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Model for Basin Effects on Long-Period Response Spectra in Southern California

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We propose a model for the effect of sedimentary basin depth on long- period response spectra. The model is based on the analysis of 3-D numerical simulations (finite element and finite difference) of long-period 2-10 s ground motions for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin region. We find depth to the 1.5 km/s S-wave velocity isosurface to be a suitable predictor variable, and also present alternative versions of the model based on depths to the 1.0 and 2.5 km/s isosurfaces. 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 1-D 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). DOI: 10.1193/1.2857545
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Model for Basin Effects on Long-Period
Response Spectra in Southern
California
StevenM.Day,
a)
Robert Graves,
b)
Jacobo Bielak,
c)
Douglas Dreger,
d)
Shawn Larsen,
e)
Kim B. Olsen,
a)
Arben Pitarka,
b)
and
Leonardo Ramirez-Guzman
c)
We propose a model for the effect of sedimentary basin depth on long-
period response spectra. The model is based on the analysis of 3-D numerical
simulations (finite element and finite difference) of long-period
2–10 s
ground motions for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1)
within the Los Angeles basin region. We find depth to the
1.5 km/s S-wave
velocity isosurface to be a suitable predictor variable, and also present
alternative versions of the model based on depths to the 1.0 and
2.5 km/s
isosurfaces. 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 1-D 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
Vs
30
). DOI: 10.1193/1.2857545
INTRODUCTION
The entrapment and amplification of seismic waves by deep sedimentary basins pro-
duces important effects on seismic wavefields (e.g., King and Tucker 1984; Field 1996;
Joyner 2000) and response spectra (e.g., Trifunac and Lee 1978; Campbell 1997; Field
2000; Choi et al. 2005). These amplification effects are three-dimensional, and they are
difficult to quantify empirically with currently available strong motion data, especially
for periods longer than
1 second and sedimentary thicknesses exceeding 3kmor so
(Campbell and Bozorgnia 2008).
Numerical simulations of earthquake ground motion have the potential to comple-
ment empirical methods for the study of basin effects. A number of studies have simu-
lated 3-D seismic wave propagation in regional geological models that include basin
a)
Department of Geological Sciences, San Diego State University, San Diego CA 92182
b)
URS Corporation, 566 El Dorado Street, Pasadena CA 91101
c)
Department of Civil and Environmental Engineering, Carnegie-Mellon University, Pittsburgh PA 15213
d)
Berkeley Seismological Laboratory, University of California, Berkeley, Berkeley CA 94720
e)
Lawrence Livermore National Laboratory, Livermore CA 94550
257
Earthquake Spectra, Volume 24, No. 1, pages 257–277, February 2008; © 2008, Earthquake Engineering Research Institute
structure (e.g., Frankel and Vidale 1992; Olsen 1994; Olsen et al. 1995; Pitarka et al.
1998; Graves et al. 1998). Moreover, the recent availability of comprehensive 3-D earth
models for southern California (e.g., Magistrale et al. 2000; Kohler et al. 2003; Suss and
Shaw 2003) has substantially advanced our capability for simulating ground motion in
that region (e.g., Olsen 2000; Komatitsch et al. 2004; Olsen et al. 2006). In the current
study, we simulate ground motions for a set of earthquake scenarios for southern Cali-
fornia, in an effort to quantify the effects of sedimentar y basins on long-period
2 seconds response spectra. The study employs both finite element (FE) and finite
difference (FD) methods to compute ground motion from propagating earthquake
sources, using the Southern California Earthquake Center (SCEC) Community Velocity
Model (CVM), a 3-D seismic velocity model for southern California (Magistrale et al.
2000).
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 his-
tories 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 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 3-D seismic focusing phenomena. They are
suitable for the engineering analyses of large, long-period structures, and smaller struc-
tures 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 parametri-
cally and provided to the Next Generation Attenuation (NGA) project (Power et al.
2008) to guide development of attenuation relations in the empirical (NGA-E) phase of
the project.
COMPUTATIONAL METHODS
The computational program was a multi-institutional collaboration requiring major
computing resources. In order to make effective use of supercomputing resources avail-
able to the respective collaborators, as well as to have cross-checks on the methodology,
we employed five independently developed 3D wave propagation codes to do the nu-
merical simulations. Four of these are FD codes (Olsen 1994; Larsen and Schultz 1995;
Graves 1996; Pitarka 1999). These four are very similar in their mathematical formula-
tion. Each uses a uniform, structured, cubic mesh, with staggered locations of the ve-
locity and stress components, and a differencing scheme that is fourth-order accurate in
space and second-order accurate in time. The codes differ in their computational ap-
proaches, their implementation of absorbing boundary conditions, and their implemen-
tation of anelastic attenuation. We used a FE code (Bao et al. 1998) for some of the
simulations. The FE code uses unstructured meshing, and is second-order accurate in
space and time.
258 DAYETAL.
Two of the FD schemes (Olsen, Graves) approximate a frequency-independent seis-
mic quality factor
Q by implementing anelastic losses using the coarse memory vari-
ables representation (Day 1998; Day and Bradley 2001; Graves and Day 2003). Another
(Larsen) uses a standard linear solid formulation that represents the absorption spectrum
with a single Debye peak. The fourth FD scheme (Pitarka) represents attenuation by the
method of Graves (1996), which is equivalent to mass-proportional Rayleigh damping
and results in
Q proportional to frequency (i.e., a red absorption spectrum). The FE
scheme also uses the mass-proportional Rayleigh damping approximation to represent
anelastic loss.
Comparison of results among these codes is useful for verifying the mathematical
soundness of the five simulation codes. Such comparisons also permit assessment of any
artifacts attributable to the absorbing boundary and attenuation implementations. Day
et al. (2001, 2003) carried out a set of test simulations using all five codes. The com-
parisons between FD and FE solutions are particularly informative, as they permit an
assessment of solution variability introduced by the model discretization. We show an
example of such a comparison in a later section. The comparisons verify that all five
codes are accurate for the class of problems relevant to this study.
These tests also enabled us to improve computational efficiency by modifying the
SCEC CVM to eliminate very low seismic wavespeeds. Computing time is sensitive to
the ratio of highest to lowest wavespeed present in the model, with low-wavespeed vol-
umes requiring finer meshing than high-wavespeed volumes to ensure a given accuracy
over a given bandwidth. The unstructured meshing possible with the FE method permit-
ted us to perform a few simulations that include the very low-velocity, near-surface sedi-
ments present in the CVM (
S velocity as low as 180 m/ s). We compared these with cal-
culations in which we put a lower threshold on the velocity model to exclude
S wave
velocity values in the CVM that fall below
500 m/ s (replacing the lower values with the
500 m/ s threshold value). The tests confirm that imposing this threshold (for the sake of
computational efficiency) has negligible effect within the target bandwidth of
00.5 Hz.
Olsen et al. (2003) carried out simulations of the 1994 Northridge, California, earth-
quake, using the SCEC CVM, with the same FD method used in the current study, and
their comparisons of synthetic and recorded ground velocities demonstrate the ability of
the numerical modeling procedures to capture basin amplification effects. Further vali-
dation is provided by comparison of synthetic (FD and FE) and recorded seismic wave-
forms of small southern Califor nia earthquakes. For example, Chen et al. (2007) find
that FD synthetics computed with the SCEC CVM model give a variance reduction of
greater than 60% in both phase-delay times and log of amplitude, relative to a standard
1-D model. Additional validation for the velocity structure used in this study is provided
by sonic log data, on the basis of which Stewart et al. (2005) estimate that uncertainties
in basin depth in the SCEC CVM introduce uncertainties in ground motion (up to 0.1
natural log units) that they judge to be small compared with typical error terms in
attenuation relations.
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 259
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 3-D models is the
100 km 100 km region outlined by
the large gray 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 FD calculations, a uniform 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.
Figure 1. Map of scenario events and model region. See Table 1 for fault names and event
magnitudes. Each rectangle is the surface projection of one of the faults, with the upper edge
shown as a solid line and the other three edges shown as dashed lines. The large gray rectangle
indicates the computational domain of the simulations.
260 DAYETAL.
We use the 10 faults listed in Table 1 for the scenario calculations. The fault surfaces
are simplified representations of the f ault geometry given by the SCEC Community
Fault Model, and our choice of rupture scenarios was guided in part by the geologic con-
siderations surveyed by Dolan et al. (1995). 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 follow 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 realiza-
tions of a stochastic model, for use in the simulations. The slip distributions are gener-
ated 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 dis-
tributed random variable, then spatially filtered to give a spectral decay inversely pro-
portional to wavenumber squared, with a corner wavenumber at approximately
1/L,
where
L is f ault length. Finally, the slip values are scaled to the target moment of the
scenario. As an example, Figure 2 shows the slip distribution functions generated by this
procedure for one of the faults (Compton, fault number 8 in Figure 1). The two hypo-
center locations (shown as stars in Figure 2) are defined as follows for each fault: Hy-
pocenter 1 is located at an along-strike distance of 0.25 of the fault length and at a
down-dip 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
distance of 0.75 of the fault length and at a down-dip distance of 0.7 of the fault width.
Table 1. List of fault rupture scenarios
Fault Lon Lat M
w
Length Width Strike Dip Rake Depth
r
1)smad −118.178 34.242 7.0 61 18 288 53 90 0 1.4
2)smon1
−118.479 34.039 6.3 14 14 261 36 45 1 0.63
3)hwood
−118.343 34.099 6.4 14 19 256 69 70 0 0.71
4)raym2
−118.128 34.139 6.6 26 17 258 69 70 0 0.89
5)ph2e
−118.004 33.904 6.8 25 27 268 27 90 3 1.1
6)phla
−118.228 34.003 6.7 21 26 293 28 90 3 1.0
7)phall
−118.102 33.967 7.1 46 27 289 27 90 2 1.6
8)comp
−118.344 33.843 6.9 63 14 306 22 90 5 1.3
9)nin
−118.202 33.868 6.9 51 16 319 90 180 0 1.3
10)whitn
−117.876 33.933 6.7 35 15 297 73 180 0 1.0
(1) Lengths in kilometers, times in seconds, angles in degrees
(2)
r
is slip duration (from Equation 1)
(3) Geographical and depth coordinates refer to center of upper fault edge
(4) Faults are Sierra Madre (smad), Santa Monica (smon1), Hollywood (hwood), Puente Hills (northern segment
is ph2e, southern segment is phla, combined scenario is phall), Compton (comp), Newport-Inglewood (nin), and
Whittier (whitn).
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 261
The slip velocity function for each simulation is an isosceles triangle with a base of
duration
r
. The value of
r
is magnitude dependent and given by the empirically derived
expression (Somerville et al. 1999):
log
10
r
= 0.5M
w
3.35, 1
where M
w
is moment magnitude and
r
is in seconds. Values used for
r
are given in
Table 1. 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 un-
modified model is described in Magistrale et al. (2000). The SCEC model is modified as
follows: We 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). Den-
sity values follow the SCEC model without modification. The quality factors for
P and
S waves, respectively, Q
p
and Q
s
, are set to the preferred Q model of Olsen et al. (2003).
The 3-component time histories are saved on a
2km 2kmgrid covering the inner
80 km 80 km portion of the model area (Figure 3). No filtering is applied to the out-
put. The resulting synthetic data set contains 3-component records for 1600 sites (4800
time histories) for each scenario simulation. For all 60 scenarios, and all sites, we com-
pute response spectral acceleration (Sa), for 5% damping, as a function of period, for
Figure 2. The three slip distributions and two hypocenter locations (stars) used in combination
to provide sources for the six Compton Fault simulations. The distributions were generated by
the stochastic approach described in the text.
262 DAYETAL.
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 seconds, and
at
0.5 second intervals between 5 and 10 seconds.
The earthquake scenarios in this study are limited to events on faults near or within
the main sedimentary basins of the Los Angeles region. We have excluded earthquake
scenarios for the more distant San Andreas fault, for which several earthquake scenarios
of Mw greater than 7.5 have been proposed (e.g., Working Group on California Earth-
quake Probabilities 1995). Olsen et al. (2006; 2008) simulate large San Andreas fault
earthquakes, finding unusually strong basin effects for some events. In particular, in their
simulations the sequence of basins south of the Transverse Ranges, between the San An-
dreas and Los Angeles, acts as a waveguide. The resultant channeling of seismic energy
into the Los Angeles region produces anomalously high amplitudes at some relatively
distant basin sites.
Figure 3. Map showing the grid of time-history output sites (dots). Sites shown as triangles are
those at which we cross-checked results from difference simulation codes.
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 263
COMPARISON OF FE AND FD SOLUTIONS
As noted above, the FD simulations used a uniform grid spacing of
200 m. Since
seismic velocities as low as
500 m/ s are present in the model, and the target frequency
band of the simulations is
00.5 Hz, the FD simulations resolve the minimum wave-
length with about 5 grid intervals. At this resolution, phase-velocity errors over homo-
geneous paths are typically very small (for the fourth-order staggered-grid FD method
used here), of the order of 1% or less (Levander 1988). However, it is difficult to trans-
late this measure of accuracy into accuracy of ground motion time histories calculated
over complex paths. To confir m that the FD simulations indeed predict ground motion
time histories accurately within our target frequency band, we repeated some of them
using the FE method, with a highly oversampled mesh (feasible because of the unstruc-
tured meshing capability of the FE method). The FE simulations employed node spacing
as small as
30 m in the low-velocity parts of the model. Thus, even accounting for the
approximate factor of two difference in points-per-wavelength requirement for a given
phase-velocity accuracy between the (fourth-order accurate) FD method and the
(second-order accurate) FE method, the FE simulations can be expected to have about
three times better resolution of the minimum wavelength in the basins. Figure 4 com-
pares three-component velocity time-histories for one of the scenarios (Newport-
Inglewood fault), as computed by FE and FD methods, respectively. The time histories
are for the 16 locations denoted by triangles in Figure 3. In nearly all cases the differ-
ences between the solutions are negligible, in that relative phase-delay times for the
dominant arrivals never exceed a few tenths of a second, and their amplitude differences
rarely reach 10%.
Figure 5 provides a quantitative comparison in the frequency domain. The figure was
constructed from smoothed (
0.1 Hz band averages) Fourier spectra of the 16 FD and 16
FE EW-component velocity time histories in Figure 4. The figure shows means and stan-
dard deviations (over the 16 recordings) of the natural logarithm of the FD to FE spectral
ratio, for each independent frequency band. The FD/FE bias is less than 10% (and scat-
ter less than 25%) for all frequencies in our target band of
00.5 Hz. Given the heavy
oversampling achieved for the FE solution, this ag reement provides strong evidence that
both methods have adequate resolution to be accurate throughout the target frequency
band. It also shows that there are no significant biases introduced by the different ways
in which the two methods model anelastic attenuation.
We have made similar comparisons for 10 such simulation pairs (i.e., comparing re-
sults from either a pair of FD codes or from an FD FE pair). Because the FD and FE
computational meshes are very different, sampling the SCEC CVM at different points
(and with much higher resolution in the near surface in the case of the FE grid), the
FE/FD comparison represents the worst case for achieving agreement between codes.
Simulations of the same scenario computed with different FD codes produce time his-
tories and spectra that are almost indistinguishable.
264 DAYETAL.
REFERENCE SIMULATIONS
To aid us in quantifying the effect of sedimentary basins on the computed ground
motions, we perform several auxiliary, or “reference, simulations (using the same FE
and FD methods used for all the other simulations). For each of the 10 faults, we select
one rupture scenario, and repeat that simulation using the same source model, but re-
placing the SCEC CVM with a horizontally stratified (1-D) model. The stratified refer-
ence 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
Figure 4. Comparson of finite element and finite difference solutions for one of the Newport-
Inglewood rupture-scenario simulations. Velocity time histories are shown for the 16 sites
shown as triangles in Figure 3. North-south (NS), east-west (EW) and up-down (UD) compo-
nent traces are given. The upper number of each pair on the left designates the station number,
as given in Figure 3. The lower number of each pair gives the peak velocity (for the component
having the largest peak), in cm/s.
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 265
SCEC CVM located at (−118.08333, 34.29167), in the San Gabriel Mountains. As
noted, surface
S velocities are ar tificially high 3.2 km/ s in the resulting model, since
this part of the SCEC model does not account for a weathered layer. The principal pur-
pose of the reference simulations is to provide a spectral normalization for the results
from the simulations done in the full SCEC CMV, as an approximate means of isolating
basin effects from source effects.
Figure 6 shows velocity time histories for a Newport-Inglewood scenario (source and
recording sites are the same as used for the FD/FE comparison shown in Figure 4). The
figure compares three-component velocities for the simulation done with the SCEC
CVM with the corresponding velocities for the reference simulation. The comparison
gives an idea of the importance of 3-D structure, which introduces effects that are espe-
cially pronounced at long period and late in the time series.
RESPONSE SPECTRAL AMPLIFICATIONS
Basin amplification effects result from interaction of the wavefield with basin mar-
gins, 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 un-
derstanding 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 two effects, we aver-
age over sources. As response spectral values vary much more between ruptures on dif-
ferent 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
Figure 5. Ratio of smoothed (over 0.1 Hz bands) Fourier spectra of the EW-component FD and
FE solutions shown in Figure 4. Solid circles are averages (over the 16 sites) of the natural
logarithm of the FD to FE spectral ratio, and error bars give the corresponding standard
deviations.
266 DAYETAL.
structure, without requiring 60 reference-structure simulations. Tests using a small num-
ber of additional events confirm that source effects have been adequately removed by
this procedure.
The synthetic time histories are band limited, and, although there is no abrupt spec-
tral cutoff at the
0.5 Hz limit, the synthetics rapidly become spectrally deficient above
this frequency. This limitation will have the effect of biasing response spectral estimates
downward at frequencies near, yet still below, the
0.5 Hz cutoff (since each response
spectral ordinate is a finite-bandwidth measure of ground motion), compared with values
that would be calculated from full-bandwidth time histories. We have made a quantita-
tive estimate of this bias by calculating response spectra from 25 recordings of the 1992
Figure 6. Comparison of time histories for one of the 3D (SCEC CVM) simulations (Newport-
Inglewood rupture scenario) with the time histories for the corresponding reference (1-D rock
model) simulation.
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 267
Landers, California, earthquake. We calculated the response spectra both before and af-
ter applying a low-pass filter to remove Fourier spectral components above
0.5 Hz.Ata
period of
2s(i.e., right at the upper frequency cutoff), the low-passed case has its re-
sponse spectrum biased downward by 45%. However, at
3speriod the bias is only 15%
and falls rapidly as the period lengthens further (e.g., to 4% at
4s). The actual bias in
our case will be even lower, as the synthetics do not have as sharp a spectral cutoff as we
created by filtering the Landers earthquake data. Further more, any bias will be further
reduced because our presentation is in terms of spectral ratios. That is, in all cases we
normalize the response spectra by dividing them by response spectra for reference so-
lutions that have the same Fourier spectral limits (and as a result have similar response-
spectral bias). The effectiveness of the normalization in removing the short-period bias
is difficult to quantify, but is qualitatively supported by the consistency and smoothness
with which the
2sspectra extrapolate trends defined at longer period (as seen in the
results to be presented later). Therefore, we present the normalized response spectra for
periods as low as
2s, but the ordinates at periods below 3sshould be interpreted with
caution; only at periods of
3sand longer do we have quantitative corroboration that the
response spectra are nearly unbiased (i.e., within
15% tolerance).
METHOD
We first bin the sites according to the local basin depth D at a site, with D
j
denoting
the depth at site
j. For this purpose, we define the depth D to be the depth to a specified
S-wave velocity isosurface. We present results for the case
D=Z
1.5
, where Z
1.5
is depth
to the
1.5 km/s isosurface. Note, however, that in the SCEC CVM, the depths of dif-
ferent
S velocity isosurfaces are strongly correlated, and therefore very similar results
(apart from a scaling of the depth variable) are obtained using the 1.0 or
2.5 km/s iso-
surface (
Z
1.0
or Z
2.5
) instead of the 1.5 km/ s isosurface. The binning is represented
through a matrix
W. We define N
bin
bins by specifying depths D
q
bin
, q=1, ...N
bin
,atthe
bin centers, spaced at equal intervals
D (i.e., D
q
bin
=q −1/2D, and then form W,
W
qj
=
1ifD
q
bin
D/2 D
j
D
q
bin
+ D/2
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
Sa
ij
T
k
/Sa
ij
ref
T
k
, where Sa
ij
T
k
is the absolute spectral accel-
eration (geometrical mean of the two horizontal components) from SCEC-CVM event
i
at site j and period T
k
, and Sa
ij
ref
T
k
is the corresponding quantity for the corresponding
reference-model event. Then we form the source-averaged basin response factor
BD
q
,T
k
by taking the natural logarithm and averaging over all N
site
sites N
site
=1600, and over all N
ev
events, where in this case N
ev
is 10:
BD
q
,T
k
=
N
ev
j=1
N
site
W
qj
−1
i=1
N
ev
j=1
N
site
W
qj
lnSa
ij
T
k
/Sa
ij
ref
T
k
兲兴. 3
268 DAYETAL.
RESULTS
Figure 7 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
Sa
ij
T
k
/Sa
ij
ref
T
k
at each site by the vertically incident plane-wave amplification factor
Figure 7. Top: Natural logarithm of basin amplification versus depth (to 1.5 km/ s S-velocity
isosurface) and period, calculated from 3D simulations. Bottom: Natural logarithm of basin am-
plification calculated by same procedure, but replacing the 3D results with 1-D plane-wave am-
plification f actors calculated using the local 1-D wavespeed and density profiles (from the
SCEC CVM) at each of the 1600 sites.
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 269
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 7 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) Com-
pared with 1-D theoretical predictions, the 3-D response is in most cases substantially
higher. (4) The 3-D response is also smoother, as a function of depth and period, than is
the 1-D prediction. We attribute the smoother depth and period dependence to the pres-
ence of laterally propagating waves in the 3-D case that smooth out the resonances
present in the 1-D case.
Figure 8 shows the standard deviations
s of the logarithm of amplification, as a func-
tion of depth and period, that is,
s
2
D
q
,T
k
=
N
ev
j=1
N
site
W
qj
−1
i=1
N
ev
j=1
N
site
W
qj
lnSa
ij
T
k
/Sa
ij
ref
T
k
兲兴 BD
q
,T
k
兲其
2
. 4
Most values fall between 0.5 and 0.6, and there is a mild tendency for s to increase
at the short-period end of our range. The differences are small, but some period-
dependence of this sort is what one might expect on the basis of simple physical argu-
ments. Short-period waves are subject to short-wavelength variations due to local focus-
Figure 8. Standard deviation of the natural logarithm of basin amplification, as function of
depth and period, from the 3D simulations.
270 DAYETAL.
ing 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 9 presents the basin-depth dependence of
B in the form of mean amplification
values (open circles) and their standard deviations (vertical bars) for each of 3 periods
(2, 4, and
8s). For depths Z
1.5
in the range of roughly 5001000 m, mean amplifica-
tion tends to decrease slightly with period, though the effect is small compared with the
scatter. This result is, at least qualitatively, in agreement with expectations from 1-D
theory: Shallow sediments will have diminished effect as the wavelength becomes long
relative to sediment depth. For depths exceeding about
2000 m, mean amplification in-
creases systematically with period. This is a 3-D effect: Higher-mode resonances present
in the 1-D case are smoothed out by lateral scattering, so that the longer-period reso-
nances dominate. Numerical values of
B are given in Table 2 for a range of representa-
tive periods and depths.
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
Figure 9. Natural logarithm of the basin amplification factor, as a function of depth to the
1.5 km/ s S velocity isosurface. Solid circles of a given color represent the mean amplification
factor for one response-spectral period, and the error bars give the standard deviations. For clar-
ity, only three periods (2, 4, and 8 s) are shown, out of the 26 periods calculated. Further nu-
merical results are given in Table 2. The dashed curves are the corresponding basin amplifica-
tion factors calculated from the parametric model (Equation 5a and 5b and Table 3) fit to the 3D
simulation results.
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 271
preliminary representation of this sort to provide guidance to the NGA development
teams. Our approximate representation,
B
˜
D , T takes the following form:
B
˜
D,T = a
0
T + a
1
T兲关1 expD/300兲兴 + a
2
T兲关1 expD/4000兲兴, 5a
where
a
i
T = b
i
+ c
i
T, i = 0,1,2, 5b
with T given in seconds and D in meters. This functional form is not itself based directly
upon physical considerations, but rather serves to summarize the practical results of the
simulations (which of course are themselves based on the physics of seismic wave
propagation). The particular function in Equation 5a and 5b was chosen because (i) it
allows for a basin-depth dependence with decreasing slope at increasing values of the
depth parameter, as required to capture the behavior shown in Figure 9, and (ii) it per-
mits the depth dependence to vary with period, as also required by Figure 9. The 6 pa-
rameters
b
i
, c
i
were calculated in a two-step procedure. Separate least squares fits (at
each period
T
k
)ofB
˜
D , T
k
to BD
q
,T
k
) gave individual estimates of the a
i
T
k
values
for each period
T
k
. Then parameters b
i
and c
i
, for each i =0,1,2, were obtained by least-
squares fitting of these 26 individual
a
i
T
k
estimates. The resulting values are shown in
Table 3. We repeated the full analysis (normalizing, binning, and parameter fitting) using
the 1.0 and
2.5 km/s isosurfaces, respectively, as depth parameters (i.e., setting
D=Z
1.0
and D=Z
2.5
, respectively), and those results are also shown in Table 3.
Table 2. Mean (and standard deviation) of natural log of amplification, versus basin depth and
period
Z
1.5
(km)
Period (s)
23456810
0.3 0.54(0.66) 0.38(0.63) 0.44(0.57) 0.52(0.55) 0.59(0.54) 0.63(0.48) 0.63(0.48)
0.5 1.00(0.65) 0.89(0.55) 0.90(0.51) 0.94(0.53) 0.97(0.54) 0.94(0.51) 0.89(0.55)
0.7 1.16(0.72) 1.07(0.57) 1.04(0.54) 1.05(0.58) 1.08(0.59) 1.03(0.60) 0.98(0.63)
0.9 1.27(0.65) 1.23(0.54) 1.22(0.54) 1.25(0.58) 1.28(0.57) 1.21(0.57) 1.13(0.64)
1.1 1.34(0.66) 1.32(0.58) 1.35(0.53) 1.37(0.53) 1.36(0.51) 1.29(0.50) 1.21(0.56)
1.3 1.37(0.65) 1.37(0.57) 1.49(0.56) 1.56(0.57) 1.55(0.53) 1.47(0.49) 1.36(0.51)
1.5 1.45(0.66) 1.44(0.56) 1.57(0.57) 1.69(0.56) 1.71(0.51) 1.64(0.48) 1.51(0.48)
1.7 1.57(0.65) 1.57(0.56) 1.64(0.54) 1.76(0.54) 1.81(0.53) 1.77(0.52) 1.65(0.53)
1.9 1.64(0.62) 1.64(0.53) 1.73(0.51) 1.83(0.54) 1.92(0.53) 1.89(0.56) 1.80(0.58)
2.1 1.64(0.65) 1.63(0.58) 1.73(0.52) 1.84(0.53) 1.92(0.53) 1.91(0.53) 1.85(0.55)
2.3 1.62(0.59) 1.65(0.51) 1.75(0.54) 1.87(0.51) 1.97(0.52) 1.98(0.56) 1.96(0.59)
2.5 1.70(0.60) 1.70(0.52) 1.79(0.55) 1.94(0.50) 1.99(0.51) 2.07(0.55) 2.06(0.56)
2.7 1.90(0.55) 1.90(0.50) 2.07(0.53) 2.13(0.56) 2.15(0.54) 2.21(0.53) 2.21(0.51)
272 DAYETAL.
Three of the resulting amplification curves (obtained by evaluating Equations 5a and
5b), for periods 2, 4, and
8s, are shown as dashed curves in Figure 9. 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 stud-
ies. Because they give a compact representation of complex wave propagation effects
captured by the numerical simulations, they provide a physical basis for extrapolation of
empirical models to periods greater than 2 or
3 seconds, where reliable data on basin
effects are especially scarce. The standard deviations
s of the simulation results, given in
Figure 9 and Table 2, provide appropriate estimates of the standard errors of prediction
for use with Equations 5a and 5b (the misfit of Equations 5a and 5b to
B is very small
compared with
s, and has negligible effect on the prediction error).
DISCUSSION AND CONCLUSIONS
We have characterized the source-averaged effect of basin depth on spectral accel-
eration using depth to the
1.5 km/s S velocity isosurface Z
1.5
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 1-D
models. For example, relative to a reference hard-rock site, sites with
Z
1.5
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
3speriod, and approximately 7.8 at
10 s period.
The basin amplification estimates described here are intended to guide the design of
functional forms for use in attenuation relationships for elastic response spectra. In par-
ticular, 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 con-
straint. 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
Vs
30
, i.e., the average S velocity in the upper 30 m). 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 Abraham-
son and Silva (1997) by a factor of 2 at long period (
5 seconds, which is much too long
a period to be affected by any response spectral biases associated with bandwidth limi-
Table 3. Coefficients for basin amplification factor (Equations 5a and 5b)
Isosurface
Depth (km)
b
0
b
1
b
2
c
0
c
1
c
2
1.0 −0.609 2.26 0.421 0.083 0.189 0.560
1.5
−1.06 2.26 1.04 0.124 0.198 0.261
2.5
−0.95 1.35 1.84 0.132 0.167 0.091
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 273
tations of the simulations, as discussed earlier). They argue that at the long periods con-
sidered, both source details and
Vs
30
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 NGA relationships all use
Vs
30
as a predictor variable. The correlation between
Vs
30
and basin depth is sufficiently strong to complicate the identification of the basin
effect in the residuals after having fit a regression model to
Vs
30
. Chiou and Youngs
(2006) tested the basin effect model proposed here (Equation 5) for three small (Mw
4-5) earthquakes in southern California, and found that the model compared very well
with spectral amplifications observed at over two hundred broadband stations of the
Southern California Seismic Network. However, they concluded that, because of the ba-
sin depth-
Vs
30
correlation, they would have had to remove the Vs
30
site term from their
NGA relationship in order to use the basin term. Doing so would make sense from a
physical standpoint, for the long periods
3–10 s considered here, because simple
wavelength arguments make it clear that
Vs
30
is unlikely to have significant physical ef-
fect at long period, and it is predictive of long-period response only to the extent that it
is statistically correlated with overall sediment thickness. However,
Vs
30
information is
widely available for strong motion recording sites, whereas
Z
1.5
(as well as Z
1.0
and Z
2.5
)
data are not available for all sites. Therefore, from a practical standpoint, Chiou and
Youngs (2008) found it expedient to develop their NGA model with
Vs
30
retained as a
predictor variable even at long period, to which they added a
Z
1.0
term to capture that
part of the basin effect not fully accounted for by the correlation between
Vs
30
and Z
1.0
.
The correlation of basin effects with
Vs
30
is discussed further by Choi et al. (2005), who
propose data analysis procedures for separating these effects.
For their NGA model, Campbell and Bozorgnia (2008) were able to empirically
identify a residual basin-depth effect after applying the
Vs
30
term in their model, but
only for sites for which
Z
2.5
3km (corresponding to Z
1.5
1.5 km). For
Z
2.5
3km, they found existing data too sparse to extend the empirical model and its
period dependence to greater sediment depth. Campbell and Bozorgnia’s NGA model
uses the parametric basin-effect model from the current study (Equations 5a and 5b) to
extrapolate the basin term into the
Z
2.5
3kmregime.
Our parametric model is based on simulations for the southern California region.
That region is characterized by deep sedimentary basins with relatively low
S wa ve ve-
locity. Sedimentary basins in other regions can have significantly different characteris-
tics. For example, the San Francisco Bay region of California is characterized by later-
ally juxtaposed geologic blocks having relatively high
S velocity and relatively shallow
basins (e.g., Santa Clara basin). There is thus a need for additional region-specific stud-
ies of basin amplification effects, including empirical analysis as well as further
simulation-based analysis. In addition, simulations, including the ones done for this
study, should be used to assess the utility of other predictor variables besides basin
depth. As an example, Choi et al. (2005) have taken a step in this direction by examining
the effect on spectral amplification of source location relative to basin boundaries.
274 DAYETAL.
ACKNOWLEDGMENTS
We benefited from helpful reviews by Roberto Paolucci, Charles Langston, and an
anonymous reviewer. This work was supported by Pacific Earthquake Engineering Re-
search (PEER) Center Lifelines Program (Tasks 1A01, 1A02, and 1A03), the National
Science Foundation under the Southern California Earthquake Center (SCEC) Commu-
nity Modeling Environment Project (grant EAR-0122464), and by SCEC. SCEC is
funded by NSF Cooperative Agreement EAR-0106924 and USGS Cooperative Agree-
ment 02HQAG0008. The SCEC contribution number for this paper is 1101.
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(Received 1 July 2007; accepted 15 November 2007
MODEL FOR BASIN EFFECTS ON LONG-PERIOD RESPONSE SPECTRA IN SOUTHERN CALIFORNIA 277
... For the purposes of site response modeling using ergodic procedures, these effects are averaged over many sites globally with conditioning on time-averaged shear wave velocity in the upper 30 m (V S30 ) and, in some cases, on isosurface depth parameters. These depths indicate the vertical distance from the ground surface to the first crossing of a shear wave velocity isosurface; the most widely used values are z 1 and z 2.5 for depths to 1.0 km/s and 2.5 km/s isosurfaces (Day et al., 2008;Bozorgnia et al., 2014). ...
... For long-period ground motions, such models predict relative de-amplification (less than that provided by the V S30 -scaling function) for shallower depths, and relative amplification for larger depths. The efficacy of depth as an independent variable correlated to site response in basins has also been demonstrated by simulations (Wald and Olsen, 2000;Day et al., 2008;Rodgers et al., 2020), despite the fact that some mechanisms of site response in two-or three-dimensional basin structures (e.g. focusing, basin edge-generated surface waves; Graves, 1993;Kawase, 1996;Graves et al., 1998;Pitarka et al., 1998;Stephenson et al., 2000;Baher and Davis, 2003) are related to more complex geometric attributes such as the shape of the sediment-rock interface at the base of the basin. ...
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Deep sedimentary basins often increase the intensity of ground motions, but this effect is not considered explicitly in most codal provisions. The effect of basin amplification on structures to the fragility level is significant to study. For the first time, the effect of basin amplification on Steel Moment Resisting Frames (SMRF) is presented as a function of the basin material and geometry. This paper evaluates the effect of basin material, basin depth, and basin width on Peak Ground Velocity (PGV), Spectral Acceleration (Sa), and fragility of 4, 8, 12, and 20 story steel structures using synthetic ground motions simulated in SPECFEM3D. It has been found that the variation in basin width and impedance ratio can increase the spectral acceleration by a factor of 4 and 2.5, respectively. The response of SMRF is computed by incremental dynamic analysis, and fragility curves are derived for the collapse limit state. Results of fragility analysis reveal that SMRF structure is more fragile to variation in impedance contrast between basin-bedrock. It has been observed from the results that the collapse intensity measure for impedance ratio variation is 40% and 19% lesser on average than the width and depth variation, respectively. Comparison between the present fragility analysis results and HAZUS fragility parameters indicates that the vulnerability of structure located in the basin is underestimated in its current provisions, and the SMRF would need to increase its strength two times to account for basin amplification.
... While the IM-based ground motion simulation (GMS) has been the mainstream method for regional seismic hazard simulation, the state-ofthe-art GMPEs still embody a large amount of epistemic and aleatory uncertainties that dominate the uncertainty propagation [127,304]. The large IM prediction uncertainties largely stem from the ergodic assumption and the unexplained source complexity and 3D path effects [305,306], which is largely due to the limited number of recorded ground motions in conjunction with the conventional functional forms adopted in the development of the GMPEs. Recent studies have steered toward leveraging advanced machine learning techniques in developing data-driven GMPEs [307][308][309][310][311], to better characterize the sophisticated input-output relationships and to further reduce the prediction bias and uncertainties. ...
... Examples of data-based studies of specific basins include Pratt et al. (2003) (Seattle, U.S.A.), Bindi et al. (2009) (Gubbio, Italy), and Yoshimoto and Takemura (2014) (Kanto, Japan). These studies provide measurements and catalogs of earthquakes for testing theoretical and numerical models for basin effects (Bard et al., 1988;Sánchez-Sesma and Luzón, 1995;Wald and Graves, 1998;Day et al., 2008;Cruz-Atienza et al., 2016;Bowden and Tsai, 2017;Tsai et al., 2017;Wirth et al., 2019). A second objective is to better understand events within the tectonically active setting of Minto Flats-a region that has produced exotic events, such as very-lowfrequency earthquakes and also earthquakes preceded by a nucleation signal . ...
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Nenana basin in central Alaska is a long (90 km), narrow (12 km), and deep (7 km) sedimentary basin aligned with an active fault zone producing Mw≥6 earthquakes. From 2015 to 2019, 13 broadband seismic stations were deployed in the region as part of the Fault Locations and Alaska Tectonics from Seismicity project. These stations recorded a wide range of earthquakes, including Mw 3–4 directly below the basin as well as several regional earthquakes Mw>6. These 43 local and regional earthquakes, in addition to five teleseismic events and continuously recorded ambient noise, provide a data set that we use to quantify the response of Nenana basin to the seismic wavefield. We calculate spectral ratios between each station and a bedrock reference station for 48 earthquakes. We find amplification of 11–14 dB (amplification ratio 3.5–5.0) for low frequencies (0.1–0.5 Hz), and 8–15 dB (amplification ratio 2.5–5.6) for high frequencies (0.5–4.0 Hz) on the vertical component. At low frequencies, amplification of the earthquake wavefield agrees well with amplification of seismic noise, with both data sets exhibiting stronger amplification on the horizontal components, in comparison with the vertical component. Furthermore, stations overlying the deeper part of the basin exhibit stronger amplification, whereas stations at the margin of the basin exhibit minimal low-frequency amplification. At higher frequencies, amplification occurs at both deeper basin stations and also marginal basin stations. Our study establishes a catalog of diverse events for future theoretical and numerical studies that can use Nenana basin to better understand the complex influence of sedimentary basins on the seismic wavefield.
... Ho wever , in the vertical direction, higher basin amplification is observed at the region where sediments are thicker. A similar observation is also reported in Day et al. ( 2008 ), where the spectral amplitudes are analyzed as a function of period and basin depths. The y hav e obtained the highest amplification of 8 at the greatest basin depth relative to the very hard rock site basement. ...
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The present study focuses on developing a 3D computational model of the Indo Gangetic basin (IG basin) using the spectral element method (SEM). The region includes the subcontinent's most densely populated areas. The basin is unique as it consists of geologically younger sedimentary layers along with several ridges and depressions in its domain. However, the proximity of great Himalayan earthquakes and the presence of thick sedimentary layers of the basin results in higher seismic hazards. The limited instrumentation of the domain poses challenges in understanding the response of the basin due to a seismic event. This motivated us to develop a computational model of the IG basin by incorporating the best-known geometry, material properties, and fine resolution topography. In the lateral direction, the modelled part of IG basin spans over ∼60 ×40 (between longitude 80.50-86.50E and latitude 250-290N). The validation of the developed basin model is performed by simulating the ground motions for the 2015 Mw 7.9 Nepal mainshock and five of its aftershocks. Both qualitative and quantitative comparison of the simulated time histories suggests that the developed model could accurately simulate ground motions over a frequency range of 0.02-0.5Hz. The developed basin model is then used to understand the seismic wavefield characteristics during the 2015 Mw 7.9 Nepal mainshock. The spatial variation of PGV, as well as amplification, are investigated at a 0.20×0.20 grid and selected cities in the basin. The contours of PGV amplification indicate a higher value of ∼8-10 in the horizontal direction and ∼2.5-3.5 in the vertical direction for sediment depth >4km. A comprehensive comparison of the simulated PGVs and the ground motion prediction equations (GMPEs) shows that, while the simulations agree with the prediction, they also show heterogeneity of ground-motion distribution that cannot be fully described by empirical prediction relations. Hence the results from the present study are more reliable and find applications in seismic hazard assessment of the cities in the basin. Besides, the results can be used to guide the installation of future seismic stations in the region.
... Nevertheless, the impacts of the basin effects are not explicitly considered for periods less than 1 s due to the implementation of a stochastic procedure to generate the ground motions assuming a constant geological profile for periods below 1s . While many studies in the literature characterize deep sedimentary basin depth as the depth from the surface to soils with a shear wave velocity of 1.0, 1.5, and 2.5 km/s, denoted as Z1.0, Z1.5, and Z2.5 (Day et al., 2008), respectively, recent studies recommend the use of Z2.5 for computing basin amplification in the Pacific Northwest where sites with a shallow Z1.0 value can still have a deep Z2.5 value Wirth et al. (2018). Therefore, as supported by other studies (e.g. ...
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Modern tall residential Reinforced Concrete Shear Wall (RCSW) buildings in Metro Vancouver are exposed to a considerable hazard due to the proximity of various seismic sources, such as the Cascadia Subduction Zone (CSZ), and the presence of Georgia sedimentary basin, which can amplify the intensity of ground motions at medium-to-long periods. Current building codes do not account for basin amplification effects, they intend to ensure life-safety in extreme earthquakes and do not explicitly minimize damage to building components that preserve building functionality. This study aims to provide insights into the expected loss and functional recovery time of tall RCSW buildings in Metro Vancouver under a variety of earthquake intensities. To this end, nonlinear models of archetype RCSW buildings are developed for eight different locations in Metro Vancouver. These models are subjected to ground motions representative of a range of hazard levels as per Canada’s 2015 National Seismic Hazard Model, which neglects basin effects, as well as a suite of simulated ground motions of M9 CSZ earthquake scenarios, which explicitly accounts for basin amplification. The structural responses are employed to conduct a loss assessment using a well-established methodology and a downtime assessment using a recently developed framework. Loss estimates show that the mean loss ratios under the M9 motions vary between 1.4% and 32% across Metro Vancouver and range from 0.7% to 14% for the range of hazard levels considered in this study. Downtime estimates show that the functional recovery time of buildings subjected to the M9 motions can range from 175 to 543 days and vary between 164 to 491 days for the range of hazard levels considered. The archetype buildings do not meet the robustness criteria of ensuring that there is a probability of less than 10% of not achieving sheltering capacity under the functional level earthquake (~ 475 year return period). Similarly, the archetype buildings do not meet the rapidity criteria of observing less than a 10% probability of not achieving functional recovery within four months after the functional level earthquake. Downtime deaggregation shows that the main contributor to functional recovery time is attributed to slab-column connection damage.
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To incorporate basin effects into seismic hazard assessment of urban areas and infrastructure, basin‐depth effect models that are the dependence of basin amplification factor on basin depth have been derived via numerical and empirical approaches. However, commonly observed quantitative and qualitative differences between numerical and empirical models remain unresolved. In particular, empirical models tend to predict smaller basin amplification factors. In this study, a modified empirical approach from Choi et al. was applied to the derivation of basin‐depth effect models for four deep basins in Japan using a database consisting of 71 MJ > 6 (Mw > 5.7) earthquakes and 13,562 records from strong‐motion seismograph networks (K‐NET and KiK‐net). The obtained basin‐depth models vary among basins and crustal‐subduction earthquake pairs, which confirms the recent trend of accounting for regional‐seismotectonic basin amplification in seismic hazard analysis. The basin amplification observed for crustal earthquakes is generally larger than that for subduction earthquakes. Moreover, the differences between the numerical and empirical models can be explained by changing the options of basin or outside‐basin stations for computing the inter‐event residuals. These results bridge a knowledge gap in seismic hazard analysis between ground‐motion prediction equations and those using large‐scale seismic wave simulations, which are now the main tools for regions lacking seismic records.
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The main objective of this study is to understand the dependency of basin amplification on-site and source parameters employing high computational numerical simulations. This study mainly addresses the effect of fault dip, size of the basin, site classification, and position of the basin on wave amplification. Two dip angles are considered, 7 and 9 degrees in this study to estimate the factor of amplification. Amplifications observed at the basin center and basin edge station for three different sizes of the basin are analyzed. Simulation results obtained from three different models with the ASCE site class C, D, and E basin sediment specifications are compared. To analyze the effect of basin relative position on amplification, we studied a model with two different basins embedded in bedrock, back and forth of the fault. This study observed multiple peaks at different time periods in response spectra drawn to amplification ratio versus time periods.
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We have simulated 0-5 Hz deterministic wave propagation for a suite of 17 models of the 2014 Mw 5.1 La Habra, CA, earthquake with the Southern California Earthquake Center Community Velocity Model Version S4.26-M01 using a finite-fault source. Strong motion data at 259 sites within a 148 km by 140 km area are used to validate our simulations. Our simulations quantify the effects of statistical distributions of small-scale crustal heterogeneities (SSHs), frequency-dependent attenuation Q(f), surface topography, and near-surface low velocity material (via a 1D approximation) on the resulting ground motion synthetics. The shear wave quality factor QS(f) is parameterized as QS, 0 and QS, 0fγ for frequencies less than and higher than 1 Hz, respectively. We find the most favorable fit to data for models using ratios of QS, 0 to shear-wave velocity VS of 0.075-1.0 and γ values less than 0.6, with the best-fitting amplitude drop-off for the higher frequencies obtained for γ values of 0.2-0.4. Models including topography and a realistic near-surface weathering layer tend to increase peak velocities at mountain peaks and ridges, with a corresponding decrease behind the peaks and ridges in the direction of wave propagation. We find a clear negative correlation between the effects on peak ground velocity amplification and duration lengthening, suggesting that topography redistributes seismic energy from the large-amplitude first arrivals to the adjacent coda waves. A weathering layer with realistic near-surface low velocities is found to enhance the amplification at mountain peaks and ridges, and may partly explain the underprediction of the effects of topography on ground motions found in models. Our models including topography tend to improve the fit to data, as compared to models with a flat free surface, while our distributions of SSHs with constraints from borehole data fail to significantly improve the fit. Accuracy of the velocity model, particularly the near-surface low velocities, as well as the source description, controls the resolution with which the anelastic attenuation can be determined. Our results demonstrate that it is feasible to use fully deterministic physics-based simulations to estimate ground motions for seismic hazard analysis up to 5 Hz. Here, the effects of, and trade-offs with, near-surface low-velocity material, topography, SSHs and Q(f) become increasingly important as frequencies increase toward 5 Hz, and should be included in the calculations. Future improvement in community velocity models, wider access to computational resources, more efficient numerical codes and guidance from this study are bound to further constrain the ground motion models, leading to more accurate seismic hazard analysis.
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We develop empirical estimates of site response at seismic stations in the Los Angeles area using recorded ground motions from 414 M 3–7.3 earthquakes in southern California. The data are from a combination of the Next Generation Attenuation-West2 project, the 2019 Ridgecrest earthquakes, and about 10,000 newly processed records. We estimate site response using an iterative mixed-effects residuals partitioning approach, accounting for azimuthal variations in anelastic attenuation and potential bias due to spatial clusters of colocated earthquakes. This process yields site response for peak ground acceleration, peak ground velocity, and pseudospectral acceleration relative to a 760 m/s shear-wave velocity (VS) reference condition. We employ regression kriging to generate a spatially continuous site response model, using the linear site and basin terms from Boore et al. (2014) as the background model, which depend on VS30 and depth to the 1 km/s VS isosurface. This is different from past approaches to nonergodic models, in which spatially varying coefficients are regressed. We validate the model using stations in the Community Seismic Network (CSN) that are in the middle of our model spatial domain but were not considered in model development, finding strong agreement between the interpolated model and CSN data for long periods. Our model could be implemented in regional seismic hazard analyses, which would lead to improvements especially at long return periods. Our site response model also has potential to improve both ground-motion accuracy and warning times for the U.S. Geological Survey ShakeAlert earthquake early warning (EEW) system. For a point-source EEW simulation of the 1994 M 6.7 Northridge earthquake, our model produces ground motions more consistent with the ground-truth ShakeMap and would alert areas with high population density such as downtown Los Angeles at lower estimated magnitudes (i.e., sooner) than an ergodic model for a modified Mercalli intensity 4.5 alerting threshold.
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The 1994 Northridge earthquake produced ground motions in the northwest portion of the Los Angeles basin that were significantly larger than rock-site motions observed at locations just north of the basin. The Santa Monica area was hit particularly hard, with numerous structures being damaged or destroyed by the strong ground shaking. In this region, the basin-edge geology is controlled by the active strand of the east-west-striking Santa Monica fault, and virtually all of the structural damage occurred at or south of the fault location. We have used 2D finite-difference ground-motion simulations to investigate the effect of the basin-edge structure in amplifying ground response. Constraints on the basin-edge structure come from geologic cross sections, geophysical data, and seismological observations. Our simulations indicate that the shallow basin-edge structure (1 km deep) formed by the active strand of the Santa Monica fault creates a large amplification in motions immediately south of the fault scarp, in very good agreement with mainshock damage patterns, recorded ground motions, and locations of elevated site response. This large amplification results from constructive interference of direct waves with the basin-edge-generated surface waves and is quite similar to the basin-edge effect associated with the 1995 Kobe earthquake. In addition, we find that focusing effects created by the deeper basin structure (3 to 4 km deep) cannot explain the large motions observed immediately south of the fault scarp. This strongly suggests that the deep-basin focusing models proposed by Gao et al. (1996) and Alex and Olsen (1998) are not likely explanations of the observed pattern of ground-motion amplification in the Santa Monica area.
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INTRODUCTION A large amount of work has been done in recent years to estimate the distribution of slip on the fault surface during earthquakes. Generally, these slip models are derived from longer period ground motions: strong-motion velocity and displacement, and teleseismic velocity seismograms. At these longer periods, ground motions are predominantly deterministic and their waveforms can in general be accurately modeled using simple descriptions of the source and crustal structure. The opposite situation exists for the prediction of high-frequency strong ground motions. Ground motions at high frequencies are predominantly stochastic, and their waveforms in general cannot be accurately modeled using simple descriptions of the source and crustal structure. However, preliminary evidence ( e.g. , Hartzell et al. , 1996; Kamae and Irikura, 1998; Somerville, 1993; Somerville et al ., 1996; Wald et al. , 1988) suggests that variable slip models derived from longer-period ground-motion recordings are relevant for the prediction of higher-frequency ground motions. For...
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A consistent set of empirical attenuation relationships is presented for predicting free-field horizontal and vertical components of peak ground acceleration (PGA), peak ground velocity (PGV), and 5% damped pseudo-absolute acceleration response spectra (PSA). The relationships were derived from attenuation relationships previously developed by the author from 1990 through 1994. The relationships were combined in such a way as to emphasize the strengths and minimize the weaknesses of each. The new attenuation relationships are considered to be appropriate for predicting free-field amplitudes of horizontal and vertical components of strong ground motion from worldwide earthquakes of moment magnitude (MW) ≥ 5 and sites with distances to seismogenic rupture (RSEIS) ≤ 60 km in active tectonic regions.
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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 Vs 30).
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The response to earthquake motion of a site in one sediment-filled valley was observed to depend strongly on frequency and the position of the site within the valley and weakly on the input signal's azimuth and incidence angles. The observed input motion was weak, varying between 10−5 and 10−3g. Measurements of ground velocity were made on profiles across and along the valley and simultaneously on two nearby rock sites. The valley was 400 m wide and 700 m long, with a maximum sediment thickness of 60 m. The average seismic impedance contrast between the sediments and underlying basement rock was about 6:1. Ratios of Fourier spectra from soil sites to spectra from nearby rock sites showed apparent site amplifications of as much as a factor of ten, depending strongly on frequency and the distance of the site from the valley edge. The scatter in spectral ratios for earthquakes with different azimuths and angles of incidence was about a factor of two; thus local site effects that changed the amplitude of incident motion by a factor of two or more could be identified in the records of most earthquakes. Ground motion at valley-edge and mid-valley sites, separated by less than 100 m, differed by as much as a factor of five. This difference could cause large differential motion in structures spanning these sites. A theoretical, flat layer model of sediment response predicts the average behavior of the middle of the valley but not that of the valley edge. The lowest frequency responance apparently involves the sediments across the width of the valley, not just the vertical column of soil beneath each site.
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This article provides an overview of the application of the staggered-grid finite-difference technique to model wave propagation problems in 3D elastic media. In addition to presenting generalized, discrete representations of the differential equations of motion using the staggered-grid approach, we also provide de-tailed formulations that describe the incorporation of moment-tensor sources, the implementation of a stable and accurate representation of a planar free-surface boundary for 3D models, and the derivation and implementation of an approximate technique to model spatially variable anelastic attenuation within time-domain finite-difference computations. The comparison of results obtained using the staggered-grid technique with those obtained using a frequency-wavenumber algorithm shows excellent agreement between the two methods for a variety of models. In addition, this article also introduces a memory optimization procedure that allows large-scale 3D finite-difference problems to be computed on a conventional, single-processor desktop workstation. With this technique, model storage is accommodated using both external (hard-disk) and internal (core) memory. To reduce system overhead, a cascaded time update procedure is utilized to maximize the number of computations performed between I/O operations. This formulation greatly expands the applicability of the 3D finite-difference technique by providing an efficient and practical algorithm for implementation on commonly available workstation platforms.
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Empirical relationships are developed to predict amplification factors for 5% damped response spectral acceleration that incorporate basin response effects. The parameters considered are depth to the 1.5 km/sec shear-wave isosurface ( z 1.5 ) as well as the location of the source beneath or outside the perimeter of the basin in which the site is located. Sites located in a basin overlying the source are denoted as having coincident source and site basin locations (cbl) and are differentiated from distinct source and site basin locations (dbl). Amplification factors for cbl and dbl sites are evaluated from simulated data (developed by others) and strong-motion data. Amplification factors derived from strong-motion recordings are taken as residuals of rock attenuation relations coupled with amplification factors for shallow-site conditions. Models relating amplification to z 1.5 were developed separately for the cbl and dbl data groups. The results indicate that the use of basin models is generally worthwhile for periods T ≥ 0.75 sec. At those long periods, residuals are significantly sensitive to z 1.5 for cbl but not for dbl. The standard deviation is also reduced for long periods to an extent that the standard deviations for long and short periods are similar.