Description of selected broadband
ground motion simulation methods
Paul Somerville, URS
Yuehua Zeng, USGS Golden
Simulation Methods Described:
1. URS
2. Zeng
3. UCSB
4. SDSU
1. URS Hybrid Approach to Broadband
Ground Motion Simulations
(Graves and Pitarka, 2004)
For f < 1 Hz:
• Kinematic representation of heterogeneous rupture on a
finite fault
– Slip amplitude and rake, rupture time, slip function
• 1D FK or 3D FDM approach for Green’s function
For f > 1 Hz:
• Extension of Boore (1983) with limited kinematic
representation of heterogeneous fault rupture
– Slip amplitude, rupture time, conic averaged radiation pattern,
Stochastic phase
• Simplified Green’s functions for 1D velocity structure
– Geometrical spreading, impedance effects
Both frequency ranges have the nonlinear site amplification based on
Vs30 (Campbell and Bozorgnia, 2008)
Kinematic Rupture Generator
–Unified scaling rules for rise time, rupture speed and corner frequency
–Depth scaling for shallow (< 5 km) moment release: rise time (increase)
and rupture speed (decrease)
Scenario Earthquake
• Begin with uniform slip having
mild taper at edges.
• Use Mai and Beroza (2002)
spatial correlation functions (Mw
dependent, K-2 falloff) with
random phasing to specify entire
wavenumber spectrum.
Validation Earthquake
• Validation events begin with
coarse representation from slip
inversion.
e.g., Loma Prieta, Wald et al (1991)
Validation Earthquake
• Validation events begin with
coarse representation from slip
inversion.
e.g., Loma Prieta, Wald et al (1991)
• Low-pass filter to retain only long
wavelength features. Preserves
gross asperity locations.
Validation Earthquake
• Validation events begin with
coarse representation from slip
inversion.
e.g., Loma Prieta, Wald et al (1991)
• Low-pass filter to retain only long
wavelength features. Preserves
gross asperity locations.
• Extend to fine grid using Mai and
Beroza (2002) spatial correlation
functions with random phasing
for shorter wavelengths.
Rupture Initiation Time
Ti = r / Vr – dt(D)
Vr = 80% local Vs depth > 8 km
= 56% local Vs depth < 5 km
linear transition between 5-8 km
dt scales with local slip (D) to
accelerate or decelerate rupture
dt(Davg) = 0
Rise Time
t
= k · D1/2
depth > 8 km
= 2 · k · D1/2 depth < 5 km
linear transition between 5-8 km
Scales with square root of local slip
(D) with constant (k) set so
average rise time is given by the
Somerville et al (1999, 2009)
relations:
tA = 1.6e-09 · Mo1/3
tA = 3.0e-09 · Mo1/3
(WUS)
(CEUS)
Rake
l = lo + e
-60o <
e < 60o
Random perturbations of rake
follow spatial distribution given by
K-2 falloff.
High Frequency Subfault Source Spectrum
• Apply Frankel (1995) convolution operator:
S(f) = C · [ 1 + C · f 2 / fc2 ]-1
C = Mo / (Nspdl3)
N = number of subfaults
sp = stress parameter (50 - WUS),
(125 – CEUS)
dl = subfault dimension
– scales to target mainshock moment
– scales to mainshock rise time
– results generally insensitive to subfault size
• Corner frequency scales with local rupture speed (Vr):
fc = co · Vr / (pdl)
co = 2.1 (WUS), 1.15 (CEUS)
(empirically constrained)
Vr = 80% local Vs depth > 8 km
= 56% local Vs depth < 5 km
linear transition between 5-8 km
1994 Northridge EQ
1994 Northridge EQ
Spectral Acceleration
Goodness of Fit
Ri = ln(Oi /Si)
Bias = (1/N) S Ri
s = [(1/N) S (Ri – Bias)2]1/2
2. Composite Source Model (Zeng et al., 1994)
A source composes of a superposition of smaller subevents.
The distribution of subevents with radius R follows a power law
distribution (Frankel, 1991)
dN
d (ln R )
 pR
D
S-velocity
P-velocity
3. UCSB Broadband Strong Motion Synthetics Method
Archuleta, Hartzell, Lavallée, Liu, Schmedes
Liu, P., R. J. Archuleta and S. H. Hartzell (2006). Prediction of broadband ground-motion
time histories: Hybrid low/high-frequency method with correlated random source
parameters, Bull. Seismol. Soc. Am. vol. 96, No. 6, pp. 2118-2130, doi:
10.1785/0120060036.
Schmedes, J., R. J. Archuleta, and D. Lavallée (2010). Correlation of earthquake source
parameters inferred from dynamic rupture simulations, J. Geophys. Res., 115, B03304,
doi:10.1029/2009JB006689.
Flowchart for Generating
Broadband Strong Motion Synthetics
Liu, Archuleta, Hartzell, BSSA
Correlated
Source Parameters (LAH)
Slip
Spatial correlation 30%
Average rupture
velocity
Spatial correlation 60%
Rise time
(Liu, Archuleta, Hartzell, 2006)
New Kinematic Model (SAL)
Schmedes, J., R. J. Archuleta, and D. Lavallée (2010), Correlation of earthquake source parameters inferred from
dynamic rupture simulations, J. Geophys. Res., 115, B03304, doi:10.1029/2009JB006689.
High Frequencies
Frequency dependent perturbation of strike, dip
and rake (Pitarka et al, 2000)

0

 i   0  ( f  f1 ) /( f 2  f1 )(( 2 ri  1) p ,

 0  (2 * ri  1) *  p
f  f1
f1  f  f 2
f2  f
With f1=1.0 Hz, f2=3.0 Hz

Randomness of the high frequencies is generated in
the source description.
Ground Motion Computation: 3D
Fourth-order viscoelastic FD code:
•Perfectly matched layers
•Coarse grained method
•Allows for two regions of different grid
spacing
Combination of 1D and 3D:
1. Cross correlation at matching frequency fm
to align seismograms.
2. Use 3D at frequencies
0  f  f low
3. Use 1D at frequencies
f up  f  f max
4. For
f low  f  f up

Re( S ( f ))  r( f ) Re(3D ( f ))  (1  r( f )) Re( 1D ( f ))
Im( S ( f ))  r( f ) Im( 3D ( f ))  (1  r ( f )) Im( 1D ( f ))

r( f )  1 
f  f low
f up  f low
4. Hybrid Broadband Ground-Motion
Simulations: Combining Long-Period
Deterministic Synthetics with High-Frequency
Multiple S-to-S Backscattering
Martin Mai, Walter Imperatori, and Kim Olsen
Mai, P.M., W. Imperatori, and K.B. Olsen (2010). Hybrid broadband ground-motion simulations:
combining long-period deterministic synthetics with high-frequency multiple S-to-S backscattering, Bull. Seis. Soc. Am. 100, 5A, 2124-2142.
Mena, B., P.M. Mai, K.B. Olsen, M.D. Purvance, and J.N. Brune (2010). Hybrid broadband
ground motion simulation using scattering Green's functions: application to large magnitude
events, Bull. Seis. Soc. Am. 100, 5A, 2143-2162.
Combines low-frequency deterministic synthetics (f ~ 1 Hz) with high-frequency
scattering operators
Site effects:
• Soil structure
• (De-)amplification of ground motions
• Non-linear soil behavior
Scattering effects:
• inhomogeneities in Earth structure at all scales
• scattering model, based on site-kappa, Q, scattering and intrinsic
attenuation, hs and hi
Site-Specific Scattering Functions
Scattering Green’s functions computed for each component of motion based on Zeng et al.
(1991, 1993) and and P and S arrivals from 3D ray tracing (Hole, 1992) convolved with a
dynamically-consistent source-time function, generating 1/f spectral decay
Site-Scattering parameters (scattering and attenuation coefficient, site kappa, intrinsic
attenuation) are taken from the literature and are partly based on the site-specific velocity
structure.
Assuming scattering operators and moment release originate throughout the fault, but
starts at the hypocenter
Generation of hybrid broadband seismograms
Hybrid broadband seismograms are
calculated from low-frequency and highfrequency synthetics in the frequency
domain using a simultaneous amplitude and
phase matching algorithm (Mai and Beroza,
2003)
Example BB calculation
BB
LF
SC
BB = broadband
LF = low frequency
SC = scattering functions
1/f
Verification and Validation
Method implemented on the SCEC
Broadband platform
Validations include Northridge, Landers
and Loma Prieta, and NGA relations at
selected sites
NGA validation at Precariously Balanced Rock
sites (Mena et al., 2010)
Northridge Validation
(Mai et al., 2010)
Comments and issues:
• URS and Zeng’s models have considered scaling of rise-time/stress-drop and
rupture speed for the upper 5 km depth.
• URS, UCSB, Zeng, and SDSU have variable rupture velocities, subevent rakes,
rise-time ~ local slip, K-2 fall off in slip distribution
• UCSB considered dynamic rupture characteristics for slip time function,
correlations between rupture speed, rise time, local slip, …
• Matched filter for the hybrid approaches:
- amplitude match
- phase match
- wavelet match
1 Hz
Comments and issues:
• URS, UCSB, and SDSU use Green’s functions from 1D/3D wave propagation.
Zeng uses 1D Green’s function. They all naturally include body waves and
surface waves, Lg and Rg phases for regional wave propagation
• Zeng and SDSU use scattering functions for high frequency coda waves
• URS, UCSB, Zeng, and SDSU explicitly consider nonlinear soil responses.
• URS, UCSB, and SDSU are included in the SCEC computation platform. Zeng
is planning to included his.
Input:
For all the models:
Fault geometry, hypocenter, P- and S-wave velocities, Qp and Qs,
fmax, seismic moment, site condition based on Vs30 (nonlinearity),
site kappa
For URS, UCSB, Olsen, Zeng (except slip):
Slip, rise-time, and rupture-time distribution;
correlation between these source parameters
Variable rake, strike, …
In Zeng’s model: slip distribution is defined by subevent stress-drop with
random distribution on subevent locations