SMSIM Calibration for the SCEC Validation Project NGA-East Workshop Berkeley 12/11/12

Transcription

1 SMSIM Calibration for the SCEC Validation Project NGA-East Workshop Berkeley 12/11/12 SWUS GMC SSHAC Level 3 Carola Di Alessandro GeoPentech with inputs from D.M. Boore OUTLINE Introduce SMSIM (Stochastic Model SIMulation) method Input parameters and criteria to choose them Why is this method different than the previously presented ones? Calibration of the method (Part B) Currently performed outside of the BBP and for Western US. Current attempts and proposed activities Optimization vs. real events (Part A) Proposed approach Conclusions 1

2 SMSIM: Point source stochastic simulation method The radiation from a fault is distributed randomly over a duration dependent on source size and propagation distance The geometry of the fault is reduced to a point The ground motion is prescribed by empirical equations (region-specific parameters) Source spectrum Crustal amplification Anelastic attenuation (includes Qeff) Near surface attenuation Geometric spreading (GS) factor SMSIM: Region-specific treated as Fixed Freq. - independent Density near the source Freq. - dependent Constants Shear-wave velocity near the source Average radiation pattern Partition factor of motion into two components Free surface factor Source Spectral shape Scaling of shape with magnitude Geometrical spreading Path Site Duration Q Crustal/Site amplification Site diminution (fmax? κ0?) 2

3 SMSIM: Region-specific treated as Fixed From Atkinson and Silva (2000) Freq. - independent Density near the source Freq. - dependent Site Path Source Constants Shear-wave velocity near the source Average radiation pattern Partition factor of motion into two components Free surface factor Atkinson and Silva (2000) double-corner source model Geometrical spreading - The two corners depend only on the Mw, as derived Q from empirical and simulated data - Advantage Duration to be already calibrated for California events - Constrained to match Brune single-corner model for 80 bars at high frequencies Spectral shape Scaling of shape with magnitude Crustal/Site amplification Site diminution (fmax? κ0?) SMSIM: Region-specific treated as Fixed Freq. - independent Density near the source Freq. - dependent Constants Shear-wave velocity near the source Consistent with Average Atkinson radiation and pattern Silva (2000) as described by Raoof at al. (1999) for Partition factor of motion into two California components Free surface factor Source Spectral shape Scaling of shape with magnitude Path Geometrical spreading Duration Q Associated anelastic attenuation: Q = 180f^(0.45) Site T = To R Crustal/Site amplification T0 = Source duration Site diminution (Boatwright(fmax? & Choy, κ0?) 1992) 3

4 SMSIM: Region-specific treated as Fixed Velocity Profile (8 Freq. - independent km) Density near the source Shear-wave velocity near the source Constants Source Path Average radiation pattern Partition Crustal factor of amplification motion into model two components consistent with Vs30 = 863 m/s Free surface factor Geometrical spreading Q Duration Freq. - dependent Velocity Profile (First 30 m - Vs30 = 863 m/s) Spectral shape Scaling of shape with magnitude Not included: Fmax = 0 and Kappa = 0.04 Site Crustal/Site amplification Site diminution (fmax? κ0?) CALIBRATION Initiated 2 weeks ago outside of the BBP and currently for Western US Focus on proposed approach rather than on interim results Performed Random Vibration (RV) simulations consistent with Boore & Thompson (2012) approach Decision to start from PART B: C0mparison with NGA08 GMPEs in the range where they are well constrained (Mw: 6-7, R: km) Calibration of a Working model Planning for validation for PART A: Optimization of the Working model and characterization of jointdistribution of parameters for future events (forward sense) 4

5 CALIBRATION: Source Working Hypothesis Source: Spectral shape Preliminary analyses confirm Atkinson and Silva (2000):. Despite its success in modeling high-frequency ground motions, the single-cornerfrequency point source consistently overpredicts ground motions from moderate-to-large earthquakes at low-tointermediate frequencies (0.1 to 2 Hz) Good agreement at highfrequencies for single and double-corner source. Single-corner overpredicts longer periods CALIBRATION: Source Working Hypothesis Source: Scaling of AS2002 source shape with Mw Lower corner frequency, determined by the source duration T0 = 1/(2fa) From empirical data For simulated events (M ) Relative weighting parameter (between 0 and 1). If e = 1, the two-corner model is identical to a single-corner Brune model). At higher corner frequency the spectrum attains 1/2 of the high-frequency amplitude level. Parameters Fixed 5

6 FUTURE OPTIMIZATION: Validation Part B Finite Fault Effect: Needed to account for effective distance saturation, as caused by the finite-fault geometry Implies the presence of and effective equivalent point-source focal depth (h) h is a function of fault size, and hence earthquake magnitude. FUTURE OPTIMIZATION: Validation Part B R = sqrt (d^2 + h^2) R = d + h Finite Fault Effect: SMSIM allows FFE correction by providing an equivalent point-source distance R, function of d (closest distance to the fault) and h (equivalent point-source depth) Proposed approach: Optimize FFE correction by deriving new function for h (equivalent point-source depth) may be period dependent log h = M Atkinson Distances and Boore in next (2003) plots log h = M Atkinson and Silva (2000) R = sqrt (Rrup^2 + h^2) log h = M Toro (2002) from GMPEs log h = c1 + c2m 6

7 Evidence for FFE correction revision Double-corner spectral shape adequate High-frequency scaling with distance seems problematic Mw km Mw km Mw km Distance scaling FFE correction FUTURE OPTIMIZATION: Validation Part A Proposed approach: Freeze FFE correction Optimize spectral source scaling ( event term -like approach) Calibrate fa and fb for a generic double- corner model (implies characterizing the joint distribution of the two parameters for future earthquakes) Optimized parameters 7

8 FUTURE OPTIMIZATION: Proposed approach Source Model FFE Part B AS 2000 R = f(rrup, h, M, t?) Part A Generic doublecorner R = f(rrup, h, M, t?) Focus on the envisioned process to perform validation, in view of forward application Optimized Fixed parameters QUESTIONS? Thanks! 8

9 SMSIM: method description 100 M = 7.0 SMSIM = Stochastic Model SIMulation Fourier acceleration spectrum (cm/sec) M = 5.0 f 0 f Frequency (Hz) M = 7.0 Point source stochastic simulation method: - The radiation from a fault is assumed to be distributed randomly over a time interval whose duration is related to the source size and the distance from the source to the site. Acceleration (cm/sec 2 ) M = 5.0 R=10 km; =70 bars; hard rock; f max=15 Hz Time (sec) SMSIM: method description In the RVT approach, yrms is obtained from amplitude spectrum: T d 1 2 y u t dt U f df D D ( ) 2 [ ()] 2 ( ) 2 rms = = yrms rms 0 rms 0 is root-mean-square motion Is ground-motion time series (e.g., u (t) accel. or osc. response) D rms is a duration measure 2 ( ) is Fourier amplitude spectrum of ground motion U f Needs extreme value statistics to relate rms acceleration to peak timedomain ground-motion intensity measure (ymax) 9

10 SMSIM: method description Ground motion and response parameters can be obtained via two separate approaches: Time-series simulation: Superimpose a quasi-random phase spectrum on a deterministic amplitude spectrum and compute synthetic record All measures of ground motion can be obtained Not used in current validation Random vibration (RV) simulation: Probability distribution of peaks is used to obtain peak parameters directly from the target spectrum Very fast Can be used in cases when very long time series, requiring very large Fourier transforms, are expected (large distances, large magnitudes) Elastic response spectra, PGA, PGV, PGD, equivalent linear (SHAKE-like) soil response can be obtain SMSIM: Frequency-independent parameters Density near the source (2.72) Shear-wave velocity near the source (3.5) Average radiation pattern (0.55) Partition factor of motion into two components ( 1/sqrt(2) ) Free surface factor (2) Parameters Fixed Consistent with Western Rock 10

11 SMSIM: Frequency-dependent parameters Source: Spectral shape (e.g., single corner frequency; two corner frequency) Scaling of shape with magnitude (controlled by the stress parameter Δσ for single-corner-frequency models) Path (and site): Geometrical spreading (multi-segments?) Q (not frequency-dependent in this validation. What shear-wave and geometrical spreading model used in Q determination?) Duration Crustal amplification (can include local site amplification) Site diminution (fmax? κ0?) correlated SMSIM: RV or TD parameters Low-cut filter RV Integration parameters Method for computing D rms Equation for y max /y rms TD Type of window (e.g., box, shaped?) dt, npts, nsims, etc. Parameters Fixed Consistent with Boore & Thompson (2012) approach 11

12 Consistency with SCEC rock condition: 1) Velocity profile interpolated from 618 m/s and CENA specific 2) Square Root Impedance (SRI) Crustal Amplification derived from interpolated profile 3) Log-space re-sampling of Crustal Amplification for SMSIM input parameters Velocity Profile (8 km) Amplification Velocity Profile (First 30 m - Vs30 = 863 m/s) Frequency (hz) CALIBRATION: Path and Site Working Hypothesis - Path (and site): Geometrical spreading and Q Consistent with Atkinson and Silva (2000) as described by Raoof at al. (1999) for California Geometric spreading of R-1 to a distance of 40 km, with R-0.5 spreading for R greater than 40 km. Associated anelastic attenuation: Q = 180f^(0.45) Parameters Fixed 12