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NUMERICAL SIMULATION OF BASIN EFFECTS ON LONG-PERIOD GROUND
MOTION
S. M. Day1, J. Bielak2, D. Dreger3, R. Graves4, S. Larsen5, K. B. Olsen1, A. Pitarka4, and L.
Ramirez-Guzman2
ABSTRACT
We simulate long-period (0-0.5 Hz) ground motion time histories for a suite of
sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin
region. Fault geometries are based upon the Southern California (SCEC)
Community Fault Model, and 3D seismic velocity structure is based upon the
SCEC Community Velocity Model. The ground motion simulations are done
using 5 different 3D finite difference and finite element codes, and we perform
numerous cross-check calculations to insure consistency among these codes. The
nearly 300,000 synthetic time histories from the scenario simulations provide a
resource for ground motion estimation and engineering studies of large, long-
period structures, or smaller structures undergoing large, nonlinear deformations.
By normalizing spectral accelerations to those from simulations performed for
reference hard-rock models, we characterize the source-averaged effect of basin
depth on spectral acceleration. For this purpose, we use depth (D) to the 1.5 km/s
S velocity isosurface as the predictor variable. The resulting mean basin-depth
effect is period dependent, and both smoother (as a function of period and depth)
and higher in amplitude than predictions from local 1D models. The main
requirement for the use of the results in construction of attenuation relationships is
determining the extent to which the basin effect, as defined and quantified in this
study, is already accounted for implicitly in existing attenuation relationships,
through (1) departures of the average “rock” site from our idealized reference
model, and (2) correlation of basin depth with other predictor variables (such as
Vs30).
Introduction
We apply 3D numerical modeling to improve understanding of the effects of sedimentary
basins on long-period (≥ ~2 seconds) earthquake ground motion. The study employs both finite
element (FE) and finite difference (FD) methods to compute ground motion from propagating
earthquake sources in the Southern California Earthquake Center (SCEC) Community Velocity
Model (CVM), a 3D seismic velocity model for southern California (Magistrale et al., 2000).
1Dept. of Geological Sciences, San Diego State University, San Diego CA 92182
2Dept. of Civil and Environmental Engineering, Carnegie-Mellon University, Pittsburgh PA 15213
3Berkeley Seismological Laboratory, University of California, Berkeley, Berkeley CA 94720
4URS Corporation, 566 El Dorado Street, Pasadena CA 91101
5Lawrence Livermore National Laboratory, Livermore CA 94550
Previous work (Day et al, 2001; 2003) documented the mathematical soundness of the five
simulation codes used for the project by comparing results from a set of test simulations. The
comparisons show that all five codes are accurate for the class of problems relevant to this study
(Day, 2003). These tests also demonstrated the validity of putting a lower threshold on the
velocity model to exclude S wave velocity values in the CVM that fall below 500 m/s. The tests
confirmed that imposing this threshold (for the sake of computational efficiency) had negligible
effects within the target bandwidth of 0-0.5 Hz. Validations of these numerical modeling
procedures using recorded strong ground motions for the 1994 Northridge, California,
earthquake are reported in Olsen et al. (2003).
For the current investigation, we compute long-period ground motion in the SCEC CVM
for a suite of 60 earthquake scenarios. The 3-component ground motion time histories from these
scenarios are saved on a grid of 1600 sites covering the Los Angeles region, including sites in the
Los Angeles, San Fernando, and San Gabriel basins, as well as rock sites in the intervening
areas. The results from the current study take 2 forms: (1) We have saved and archived a library
of time histories from the 60 scenarios. In cooperation with the SCEC Community Modeling
Environment project, these time histories are available online, through a web interface
specialized to engineering applications (http://sceclib.sdsc.edu/LAWeb). These long-period time
histories capture basin amplifications, rupture-propagation-induced directivity, and 3D seismic
focusing phenomena. They are suitable for the engineering analyses of large, long-period
structures, and smaller structures undergoing large, nonlinear deformations. (2) The results of the
simulation suite have been analyzed to estimate response spectral amplification effects as a
function of basin depth and period. The resulting mean response has been characterized
parametrically and provided to the Next Generation Attenuation (NGA) project to guide
development of attenuation relations in the empirical (NGA-E) phase of the project.
Earthquake Scenarios
We model sources on ten different faults, or fault configurations (for example, the Puente
Hills fault is modeled in 3 different segmentation configurations). For each fault, we simulate 6
sources, using combinations of 3 different static slip distributions and 2 hypocenter locations.
These are kinematic simulations: rupture velocity, static slip, and the form of the slip velocity
function are all specified a priori.
The areal coverage for the 3D models is the 100 km x 100 km region outlined by the green
box in Figure 1. In all simulations, the boundaries of the computational domain (i.e. absorbing
boundaries) lie at or outside of this area and extend to a depth of at least 30 km. For the uniform
grid FD modelers, a grid spacing of 200 m was used. The FE grid uses a variable element size,
with near-surface elements as small as 30 m in dimension.
We use the 10 faults listed in Table 1 for the scenario calculations. The surface
projections of these faults are also shown in Figure 1. The longitude and latitude coordinates in
this table refer to the geographic location of the top center of the fault, that is, the point on the
surface that is directly above the midpoint of the top edge of the fault. Strike, dip and rake
follows Aki and Richards' (1980) convention. Length, width and depth are all given in km. The
depth refers to the depth below the surface of the top edge of the fault (0 corresponding to a
surface-rupturing event).
For each of the fault geometries, we generate 3 random slip distributions, as realizations
of a stochastic model, for use in the simulations. The slip distributions are generated following
some empirical rules for the size and distribution of asperities as given by Somerville et al.
(1999). The slip values on the fault are drawn from a uniformly distributed random variable, then
spatially filtered to give a spectral decay inversely proportional to wavenumber squared, with a
corner wavenumber at approximately 1/L, where L is fault length. Finally, the slip values are
scaled to the target moment of the scenario. The two hypocenter locations are defined as follows
for each fault: Hypocenter 1 is located at an along-strike (AS1) distance of 0.25 of the fault length
and at a down-dip (DD1) distance of 0.7 of the fault width (measured within the fault plane from
the top edge of the fault, not the ground surface). Hypocenter 2 is located at an along strike (AS2)
distance of 0.75 of the fault length and at a down-dip (DD2) distance of 0.7 of the fault width.
Figure 1. Map of scenario events and model region. See Table 1 for fault names
and event magnitudes.
The slip velocity function for each simulation is an isosceles triangle with a base of
duration Tr. The value of Tr is magnitude dependent and given by the empirically derived
expression (Somerville et al., 1999):
log10(Tr) = 0.5(Mw + 10.7) + log10(2.0 x10–9) , (1)
where log10 is base 10 logarithm and Mw is moment magnitude. Rupture velocity is constant for
all faults and all slip models. This value is set at 2.8 km/s. The rupture starts at the hypocenter
and spreads radially outward from this point at the specified velocity. The simulated duration for
each scenario is 80 seconds.
All simulations use the SCEC CVM, Version 2, except for modifications described below
to impose a lower limit on the velocities and add anelastic attenuation. The unmodified model is
described in Magistrale et al. (2000). The SCEC model is modified as follows: Replace the
SCEC model S velocity with the value 500 m/s whenever the SCEC model value falls below 500
m/s. Whenever this minimum S velocity is imposed, the P wave velocity is set equal to 3 times
the S velocity (1500 m/s in this case). Density values follow the SCEC model without
modification. The quality factors for P and S waves, respectively, Qp and Qs, are set to the
preferred Q model of Olsen et al. (2003).
The 3-component time histories are saved on a 2 km x 2 km grid covering the inner 80
km x 80 km portion of the model area. No filtering is applied to the output. The result is 1600
sites (4800 time histories) for each scenario simulation. For all 60 scenarios, and all sites, we
compute response spectral acceleration (Sa), for 5% damping, as a function of period, for each
component of motion. This is done for 26 periods in the range 2-10 seconds: spectral
acceleration is computed at 0.2 second intervals between 2 and 5 second, and at 0.5 second
intervals between 5 and 10 seconds.
Table 1. List of Fault Rupture Scenarios
Reference Simulations
To aid us in quantifying the effect of sedimentary basins on the computed ground
motions, we perform several auxiliary, or “reference,” simulations. For each of the 10 faults, we
select one rupture scenario, and repeat that simulation using the same source model, but
replacing the SCEC CVM with a horizontally stratified model. The stratified reference model
corresponds to an artificially high-velocity, unweathered hard-rock site. This reference velocity
model was constructed by laterally extending a vertical profile of the SCEC CVM located at (–
118.08333, 34.29167), in the San Gabriel Mountains. As noted, surface S velocities are
artificially high (3.2 km/s) in the resulting model, since this part of the SCEC model does not
account for a weathered layer. The purpose of the reference simulations is solely to provide a
normalization for the results from the simulations done in the full SCEC CMV, as an
approximate means of isolating basin effects from source effects.
Response Spectral Amplifications
Basin amplification effects result from interaction of the wavefield with basin margins,
and depend in a complex, poorly understood manner on period, source location, source distance,
basin geometry, sediment velocity distribution, and site location within the basin. The 60
scenarios provide synthetic data that can be used to improve our understanding of these effects.
We take an initial step in this direction by attempting to isolate the effects of period and local
basin depth. To isolate these 2 effects, we average over sources. As response spectral values vary
much more between ruptures on different faults than between ruptures on a given fault, we have
computed averages using only 1 of the 6 scenarios from each fault, giving us a 10-event subset of
the simulations. This subset misses a small amount of the variability in basin response present in
the full 60-event suite, but allows us to work with spectral values normalized to the reference
structure, without requiring 60 reference-structure simulations. Tests using a small number of
additional events confirm that source effects have been adequately removed by this procedure.
Method
We first bin the sites according to the local basin depth D at a site, with Dj denoting the
depth at site j. For this purpose, we define the depth D to be the depth to the 1.5 km/s S wave
velocity isosurface. Note, however, that in the SCEC CVM, the depths of different S velocity
isosurfaces are strongly correlated, and therefore very similar results are obtained using the 1.0
or 2.5 km/s isosurface instead of the 1.5 km/s isosurface. The binning is represented through a
matrix W. We define Nbin bins by specifying depths
Dq
bin
, q=1, . . . Nbin, at the bin centers, spaced
at equal intervals
!D
(i.e.,
Dq
bin == q!1 2
( )
"D
, and then form W,
Wqj =
1 if Dq
bin ! "D2
( )
#Dj<Dq
bin +"D2
( )
0 otherwise
$
%
&
'
&
. (2)
For consistency with most empirical attenuation relations, we work with response
spectral values averaged over the two horizontal components. For the ith event and jth site, we
form the ratio
Saij (P
k)Saij
ref (P
k)
, where
Saij (P
k)
is the absolute spectral acceleration (averaged
over horizontal components) from SCEC-CVM event i at site j and period Pk, and
Saij
ref (P
k)
is
the corresponding quantity for the corresponding reference-model event. Then we form the
source-averaged basin response factor B(Dq, Pk) by averaging over all Nsite sites (Nsite=1600), and
over all Nev events, where in this case Nev is 10:
B(Dq,P
k)=Nev Wqj
j=1
Nsite
!
"
#
$%
&
'
(1
Wqj Saij (P
k)Saij
ref (P
k)
j=1
Nsite
!
i=1
Nev
!
. (3)
Results
Figure 2 summarizes the results of this procedure for (200 m bins). The upper frame
shows B as a function of depth and period. The lower frame shows basin amplification calculated
by the same procedure, but replacing the spectral acceleration ratio
Saij (P
k)Saij
ref (P
k)
at each
site by the vertically-incident plane-wave amplification factor for that site. The latter factors
were computed using a plane-layered structure specific to each site, and corresponding to the
SCEC-CVM shear wavespeed and density depth-profiles directly beneath that site. The main
results from Figure 2 are the following: (1) Source-averaged basin amplification is period-
dependent, with the highest amplifications occurring for the longest periods and greatest basin
depths. (2) Relative to the very-hard rock reference structure, the maximum amplification is
about a factor of 8. (3) Compared with 1D theoretical predictions, the 3D response is in most
cases substantially higher. (4) The 3D response is also smoother, as a function of depth and
period, than is the 1D prediction, since laterally propagating waves in the former smooth out the
resonances present in the latter.
Figure 2. Top: Basin amplification versus depth and period, calculated from 3D simulations.
Bottom: Basin amplification calculated by same procedure, but replacing the 3D results with 1D
plane-wave amplification factors calculated using the local 1D wavespeed and density profiles
(from the SCEC CVM) at each of the 1600 sites.
Figure 3 presents the results in the form of amplification curves for each of 6 periods. For
depths in the range of roughly 500-1000 m, amplification decreases with period. This is, at least
qualitatively, in agreement with expectations from 1D theory: shallow sediments will have
diminished effect as the wavelength becomes long relative to sediment depth. For depths
exceeding about 1000 m, amplification increases with period. This is a 3D effect: higher-mode
resonances present in the 1D case are smoothed out by lateral scattering, so that the longer-
period resonances dominate.
Figure 3. Basin amplification as a function of depth to 1.5 km/s S wave isosurface.
Parametric Model
It is useful to have a simple functional form that captures the main elements of the
period- and depth-dependent basin amplification behavior observed in the simulations. One
purpose of such a representation is to provide a functional form for representing basin effects in
regression modeling of empirical ground motion data. We constructed a preliminary
representation of this sort to provide immediate guidance to the NGA development team. Our
approximate representation,
!
B D,P
( )
takes the following form:
!
B(D,P)=a0(P)+a1(P) 1 !exp(D300)
[ ]
+a2(P) 1 !exp(D4000)
[ ]
, (4a)
where
ai(P)=bi+ciP, i=0,1,2
, (4b)
The 6 parameters bi, ci were calculated in a two-step procedure. Separate least squares fits at
each period Pk of
!
B D,P
k
( )
to B(Dq,Pk) gave individual estimates of the ai(Pk) values for each
period Pk. Then parameters bi and ci, for each i=0,1,2, were obtained by least-squares fitting of
these 26 individual ai(Pk) estimates. The resulting values are
b0 = –1.06, c0 = 0.124,
b1 = 2.26, c1 = –0.198, (4c)
b2 = 1.04, c2 = 0.261.
The resulting amplification curves are shown in Figure 4. These expressions, despite their
simplicity, represent the mean predictions of the numerical simulations quite well, and can serve
as a starting point for modeling basin effects in empirical studies. In particular, they provide, in
simple form, a physical basis for extrapolation of empirical models to periods greater than 2 or 3
seconds, where reliable data on basin effects are extremely scarce.
Figure 4. Parametric model
!
B
(dashed curves) fit to basin amplification curves B (solid curves)
derived by averaging 3D simulations.
Figure 5 shows the root mean square residual of
Saij (P)Saij
ref (P)
, relative to
!
B D,P
( )
, as
a function of period. That is, the figure depicts R, where
R2P
k
( )
=Nev Wqj
j=1
Nsite
!
"
#
$%
&
'
(1
Saij (P
k)Saij
ref (P
k)(!
B Dj,P
k
( )
)
*+
,
2
j=1
Nsite
!
i=1
Nev
!
. (5)
The residuals decrease systematically with period. This period-dependence is what one would
expect on the basis of simple physical arguments. Short-period waves are subject to short-
wavelength variations due to local focusing and interference effects. Very long-period waves, in
contrast, represent oscillations that are coherent over large scale lengths and are influenced
principally by large-scale averages of the seismic velocity structure.
Figure 5. Root-mean-square residual of spectral acceleration amplification, relative to predictions
from parametric model.
Discussion and Conclusions
We characterize the source-averaged effect of basin depth on spectral acceleration using
depth (D) to the 1.5 km/s S velocity isosurface as the predictor variable. The resulting mean
basin-depth effect is period dependent, and both smoother (as a function of period and depth) and
higher in amplitude than predictions from local 1D models. For example, relative to a reference
hard-rock site, sites with D equal to 2.5 km (corresponding to some of the deeper L.A. basin
locations) have a predicted mean amplification factor of approximately 5.5 at 2 s period, and
approximately 7.5 at 10 s period.
The basin amplification estimates described in this report are intended to guide the design
of functional forms for use in attenuation relationships for elastic response spectra. In particular,
they should be useful guides for extrapolating the period-dependence of basin terms to periods
longer than a few seconds, where empirical data provide little constraint. More direct,
quantitative use of the results may become possible in the future, however. The main
requirement is that we first carefully assess the extent to which the basin effect, as defined and
quantified in this study, is already accounted for implicitly in existing attenuation relationships,
through (1) departures of the average “rock” site from our idealized reference model, and (2)
correlation of basin depth with other predictor variables (such as Vs30). A preliminary assessment
of the reference model bias is presented in Day et al. (2005). They find that the reference-model
simulations under-predict the rock regression model of Abrahamson and Silva (1997) by a factor
of 2 at long period (5 seconds). They argue that at the long periods considered, both source
details and Vs30 will have minimal effects, and that this factor of 2 is likely representative of a
seismic velocity shift (between the average engineering rock-site and the reference model)
extending to depths of the order of half a kilometer or more. The correlation of basin effects with
Vs30 is discussed by Choi et al. (2005), who propose data analysis procedures for separating
these effects.
Acknowledgments
This work was supported by Pacific Earthquake Engineering Research (PEER) Center
Lifelines Program (Tasks 1A01, 1A02, and 1A03), the National Science Foundation under the
Southern California Earthquake Center (SCEC) Community Modeling Environment Project
(grant EAR-0122464), and by SCEC. SCEC is funded by NSF Cooperative Agreement EAR-
0106924 and USGS Cooperative Agreement 02HQAG0008.
References
Abrahamson, N. A., and W. J. Silva (1997). Empirical response spectral attenuation relations for shallow
crustal earthquakes, Seism. Res. Lett. 68, 94-127.
Aki, K., and P. G. Richards (1980). Quantitative Seismology, Theory and Methods, W. H. Freeman and
Co., New York.
Choi, Y., J. P. Stewart. And R. W. Graves (2005). Empirical model for basin effects accounts for basin
depth and source location, Bull. Seism. Soc. Am., Vol. 95, 1412-1427, doi: 10.1785/0120040208.
Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2001). Tests of 3D
elastodynamic codes: Final report for Lifelines Project 1A01, Pacific Earthquake Engineering
Research Center.
Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2003). Tests of 3D
elastodynamic codes: Final report for Lifelines Project 1A02, Pacific Earthquake Engineering
Research Center.
Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2005). 3D ground
motion simulation in basins: Final report for Lifelines Project 1A03, Pacific Earthquake
Engineering Research Center.
Magistrale, H., S. M. Day, R. Clayton, and R. W. Graves (2000). The SCEC southern California reference
three-dimensional seismic velocity model version 2, Bull. Seism. Soc. Am., 90, S65-S76.
Olsen, K. B., S. M. Day, and C. R. Bradley (2003). Estimation of Q for long-period (>2 s) waves in the
Los Angeles Basin, Bull. Seism. Soc. Am., 93, 627-638.
Somerville, P.G., K. Irikura, R. Graves, S. Sawada, D. Wald, N. Abrahamson, Y. Iwasaki, T. Kagawa, N.
Smith and A. Kowada (1999). Characterizing crustal earthquake slip models for the prediction of
strong ground motion, Seism. Res. Lett. 70, 59-80.
