GMPE Development: Duration Model Development

Transcription

1 GMPE Development: Model Development Nicolas Kuehn, Sanjay Singh Bora, Frank Scherbaum, Peter Stafford 3 PEER, University of Potsdam, 3 Imperial College London 4 July 04 NGA East Workshop Motivation The Fourier spectrum is easier to understand than the response spectrum. Build an empirical model for the Fourier spectrum Combine with a model for duration to get the response spectrum is optimized to give the smallest misfit between empirical response spectrum and RVT response spectrum Basic idea: Bora et al. (04): Fourier spectral- and durationmodels for the generation of response spectra adjustable to different source-, propagation-, and site conditions, BEE

2 RVT Recap We want to calculate the maximum response of a system y max calculate root-mean-squared response y rms y rms = m0 D rms D rms is the RMS-duration (duration of oscillator m 0 is zeroth spectral moment calculate peak factor p = y max y rms m k = (πf) k Y (f,f osc ) df 0 RVT Recap There are different relations for the peak factor Cartwright and Longuet-Higgins (956) y max = ( ( N ) ) z exp( z ) dz y rms N e with N z the number of zero crossings N z = π D m gm, m 0 N e the number of extrema N e = π D gm D gm the duration of ground-motion. m4 m,

3 RVT Two durations are needed, rms-duration D rms and ground-motion duration D gm. D rms = f(d gm ) (Joyner and Boore, 984; Liu and Pezeshk, 999; Boore and Thompson, 0) possible choices for D gm : D 5 95, D 5 75,... (For this application), we don t care about the (values of the) duration per se, we care about the response spectrum. use duration that minimizes the misfit between the response spectrum calculated from acceleration time series and the response spectrum calculated by RVT this is not a physical duration In Bora et al. (984), applied to the RESORCE database (Akkar et al., 04) Fit to Response Spectra target: record response spectrum predictor: record FAS parameter: duration D gm SMSIM duration:.638s. 0.5 A m s misfit: log 0 (SA) log 0 (predictedsa)

4 Fit to Response Spectra target: record response spectrum predictor: record FAS parameter: duration D gm SMSIM duration:.638s. 0.5 A m s misfit: log 0 (SA) log 0 (predictedsa) Fit to Response Spectra target: record response spectrum predictor: record FAS parameter: duration D gm SMSIM duration:.638s NGA ID.00 SA m s observed RVT optimized F Hz misfit: log 0 (SA) log 0 (predictedsa)

5 lnhdexl lnhdexl Model MW RRUP ln Dgm = a0 + a MW + (a + a3 MW ) ln q RRUP + a4 + a5 ln VS30 + a6 ZTOR + η + ε Is that appropriate? Different form? lnhdexl lnhdexl Model MW MW DEX Bommer et al H5-95L Bommer et al H5-75L ln Dgm = a0 + a MW + (a + a3 MW ) ln + a5 ln VS30 + a6 ZTOR q RRUP + a

6 Response Spectrum from Fourier and Model Fourier model gives median prediction needs to be adjusted for mean Combine with duration from duration model response spectrum Bora et al., 04 Response Spectrum from Fourier and Model Fourier model gives median prediction needs to be adjusted for mean Combine with duration from duration model response spectrum Fig. 6 Residual plots for response spectral ordinates at different oscillator frequencies Bora et al., 04

7 Response Spectrum from Fourier and Model Fourier model gives median prediction needs to be adjusted for mean Combine with duration from duration model response spectrum Fourier spectrum smoothing: constant frequency band, no overlap σ = σ reg + σ smooth Bora et al., 04 Model Issues usable frequency range for estimation of duration extend FAS usable frequency range? model for relation between D rms and D gm frequency dependent duration? peak factor needs to be consistent between inversion of duration and estimating response spectrum from model need to be generally consistent with empirical Fourier spectral model any issues will be absorbed into the duration(?)

8 Model Issues Left panel, depicts the distribution of the dataset (RESORCEusable frequency range for estimation of durationof 5 records from 3 t to magnitude and distance which consists extend FAS usable frequency range? panel, depicts theoriginal geometrical model betweenspreading Hz regime determined from th owards the Generation of Response iction Equations for Seismic Hazard A Scherbaum- Institute of Earth and Environmental Sciences, Universit plots indicating theresearch fit between model FAS andofobserv -epresentative Pacific Earthquake Engineering Center, University Califo ord - Department of Civil and Environmental Engineering, Imperial Coll Ben Edwards-Swiss Seismological Service, ETH Zürich ntation Bora et al., 04 SSA Model A frequency dependent duration model Issues mine the stochastic model We propose a unique measure of ground motion duration which is. Subsequently, spectrum different functional formthe misfit between the RVT based and classical re optimize ce is extrapolated to 400 spectral ordinates at each oscillator frequencies. q del for each record. ( 0.5McW ) 3 Dgm = c0 + + c RJB + c3 + c4 VS30 + c5 κ () el adjustable to different β ( ) = c ourier amplitude spectrum frequency dependent duration Where =3.5 km/s is the shear wave velocity in the vicinity of the s ismological conditions at ft panel, depicts the fc-mw plot. Right panel, depicts the inverted t* va meters Rhyp. The t* values have been averaged in 0 samples bin of sorted d rd by the constrained non: region and the Middle East. Seismol Res Lett 8(): tion models. Bull Seismol Soc Am 00: of earthquake ground motion. Bull Seismol Soc Am 99: ble to different source-,path-and site conditions. Bull. Eq. Eng. (): Bora et al., 04 SSA tra :

9 References S. Akkar, M. A. Sandikkaya, M. Senyurt, A. Azari Sisi, B. Ö. Ay, P. Traversa, J. Douglas, F. Cotton, L. Luzi, B. Hernandez, and S. Godey (04). Reference database for seismic ground-motion in Europe (RESORCE), Bulletin of Earthquake Engineering (): S. S. Bora, F. Scherbaum, N. Kuehn, and P. Stafford (04). Fourier spectral- and duration models for the generation of response spectra adjustable to different source-, propagation-, and site conditions, Bulletin of Earthquake Engineering, (): S. S. Bora, F. Scherbaum, N. Kuehn, P. Stafford and B. Edwards (04). A New Perspective towards the Generation of Response Spectral Ground Motion Prediction Equations for Seismic Hazard Analysis, SSA Annual Meeting, Anchorage, Al