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Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra

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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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Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
Empirical Near-Source Attenuation Relationships for
Horizontal and Vertical Components of Peak Ground
Acceleration, Peak Ground Velocity, and Pseudo-
Absolute Acceleration Response Spectra
Kenneth W. Campbell
EQE International
ABSTRACT
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.
INTRODUCTION
The development of design ground motions is a critical part of the seismic design of engineered
structures. Methods commonly used to develop these ground motions include: (1) seismic
zoning maps, (2) site-specific deterministic analyses, and (3) site-specific probabilistic seismic
hazard analyses (e.g., Campbell, 1992a). All of these methods require a strong motion
attenuation relationship to estimate earthquake ground motions from simple parameters
characterizing the earthquake source, the propagation path between the earthquake source and
the site, and the geologic conditions beneath the site. See Campbell (1985) for a general
discussion of attenuation relationships and their parameters.
Design ground motions are often controlled by an hypothesized occurrence of a large earthquake
on a nearby fault. Therefore, it is important that the seismological model or attenuation
relationship used to predict these design ground motions specifically address this requirement.
This study describes a set of empirical attenuation relationships that were specifically developed
to predict horizontal and vertical components of peak ground acceleration (PGA), peak ground
velocity (PGV), and 5%-damped pseudo-absolute acceleration response spectra (PSA) in the
near-source region of moderate-to-large earthquakes.
The attenuation relationships presented in this paper represent a compendium and synthesis of
near-source attenuation relationships previously developed by the author (e.g., Campbell, 1981,
1987, 1989a, 1990, 1992a, 1993; Campbell and Bozorgnia, 1994a). The 1989 and 1990 studies
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provided the only coherent set of attenuation relationships for both the horizontal and vertical
components of PGA, PGV, and PSA—the 1989 study for Soil sites and the 1990 study for both
Soil and Soft Rock sites. In 1993, these studies were extended to include Hard Rock recordings,
but only for the horizontal components of PGA and PSA. In the 1994 study, the attenuation
relationship for the horizontal component of PGA underwent a major revision with the addition
of recordings on Soil, Soft Rock, and Hard Rock from significant worldwide earthquakes that
occurred from 1987 to 1992 and from selected worldwide earthquakes that occurred prior to
1987.
Recommended Ground Motion Models
Engineering applications require ground motion predictions for all strong motion parameters and
local site conditions. Therefore, it is desirable to have a single coherent set of near-source
attenuation relationships. With this in mind, the attenuation relationships of Campbell (1990,
1993) and Campbell and Bozorgnia (1994a) were combined in such a way as to incorporate the
strengths and minimize the weaknesses of each. As described later in the paper, the relationship
for the horizontal component of PGA was developed from the study of Campbell and Bozorgnia
(1994a); the relationships for the horizontal components of PGV and PSA were developed from
the studies of Campbell (1990, 1992b) for Soil and Soft Rock and from Campbell (1993) for
Hard Rock; and the relationships for the vertical components of PGA, PGV, and PSA were
developed from the study of Campbell (1990).
MODEL PARAMETERS
Strong Motion Parameters
The strong-motion parameters of interest in this study include the horizontal and vertical
components of peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped
pseudo-absolute acceleration response spectra (PSA), hereafter referred to as spectral
acceleration. The horizontal and vertical components of PGA are denoted AH and AV , the
horizontal and vertical components of PGV are denoted VH and VV, and the horizontal and
vertical components of PSA are denoted SAH and SAV, respectively. The horizontal ground
motion parameters, defined as the geometric mean (i.e., the mean of the logarithm) of the peaks
of the two horizontal components, are approximately 12% and 17% less than the largest
horizontal component of PGA and PGV, respectively (Campbell, 1981; Joyner and Fumal,
1984). For PSA, the relationship between the geometric mean and the peak is a function of the
oscillator period (e.g., see Boore and others, 1993).
Earthquake Magnitude (M)
Moment magnitude (MW) was used to define earthquake magnitude in the study by Campbell
and Bozorgnia (1994a). The use of moment magnitude avoids the “saturation” of the more
traditional band-limited magnitude measures at large seismic moments and, therefore, is
considered to be a better measure of the true size of an earthquake (e.g., Bolt, 1993).
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Earlier studies (e.g., Campbell, 1989a, 1990, 1992b, 1993) used surface-wave magnitude (MS) to
define earthquake magnitude for earthquakes with MS 6 and local magnitude (ML) to define
earthquake magnitude for earthquakes with MS < 6. A comparison of magnitude scales
presented by Heaton and others (1986) indicates that ML is approximately equal to MW for ML <
6.5 (see also Bakun, 1984; Hanks and Boore, 1984) and that MS is approximately equal to MW
for MS ranging from 6.0 to 8.0. Thus, the magnitude measures used in these eariler studies are
consistent with MW over the range of magnitudes of engineering interest and the magnitude
measure used in the attenuation relationships recommended in this study can be considered to be
MW for all intents and purposes.
Source-to-Site Distance (RSEIS)
Source-to-site distance is defined as the shortest distance between the recording site and the
presumed zone of seismogenic rupture on the fault. Implicit in this definition is the assumption
that fault rupture within the softer sediments and within the upper 2 to 4 km of the fault zone is
primarily non-seismogenic (Marone and Scholz, 1988). Therefore, this shallow rupture is not
believed to contribute significantly to recorded ground motions at oscillator periods of
engineering interest. The seismogenic part of the rupture zone was estimated from several types
of information, including the mapped surface trace of the fault rupture, the spatial distribution of
aftershocks, the inversion of strong motion and teleseismic recordings, regional crustal velocity
profiles, and regional geodetic and geologic data.
Other distance measures that have been proposed for use in empirical attenuation relationships
include the shortest distance between the recording site and the observed or inferred rupture on
the fault, even if this rupture is within the softer sediments (e.g., Campbell, 1981; Idriss,
1991a,b; Sadigh and others, 1993; Abrahamson and Silva, 1995, 1996); and the shortest distance
between the recording site and the horizontal projection of the rupture zone on the surface of the
earth (e.g., Joyner and Boore, 1981; Boore and others, 1993, 1994).
Shakal and Bernreuter (1981) recommended that the source-to-site distance should be measured
from the recording site to the closest asperity—that part of the fault rupture that releases the
greatest amount of radiated energy. They suggested that ground motion predictions made using
attenuation relationships that use distance measures based on the closest-distance to the fault
rupture will “at best be accurate and at worst may significantly under-predict ground-motion
levels.” Although their proposed distance measure is admittedly more seismologically based
than the closest-distance measures proposed by other investigators, their statement regarding the
bias in these distance measures is true only if the relationships are developed in terms of a
closest-distance measure then applied in terms of the distance to the closest asperity. Because it
is not known in advance where the true source of the strongest ground motion will come from, it
is not feasible to make ground-motion predictions in terms of the distance measure
recommended by Shakal and Bernreuter. On the other hand, RSEIS has a reasonable
seismological basis, can be reliably and easily determined for most significant earthquakes, and
can be easily defined for a hypothetical design earthquake. If correctly applied, it appropriately
accounts for uncertainty in the location of the actual source of the strongest recorded ground
motions by including it as random variability.
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Unlike the distance measures defined by Campbell (1981), Sadigh and others (1986, 1993),
Idriss (1991a,b), Abrahamson and Silva (1995, 1996), and Shakal and Bernreuter (1981), RSEIS
avoids ambiguities associated with identifying and predicting the location of asperities for large
earthquakes and the shallowest extent of rupture for moderate-size earthquakes, which are often
accompanied by limited surface cracking but no clear identification of surface rupture. Also,
Anderson and Luco (1983) have found from theoretical ground motion modeling studies that
RSEIS is analytically superior to the distance measure proposed by Joyner and Boore (1981) and
later used by Boore and others (1993, 1994) for characterizing the attenuation of ground motion
from dipping faults.
By definition, RSEIS cannot be less than the depth to the top of the seismogenic part of the earth’s
crust. Based on observations by Marone and Scholz (1988), this depth should be no shallower
than about 2 to 4 km. It can, however, be greater than this range. For example, in the Imperial
Valley of California, the depth to the seismogenic portion of the crust has been determined to be
at least 5 km from accurate hypocenter determinations and from the inferred principal zone of
rupture during the 1979 (MW = 6.5) Imperial Valley earthquake (Doser and Kanamori, 1986). If
no other information is available, an estimate of the average depth to the top of the seismogenic
rupture zone for a hypothetical earthquake can be derived by assuming that its expected rupture
zone is equally likely to occur anywhere within the seismogenic part of the fault zone. This can
be calculated from the expression,
dSEIS = HTOP + ½ [HBOT – HTOP – W sin(α)]; dSEIS HTOP
= HTOP; Otherwise (1)
where dSEIS is the average depth to the top of the seismogenic rupture zone, HTOP and HBOT are
the depth to the top and bottom of the seismogenic part of the crust, α is the dip of the fault
plane, and W is the expected width (down-dip dimension) of the fault rupture. Rupture width
can be estimated from moment magnitude from the following relationship (Wells and
Coppersmith, 1994),
log(W) = –1.01 + 0.32 MW (2)
for W in kilometers. Table 1 gives expected minimum values of dSEIS for several values of MW
and α and for depths to the top and bottom of the seismogenic crust typical of California, i.e.
HTOP = 3 km and HBOT = 15 km. Values of dSEIS greater than these should not be used unless
supported by the specific geometry of the fault plane or the depth and thickness of the
seismogenic crust.
Style of Faulting (F)
Style of faulting, or fault type, is defined by the index variable F, where F = 0 for strike-slip
faulting and F = 1 for reverse, thrust, reverse-oblique, and thrust-oblique faulting. Reverse
faulting is distinguished from thrust faulting by the value of the dip angle of the fault plane, with
reverse faulting having a dip angle greater than or equal to 45°. To be consistent with the way F
was determined in this study, strike-slip faulting is defined as an event whose absolute value of
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the slip direction (rake) is no more than 22.5° from horizontal as measured along the fault plane.
A rake of 0° represents left-lateral strike-slip faulting, 180° represents right-lateral strike-slip
faulting, 90° represents reverse or thrust faulting, and –90° represents normal faulting.
Based on theoretical and empirical studies, McGarr (1984) concluded that normal-faulting
earthquakes located in extensional stress regimes are associated with lower ground motions than
either strike-slip or reverse-faulting earthquakes located in compressional stress regimes.
However, Westaway and Smith (1989) and Spudich and others (1995) have found that
attenuation relationships developed from primarily California and other western United States
strike-slip and reverse-faulting earthquakes provide a reasonable estimate of PGA from normal-
faulting earthquakes located worldwide. A similar result was found from an analysis of strong
ground motions from the 1992 Little Skull Mountain, Nevada, normal-faulting earthquake by
Hofmann and Ibrahim (1994).
There was only two normal-faulting earthquakes included in the current database used to
determine the coefficient of F—the 1935 (ML = 5.5) Helena, Montana earthquake, and the 1975
(MW = 6.0) Oroville, California earthquake. Therefore, there is no statistical basis in this study
for concluding whether strong ground motions from normal-faulting earthquakes are different
from those of other types of earthquakes. However, considering the recent empirical results
cited above, it is recommended that normal-faulting earthquakes be assigned a value of F
halfway between that of strike-slip and reverse-faulting earthquakes, or F = 0.5, until more
definitive studies become available.
Local Site Conditions (SSR and SHR)
Local site conditions are defined by the index variables SSR, and SHR; where SSR = SHR = 0 for
Alluvium or Firm Soil; SSR = 1 and SHR = 0 for Soft Rock; and SSR = 0 and SHR = 1 for Hard
Rock. Alluvium and Firm Soil is defined as firm or stiff Quaternary deposits with depths greater
than 10 m. Soft Rock is defined as primarily Tertiary sedimentary deposits and soft volcanic
deposits (e.g., ash deposits). Hard Rock is defined as primarily Cretaceous and older
sedimentary deposits, metamorphic rock, crystalline rock, and hard volcanic deposits (e.g.,
basalt). The approximate relationship between the site classifications defined above and similar
classifications defined in terms of shear-wave velocity (e.g., Boore and others, 1993; Borcherdt,
1994) and simpler Soil and Rock site classifications (e.g., Sadigh and others, 1986, 1993; Idriss,
1991a,b; Abrahamson and Silva, 1995, 1996) are given in Table 2.
Depth to Basement Rock (D)
Long-period site response is modeled by depth to basement rock. The importance of this
parameter has been noted by several investigators (e.g., see the list of references in Campbell,
1990). It has been explicitly included in empirical attenuation relationships developed by
Trifunac and Lee (1978, 1979) and Campbell (1987, 1989a, 1990, 1991a, 1992b, 1993). For
shallow sediments, D is defined as the depth to the top of Cretaceous or older deposits. For deep
sediments, D is determined from crustal velocity profiles where basement is defined as
crystalline basement rock or sedimentary deposits having a P-wave velocity of least 5 km/sec or
a shear-wave velocity of at least 3 km/sec. These high-velocity sediments are typically referred
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to as “seismic basement” by geophysicists. They are typically underlain by deposits
characterized by a low velocity gradient and a relatively small velocity impedance.
When direct estimates of D are not available, this depth can be inferred from gravity and
aeromagnetic data, from stratigraphic sequences, and from extrapolation of bedrock slopes. For
the majority of sites in the database compiled for this study (e.g., the Los Angeles Basin),
basement was identified as the top of crystalline or metamorphic rock. However, in some cases
(e.g., parts of the Livermore Basin in central California), deposits representing seismic basement
were identified within the sedimentary sequence.
Soil-Structure Interaction Parameters (Ki)
Because recordings from embedded and tall buildings were included in the database for PGV
and PSA, it was necessary to remove soil-structure interaction (SSI) effects by including the
index parameters Ki in the analyses involving these strong motion parameters. These SSI
parameters were defined as K1 = 1 and K2 = K3 = 0 for embedded buildings 3 to 11 stories high;
K1 = 0, K2 = 1, and K3 = 0 for embedded buildings greater than 11 stories high; K1 = K2 = 0 and
K3 = 1 for ground-level buildings greater than 2 stories high, and K1 = K2 = K3 = 0 for all other
recording sites (Campbell, 1989a, 1990). Because the recommended attenuation relationships
developed in this study are for free-field sites, these parameters have not been explicitly included
in these relationships. They are presented as a means of understanding the definition of “free-
field” in these earlier studies.
STRONG MOTION DATABASE
A description of the strong motion database is given in Table 3. Table 4 gives a listing of the
earthquakes and the number of recordings for each of the strong motion parameters. The
recordings were restricted to near-source distances to minimize the influence of regional
differences in crustal attenuation and to avoid the complex propagation effects that have been
observed at longer distances during, for example, the 1987 (MW = 6.1) Whittier Narrows, the
1989 (MW = 6.9) Loma Prieta, and the 1992 (MW = 7.3) Landers, California earthquakes
(Campbell, 1988, 1991c; Campbell and Bozorgnia, 1994b). Recordings from small earthquakes
were restricted to shorter distances than large earthquakes, depending on the magnitude and style
of faulting of the earthquake and the geology of the recording site, in order to mitigate the bias
associated with non-triggering instruments. The magnitudes were restricted to about MW 5 to
emphasize those ground motions of greatest engineering interest and to limit the analyses to the
more reliable, well-studied earthquakes.
Previous analyses have indicated that embedded and large structures can have accelerations
significantly less than those at free-field sites (e.g., Campbell, 1987, 1989a,b). However, these
recordings were included in the 1990 and 1993 studies because there were too few free-field
values of PGV and PSA with which to perform a reliable statistical analysis. Because of the
larger database, Campbell and Bozorgnia (1994a) excluded those recordings which were
believed to be adversely affected by soil-structure interaction (Table 3). Although excluded by
Boore and others (1993, 1994), recordings from dam abutments were included because such sites
comprise a significant number of the rock recordings in the database and, due to their stiff
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foundation conditions, are expected to be only minimally affected by the presence of the dam.
Although not addressed in this study, some of these abutment recordings could be affected by
local topography.
Recordings on Shallow Soil and Soft Soil were excluded from the database based on previous
analyses that showed that these sites have accelerations significantly higher than those on
deeper, firmer soil (e.g., Campbell, 1987, 1988, 1989b, 1991c). Shallow Soil is defined as
Quaternary deposits with depths less than 10 m. Soft Soil is defined as soft to very soft clay
(e.g., San Francisco Bay Mud) and loose to very loose granular soils (e.g., hydraulic fill).
Earthquakes were included only if they had seismogenic rupture within the shallow crust (depths
less than about 25 km) in order to avoid the potential differences in attenuation characteristics
and tectonic stresses associated with deeper earthquakes (e.g., Youngs and others, 1988).
Several large, shallow subduction interface earthquakes were included in the database based on
previous studies that found that these events had source characteristics and near-source ground
motions similar to those of shallow crustal earthquakes (e.g., Boore, 1986; Youngs and others,
1988).
HORIZONTAL ATTENUATION RELATIONSHIPS
Peak Ground Acceleration
The attenuation relationship developed by Campbell and Bozorgnia (1994a) is recommended for
predicting AH. The coefficients in this relationship were determined from an unweighted
generalized nonlinear least-squares regression analysis. The distribution of the recordings with
respect to magnitude and distance plotted by style of faulting and local site conditions is shown
in Figures 1 through 3.
To avoid the bias associated with non-triggering instruments, the analysis was done in two
stages. In the first stage, all selected recordings were used to determine the regression
coefficients. The resulting attenuation relationship was then used to compute the predicted value
of AH as a function of magnitude, distance, style of faulting, and local site conditions. A
distance threshold was then selected for each value of magnitude, style of faulting, and local site
condition such that the 16th-percentile estimate of AH was equal to 0.02g. This threshold value
of AH was chosen because it corresponds approximately to a peak vertical acceleration of 0.01g,
the nominal trigger threshold of modern strong motion accelerographs. In stage 2, recordings
not meeting the calculated distance thresholds were removed from the database and the
regression analysis was repeated. Ideally, this process should be repeated until the distance
thresholds become stable. However, a repeat of stage 1 indicated that there would be little
gained in repeating the two-stage analysis.
The final attenuation relationship is given by the expression,
ln(AH) = –3.512 + 0.904 M – 1.328 ln[{RSEIS2 + [0.149 exp(0.647 M)]2}½]
+ [1.125 – 0.112 ln(RSEIS) – 0.0957 M] F + [0.440 – 0.171 ln(RSEIS)] SSR
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+ [0.405 – 0.222 ln(RSEIS)] SHR + ε (3)
where AH has units of g (g = 981 cm/sec2), ε is a random error term with a mean of zero and a
standard deviation equal to the standard error of estimate of ln(AH), and all other parameters are
defined in the previous section.
Some studies have found that the dispersion in the predicted value of PGA is dependent on
earthquake magnitude (e.g., Sadigh and others. 1986, 1993; Idriss, 1991a,b; Abrahamson and
Silva , 1995, 1996), whereas others have found it to be a function of PGA (e.g., Donovan and
Bornstein, 1978). Campbell and Bozorgnia (1994a) investigated both of these hypotheses by
plotting the running value of the standard error of estimate of ln(AH) as a function of mean
earthquake magnitude and mean predicted value of ln(AH) and fitting a simple equation to these
observations using the method of least squares. The running values were calculated using 30
observations. The resulting relationship between σ, the standard error of estimate of ln(AH), and
ln(AH) is given by the expression,
σ = 0.55; AH < 0.068g
= 0.173 – 0.140 ln(AH); 0.068g AH 0.21g
= 0.39; AH > 0.21g (4)
The relationship relating σ to M is given by the expression,
σ = 0.889 – 0.0691 M; M < 7.4
= 0.38; M 7.4 (5)
Equation (4) is more statistically robust than Equation (5) with an r-squared value of 0.89 (i.e.,
89 percent of the variance is explained by the model) and a standard error of estimate of 0.021.
By comparison, Equation (5) has an r-squared value of 0.56 and a standard error of estimate of
0.044.
The statistical robustness of the results are demonstrated in Figures 4 through 7. These figures
show plots of the normalized residuals—the observed value minus the predicted value of ln(AH)
divided by the standard error of estimate of ln(AH)—as a function of source-to-site distance and
magnitude. The plots are segregated by style of faulting and local soil conditions.
Peak Ground Velocity and Spectral Acceleration
The recommended attenuation relationships for the horizontal components of PGV and PSA
were developed by combining the relationships of Campbell (1990) and Campbell (1993). The
coefficients in these relationships were determined from a weighted generalized nonlinear least-
squares regression analysis. Weights were used to reduce the potential bias in distance and site
location. The bias in distance results from the vastly different numbers of recordings between
earthquakes. To reduce this bias, recordings from a given earthquake that fell within a specified
distance interval were assigned the same weight as those recordings from other earthquakes that
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fell within the same distance interval. The potential bias in site location results from the
virtually identical source, path, and site effects that are common to recordings obtained at the
same location during the same earthquake. To reduce this bias, recordings from a given
earthquake that occurred at the same site location were given the same cumulative weight as a
single recording at that distance. Ten distance intervals of equal logarithmic increments between
0 and 56.6 km were used to establish the weights.
The weight of each recording was computed from the following expression,
wi = (N/Ni) 1/Nj (6)
where i is the index representing the recording; Ni = Ni,1 Ni,2; Ni,1 is the number of recordings
from the same earthquake and distance interval as the ith recording; Ni,2 is the number of
recordings from the same earthquake and site location as the ith recording; and N is the total
number of recordings. The above expression has been normalized such that the sum of the
weights equals N, a constraint required in order to maintain the correct number of degrees of
freedom and, thus, the correct weighted value of the standard error of estimate.
Other investigators have proposed different statistical methods to compensate for the potential
bias associated with the uneven distribution of recordings between earthquakes. The two most
notable are the two-step regression procedure proposed by Joyner and Boore (1981) and Boore
and others (1993), and the random-effects regression procedure proposed by Brillinger and
Preisler (1984) and Abrahamson and Youngs (1992) and later applied by Campbell (1991d) and
Abrahamson and Silva (1995, 1996).
After correctly weighting the second stage of their two-stage regression analysis, Joyner and
Boore (1993) found that the two-stage and random-effects approaches gave similar results.
TERA Corporation (1982) found that both a single and two-stage regression analysis of the
Joyner and Boore (1981) database gave virtually identical results. Campbell (1991d), using the
same database as Campbell (1990), found that a random-effects analysis resulted in predicted
strong-motion parameters that were generally within about 10% of those given by the traditional
variance-weighted model used by Campbell (1990). Larger differences at oscillator periods of
0.5 sec and longer were attributed to differences in magnitude and depth-to-basement-rock
scaling characteristics, which were determined independently of period. In constrast, Campbell
(1990) used period-independent scaling characteristics for these parameters. Differences among
the three regression procedures are sufficiently small for the robust databases available for the
western United States that one method is not preferred over the other based on differences in
regression results alone.
The regression analysis of PSA was considerably more complicated than the analyses of PGA
and PGV. An attempt to perform a direct regression on ln(PSA) led to an unacceptably large
period-to-period variability in the regression coefficients and in the resulting predicted response
spectra (e.g., see Campbell, 1991d). This variability is believed to have been caused by three
factors: (1) the relatively large number of independent variables included in the attenuation
relationship, (2) the relatively small number of available recordings, and (3) the period-to-period
variability in the number of recordings and associated earthquakes.
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When confronted with similar variability, Joyner and Boore (1982), Joyner and Fumal (1984),
and Boore and others (1993) smoothed the regression coefficients to obtain well-behaved
predicted response spectra. However, Campbell (1990, 1993) noted several unique factors that
made this type of approach virtually impossible. First, some of the regression coefficients were
found to be strongly correlated with one another, making it difficult to smooth them without
many iterations. Second, the nonlinearity and relatively large number of coefficients in these
attenuation relationships made each iteration extremely time consuming.
Therefore, instead of attempting to smooth the regression coefficients, the analyses were
simplified by performing the regression on the logarithm of the spectral ratio, ln(PSA/PGA),
rather than directly on ln(PSA). This approach has been adopted by many previous investigators
(e.g., Newmark and Hall, 1982; Sadigh, 1983, Sadigh and others, 1986, 1993; also see references
in Campbell, 1985 and Joyner and Boore, 1988). Besides giving more stable results, the analysis
of the spectral ratio has several advantages that makes it suitable for developing spectral
attenuation relationships: (1) it simplifies the analysis by reducing the number of coefficients to
be evaluated, (2) it minimizes the impact of the period-to-period variability in the number of
recordings and associated earthquakes, and (3) it can be used with a PGA attenuation
relationship based on a significantly larger number of recordings than those used to develop the
relationships for the spectral ratios.
The prediction of spectral ordinates from spectral ratio has been recently criticized by Joyner and
Boore (1988) and Bender and Campbell (1989). The major criticism concerns the use of peak
acceleration to scale a fixed spectral shape, which neglects observed differences in the period-
dependence of PSA on magnitude, source-to-site distance, and local site conditions. This
criticism was avoided by allowing the spectral ratio to scale freely with all of the independent
variables discussed in the previous section.
Even with the simpler analysis on spectral ratio, there were too many regression coefficients to
insure convergence of the nonlinear algorithms. Therefore, it was necessary to perform the
analysis in several steps, with each step used to evaluate a different set of independent variables,
until all of the regression coefficients were determined. With each successive step, the observed
values were de-trended using the regression coefficients determined in all of the previous steps
and the resulting residuals were inspected to re-validate the appropriateness of the previous
coefficients. The procedure is similar to a stepwise regression analysis. The order in which the
coefficients were determined was selected based on the significance of the observed trends.
Before each step, the de-trended residuals of the previous step were plotted and analyzed to
identify trends and suggest appropriate functional forms for the next step. The steps involved the
following analyses in the order indicated: (1) scaling with magnitude, (2) scaling with depth to
basement rock, (3) scaling with local site conditions (Campbell, 1993 only), and (4) scaling with
soil-structure interaction parameters. There was no statistically significant dependence of the
spectral ratio on source-to-site distance or style of faulting, although the Campbell (1993) study
included a distance-scaling term based on a theoretical model of anelastic attenuation developed
by Campbell (1991b).
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After the final step was completed, weighted residuals were calculated directly in terms of
ln(PSA) and were plotted against magnitude, source-to-site distance, depth to basement rock,
and local site conditions to insure that there were no significant trends with respect to these
variables. These residuals were also used to develop standard errors of estimate for ln(PSA) as a
function of magnitude and oscillator period.
In order to combine the strengths and minimize the weaknesses of the Campbell (1990, 1993)
studies, after considerable review and comparison, the recommended attenuation relationship for
the spectral ratio was developed as indicated below:
Scaling characteristics with respect to magnitude (M) were taken from Campbell (1990),
Scaling characteristics with respect to distance (RSEIS) were taken from Campbell (1993),
Scaling characteristics with respect to depth to basement rock (D) for Firm Soil and for D
1 km were taken from Campbell (1993) and were normalized to have the amplitude of
the spectral ratio given by Campbell (1990) at D = 5 km,
Scaling characteristics with respect to depth to basement rock (D) for Soft Rock and for
D 1 km were taken from Campbell (1993) and were normalized to the amplitude of the
spectral ratio given by Campbell (1993) at D = 5 km and long periods,
The amplitude of the spectral ratio at D = 0 km (Hard Rock) was taken from Campbell
(1993),
The amplitude of the spectral ratio for Soft Rock at short periods was taken to be halfway
between the amplitudes for Hard Rock and for Firm Soil for D < 1 km, and
The transition between the logarithm of the spectral ratios at D = 0 and at D = 1 km was
assumed to be a linear function of D.
Recommended Attenuation Relationships. In order to take advantage of the updated attenuation
relationship for AH developed by Campbell and Bozorgnia (1994a), the recommended
attenuation relationships for VH and SAH were developed by first normalizing by AH, then
multiplying these normalized values by the value of AH from the Campbell and Bozorgnia
(1994a) study. The resulting attenuation relationship for VH is given by the expression,
ln(VH) = ln(AH) + 0.26 + 0.29 M – 1.44 ln[RSEIS + 0.0203 exp(0.958 M)]
+ 1.89 ln[RSEIS + 0.361 exp(0.576 M)] + (0.0001 – 0.000565 M) RSEIS
– 0.12 F – 0.15 SSR – 0.30 SHR + 0.75 tanh(0.51 D) (1 – SHR) + fV(D) + ε (7)
where,
fV(D) = 0; D 1 km
= –0.30 (1 – SHR) (1 – D) – 0.15 (1 – D) SSR;D < 1 km
The attenuation relationship for SAH is given by the expression,
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
12
ln(SAH) = ln(AH) + c1 + c2 tanh[c3 (M – 4.7)] + (c4 + c5 M) RSEIS + 0.5 c6 SSR
+ c6 SHR + c7 tanh(c8 D) (1 – SHR) + fSA(D) + ε
(8)
where,
fSA(D) = 0; D 1 km
= c6 (1 – SHR) (1 – D) + 0.5 c6 (1 – D) SSR;D < 1 km
In all of the above relationships, VH has units of cm/sec; SAH has units of g; AH is the mean
horizontal component of PGA from Equation (3); and all other variables are defined in Equation
(3) or in the section Model Parameters. The regression coefficients for Equation (8) are
summarized in Table 5.
Consistent with the way Equations (7) and (8) were developed, the square of the standard errors
associated with these relationships were developed by adding the difference between the square
of the standard error of the desired strong motion parameter and ln(AH) to the square of the
standard error of ln(AH) from the Campbell and Bozorgnia (1994a) attenuation relationship. The
resulting standard errors are given by the following expressions,
σH = (σ2 + 0.062)0.5; for VH (9)
σH = (σ2 + 0.272)0.5; for SAH (10)
where σ is the standard error of estimate of ln(AH) from Equations (4) or (5). A single value of
σH was used for SAH for all oscillator periods because there was no clear trend in the calculated
values for the individual periods.
VERTICAL ATTENUATION RELATIONSHIPS
Only Campbell (1990) included an analysis of the vertical components of strong ground motion.
In order to take advantage of the increased reliability of the recommended attenuation
relationships for the horizontal components, the recommended attenuation relationships for AV,
VV and SAV were developed by taking the ratio of the vertical to the mean horizontal
components from the 1990 study and multiplying this ratio by the value of AH, VH, or SAH from
the recommended horizontal attenuation relationships. The resulting attenuation relationships
are given by the expressions,
ln(AV) = ln(AH) – 1.58 – 0.10 M – 1.50 ln[RSEIS + 0.079 exp(0.661 M)]
+ 1.89 ln[RSEIS + 0.361 exp(0.576 M)] – 0.11 F + ε, (11)
ln(VV) = ln(VH) – 2.15+ 0.07 M – 1.24 ln[RSEIS + 0.00394 exp(1.17 M)]
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
13
+ 1.44 ln[RSEIS + 0.0203 exp(0.958 M)]+ 0.10 F
+ 0.46 tanh(2.68 D) – 0.53 tanh(0.47 D) + ε, (12)
ln(SAV) = ln(SAH) + c1 – 0.10 M + c2 tanh[0.71 (M – 4.7)]
+ c3 tanh[0.66 (M – 4.7)] – 1.50 ln[RSEIS + 0.079 exp(0.661 M)]
+ 1.89 ln[RSEIS + 0.361 exp(0.576 M)] – 0.11 F + c4 tanh(0.51 D)
+ c5 tanh(0.57 D) + ε, (13)
where AV and SAV have units of g; VV has units of cm/sec; AH, VH, and SAH are the mean
horizontal components of PGA, PGV and PSA from Equations (3), (7) and (8); and all other
variables are defined in Equations (3) and in the section Model Parmaeters. The regression
coefficients for Equation (13) are summarized in Table 6.
Consistent with the way that Equations (11) through (13) were developed, the square of the
standard errors associated with these relationships were developed by adding the difference
between the square of the standard errors of the vertical and horizontal components from
Campbell (1990) to the square of the standard errors of the recommended horizontal attenuation
relationships given by Equations (4) or (5), (9) and (10). The resulting standard errors are given
by the following expressions,
σV = (σ2 + 0.362)0.5; for AV, (14)
σV = (σH2 + 0.302)0.5; for VV, (15)
σV = (σH2 + 0.392)0.5; for SAV, (16)
where σ is the standard error of estimate of ln(AH) from Equations (4) or (5), and σH is the
standard error of estimate of ln(VH) and ln(SAH) from Equations (9) and (10), respectively. A
single value of σV was used for SAV for all oscillator periods because there was no clear trend in
the calculated values for the individual periods.
DISCUSSION
The recommended attenuation relationships presented in this paper were developed by
combining the results of three previous studies (Campbell, 1990, 1993; Campbell and Bozorgnia,
1994a) in such a way as to maximize the strengths and to minimize the weaknesses of each. The
recommended attenuation relationship for the horizontal component of PGA was taken from the
Campbell and Bozorgnia (1994a) study, which included twice the number of earthquakes and
triple the number of recordings than the earlier studies. The recommended attenuation
relationships for the vertical component of PGA and for the horizontal components of PGV and
PSA were developed in terms of the ratio of these parameters with respect to the horizontal
component of PGA, then combined with the horizontal component of PGA from the Campbell
and Bozorgnia (1994a) study, in order to take advantage of the increased reliability of the 1994
results. The recommended attenuation relationships for the vertical components of PGV and
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
14
PSA were developed in terms of the ratio of these parameters with respect to their horizontal
components, then combined with the horizontal components from the recommended horizontal
attenuation relationships in order to take advantage of the increased reliability of these latter
relationships.
The results for Firm Soil and for thick sedimentary deposits were taken from Campbell (1990).
The results for Hard Rock were taken from Campbell (1993). Because neither study adequately
modeled Soft Rock recordings, these sites were assumed to have amplitudes halfway between
those of Firm Soil and Hard Rock at short periods and consistent with the Campbell (1993)
results for Soft Rock at D = 5 km and long periods. Although the approach of combining several
attenuation relationships takes advantage of the strengths of each, it unavoidably results in a set
of relationships which do not have the same statistical robustness as the individual relationships.
However, until a thorough, consistent analysis of PGA, PGV, and PSA can be conducted using
an up-to-date strong-motion database, these recommended attenuation relationships can be used
to predict near-source ground motions for engineering purposes. The recommended attenuation
relationships for PGA are shown in Figures 8 through 10. Predicted PSA spectra are shown in
Figures 11 through 16.
Since the original studies were published, there have been several earthquakes that have
produced significant near-source recordings. Notable earthquakes that have occurred since the
Campbell and Bozorgnia (1994a) study include the 1994 (MW = 6.7) Northridge, California and
the 1995 (MW = 6.9) Hyogo-ken Nanbu (Kobe), Japan earthquakes. Additional notable
earthquakes that have occurred since the Campbell (1990, 1993) studies include the 1989 (MW =
6.9) Loma Prieta, California, the 1992 (MW = 7.3) Landers, California, and the 1992 (MW = 7.1)
Petrolia, California earthquakes.
Other than the Northridge earthquake, the earthquakes noted above have been shown to have
near-source amplitudes relatively consistent with those predicted from previously published
attenuation relationships (e.g., Campbell, 1991c; Campbell and Bozorgnia, 1994b; EQE
International, 1995; Geomatrix Consultants, 1995). The Northridge earthquake is unique among
these earthquakes in that its near-source accelerations were approximately 50% higher than those
predicted from previous attenuation relationships (Campbell, 1995). A similar result was found
for the 1987 (MW = 6.1) Whittier Narrows, California earthquake (Campbell, 1988), another
relatively deep blind thrust-faulting earthquake. These results indicate that, taken as a whole, the
new recordings are not expected to result in significant changes to the near-source attenuation
relationships recommended in this paper. However, it is possible that relatively deep blind thrust
faults could systematically produce ground motions that are roughly 50% higher than those from
shallower blind and surface faults with the same style of faulting, but additional recordings will
be required to confirm this hypothesis.
Only one earthquake in the database—the 1985 (MW = 6.8) Nahanni, Canada earthquake—can
arguably be considered to have occurred in a stable continental region (SCR), similar to eastern
North America. The earthquake occurred along the eastern front of the Rocky Mountains in a
region considered to be a transition zone between the North American SCR and the more
seismically active and tectonically deformed region of western North America. Therefore, there
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
15
is no statistical basis for determining whether the attenuation relationships presented in this
paper can be used to estimate ground motions in the near-source region of SCR earthquakes.
Earthquakes from stable continental regions have been shown to have higher near-source ground
motions than those from more tectonically active regions due primarily to differences in stress
drop (e.g., EPRI, 1993a,b). Therefore, it is possible that ground motions from earthquakes with
similar stress drops in stable continental and active tectonic regions might also be similar, unless,
of course, there are systematic differences in source scaling relations between the two regions
(e.g., Atkinson, 1993; Atkinson and Boore, 1995). In any case, the author has proposed a
relatively simple technique based on stochastic simulation/random vibration procedures that can
be used to modify empirical attenuation relationships, such as those presented in this paper, for
use in stable continental regions (Campbell, 1994). These modified empirical attenuation
relationships serve as an alternative to the more conventional attenuation relationships developed
for these regions using theoretical ground motion models.
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
16
CONCLUSIONS
The recommended attenuation relationships presented in this paper are considered to be
appropriate for predicting free-field amplitudes of horizontal and vertical components of peak
ground acceleration, peak ground velocity, and 5%-damped pseudo-absolute acceleration
response spectra from worldwide earthquakes of MW 5 and sites with RSEIS 60 km in active
tectonic regions.
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Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
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Table 1
RECOMMENDED MINIMUM
VALUES FOR THE AVERAGE VALUE OF dSEIS
(HTOP = 3 km, HBOT = 15 km)
Magnitude Rupture Width dSEIS (km)
(MW)(W, km) α = 30° α = 45° α = 90°
5.00 3.2 8.0 7.6 7.1
5.25 4.2 7.8 7.3 6.7
5.50 5.6 7.6 7.0 6.2
5.75 7.5 7.3 6.6 5.6
6.00 10.0 7.0 6.1 4.9
6.25 13.3 6.6 5.5 4.1
6.50 17.8 6.1 4.8 3.1
6.75 23.7 5.5 4.0 3.0
7.00 31.6 4.8 3.0 3.0
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Table 2
COMPARISON OF SITE CLASSIFICATIONS
Borcherdt
Site Class Boore and Others
Site Class Sadigh, Idriss &
Abrahamson
Site Class
Campbell
Site Class
SC-Ib AROCK HARD ROCK
SC-II BROCK SOFT ROCK
SC-III CSOIL FIRM SOIL
SC-IV DSOFT SOIL SOFT SOIL
SHALLOW SOIL
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24
Table 3
GROUND MOTION DATABASE CHARACTERISTICS
Description PGA PGV and PSA
Dates 1957 – 1993 1933 – 1987
No. of Recordings 645 (Horizontal);
225 (Vertical) 226 (Horizontal);
173 (Vertical)
No. of Earthquakes 47 (Horizontal);
26 (Vertical) 30 (Horizontal);
22 (Vertical)
Component Mean of horizontal components;
Vertical component Mean of horizontal components;
Vertical component
Magnitude Measure MWMS for MS < 6;
ML for MS 6
Magnitude Range 4.7 – 8.0 (Horizontal);
4.7 – 8.1 (Vertical) 4.7 – 8.1
Distance Measure Closest distance to seismogenic
rupture (RSEIS)Closest distance to seismogenic
rupture (RSEIS)
Distance Range (km) 3.0 – 60.0 3.0 – 30.0 for M < 6.25;
3.0 – 50.0 for M 6.25
Local Site Conditions Firm Soil > 10m deep;
Soft and Hard Rock Firm Soil > 10m deep;
Soft and Hard Rock
Style of Faulting Strike Slip;
Reverse and Thrust Strike Slip;
Reverse and Thrust
Depth of Rupture (km) Upper crust (< 25 km) Upper crust (< 25 km)
Recordings Excluded Basement of buildings;
> 2 stories (Soil & Soft Rock);
> 5 stories (Hard Rock);
Toe and base of dams;
Base of bridge columns
Toe and base of dams
Regions Active tectonic regions;
Worldwide Active tectonic regions;
Worldwide
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Table 4
EARTHQUAKES USED IN THE ANALYSIS
Earthquake Year MFault Type Number of Recordings
AHAVVH
SAH
VV
SAV
Long Beach, CA 1933 6.2 Strike Slip 0333
Helena, MT 1935 5.5 Normal 0010
Imperial Valley, CA 1940 7.2 Strike Slip 0111
Kern County, CA 1952 7.8 Reverse Oblique 0111
Daly City, CA 1957 5.4 Reverse Oblique 1444
Parkfield, CA 1966 6.1 Strike Slip 4444
Borrego Mtn., CA 1968 6.8 Strike Slip 0111
Koyna, India 1967 6.3 Strike Slip 1010
Lytle Creek, CA 1970 5.3 Reverse 6564
San Fernando, CA 1971 6.6 Reverse 12 55 60 55
Sitka, AK 1972 7.7 Strike Slip 1010
Stone Canyon, CA 1972 4.7 Strike Slip 3222
Managua, Nicaragua 1972 6.2 Strike Slip 1111
Point Mugu, CA 1973 5.6 Reverse 1100
Hollister, CA 1974 5.1 Strike Slip 1222
Oroville, CA 1975 6.0 Normal 4010
Kalapana, HI 1975 7.1 Thrust 0010
Gazli, Uzbekistan 1976 6.8 Reverse 1111
Caldiran, Turkey 1976 7.3 Strike Slip 1000
Mesa de Andrade, Mexico 1976 5.6 Strike Slip 2000
Santa Barbara, CA 1978 6.0 Thrust 3644
Tabas, Iran 1978 7.4 Thrust 3333
Bishop, CA 1978 5.8 Strike Slip 4100
Malibu, CA 1979 5.0 Reverse 1300
St. Elias, AK 1979 7.6 Thrust 1121
Coyote Lake, CA 1979 5.8 Strike Slip 17 810 8
Imperial Valley, CA 1979 6.5 Strike Slip 43 41 43 38
Livermore, CA #1 1980 5.8 Strike Slip 7000
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
26
Table 4 (Continued)
Earthquake Year MFault Type Number of Recordings
AHAVVH
SAH
VV
SAV
Livermore, CA #2 1980 5.4 Strike Slip 6000
Westmorland, CA 1981 6.0 Strike Slip 22 000
Morgan Hill, CA 1984 6.2 Strike Slip 40 25 29 24
Valparaiso, Chile 1985 8.0 Thrust 3242
Michoacan, Mexico 1985 8.1 Thrust 0111
Zihuatanejo, Mexico 1985 7.6 Thrust 3030
Nahanni, Canada 1985 6.8 Thrust 3020
N. Palm Springs, CA 1986 6.1 Strike Slip 35 14 16 4
Chalfant Valley, CA 1986 6.3 Strike Slip 14 610 0
Whittier Narrows, CA #1 1987 6.1 Thrust 74 33 48 9
Whittier Narrows, CA #2 1987 5.3 Reverse Oblique 37 000
Elmore Ranch, CA 1987 6.2 Strike Slip 25 000
Superstition Hills, CA 1987 6.6 Strike Slip 31 000
Spitak, Armenia 1988 6.8 Reverse Oblique 1000
Pasadena, CA 1988 5.0 Strike Slip 8000
Loma Prieta, CA 1989 6.9 Reverse Oblique 51 000
Malibu, CA 1989 5.0 Thrust 3000
Manjil, Iran 1990 7.4 Strike Slip 4000
Upland, CA 1990 5.6 Strike Slip 34 000
Sierra Madre, CA 1991 5.6 Reverse 61 000
Landers, CA 1992 7.4 Strike Slip 18 000
Big Bear, CA 1992 6.6 Strike Slip 22 000
Joshua Tree, CA 1992 6.2 Strike Slip 13 000
Petrolia, CA #1 1992 7.1 Thrust 13 000
Petrolia, CA #2 1992 7.0 Strike Slip 5000
Erzincan, Turkey 1992 6.7 Strike Slip 1000
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
27
Table 5
REGRESSION COEFFICIENTS FOR SAH
Period (sec) c1c2c3c4c5c6c7c8
0.05 0.05 0 0 –0.0011 0.000055 0.20 0 0
0.075 0.27 0 0 –0.0024 0.000095 0.22 0 0
0.1 0.48 0 0 –0.0024 0.000007 0.14 0 0
0.15 0.72 0 0 –0.0010 –0.00027 –0.02 0 0
0.2 0.79 0 0 0.0011 –0.00053 –0.18 0 0
0.3 0.77 0 0 0.0035 –0.00072 –0.40 0 0
0.5 –0.28 0.74 0.66 0.0068 –0.00100 –0.42 0.25 0.62
0.75 –1.08 1.23 0.66 0.0077 –0.00100 –0.44 0.37 0.62
1.0 –1.79 1.59 0.66 0.0085 –0.00100 –0.38 0.57 0.62
1.5 –2.65 1.98 0.66 0.0094 –0.00100 –0.32 0.72 0.62
2.0 –3.28 2.23 0.66 0.0100 –0.00100 –0.36 0.83 0.62
3.0 –4.07 2.39 0.66 0.0108 –0.00100 –0.22 0.86 0.62
4.0 –4.26 2.03 0.66 0.0112 –0.00100 –0.30 1.05 0.62
Note: SAH has units of g
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
28
Table 6
REGRESSION COEFFICIENTS FOR SAV
Period (sec) c1c2c3c4c5
0.05 –1.32 0 0 0 0
0.075 –1.21 0 0 0 0
0.1 –1.29 0 0 0 0
0.15 –1.57 0 0 0 0
0.2 –1.73 0 0 0 0
0.3 –1.98 0 0 0 0
0.5 –2.03 0.46 –0.74 0 0
0.75 –1.79 0.67 –1.23 0 0
1.0 –1.82 1.13 –1.59 0.18 –0.18
1.5 –1.81 1.52 –1.98 0.57 –0.49
2.0 –1.65 1.65 –2.23 0.61 –0.63
3.0 –1.31 1.28 –2.39 1.07 –0.84
4.0 –1.35 1.15 –2.03 1.26 –1.17
Note: SAV has units of g
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
29
FIGURE CAPTIONS
Figure 1. The distribution of recordings in the PGA database of Campbell and Bozorgnia
(1994a) plotted as a function of magnitude, distance, and style of faulting.
Figure 2. The distribution of recordings in the PGA database of Campbell and Bozorgnia
(1994a) plotted as a function of magnitude, distance, and local site conditions for
strike-slip earthquakes.
Figure 3. The distribution of recordings in the PGA database of Campbell and Bozorgnia
(1994a) plotted as a function of magnitude, distance, and local site conditions for
reverse and thrust earthquakes.
Figure 4. The distribution of residuals in the PGA analysis of Campbell and Bozorgnia (1994a)
plotted as a function of distance and style of faulting.
Figure 5. The distribution of residuals in the PGA analysis of Campbell and Bozorgnia (1994a)
plotted as a function of distance and local site conditions.
Figure 6. The distribution of residuals in the PGA analysis of Campbell and Bozorgnia (1994a)
plotted as a function of magnitude and style of faulting.
Figure 7. The distribution of residuals in the PGA analysis of Campbell and Bozorgnia (1994a)
plotted as a function of magnitude and local site conditions.
Figure 8. Scaling of peak ground acceleration with magnitude, distance, and ground motion
component predicted by the attenuation relationship recommended in this study.
Figure 9. Scaling of peak ground acceleration with magnitude, distance, and style of faulting
from the attenuation relationship recommended in this study.
Figure 10. Scaling of peak ground acceleration with distance and local site conditions from the
attenuation relationship recommended in this study.
Figure 11. Scaling of 5%-damped pseudo-absolute acceleration with magnitude and ground
motion component from the attenuation relationship recommended in this study.
Figure 12. Scaling of 5%-damped pseudo-absolute acceleration with distance and ground
motion component from the attenuation relationship recommended in this study.
Figure 13. Scaling of 5%-damped pseudo-absolute acceleration with depth to basement rock and
ground motion component from the attenuation relationship recommended in this
study.
Figure 14. Scaling of horizontal 5%-damped pseudo-absolute acceleration with local site
conditions at a distance of 10 km from the attenuation relationship recommended in
this study.
Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997
30
Figure 15. Scaling of horizontal 5%-damped pseudo-absolute acceleration with local site
conditions at a distance of 25 km from the attenuation relationship recommended in
this study.
Figure 16. Scaling of horizontal 5%-damped pseudo-absolute acceleration with local site
conditions at a distance of 50 km from the attenuation relationship recommended in
this study.
... In general, ground motion prediction equations (GMPEs) or attenuation relationships form a key input for the earthquake hazard assessment of any region (Joyner and Boore, 1993;Ambraseys et al. 1996;Campbell, 1997). In general, the linear regression analysis is applied on the observed and/or synthetic peak ground acceleration data to determine GMPEs (Joyner and Boore, 1993;Ambraseys et al. 1996;Campbell, 1997;Boore and Atkinson, 2008;Nath et al. 2009;Anbazhagan et al. 2013). ...
... In general, ground motion prediction equations (GMPEs) or attenuation relationships form a key input for the earthquake hazard assessment of any region (Joyner and Boore, 1993;Ambraseys et al. 1996;Campbell, 1997). In general, the linear regression analysis is applied on the observed and/or synthetic peak ground acceleration data to determine GMPEs (Joyner and Boore, 1993;Ambraseys et al. 1996;Campbell, 1997;Boore and Atkinson, 2008;Nath et al. 2009;Anbazhagan et al. 2013). However, this method introduces errors in ground motion predictability due to the assumption of prior functional form. ...
Article
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The uncertainty in the empirical ground motion prediction models (GMMs) for any region depends on several parameters. In the present work, we apply an artificial neural network (ANN) to design a GMM of peak ground acceleration (PGA) for Kachchh, Gujarat, India, utilizing independent input parameters viz., moment magnitudes, hypocentral distances, focal depths and site proxy (in terms of average seismic shear-wave velocity from the surface to a depth of 30 m (Vs30)). The study has been performed using a PGA dataset consisting of eight engineering seismoscope records of the 2001 Mw7.7 Bhuj earthquake and 237 strong-motion records of 32 significant Bhuj aftershocks of Mw3.3–5.6 (during 2002–2008) with epicentral distances ranging from 1.0 to 288 km. We apply a feed-forward back propagation ANN method with 8 hidden nodes, which is found to be optimal for the selected PGA database and input–output mapping. The standard deviation of the error has been utilized to examine the performance of our model. We also test the ground motion predictability of our ANN model using real recordings of the 2001 Bhuj mainshock, two Mw5.6 Kachchh aftershocks and the 1999 Mw6.4 Chamoli mainshock. The standard deviation of PGA prediction error estimates in log10 units is found to be ± 0.2554. Also, the model predictability of our ANN model suggests a good prediction of the PGA for earthquakes of Mw5.6–7.7, which are occurring in Kachchh, Gujarat, India.
... In general, ground motion prediction equations (GMPEs) or attenuation relationships form a key input for the earthquake hazard assessment of any region (Joyner and Boore, 1993;Ambraseys et al., 1996;Campbell, 1997). In general, the linear regression analysis is applied on the observed and/or synthetic peak ground acceleration data to determine GMPEs (Joyner and Boore, 1993;Ambraseys et al., 1996;Campbell, 1997 which provided an excellent dataset for the robust estimation of moment magnitude, focal depths, hypocentral distances and focal mechanisms. ...
... In general, ground motion prediction equations (GMPEs) or attenuation relationships form a key input for the earthquake hazard assessment of any region (Joyner and Boore, 1993;Ambraseys et al., 1996;Campbell, 1997). In general, the linear regression analysis is applied on the observed and/or synthetic peak ground acceleration data to determine GMPEs (Joyner and Boore, 1993;Ambraseys et al., 1996;Campbell, 1997 which provided an excellent dataset for the robust estimation of moment magnitude, focal depths, hypocentral distances and focal mechanisms. Further toward hazard assessment, several micro-zonation studies have been carried in Kachchh, which provided V s30 estimates for the different regions of Kachchch that enabled us to construct maps of Vs at shallow depths below the Kachchh basin (Mandal and Asano, 2019). ...
Preprint
Full-text available
The uncertainty in the empirical ground motion prediction models (GMMs) for any region depends on several parameters. In the present work, we apply an artificial neural network (ANN) to design a GMM of peak ground acceleration (PGA) for Kachchh, Gujarat, India, utilizing independent input parameters viz., moment magnitudes, hypocentral distances, focal depths and site proxy (in terms of average seismic shear-wave velocity from the surface to a depth of 30m (Vs30)). The study has been performed using a PGA dataset consisting of eight engineering seismoscope (SRR) records of the 2001 Mw7.7 Bhuj earthquake and 237 strong-motion records of 32 significant Bhuj aftershocks of Mw3.3-5.6 (during 2002-2008) with epicentral distances ranging from 1.0 to 288 km. We apply a feed-forward back propagation ANN method with 8 hidden nodes, which is found to be optimal for the selected PGA database and input-output mapping. The standard deviation of the error has been utilized to examine the performance of our model. We also test the ground motion predictability of our ANN model using real recordings of the 2001 Bhuj mainshock, two Mw5.6 Kachchh aftershocks and the 1999 Mw6.4 Chamoli mainshock. The standard deviation of PGA prediction error estimates in log10 units is found to be ±0.2554. Also, the model predictability of our ANN model suggests a good prediction of the PGA for earthquakes of Mw5.6-7.7, which are occurring in Kachchh, Gujarat, India.
... The 2001 NSHM considered several alternative GMMs all weighted equally. For earthquakes between M5 and 7, the 2001 model considered the following GMMs: for PGA, they applied the Boore et al. (1997), Sadigh et al. (1997), Campbell (1997), and Munson and Thurber (1997); for 0.2-s SA, they used the same suite but excluded the Campbell (1997) equation and applied a factor of 2.2 to the Munson and Thurber (1997) PGA GMM to estimate this high-frequency shaking; and for 1.0-s SA, they used the Boore et al. (1997) and Sadigh et al. (1997) equations. They considered similar models for earthquakes larger than M7: for PGA and 0.2-s SA, they applied the Sadigh et al. (1997) GMM and a modified version of Munson and Thurber (1997) GMM that considered alternative magnitude scaling parameters; for 1.0-s SA, they only used the Sadigh et al. (1997) GMM. ...
... The 2001 NSHM considered several alternative GMMs all weighted equally. For earthquakes between M5 and 7, the 2001 model considered the following GMMs: for PGA, they applied the Boore et al. (1997), Sadigh et al. (1997), Campbell (1997), and Munson and Thurber (1997); for 0.2-s SA, they used the same suite but excluded the Campbell (1997) equation and applied a factor of 2.2 to the Munson and Thurber (1997) PGA GMM to estimate this high-frequency shaking; and for 1.0-s SA, they used the Boore et al. (1997) and Sadigh et al. (1997) equations. They considered similar models for earthquakes larger than M7: for PGA and 0.2-s SA, they applied the Sadigh et al. (1997) GMM and a modified version of Munson and Thurber (1997) GMM that considered alternative magnitude scaling parameters; for 1.0-s SA, they only used the Sadigh et al. (1997) GMM. ...
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The 2021 US National Seismic Hazard Model (NSHM) for the State of Hawaii updates the previous two-decade-old assessment by incorporating new data and modeling techniques to improve the underlying ground shaking forecasts of tectonic-fault, tectonic-flexure, volcanic, and caldera collapse earthquakes. Two earthquake ground shaking hazard forecasts (public policy and research) are produced that differ in how they account for declustered catalogs. The earthquake source model is based on (1) declustered earthquake catalogs smoothed with adaptive methods, (2) earthquake rate forecasts based on three temporally varying 60-year time periods, (3) maximum magnitude criteria that extend to larger earthquakes than previously considered, (4) a separate Kīlauea-specific seismogenic caldera collapse model that accounts for clustered event behavior observed during the 2018 eruption, and (5) fault ruptures that consider historical seismicity, GPS-based strain rates, and a new Quaternary fault database. Two new Hawaii-specific ground motion models (GMMs) and five additional global models consistent with Hawaii shaking data are used to forecast ground shaking at 23 spectral periods and peak parameters. Site effects are calculated using western US and Hawaii specific empirical equations and provide shaking forecasts for 8 site classes. For most sites the new analysis results in similar spectral accelerations as those in the 2001 NSHM, with a few exceptions caused mostly by GMM changes. Ground motions are the highest in the southern portion of the Island of Hawai’i due to high rates of forecasted earthquakes on décollement faults. Shaking decays to the northwest where lower earthquake rates result from flexure of the tectonic plate. Large epistemic uncertainties in source characterizations and GMMs lead to an overall high uncertainty (more than a factor of 3) in ground shaking at Honolulu and Hilo. The new shaking model indicates significant chances of slight or greater damaging ground motions across most of the island chain.
... When conducting a probabilistic prediction of ground-motion intensity, a ground-motion prediction equation (GMPE) is typically required for ground-motion intensity estimation at a site of interest using measures such as peak ground acceleration (PGA) or spectral acceleration (SA) [4][5][6][7][8]. The GMPEs are typically derived based on regression analysis of earthquake data, considering several predictive variables (such as magnitude, and source-to-site distance, etc.) and a functional form [9][10][11][12][13][14][15][16][17][18][19]. This process is usually available for seismically active regions with earthquake data [16]. ...
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Probabilistic prediction of ground-motion intensity in regions lacking strong ground-motion records is a vital issue for seismic structural design. Several approaches have been suggested for this purpose, and nearly all of them directly import and adjust the ground-motion prediction equation (GMPE) of ground-motion measures such as the peak ground acceleration (PGA) or spectral acceleration (SA) from data-rich regions. However, as the transmissions of PGA and SA from the source to the site correspond to nonlinear processes, this import and adjustment may lead to an unrealistic evaluation of ground motion. In this study, a novel probabilistic prediction method of ground-motion intensity for such regions is proposed. In contrast to the current approach wherein the GMPE of ground-motion measures such as PGA or SA is directly used, a Fourier amplitude spectral (FAS) model is suggested to express the seismic transmission process from the source to the site. The ground-motion intensities of PGA or SA are obtained from the FAS model using the random vibration theory. The exceedance probability of ground-motion intensity is calculated based on Monte Carlo simulations. As the FAS conforms to the linear system theory and the determination of FAS model does not require too many ground-motion records, the proposed method should be convenient for the probabilistic prediction of ground-motion intensity in regions lacking strong ground-motion records.
... The concept developed by the United States Geological Survey (USGS) was adopted to correlate the data obtained from this analysis [20,21,22,23]. This correlation portrays ( Table 8) the intensity of damage caused due to the respective earthquake considered in this study. ...
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In India, coal ash is produced in quantities of over 70 million tons per year by NTPC plants with a global coal reserve of 8%. This coal ash will be held in ash ponds, which will be closed out when their capacity is reached. It can be decided whether to use the current ash pond or leave it unaltered based on the physical attributes and seismic characterization of the pond. Therefore, the characterization of coal ash ponds situated at NTPC Korba, Ramagundam, Singrauli, Sipat, and VTPS Vijayawada is presented in this research by considering shear wave velocity and penetration number. The seismic characterization of these sites is carried out in Deep-Soil employing equivalent linear analysis by considering the moment magnitude of four different earthquakes (Bhuj, Chamoli, India-Burma, and Kobe) through which peak surface accelerations and maximum strains are inferred. With the magnitudes of factor of safety and acceleration, respectively, it is determined that the ash ponds examined in this research are susceptible to liquefaction. The results of the Mercalli scale are compared to show the potentiality of vibrations induced by the earthquakes evaluated in this study. The ranges of accelerations determined from the final analysis show that the Kobe earthquake produced moderate to heavy damage while inflicting severe perceived shaking.
... The characteristics of the components for different seismic zones were explored using this approach in past studies carried out by Refs. [59][60][61][62], and [63]. A mean PGA ratio of 0.78 was found for the 248 sets of records, which is 16.9% larger than the 2/3 empirical ratio recommended in NBC and other codes and standards. ...
Article
This study aims to provide an estimate of vertical-to-horizontal (V/H) pseudo-spectral acceleration (PSA) ratios in the Eastern Canada seismic zone for firm soils (360 < Vs30 < 760 m/s) referred to as Site Class C in the National Building Code of Canada (NBC). According to previous studies, the 2/3 V/H empirical ratio prescribed in NBC is deemed overestimated for far-field areas and underestimated for near-field areas. In this study, the V/H PSA ratios were computed for 248 records from 67 historic earthquakes in the Eastern Canada region with a magnitude Mw ≥ 3.0 and an epicentral distance (Repi) < 150 km. Given the lack of available records for Site Class C in this region, sets of records from other site classes, mostly Site Class A (Hard rock), were selected and converted to the corresponding records on Site Class C. To this end, the equivalent linear method, using the Pressure-Dependent Modified Kondner Zelasko (MKZ) model of analysis in the frequency domain was selected using the software DEEPSOIL. Computed V/H PSA ratios were then calibrated with those obtained from available Ground Motion Prediction Equations (GMPEs) compatible with Site Class C of the studied region. The computed mean V/H PSA ratios were found to exceed the common value of 2/3 recommended in most codes, especially for short periods up to 1.3 sec, and new V/H ratios were proposed as a function of the fundamental period of the building. Finally, a profile of vertical acceleration design spectra (ADSver) was proposed for Site Class C in Montreal and compared with those obtained by ASCE/SEI 7–16 and ASCE 41-17 provisions.
... Kowsari et al. [4,5] recalibrated the ground motion models (GMMs) to the dataset using Bayesian regression and Markov Chain Monte Carlo simulations which allow limited strong motion data to be combined with the prior information, and can well overcome sparse data in the research region. With the improvement of regression methods [6,7] and the accumulation of strong motion recordings, GMPEs gradually considered the influence of style-of-faulting, hanging-wall effect, or linear and nonlinear site response [8][9][10][11]. In 2008 and 2014, PEER NGA-West1 and NGA-West2 established a database containing strong motion data and related metadata in shallow crustal active tectonic regions worldwide. On this basis, five teams considered the earthquake source characteristic (magnitude, style-of-faulting, hanging-wall effect), path effect (distance), site effect (linear/nonlinear response of soil, basin response), and regional differentiation. ...
Article
In this paper, we collect and process free-field strong motion recordings from 70 earthquakes for 4.2 ≤ MW ≤ 7.9 at 0 < Rrup < 300 km between 2008 and 2018 in the active tectonic regions of southwest China, and then establish a dataset containing 1324 average horizontal ground motion (ROTD50) and corresponding metadata such as parameters of the earthquake source, distance, and site. A new ground motion prediction equation (GMPE) for the average horizontal component of peak ground acceleration (PGA), peak ground velocity (PGV), and 5% damped acceleration response spectra at periods ranging from 0.033 to 8.0 s (SA (T = 0.033–8.0 s)) is introduced. This GMPE considers multiple influencing factors such as magnitude and distance saturation effect, geometric attenuation, style-of-faulting, hanging-wall effect, linear/nonlinear site response, and anelastic attenuation. The residual evaluation and median ground motion are presented. The predicted ground motions using the new GMPE are compared with predictions from the GMPE in western China and five NGA-West2 GMPEs, and the observed ground motions of strong earthquakes which occurred in southwest China. The results show that the proposed GMPE can better reflect the influence of the earthquake source characteristic, propagation media, site effect on the ground motion attenuation characteristic in southwest China, and works well versus independent strong motion data of earthquakes in southwest China, and well reflects the general feature of ground motions for the Wenchuan and Lushan earthquakes that is rich at short-period and weak at long-period. The new GMPE shows outstanding performance estimating the horizontal ground motion of the earthquakes in southwest China for MW 4.2–7.9 (related to style-of-faulting) and Rrup = 10–200 km, at sites with VS30 = 140–1130 m/s.
... In an independent study, Si and Midorikawa (2000) proposed the above attenuation relation for PGV on the stiA ground and PGA on the surface as well. A few studies Campbell 1997;Nozu 1997) indicated that the average amplitude of PGA at a site having soil is about 1.4 times greater than that of the rock site. The base rock motion both for the PGA and PGV are calculated at each shell by introducing the model parameters such as closest fault distance, magnitude and focal depth in the above attenuation equation for the three different earthquake scenarios. ...
Article
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... A large number of worldwide GMPEs have been developed in the past two decades that can be paired with compatible horizontal GMPEs to estimate the V/H ratio. Examples of vertical GMPEs are studies by Abrahamson and Silva (1997), Campbell (1997), Sadigh et al. (1997), Bozorgnia and Campbell (2004), Ambraseys et al. (2005), Chiou and Youngs (2013), Bozorgnia and Campbell (2016a), Stewart et al. (2016), and Gu¨lerce et al. (2017). The second approach is to develop a GMPE directly for the V/H ratios obtained from the empirical data. ...
Article
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We develop a ground motion prediction equation (GMPE) for estimating the vertical ground motion amplitudes for crustal earthquakes in Taiwan. The data set used for the development includes strong-motion recordings mainly from Taiwan earthquakes (M3.5–7.6) and supplemented with large-magnitude earthquakes (M6.5–7.9) from other regions in the Pacific Earthquake Engineering Research Center (PEER) next generation attenuation (NGA)-West2 database. The functional form of the GMPE is similar to that of Phung et al. developed for the horizontal component (P20). The GMPE provides median and standard deviations of peak ground acceleration (PGA) and 5% damped pseudo spectral acceleration response ordinates of the orientation-independent average horizontal component of ground motion (RotD50) for the spectral period of 0.01–10 s. The vertical ground motion developed in this study can be paired with the P20 horizontal component model to estimate a vertical-to-horizontal (V/H) ratio that is unbiased. In the vertical component, we observe significant nonlinear site effects in the period of about 0.2–0.5 s, moderate nonlinear site effects in the period of about 0.01–0.04 s, and small nonlinear site effects in the period of about 0.05–0.075 s. Compared to our horizontal GMPE, anelastic attenuation is faster, V S30 -scaling is reduced, and nonlinear site response is weaker for the vertical component.
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Full-text available
Most seismic hazard analyses combine probabilistic ground motions from all earthquakes within some magnitude range, Mmin < M < Mmax, to estimate levels of peak horizontal acceleration or peak horizontal velocity that have a specified probability of being exceeded at a site during various time periods (e.g., Algermissen et al., 1982). However, engineers have observed that high peak accelerations from smaller magnitude earthquakes may not cause significant damage to well-engineered structures (e.g., Kennedy, 1986), and therefore, it is arguable whether ground motions from small-magnitude earthquakes should be included in seismic hazard calculations (e.g., EPRI, 1987). The choice of minimum magnitude is particularly important in estimates of hazard at sites in Eastern North America (ENA) because peak accelerations associated with ground motions in this region are typically high in amplitude, even when the motions result from small-magnitude earthquakes. However, the ground motions of ENA are extremely rich in high frequencies because of a relatively high Mmax in this region (Atkinson, 1984; Boore and Atkinson, 1987; Toro and McGuire, 1987), and may be less hazardous than ground motions of the same amplitude with more low-frequency energy. There is no consensus among seismic hazard analysts as to an appropriate value of minimum magnitude to use in hazard calculations. Reflecting different opinions regarding the choice of a minimum magnitude to use in seismic hazard analyses for sites in ENA, Bernreuter et al. (1985) adopted the value mb = 3.75, for example, whereas EPRI (1986) selected the value mb = 5.0. A comparison of results obtained by the two groups named above for the same sites suggests that differences in the minimum magnitude may significantly affect the ground motion estimates at some probability levels (Bernreuter et al., 1987). In part because a single scalar, such as peak horizontal acceleration, cannot adequately represent the distribution of ground-motion amplitudes with respect to frequency, some recent seismic hazard studies have estimated response spectra in addition to peak horizontal acceleration (e.g., Bernreuter et al., 1985; EPRI, 1986). However, as we shall illustrate, the choice of minimum magnitude is still important, inasmuch as the minimum magnitude used in the calculations can affect both the shape and level of probabilistic response spectra.
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Probabilistic and statistical methods are being more widely used in seismic risk analyses. These procedures allow the maximum usage of geologic and seismological input into the evaluation of probable risk levels expected at a site. The seismic parameters used in an analysis must be based upon as complete and accurate a data set as possible and the relationships derived from the data must be consistent and representative of that data base. Several case histories are presented. Each one demonstrates some of the difficulties inherent in most data sets and the methods available to overcome them.
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Near-source attenuation relationships for predicting peak horizontal acceleration and velocity in terms of earthquake magnitude, source-to-site distance, and several source and site parameters are used to estimate strong ground motion in north-central Utah. The range of estimates provided reflects uncertainty in the state of knowledge regarding the effects of stress regime, fault type, anelastic attenuation, and local site conditions. Regional data were used to quantify these effects when possible. For a site located directly above the rupture zone of an hypothesized MS=7.5 earthquake on the Wasatch fault (a distance of approximately 5 km), median estimates of peak horizontal acceleration and velocity were found to range from 0.55 to 1.1 g and 45 to 120 cm/s, respectively. These ground-motion estimates, when translated into median estimates of 5-percent-damped response spectral values using the Newmark-Hall procedure, result in estimates of pseudo-absolute acceleration for the 0.1- to 0.5-s period band that range from 1.05 to 2.1 g and estimates of pseudo-relative velocity for the 0.5- to 3.0-s period band that range from 70 to 200 cm/s.
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Attenuation relationships are presented for estimating peak acceleration and spectral velocities on rock sites in the near field of large subduction zone earthquakes. The attenuation relationships were developed from regression analysis of recorded ground motions and numerical simulations of ground motions for large earthquakes. The empirical data consists of the available recordings obtained on rock from 60 earthquakes including the 1985 events in Chile and Mexico. Near field, ground motions for events were simulated by superposition of a large number of subevents. The source models for the subevents were derived from finite difference simulations of faulting and wave propagation was modeled using ray theory.
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Predictive relations are developed for ground motions from eastern North American earthquakes of 4.0≤ M ≤ 7.25 at distances of 10 ≤ R ≤ 500 km. The predicted parameters are response spectra at frequencies of 0.5 to 20 Hz, and peak ground acceleration and velocity. The predictions are derived from an empirically based stochastic ground-motion model. The relations are in demonstrable agreement with ground motions from earthquakes of 4-5. There are insufficient data to adequately judge the relations at larger magnitudes, although they are consistent with data from the Saguenay (M 5.8) and Nahanni (M 6.8) earthquakes. The underlying model parameters are constrained by empirical data for events as large as M 6.8. -from Authors
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A new computational method for implementing Brillinger and Preisler's one-stage maximum-likelihood analysis of strong-motion data is introduced. Analysis by Monte Carlo methods shows that both one-stage and two-stage methods, properly applied, are unbiased and that they have comparable uncertainties. Both give the same correct results when applied to the data that Fukushima and Tanaka (1990) have shown cannot be satisfactorily analysed by ordinary least squares. The two-stage method is more efficient computationally, but for typical problems neither method requires enough time to make efficiency important. Of the two methods, only the two-stage method can readily be used with the techniques described by Toro (1981) and MaLaughlin (1991) for overcoming the bias due to instruments that do not trigger. -from Authors
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A number of predictive relationships derived from regression analysis of strong-motion data are available for horizontal peak acceleration, velocity, and response spectral values. Theoretical prediction of ground motion calls for stochastic source models because source heterogeneities control the amplitude of ground motion at most, if not all, frequencies of engineering interest. Theoretical methods have been developed for estimation of ground-motion parameters and simulation of ground-motion time series. These methods are particularly helpful for regions such, as eastern North America where strong-motion data are sparse. The authors survey the field, first reviewing developments in ground-motion measurement and data processing. The authors then consider the choice of parameters for characterizing strong ground motion and describe the wave-types involved in strong ground motion and the factors affecting ground-motion amplitudes. They conclude by describing methods for predicting ground motion.