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.