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

Transcription

1 5 th IASPEI / IAEE International Symposium Effects of Surface Geology on Seismic Motion SELECTION OF GROUND-MOTION PREDICTION EQUATIONS FOR PROBABILISTIC SEISMIC HAZARD ANALYSIS : CASE STUDY OF TAIWAN Phung-Van Bang, Chin-Hsiung Loh, Norman Abrahamson University of California, Berkeley USA Taipei, TAIWAN NTU UC-Berkeley August 15-17, 216 Taipei, TAIWAN

2 Background In 215-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) 1

3 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 2

4 Introduction Peak Ground Acceleration (PGA) Attenuation Hazard Curve 3

5 Introduction 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 of 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), Sensitivity analysis of the proposed weights for GMPEs on the seismic hazard. 4

6 General Feature of Candidate GMPEs GMPE (Abrahamson, N. A., Silva, W. J., and Kamai, R., 214) (Boore, D. M., Stewart, J. P., Seyhan, E., and Atkinson, G. M., 214) (Campbell, K. W., and Bozorgnia, Y., 214) (Chiou, B. S-J., and Youngs, R. R., 214) GMPE Acronym Regions Magnitude Interval Primary distance Style of faulting Site effect Component ASK14 Global Mw (3.-8.5) Rrup (<3km) SS,NML,REV Vs3 BSSA14 Global Mw (3.-8.5) Rjb(<3km) U,SS,NML,REV Vs3 CB14 Global Mw ( ) Rrup (<3km) SS,NML,REV Vs3 CY14 Global Mw ( ) Rrup (<3km) SS,NML,REV Vs3 (Idriss, 214) Id14 Global Mw (5-8.5) Rrup (<15km) SS,NML,REV Vs3 (Akkar, S., Sandikkaya, M. A., and Bommer, J. J., 214) (Bindi D., Massa M., Luzi L., Ameri G., Pacor F., Puglia R., and Augliera, P., 214) (Graizer, V., and Kalkan, E., 215) ASB14 Bi14 EU and ME EU and ME GK15 Global Mw(5.-8.) Zhao et al. 216 Zhao16 Japan Mw(5.-7.3) Özkan Kale, Sinan Akkar, Anooshiravan Ansari, and Hossein Hamzehloo Ka15 Turkey and Iran Mw (4-7.5) Rjb (<2km) SS,NML,REV Vs3 Mw(4-7.6) Rjb (<3km) U,SS,NML,REV Vs3 Mw(4.-8.) Rrup (<25Km) Rrup(<3km ) Rjb(<2km) SS,NML,REV FN,SS U,SS,NML,RE V Vs3 Dummy variable Vs3 PGA,PGV,PSA in GMRotI5 PGA,PGV,PSA in GMRotI5 PGA,PGV,PSA in GMRotI5 PGA,PGV,PSA in GMRotI5 PGA,PGV,PSA in GMRotI5 PGA,PGV,PSA in GM PGA,PGV,PSA in GM PGA,PGV,PSA in GM PGA, PSA in GM PGA, PGV, PSA in GM Number of records and events 1575 and 326 ~16 and ~ and and and and and and and 76 (cr), 47(mum) 67(Tur),528(Ir) Lin, P.S et al. 211 Lin11 Taiwan Mw(5.-7.6) Rrup(<24km) - no PGA,PSA in GM 5268 and 52 (Cauzzi, C., Faccioli, E., Vanini, M., and Bianchini, A., 214) Ca14 Global Mw( ) Rrup (<15km) U,SS,NML,REV Vs3 PGA,PGV,PSA in GM 188 and 98 6

7 Selection of candidate GMPE PSA(T=.1s),g Selected GMPEs: ASK14, BSSA14, CB14, CY14, Id14, GK15, M=6; Sof= (strike slip fault) R JB =1km; Vs3=76 m/s ASB14, Bi14, Ca M Lin11, KAAH15-Turkey, KAAH15-Iran, Zhao16 (total of 13 models) PSA(T=.1s),g M=6; Vs3=76 m/s Sof= R RUP,km ASK14 BSSA14 CB14 CY14 Id14 ASB14 Bi14 Ca14 GK15 LLCS11 KAAH15-Turkey KAAH15-Iran Zhao16 Use of multiple models with alternative functional forms is required to properly capture uncertainties in forms as well as in amplitude. 7

8 Develop Mix Model from scenatios of candidate GMPEs 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., 5.2, 5.4, 5.5, 5.6, 5.8, 6., 6.2, 6.4, 6.5, 6.6, 6.8, 7., 7.2, 7.4, 7.5, 7.6, 7.8, 8. for strike slip and reserve faulting. M = 5., 5.2, 5.4, 5.5, 5.6, 5.8, 6., 6.2, 6.4, 6.5, 6.6, 6.8, 7. for normal faulting. Rx=-2,-15,-1,-85,-7,-65,-6,-55,-5,-45,-4,-35,-3,-28,-26,-24,-22,-2,- 18,-16,-15,-14,-12,-1,-8,-6,-5,-4,-2. (foot wall) From fault geometry, Rrup, and Rjb can be calculated. Vs3 = 76 m/s. Dip =9 o for strike slip, and dip = 45 o for normal and reverse faulting events. Other parameters are set to default (Ztor, W,...) N Mix wigmpeim, R, i1 9

9 Reference to the set of 13GMPEs Add the reference to the set of 13GMPEs: Mix Model (average of all models) : Up-Down Scaled models : Magnitude Scaled models : Distance Scaled models: N Mix wigmpeim, R, i1 Mix log, with =.67,.8, 1.25, 1.5 S--, S-,S+,S++ Mix M 6.5, with = -.4, -.2,.2,.4 M--, M-, M+, M++ Mix R 7, with = -.1, -.5,.5,.1 R--, R-, R+, R++ 8

10 Reference to the set of 13GMPEs Add the reference to the set of 13GMPEs: Mix Model (average of all models) : Up-Down Scaled models : Magnitude Scaled models : Distance Scaled models: N Mix wigmpeim, R, i1 Mix log, with =.67,.8, 1.25, 1.5 S--, S-,S+,S++ Mix M 6.5, with = -.4, -.2,.2,.4 M--, M-, M+, M++ Mix R 7, with = -.1, -.5,.5,.1 R--, R-, R+, R++ 8

11 Reference to the set of 13GMPEs lnpsa(t=.1) Mix S-- S- S+ S++ Up-Down Scaled models M=6.5, sof=, Vs3=76m/s R JB,km,km 1 Distance Scaled models 1 Magnitude Scaled models lnpsa(t=.1) M=6.5, sof=, Vs3=76m/s lnpsa(t=.1) R JB =7km, sof=, Vs3=76m/s R JB,km M 1

12 Generate Sammon Map (13 Candidate GMPEs) + (13 Reference models: mix & scale models) GMPE i = f(m, R) M = 5., 5.2,, 7.8, 8. (for SS & NF) Rx=-2,-15,., -4,-2. (foot wall) 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 11

13 Visualization technique-gmpes Calculation Combined the embedded GMPEs and the Mix Model & Scaled Models into the [X] matrix considered to be N-dimensional space μ GMPE 13xN [ μ scales ] 13xN ASK14( M, R) BSSA14( M, R) CY14( M, R) Lin11( M, R) Mix [ S] [ M ] [ R] 1xN 4xN 4xN 4xN 13xN 13xN 2D visualization (preliminary) X 26xN μgmpe 13xN μ Scaled 13xN T XX ~, 2 D pca N 1 X Construct the initial PCA-based map [ X pca 1 2 ] 2 DPCA x x x y y y

14 Visualization technique-gmpes Calculation To construct the Sammon map 26x2 Using X 26xN and define to construct X [ X } 26x26 μgmpe 13xN μ Min. Scaled Calculate inter-point distance X 21 X xN 2 X X ) ) N N ij ( ( k ik jk / 1 X 12 X 262 E 1 i j X 126 X 226 ij 26x26 i j ( ij Define ij PCA Map 26x26 map ij 2 ) 2 2 Xi, j ( x 1,, ) p Xi p xxj p X 2,1 X 26,1 X 1,2 X 26,2 X 1,26 X 2,26 26x26 Determine : Map PCA to construct the Sammon map X Sammon map 26x2 13

15 Visualization technique-gmpes Calculation 2 GMPE GMPE ) ) N N ij ( ( k ik jk / 1 [ X } 26x26 X 21 X 261 X 12 X 262 X 126 X x26 N 2 w GMPE GMPE GMPE ij k ik jk k w.5 DEAGG M, R k k k 1 NS 14

16 GMPE Distribution Visualization of models in 2-Ddimension.6.4 Candidate GMPEs Distribution T1 M-- [ X ] SammonMap x1 x2 x 26 y y y ln (units) R++ M- KAAH15-Iran S-- Ca14 R+ GK15 S- ASK14 Id14 Average S+ KAAH15-Turkey Lin11 CY14 BSSA14 R- CB14 M+ ASB14 R-- Bi14 M++ S++ Zhao ln (units) The considered GMPE models are not adequate to fully capture the range of epistemic uncertainty because of the existing gaps among models. 15

17 Selection of candidate GMPE common form Model A - based on rupture distance, R RUP ln SA R Z exp( ) F exp( ) F M R Rrup based rup 9 tor 11 NML 1 REV 5 6 rup 7 M for M M 2 3 M-5.5 for 5.5 M 6.5 M 2 3M M 6.5 for M 6.5 Model B - based on rupture distance, R JB ln SA R exp( ) F exp( ) F M R 2 Rjb based 1 8 jb 11 NML 1 REV 5 6 jb 7 M for M M 2 3 M-5.5 for 5.5 M 6.5 M 2 3 M M 6.5 for M 6.5 (Behave differently on the hanging wall side) 16

18 Select common form to fit the synthetic data 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) Comparison between the common form GMPE with respect to the candidate GMPE PSA(T=.1s),g M=6; Sof= R JB =1km; Vs3=76 m/s M PSA(T=.1s),g M=6; Vs3=76 m/s Sof= R RUP,km (Sof=) : strike slip fault ASK14 BSSA14 CB14 CY14 Id14 ASB14 Bi14 Ca14 GK15 LLCS11 KAAH15-Turkey KAAH15-Iran Zhao16 17

19 Example : Fit common form to synthetic data. R RUP -based PSA[g] PSA[g] PSA[g] M=5 M=6 M=7 M=8 Original ASK14 T Rrup,km.5 BSSA14 T M=5 M=6 M=7 M=8 Original Rrup,km M=5 M=6 M=7 M=8 Original CB14 T Rrup,km Residual Residual Residual.4 ASK14 T M.4 BSSA14 T M.4 CB14 T M.4 ASK14 T R RUP.4 BSSA14 T R RUP.4 CB14 T R RUP

20 Example: Fit common form to synthetic data. R JB -based PSA[g] PSA[g] PSA[g] M=5 M=6 M=7 M=8 Original ASK14 T Rrup,km M=5 M=6 M=7 M=8 Original BSSA14 T Rrup,km M=5 M=6 M=7 M=8 Original CB14 T Rrup,km Residual Residual Residual.4 ASK14 T M.4 BSSA14 T M.4 CB14 T M.4 ASK14 T R RUP.4 BSSA14 T R RUP.4 CB14 T R RUP

21 Select common form to fit the synthetic data. (Assumed multivariate normal distribution) 18

22 Distribution of GMPE coefficient 2 Calculate μ θ and θ (from the fitted sets of coefficients) 2 Original Candidate GMPEs Count 1 Count lnpsa(t=.1s) M Sof=,RJB=35km Vs3=76m/s Model A Model B Original candidate GMPE lnpsa(t=.1s) M=6.5, sof= Vs3=76m/s Model A Model B Original candidate GMPE R JB, km 21

23 GMPE Distribution Visualization of models in 2D M = 4.75, 5.25,...,7.75 RJB = 1.25, 1.5, 3.75,...,87.5 Vs3=76m/s Sof =, 1 T=.1s 1.5 T1s Model A: R RUP -based Model B: R JB -based Convex hull of candidate GMPE with plus/minus 2σ AY14 ln (units) Zhao16 and KAAH-Turkey were not included -.5 Original Candidate GMPEs Original Candidate GMPEs+2 Original Candidate GMPEs-2 14 ln PSA f M, R,... M, R, F ij i j j AY j j with = {-2,, 2} ModelA ModelB ln (units) Capture the range of epistemic uncertainty. 23

24 Selection of models Approach 1 Fitting ellipse to convex hull. Scale up and down by a factor 2, 1.5 and.5 Split region covered by four ellipese into many subregion. 24

25 Selection of models Approach 1 1 T1s 1 T1s For each subregion, common forms are selected Select representative model for each subregion. 25

26 Visualization of model space: Residual analysis ~ B W ij i i j e es Mw: Strike slip Reverse faulting Normal faulting Latitude, N M Shallow Crustal Earthquake: M: Vs3>15m/s Longitude, E Distance, km 26

27 GMPE Distribution Scenarios M = 4.75, 5.25,...,7.75 RJB = 1.25, 1.5, 3.75,...,87.5 Vs3=76m/s Sof =, 1 T=.1s Data corrected to Vs3=76m/s Model evaluation. Contour using mean between event residual + Candidate GMPEs ln(units) Mean between event residual T1s Overlay the contour map of mean between residual w.r.t. the fitting ellipse ln(units) 27

28 Selection of models Approach 1 Identify the value of mean between event residual of each form from each split region. 1 T1s 1 T1s.5.5 ln(units) ln(units) For each subregion, information of mean between event residual exist. 28

29 Selection of models Approach 2 Discretizing the map using the Voronoi-Diagram. 1.5 T1s ln(units) ln(units) 29

30 GMPE Distribution Scenarios M = 4.75, 5.25,...,7.75 RJB = 1.25, 1.5, 3.75,...,87.5 Vs3=76m/s Sof =, 1 T=.1s Data corrected to Vs3=76m/s Model evaluation. Contour based on Log-likelihood value of each model ln (units) T1s Log-likelihood ln units 3

31 Selection of models Approach T1s T1s.5.5 ln (units) ln (units) ln (units) ln (units) 31

32 GMPE weightings and cells The Representative suite of common Form model The candidate GMPE models 1.5 T.1s PSA(T=.1s),g 1-1 ln (units) Sof=; R JB =1km Magnitude -.5 PSA(T=.1s),g ln (units) 1-3 M=6; Sof= Distance,km 32

33 Selection of models Approach T1s PSA(T=.1s),g PSA(T=.1s),g Sof=; R JB =1km M M=6; Sof= R RUP,km Log-likelihood ln (units) These two values will change among different sub-region in the Voronoi Diagram ln (units) 33

34 GMPE weightings and cells The weight for the selected representative model for each cell Ni 1 wi A i Lji Ni j 1 L ij 34

35 GMPE weightings and cells.12.1 wresidual wsqresidual wll.5 T.1s.8 Weight.6.4 ln (units) Model index ln (units) Capture uncertainties in form & amplitude Conduct sensitivity analysis from the proposed weights on the seismic hazard 35

36 Conclusions 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 36

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38 Introduction 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 5

39 Select common form to fit the synthetic data 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) Calculate mean μ θ and covariance θ Given μ θ and θ,, sample new sets of coefficients {} and thus generate new models 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 a i b j Interp ln SA( M, R, Vs3) w ln SA w ln SA with i j wa, wb,,,,,

40 Develop simple GMPE Simple functional form fit to Taiwan data: ln psa(t.1) c c FRV c Ztor c M c M c log R c exp c M Ztor Ztor Ztor i 2 1 1a 1b CY14 Ztor is limited to 2km 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 , February 1992 BY N. A. ABRAHAMSON AND R. R. YOUNGS Model bias and variability τ =.461. = c c1a.855 C1b.455 C C C C5.388 C Use this number to construct the log-likelihood contour 26

41 Selection of models Approach 2 PSA(T=.1s),g PSA(T=.1s),g Sof=; R JB =1km M M=6; Sof= R RUP,km Log-likelihood ln (units) T1s ln (units) 34

42 Distribution of GMPE weighting.5 1/ μ(δb), One over the absolute mean between event residual. T.1s ln (units) ln (units) 37