PEER RVT approach: Duration Model

Transcription

1 PEER RVT approach: Duration Model Nicolas Kuehn Norm Abrahamson, Christine Goulet, Justin Hollenback Pacific Earthquake Engineering Research Center NGA East Workshop 30 October 2014

2 Motivation To calculate response spectral values from the FAS, a duration D is needed. Several duration measures exist in the literature (D 5 95,D 20 80,...) For the purpose of prediction of PSA, we are not interested in the value of D itself. choose duration that provides best PSA prediction. cf. Atkinson (1993); Bora et al. (2014) Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 2 / 19

3 RVT y max = p f y rms y rms = m 0 /D rms D = D rms with p f peak factor, m k spectral moments. Invert for D. misfit function: (lnsa lny max ) 2 Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 3 / 19

4 Inversion Input: downsampled and smoothed FAS calculate spectral moments PSA Inversion: minimize misfit w.r.t. D The inverted duration is not a physical duration. It is a parameter that ensures that the PSA prediction using RVT (given all assumptions) is optimal. Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 4 / 19

5 Example left: record from Saguenay event right: record from Mineral event RecID RecID PSA g PSA g F Hz F Hz Time Series PSA RVT calculated PSA with inverted duration Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 5 / 19

6 Data D D durations, calculated for the NGA East dataset Kuehn et al (PEER) RRUP M PEER RVT approach: Duration Model NGA East WS 6 / 19

7 Data durations, calculated for the NGA East dataset D D Expand dataset: Use durations from NGA West 2 dataset Kuehn et al (PEER) RRUP M PEER RVT approach: Duration Model NGA East WS 6 / 19

8 Data NGA East 8492 durations, 75 events, 1267 stations largest event: M = 6.8, only three records, all within R JB = 20. NGA West durations, 229 events, 848 stations M = , R RUP = resolve (possible) differences: random effects model on regions Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 7 / 19

9 Models 1 lnd es = ln[f(m) + f(r) + f(s)] + δ B e + δ W es + δ S s KS D es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s 3 lnd es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s BoAl 2009, BoraAl 2014 Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 8 / 19

10 Models 1 lnd es = ln[f(m) + f(r) + f(s)] + δ B e + δ W es + δ S s KS 2006 D es = f(m)e δ B e e δ W es e δ S s + f(r)e δ B e e δ W es e δ S s + f(s)e δ B e e δ W es e δ S s 2 D es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s 3 lnd es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s BoAl 2009, BoraAl 2014 Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 8 / 19

11 Models 1 lnd es = ln[f(m) + f(r) + f(s)] + δ B e + δ W es + δ S s KS 2006 D es = f(m)e δ B e e δ W es e δ S s + f(r)e δ B e e δ W es e δ S s + f(s)e δ B e e δ W es e δ S s 2 D es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s δ B e,δ W es,δ S s are not normally distributed 3 lnd es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s BoAl 2009, BoraAl 2014 Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 8 / 19

12 Models 1 lnd es = ln[f(m) + f(r) + f(s)] + δ B e + δ W es + δ S s KS 2006 D es = f(m)e δ B e e δ W es e δ S s + f(r)e δ B e e δ W es e δ S s + f(s)e δ B e e δ W es e δ S s 2 D es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s δ B e,δ W es,δ S s are not normally distributed 3 lnd es = f(m) + f(r) + f(s) + δ B e + δ W es + δ S s BoAl 2009, BoraAl 2014 D es = e f (M) e δ B e e f (R) e δ W es e f (S) e δ S s Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 8 / 19

13 Model Model 3: lnd es = f(m) + f(r) + δ B e + δ W es + δ S s δ B N(0,σ e ) δ W N(0,σ es ) δ S N(0,σ s ) Assumption multiplicative (D = D source D path D Site ) Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 9 / 19

14 Duration Model functional Form: lnd = a 0 + a 1 M + (a 2 + a 3 M)ln δ B N(0,σ e ) δ S N(0,σ s ) δ W N(0,σ es ) R 2 RUP + a2 4 + δ B e + δ W es + δ S s To account for regional differences, coefficients are regionally dependent: a k = a k + δ a k (r) Only a 0 and a 2 are regionally dependent. Two regions (East/West) are considered. δ a k (r) N(0,σ ak ) (1) Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 10 / 19

15 Regression Most events are small and recorded at large distances source terms are small compared to path terms Regression is done in two steps. 1 Data up to 50 km is used to fix magnitude scaling (a 1 ). 2 In a second step, the rest of the parameters are estimated using all data. Regression is done by Bayesian inference via MCMC using the program Stan. priors on parameters ara normal distributions N(0, 10) priors on standard deviations are half-cuachy distributions Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 11 / 19

16 Event Terms event term = a1m + δ B event residual = δ B event term B M M Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 12 / 19

17 Event Terms event term = a1m + δ B event residual = δ B B 0.0 B PIE tectonic M M Gulf Coast Region 2 Region 3 Region 4 CA NEV other WUS Taiwan Italy Mid East China Japan Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 12 / 19

18 Record/Station Residuals within-event residual = δ W station-to-station residual = δ S W R S V S30 Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 13 / 19

19 Record/Station Residuals within-event residual = δ W station-to-station residual = δ S magnitude-dependent δ W W M 4, R RUP W M 5, R RUP Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 13 / 19

20 Record/Station Residuals within-event residual = δ W station-to-station residual = δ S magnitude-dependent δ W W M 6, RUP W M 7, RUP Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 13 / 19

21 Conversion to PSA Goal: prediction of PSA achieved via RVT y max = p f y rms input: mean FAS: µ(fas) = exp(median(fas) + σ 2 FAS /2) mean duration: µ(d) = exp(median(d) + σ 2 D /2) Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 14 / 19

22 PSA Residuals M > 4, R RUP < 300 calculation of residuals to PSA F = 1Hz B 0.0 W M R updated residuals Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 15 / 19

23 PSA Residuals M > 4, R RUP < 300 calculation of residuals to PSA F = 5Hz B 0.0 W M R updated residuals Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 15 / 19

24 PSA Residuals M > 4, R RUP < 300 calculation of residuals to PSA F = 10Hz B 0.0 W M R updated residuals Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 15 / 19

25 Scalinf of PSA Extrapolation to large magnitudes is based on simulations. Comparison between Graves and Pitarka and ExSIM PSA M 6; F 5. GP ExSIM R PSA R 100; F M Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 16 / 19

26 Discussion Duration treated as parameter of model to match PSA via RVT. Magnitude scaling constrained by Western data. Small distance scaling constrained by Western data. Multiplicative model works good. To do: Impact of duration model uncertainty on PSA predictions. To do: Calibrate duration model using model FAS Regional model for all different regions? Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 17 / 19

27 References Atkinson, G. M. (1993). Notes on ground motion parameters for eastern north America: Duration and H/V ratio, BSSA 83, Bommer, J. J. P. Stafford and J. E. Alarcon (2009). Empirical Equations for the Prediction of the Significant, Bracketed, and Uniform Duration of Earthquake Ground Motion, BSSA 99, Bora S. S. F. Scherbaum, N. Kuehn, and P. J. Stafford (2013). Fourier spectral- and durationmodels for the generation of response spectra adjustable to different source-, propagation-, and site conditions. Bull Earthq Eng. 12, Kempton, J. and J. Stewart (2006). Prediction Equations for Significant Duration of Earthquake Ground Motions Considering Site and Near-Source Effects, Earthquake Spectra 22, Stan development team (2014). Stan: A C++ Library for Probability and Sampling, Version Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 18 / 19

28 Acknowledgements Sanjay Singh Bora Frank Scherbaum Jeff Bayless Tadahiro Kishida RVT working group Kuehn et al (PEER) PEER RVT approach: Duration Model NGA East WS 19 / 19