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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

Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997

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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

Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997

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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

Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997

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

Seismological Research Letters, Vol. 68, No. 1, pp. 154–179, January/February 1997

25

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

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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

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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

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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

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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.