 T001 Residual M 2 10 100 200

0.4
0.2

0.2 0.4 CB14 T001 RRUP

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Select common form to fit the synthetic data

(Assumed multivariate normal distribution)

. . . .

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0.2
0.1

0.1 0.2 0.3 50 100 150 200

8 Count

Original Candidate GMPEs

20
10

10 20 50 100 150 200

1 Count

Distribution of GMPE coefficient

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Calculate μθ and θ (from the fitted sets of coefficients)

10

1

10

2

10

3

10

2

10

1

10

RJB, km lnPSA(T=0.01s)

Model A Model B Original candidate GMPE M=6.5, sof=0 Vs30=760m/s 5.5 6 6.5 7 7.5 8 10

3

10

2

10

1

10

M lnPSA(T=0.01s)

Model A Model B Original candidate GMPE Sof=0,RJB=35km Vs30=760m/s

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 Visualization of models in 2D

M = 4.75, 5.25,...,7.75
RJB = 1.25, 1.5, 3.75, ...,87.5
Vs30=760m/s
Sof = 0, 1
T=.001s

Convex hull of candidate GMPE with plus/minus 2σAY14

1
0.5

0.5 1

1
0.5

0.5 1

ln (units) ln (units)

T001s ModelA ModelB

Zhao16 and KAAH-Turkey were not included Model A: RRUP-based Model B: RJB-based

Original Candidate GMPEs Original Candidate GMPEs+2 Original Candidate GMPEs-2

  

GMPE Distribution

   

14

ln , ,... , ,

ij i j j AY j j

PSA f M R M R F    with = {-2, 0, 2}

Capture the range of epistemic uncertainty.

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Selection of models – Approach 1

Split region covered by four ellipese into many subregion. Fitting ellipse to convex hull. Scale up and down by a factor 2, 1.5 and 0.5

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1
0.5

0.5 1

1
0.5

0.5 1 T001s

1
0.5

0.5 1

1
0.5

0.5 1 T001s

Selection of models – Approach 1

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For each subregion, common forms

are selected

Select representative model for

each subregion.

25

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Visualization of model space: Residual analysis

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120 120.5 121 121.5 122 122.5 21.5 22 22.5 23 23.5 24 24.5 25 25.5

Mw:5-7.62

Latitude, N Longitude, E

10 10

1

10

2

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

Distance, km M

Strike slip Reverse faulting Normal faulting

e 2 2 2

~ B

ij i i j es

W             

Shallow Crustal Earthquake: M:5-7.62 Vs30>150m/s.

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 Scenarios

M = 4.75, 5.25,...,7.75
RJB = 1.25, 1.5, 3.75, ...,87.5
Vs30=760m/s
Sof = 0, 1
T=0.001s

 Data corrected to Vs30=760m/s  Model evaluation.

Contour using

mean between event residual + Candidate GMPEs Mean between event residual

GMPE Distribution

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln(units) ln(units)

1.05 -0.9 -0.75 -0.6 -0.45 -0.3 -0.15

0.15 0.3 0.45 0.6 0.75 1.05

Overlay the contour map of mean between residual w.r.t. the fitting ellipse

27

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1
0.5

0.5 1

1
0.5

0.5 1 T001s

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln(units) ln(units)

1.05 -0.9 -0.75 -0.6 -0.45 -0.3 -0.15

0.15 0.3 0.45 0.6 0.75 1.05

Identify the value of mean between event residual of each form from each split region.

For each subregion, information of

mean between event residual exist.

Selection of models – Approach 1

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SLIDE 29

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln(units) ln(units)

1.05 -0.9
0.75 -0.6
0.45 -0.3 -0.15

0.15 0.3 0.45 0.6 0.75 1.05

Selection of models – Approach 2

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 Discretizing the map using the Voronoi-Diagram. 29

SLIDE 30

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln (units) ln units

747.474-700
650
600
550
500
450
400
350
300-279.813

 Scenarios

M = 4.75, 5.25,...,7.75
RJB = 1.25, 1.5, 3.75, ...,87.5
Vs30=760m/s
Sof = 0, 1
T=.001s

 Data corrected to Vs30=760m/s  Model evaluation.

Contour based on Log-likelihood

value of each model

Log-likelihood

GMPE Distribution

National Taiwan University Department of Civil Engineering

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SLIDE 31

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln (units) ln (units)

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln (units) ln (units)

Selection of models – Approach 2

National Taiwan University Department of Civil Engineering

31

SLIDE 32

 The Representative suite of common Form model  The candidate GMPE models

5 5.5 6 6.5 7 7.5 8 10

2

10

1

10

Sof=0; RJB=10km PSA(T=0.01s),g Magnitude

2 10 100 200 10

3

10

2

10

1

10

M=6; Sof=0 PSA(T=0.01s),g Distance,km

0.5

0.5

0.5

0.5

ln (units) ln (units)

T0.01s

GMPE weightings and cells

National Taiwan University Department of Civil Engineering

32

SLIDE 33

 Log-likelihood

0.0098
280.873
0.0895
290.548
0.1419
310.989

0.0457

284.204

0.0951

299.791

0.0727

292.808

0.0278

276.865

0.0609

289.394

5 6 7 8 10

2

10

1

10

Sof=0; RJB=10km PSA(T=0.01s),g M

2 10 100 200 10

3

10

2

10

1

10

M=6; Sof=0 PSA(T=0.01s),g RRUP,km

These two values will change among different sub-region in the Voronoi Diagram

Selection of models – Approach 2

National Taiwan University Department of Civil Engineering

33

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln (units) ln (units)

SLIDE 34

 The weight for the selected representative model for each cell

Lij

1

i

N i i ji j i

w A L N





GMPE weightings and cells

National Taiwan University Department of Civil Engineering

34

SLIDE 35

GMPE weightings and cells

National Taiwan University Department of Civil Engineering

5 10 15 20 25 30 35 40 45 0.02 0.04 0.06 0.08 0.1 0.12

Model index Weight

wResidual wSqResidual wLL

35

0.5

0.5

0.5

0.5

ln (units) ln (units)

T0.01s

 Capture uncertainties in form & amplitude  Conduct sensitivity analysis from the proposed weights on the seismic hazard

SLIDE 36

National Taiwan University Department of Civil Engineering

36

1. Method on the selection of GMPE for PSHA is introduced (The above–mentioned method had been used in “Diablo Canyon SSHAC Level-3 Report”). 2. The calculated weighting value depends not only on the mean between event residual or likelihood value, but also depend on the area of each cell or the way of mapping is partitioned.

3. The proposed method can generate the quantitative value on selecting

and ranking of GMPE model and provides information for experts on the judgment of weighting factor in seismic hazard calculation

Conclusions

SLIDE 37

SLIDE 38

National Taiwan University Department of Civil Engineering

5

A Procedure of Logic Tree for GMPE (to capture uncertainties in form as well as amplitude)

Selection of candidate GMPEs  Identification of worldwide GMPEs  Review of the GMPE applicability range  Adjust for parameter compatibility  Evaluation of the GMPE Expert Judgment  Logic tree from experts Testing using data  Ranking of GMPE Proposition of logic trees Sensitivity analysis of the proposed weights on the seismic hazard

Introduction

SLIDE 39

GMPE Distribution

Develop common funtional form for each candidate GMPE

   

ln , , ,... y f M R    In order to capture the correlation between the different coefficients θ, the common form is also fitted to the interpolated ground motions from the candidate GMPEs

   

 

 

ln ( , , 30) ln ln with 1 2 1 1 2 1 , , , , , , 3 3 2 2 3 3

a i b j a b

Interp SA M R Vs w SA w SA i j w w                      

For each GMPE i, estimate the set of coefficients i (using senthetic data)

Calculate mean μθ and covariance θ Given μθ and θ, , sample new sets of coefficients {} and thus generate new models

National Taiwan University Department of Civil Engineering

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Select common form to fit the synthetic data

SLIDE 40

Simple functional form fit to Taiwan data:

– Ztor is limited to 20km because we adopt Ztor-M relation of CY14.

Method: Maximum regression using mixed – effect model

A STABLE ALGORITHM FOR REGRESSION ANALYSES USING THE RANDOM EFFECTS MODEL Bulletin of the Seismological Society of America, Vol. 82, No. 1, pp. 505-510, February 1992 BY N. A. ABRAHAMSON AND R. R. YOUNGS

Model bias and variability

– τ = 0.4061. –  = 0.5838.

 

2 1 1 1 2 3 4 5 6 14

ln (T0.01) log exp

a b i CY

psa c c FRV c Ztor c M c M c R c c M Ztor Ztor Ztor           

c1

6.3535

c1a 0.0855 C1b 0.0455 C2 2.0335 C3

0.03826

C4

2.0609

C5 0.388 C6 0.6268

Use this number to construct the log-likelihood contour

National Taiwan University Department of Civil Engineering

Develop simple GMPE

26

SLIDE 41

 Log-likelihood

1.023
440.448
1.0788
399.806
0.3595
363.047
0.7301
419.606
0.5533
488.515
0.6589
474.253
0.4225
389.43
0.5426
390.071
0.4222
376.565
0.2608
323.921
0.1877
374.395
0.1211
304.776
0.1739
326.772
0.3189
335.055
0.1726
324.308
0.0631
295.312
0.1776
391.671
0.1535
330.265
0.1453
310.945
0.076
299.143
0.1569
329.054
0.1148
316.892
0.2214
325.172
0.2319
347.509

5 6 7 8 10

2

10

1

10

Sof=0; RJB=10km PSA(T=0.01s),g M

2 10 100 200 10

3

10

2

10

1

10

M=6; Sof=0 PSA(T=0.01s),g RRUP,km

Selection of models – Approach 2

National Taiwan University Department of Civil Engineering

34

1
0.5

0.5 1

1
0.5

0.5 1 T001s

ln (units) ln (units)

SLIDE 42

National Taiwan University Department of Civil Engineering

1/ 𝜈(𝜀𝐶) , One over the absolute mean

between event residual.

0.5

0.5

0.5

0.5

ln (units) ln (units)

0.021275 0.041884 0.054706 0.043404 0.029822 0.036376 0.09716 0.047678 0.016146 0.011492 0.013961 0.024789 0.011492 0.0034191 0.025359 0.0098775 0.010922 0.024599 0.0106370.0063634 0.0085478 0.0096875 0.023839 0.0047488 0.0088327 0.01966 0.012537 0.030582 0.013866 0.0096875 0.0086428 0.026973 0.029727 0.021749 0.032672 0.019755 0.007978 0.012157 0.0051287 0.045398 0.041504 0.0068383 0.015101 0.016336 0.012252 0.014436

T0.01s

0.0063634 0.0085478 0.0096875 0.023839 0.0047488 0.0088327 0.01966 0.012537 0.030582 0.013866 0.0096875 0.0086428 0.026973 0.029727 0.021749 0.032672 0.019755 0.007978 0.012157 0.0051287 0.045398 0.041504 0.0068383 0.015101 0.016336 0.012252 0.014436 0.021275 0.041884 0.054706 0.043404 0.029822 0.036376 0.09716 0.047678 0.016146 0.011492 0.013961 0.024789 0.011492 0.0034191 0.025359 0.0098775 0.010922 0.024599 0.010637

Distribution of GMPE weighting

37