broadband simulation methodology: a hybrid deterministic and stochastic approach
DESCRIPTION
BROADBAND SIMULATION METHODOLOGY: A HYBRID DETERMINISTIC AND STOCHASTIC APPROACH. Robert Graves, Arben Pitarka, Nancy Collins, and Paul Somerville URS Corporation. Use Deterministic Methodology at Low Frequencies (f < 1 Hz) Use Stochastic Methodology at High Frequencies (f > 1 Hz) - PowerPoint PPT PresentationTRANSCRIPT
03/24/2004 NGA Workshop: Validation 1
BROADBAND SIMULATION METHODOLOGY: A HYBRID DETERMINISTIC AND STOCHASTIC APPROACH
Use Deterministic Methodology at Low Frequencies (f < 1 Hz)
Use Stochastic Methodology at High Frequencies (f > 1 Hz)
Apply Site-specific Amplification Factors Based on Vs30
Combine using matched filters (1 Hz) and summing in time domain
Robert Graves, Arben Pitarka, Nancy Collins, and Paul SomervilleURS Corporation
03/24/2004 NGA Workshop: Validation 2
Kinematic representation of heterogeneous rupture on a finite fault.
- slip amplitude - slip direction (rake) - rupture velocity - rise time
Wave propagation modeled using full waveform Green’s functions calculated for 1D or 3D velocity structure.
Site response based on Vs30 using Borcherdt’s (1994)
short- and mid-period amplification factors.
Deterministic Methodology (f < 1 Hz)
03/24/2004 NGA Workshop: Validation 3
Stochastic Methodology (f > 1 Hz)
Limited kinematic representation of heterogeneous rupture on a finite fault (extension of Boore, 1983).
- slip amplitude (stress parameter = 50)
- rupture velocity - rupture duration - average radiation pattern - stochastic phasing
Simplified Green’s functions for 1D velocity structure.
- amplitude decays as inverse of ray path - impedance effects based on Boore and Joyner (1997)
Site response based on Vs30 using Borcherdt’s (1994) short-
and mid-period amplification factors.
03/24/2004 NGA Workshop: Validation 4
Site Amplification Factors (Borcherdt, 1994)
Fa = (Vref / Vsite) ma (high-frequency) Vref = Vs
30 in simulation
Fv = (Vref / Vsite) mv (mid-frequency) Vsite = Vs
30 at site
Applied in Fourier domain, although strictly defined for response spectra.
Fv
Fa
03/24/2004 NGA Workshop: Validation 5
Tp Tr
A
h
Source Rupture Model
- slip distribution
- rupture timeTi = R / Vr - t (slip) Vr = 0.8 Vs
- slip velocity function
Tr = 2 x 10-9 Mo1/3
Tp = 0.2 Tr
h = 0.2 A
03/24/2004 NGA Workshop: Validation 6
1994 Northridge Mw 6.7- strong motion recordings at 69 sites - complex basin geology (SCEC v2.2b)
- slip distribution after Hartzell et al. (1996)
03/24/2004 NGA Workshop: Validation 7
Site type C
Site type DSite type B
Time History Comparison
03/24/2004 NGA Workshop: Validation 8
Observed and Simulated PGA and PGV
03/24/2004 NGA Workshop: Validation 9
Model Bias and Standard Error: Response Spectra
Residuals vs. distance / site typeGlobal goodness-of-fit (38 sites, avg. horizontal)
Average horizontalwithout site factors
without site factors
03/24/2004 NGA Workshop: Validation 10
Residuals show no significant azimuthal trends(slight over-prediction in SF valley)
03/24/2004 NGA Workshop: Validation 11
1989 Loma Prieta Mw 6.9- strong motion recordings at 32 sites - lateral velocity change across SAF
- slip distribution after Wald et al. (1991)
03/24/2004 NGA Workshop: Validation 12
Site type BC
Site type DSite type C
Time History Comparison
03/24/2004 NGA Workshop: Validation 13
Observed and Simulated PGA and PGV
03/24/2004 NGA Workshop: Validation 14
Model Bias and Standard Error: Response Spectra
Residuals vs. distance / site typeGlobal goodness-of-fit (32 sites, avg. horizontal)
Average horizontal
03/24/2004 NGA Workshop: Validation 15
Residuals show no significant azimuthal trends (over-prediction in Gilroy at longer periods)
03/24/2004 NGA Workshop: Validation 16
CONCLUSIONS Hybrid (deterministic + stochastic) broadband simulation methodology works well in
reproducing observed near-fault motions for the Loma Prieta and Northridge earthquakes.
Source specification requires relatively few parameters:
magnitude and geometry slip distribution global rise time hypocenter location
Wave propagation effects in complex 3D media are readily incorporated in the
deterministic calculation. Gross impedance effects are included in the stochastic calculation using quarter
wavelength theory for a specified 1D model (Boore and Joyner, 1997). Frequency dependent site amplification factors based on Vs
30 are generated following Borcherdt (1994) and are applied to the Fourier spectra of the broadband time histories.
The success of the validation exercises support the use of this methodology for
simulating broadband time histories for scenario earthquakes.