ML20010C349
| ML20010C349 | |
| Person / Time | |
|---|---|
| Site: | Diablo Canyon  |
| Issue date: | 08/07/1981 |
| From: | Boore D, Joyner W INTERIOR, DEPT. OF, GEOLOGICAL SURVEY |
| To: | |
| Shared Package | |
| ML20010C345 | List: |
| References | |
| NUDOCS 8108190374 | |
| Download: ML20010C349 (68) | |
Text
g, PEAK FORIZOP:TAL ACCELERATIOP: A!'D VELOCITY FROM STRONG-M3TIO? RECORDS INCLUDING PECOR05 FROM TPE 1979 IMPERI AL VALLEY, CALIFORNI A, FAPTH0l' AVE
- 7 rm by ga
~
4 William B. Joyner
/f occam and 3
David M. Boore AUG 131981 > 1
~~
M Utke tt ua twtt#1 U.S. Geological Survey, Menlo Park, California tqMu 4 3mka Osa Q
N ABSTRACT We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relations for peak horizontal acceleration and velocity. This new analysis uses a magnitude-indetendent shape, based on geometrical spreading and anelastic attenuation, for the attenuation curve. An innovation in technique is introduced that decouples the determination of the distance depende.
of the data frorc the maanitude depeiicence. The resulting equations are log A = -1.02 + 0.249M - log r - 0.00255r + 0.26" r = (d2 + 7.3 )1/2 5.0 1 M 1 7.7 2
log V = -0.67 + 0.489M - log r - 0.00256r + 0.175 + 0.22P r = (d2 + 4.0 )1/2 5.3 1 M 1 7.4 2
where A is peak horizontal acceleration in o, V is peak horizontal velocity in cm/sec, M is moment m'gnitude, d is the closest distance to the surface
- submitted to the Bulletin of the Seismological Society of America C108190374 810813
.PDR ADOCK 05000275
)
- PDR,
-5 s
projection of th fault rupture in km, S takes on the value of zero at rock sites and one at soil sites, and P is zero for 50 percutile values and on:.
for 84 percentile values.
We considered a nagnitude-dependent shape, but we find no basis for it in the data; we have adopted the magnitude-independent shape because it requires fewer parameters.
I NTRODUCT10':
New data, particularly from the 1979 Coyote Lake and Imperial Valley earthquakes in California, provide a much improved basis for making ground-motion predictions at small distances from the source.
In this report we update our earlier efforts (Fage and others,1972; Borre and others,1978; 1980) and we introduce some improvements in stat rtical technique that should give better deter-ination of the ef fects of bott 7;agnitude and distance on ground motion.
We examine here the dependence of peak horizontal acceleration and peak horizontal velocity un Ament magnitude (M), distance, and recordinn-site geol ogy. lhe results for velocity should be considered provisional pendinn the integration of more records. We e not intend to imply a preference for i
peak horizontal acceleration or velocity as parameters for describino earthquake ground motion; we are simply recognizing their widesoread use.
This work differs in nyeral important ways from our previous work.
Improvements in statistical analysis techniques pemit us to develop predic-tion equations with an explicit magnitude dependence. The newly available close-in data pemit us to extend the prediction equations to zero distance.
In doing this we have modified the measure of distance used in the previous work and adopted a different functional fom for the prediction equation.
2
D A
METHOD We. fit the strong motion data by multiple linear regression usino the
. equation N
a E, - log r - br + cS.
(1)
Log y =
j
'i=1 where Ej = 1 for eerthquate i
= 0 otherwise S = 1 for soil sites
= 0 for rock sites r = (d2 + h )1/2 2
j( is either peak horizontal acceleration or velocity, N is the number of earthquakes in the data sample, and d is the closest distance from the recording site to the surface projection of the fault rupture. Values for aj,
b, and c are determined by the linear regression for 3 chosen value c' h, and h is determined by a simple search procedure to minimize the sum of scuares c' the residuals. Once the aj values are determined they are used to f'nd, by least squares, a first-or second-order polynomial representing the magnitude i
dependence.
9 j = a + SMj+Y}
(2)
M
.a The use of dummy variables such as Ej and S to divide the data into classes is a well known technique in regression analysis (Draper and Smith, 1966, Weisberg,1980). Similar techniques have been used before for classifying strong-motion data according to site geology (for example, l
Trifunac, 1976; McGuire, 1978). Extension of the technique by employing the 3
'o 4
variable E, 5 s the advantage that it decouples the detemination of magnitude dc n the deterni m_ ion of distance dependence.
To see an exampte of tnis advantage, note that the data from a single earthquake is typically recorded over a limited range of distance.
If the repression analysis were done in tems of magnitude and distance simultaneously, errors in reasuring magnitude would affect the distance coe##icient obtained # rom the regression.
Another advantage of the approach is that it causes each earthquake to have the sane weight in detemining magnitude dependence and each recording to have the same weight in detemining distance dependence, which intuitively spens appropriate. The method can be considered the analytical equivalent of the graphical method employed by Richter (1035,1958) in developing the attenuation curve that foms the basis for the local magnitude scale in southern California. The method described here might prcve to he useful in the development of local magnitude scales.
The fom chosen for the regression is the eouivalent of y=Ie'9#
r where k is a function of M and q is a constant. This corresponds to simple point-source geometric spreading with constant-Q anelastic attenuation.
Strictly speaking, this form would apply only to a harmonic component of the ground rnotion, not to peak acceleration or peak velocity.
Since the coefficients are detemined eicpirically, however, we helieve the application to peak parameters is an appropriate approximation.
We realize that the rupture surface is not a point source for recording sites close to the rupture in a large earthquake. The source of the peak motion, however, is not the whole rupture eurface but rather some more 4
4-1 restricted portion of it.
Even if rupture were instantaneous over the whole surface, which would seen unlikely, the whole surface could not contribute to the motion at any one time because of finite propagation velocities.
The parameter h is introduced to allow for the fact that the source of the peak motion values may not be the closest point on the rupture.
If the source of the peak notion were directly below the nearest point on the surface projection of the rupture, the va'ue of h would. simply represent the depth of that sourca.
In reality the value obtained for h incorporates all the factors that tend to limit or reduce motion near the source, including any tendency for the peak horizontal acceleration to be limited by the finite strength of near-surface material s ( Ambraseys,1974).
The value of h also incorporates any factors that tend to enhance the motion near the source, in particular, directivity (Boore and Joyne,1978).
We use moment magnitude (Hanks and Kanamori,1979) defined as M = 2/3 log M - 10.7 (3) g where M is seismic moment in dyne cm. We prefer M to surface-wave mannitude o
or local magnitude because F corresponds to a well-defined physical property of the source.
Furthermore the rate of occurrence of earthouakes with different M can be related directly to the slip rate on faults (Erune,106P; Molnar,1979; Anderson,1979; Herd and others,1981).
It has been argued that local magnitude is preferable for use in predicting ground motion for engineering purposes because local mage itude is based on measurements at frequencies in the range.;f engineering significance.
It is not clear that local magnitude is in fact a better predictor of ground motion in that frequency range, but, even if it were, the use of local magnitude for 5
predicting ground motion in a future earthquake might merely have the effect of transferring the uncertainty fron the step of predicting ground motion given the local magritude to the step of predicting the local magnitude.
(We i
have done an analysis predicting peak horizontal acceleration and velocity in terms of Pithter local magnitude [Joyner and others,1981? similar to the analysis presented here in terrs of moment magnitude.
The results are compa rable. )
The closest distance to the surface projection of the fault rupture is taken as the horizontal component of the station distance rather than the epicentral distance or the distance to the surf ace rrojection of the center o' the rupture, because the latter twc alternatives are clearly inappropriate in such important cases as Parkfield 1966 or Imperial Valley 1979 where record.ing sites are located close to the rupture but far from both epicenter and rupture cent e r.
Ideally one would work with the distance to the point on the rupture that contributes the peak motion, but it would be difficult to deterrine the location of that point for past earthquakes and in the present state of knowledge impossible for future earthquakes. Th' use of our measure of distance in the development of prediction equations is the equivalent of considering the placement of strong-motion instrunents and the placement of structures as analogous experiments from the statistical point o' view.
In our earlier work (Page and others,1972; Roore and others,107P; inor) we used the shortest distance to the rupture as the measure of distance, whereas here we use the shortest distanc-to the surface projection of the ru pture. The reason for the change is the introduction of the parameter h, which makes allowance, among other things, for the fact that the source of the l
peak motion may lie at some depth below the surface.
If we used the former measure of distance for d, then we would be compensating twice for the effect of depth.
6
To estimate o, the standard error of a prediction made using the y
procedures described here, we use the equatior (o 2+ca) 2 o =
y s
where c is the standard deviation of the residuals from the recression 3
-described by equation (1) and o is the standard deviation o# the residuals g
from the regression described by equation (?). This is based on two assumptions: first, that the error in (etermining the attenuation curve in equation (1) is negligible conpared to the residual of an individual data point relative to that curve and second, that all the variability is due a
to the stochastic nature of the relationship between aj and M and none is due to measuring error in aj or Mj such as might be caused by inedequate sampli ng. We believe that the first assumption is probably true, and the second, though not strictly true, is close enough to give a satisfactory approximation to o.
y DATA The data set for peak acceleration consists of 197 recordings # rom 73 earthquakes and for peak velocity 62 recordings from 10 earthanakes.
Six of the earthquakes in the peak acceleration data set and four of the earthquakes 1
in the peak velocity data set were recorded at only one station. Such data are given zero weight in the analysis. The data sets are restricted to earthquakes in western Forth America with M greater than 5.0 anei to shallow earthquakes, defined as those for which the fault rupture lies ainly above a 7
6 depth of 20 km.
For peak values we use the larger of the two horizontal components in the directions as originally recorded. Others (e.g. Campbell,
1981) have used the mean of the two components. For his data set Fampbell reports that, on the average, the larger value for peak acceleration exceeds the mean by 13 percent. The small symbols on Figure I show the distribution of the peal acceleration data in magnitude and distance; the large syrhols indicate data points not included in our data set but compared with our prediction equations in Table 5.
Figure 2 shows the distribu lon of the real velocity data in magnitude and distance.
Table 1 lists the earthquakes and gives the source of de s used in assigning magnitudes and station distances.
For earthquakes through 107! the sources of strong motion data and geologic site data are aiven in a previous publication (Boore and others,1078). Many of the acceleration data for these earthquakes were taien from Volume I of the series " Strong-Motion Farthquake Accelerograms" published under the direction of D. E. Hudson by the Earthouat e Engineering Research Laboratory of the California Institute of Technology.
Volume I of that series was uted for acceleration instead of Volume 11 because the procedures used in producing Volume II tended to bias the peak acceleration toward lower values.
For more recent earthquakes sources of strong-motion data include Porter (1978), Porcella (1979), Porcel :a and others (1979), Brady and others (1980), and Poore and Porcella (1081).
In addition, unpublisted data were made available by the California Division of Fines and Geology, by J. N. Brune for the stations of the cooperative program of the University of California at San Diego and the t'niversidad Pacional Autonora de Mexico, and by Kineretrics Inc. for the Shell Oil Company station at Funday Creek, Alaska. Sources of site descriptions for records obtained since In7c include the U.S. Geological Survey (1977) and Shannon and Wilson Inc. and 8
I
p
~
t d
Agbabian Associates (1978; 1980a; 1980b).
In the base of two stations (290 Wrightwood, California, and IMC Fort Tejon, Crifornia), site clast.ifications made by Boore and others (1978) were changed on the basis of new infomation given by Shannon and Wilson Inc. and Agbabian Associates (1978; 198Da; 1980b). The strong-motion data and site classifications are given in Table 2.
For some of the recent earthquakes geoloqic data were not available for all sites. Since only acceleration data were available for those earthquakes and since earlier studies (Foore and others,1980) had shown that peak acceleration is not correlated with geologic site conditions, we proceeded with the analysis without geologic Site data for those earthaudes.
The P values (Table 1) are calculated from seisric riorents if noment determinations are available.
In cases where they are not available P is taken to be equal to ML and the values are enclosed in parentheses in Table 1.
The largest such value is 6.2 for the 1972 Managua, Nicaragua, ea rt hquake. This event had an M of 6.2 (U.S. Dept. of Commerce,1973); an Q 3
of 6.2 was
- culated fro-the strong-mtion record at the Esso Pefinery (Jennings and Kanamori,1979).
On the basis o# evidence (Poore and others,10R0; frouse,1079) suggesting that large structures may bias the ground-motion data recorded at the base of the s.ructure, we excluded from the data set records made at the base of buildings three or more stories in h?ight and on the abutments o' dams. We excluded all earthquakes for which the data were in our opinion inadequate for estimating the source distance to an accuracy better than F km (see Pat.: et al,1972, Table 5).
Bias may be introduced into the analysis of strong-motion data by the fact that some operational instruments are not triggered. To avoid this bias we employed the following procedure: For each earthquake the distance to the nearest operational instrument that did not trigger was determined or in some 9
i
4 caser estimated. All data from equal or greater distances for that earthauake were excluded.
In contrast to our earlier work the cutoff distance was different' for each earthquake. For a few records peak accelerations were reported only as "less than 0.05 c,."
In those cases we noted the smallest distance for such a record and excluded all data recorded at equal or grea+er distances for that event. There exists a possibility of bias in analyzing peak velocity data because hign-anplitude records may have been preferent ially chosen for integratior,. To avoid this bias we noted the distance of the nearest record that had not been integrated, except records for which we knew definitely that the reason they were not integrated had nothinc to do with amplitude. We then excluded all velocity data recorded at eaual or greater distances for that event.
Recording sites were classified into two categories, rock and soil, using the best available infomation in the same way as done in earlier work (Poore a nd et he rs, 1978; 1980).
Sites dascribed by such tems as " granite,"
"diorite," "gnei s s," "che rt," "graywacke," " limestone," "sa ndstone," or "siltstone" were assigned to the rock category, and sites described by such terms as " alluvium," " sand," " gravel," "cl ay," " silt," " mud," " fill," or
" glacial outwash" were assigned to the soil category, except that if the description indicated soil material less than 4 to 5 m thick overlying rock, t he s i -a was classified as a rock site. Resonant frecuencies of soil layers as thin as that would generally be greater than 10 Hz and thereby outside the range of frequencies making up the dominant part of the accelerogram.
RESULTS The aj values resulting from the regression analysis of peak acceleration data using equation (1) are plotted against M in Figure 3.
Earthquakes represented in the data set by only one record are shown in Fiqure 3 by 10
c-ta 1
l diamonds and are excluded in the fitting of the polynvial. The coefficient of the second degree tem of the )olynomial is not significant at the on percent level and the tem is omitted.
The effect on the final prediction equations of excluding the points represented by the dianonds -in Figure 3 is relatively small. The ef fect on the 50 per 2ntile values ranges from a 40-percent increase at magaitude 5.0 to a 10-percent decrease at magnitude 7.7.
The points were excluded in an ef fort to obtain the best pessible estimates of the parameters of the prediction equation. The two lowest points in Figure 3, which represent the two Santa Rosa earthouakes recorded at the same site, are not representative of the earthq uakes.
In both earthouakes instruments at eight sites recorded hieher peak horizontal acceleration than the record included in the data set even though they w?ra at greate distances (Boore and others,1979).
(These other records were exclude' use their distances exceeded the distance of the closest operational instrument that did not trigaer.)
Combining the results of the analyses using equations (1) and (2), we obtain the following prediction equation for peak horizgntal acceleration:
1og A = -1.02 + 0.249 M - 1og r - 0.00255r + 0.26P r = (d2, 7,3 )1/2 5.0 1 M i 7.7 (4) 2 where d is defined as in equation (1) and P equals zero for 50 percent probability that the prediction will exceed the real value and one for 84 i
percent probability. The value of P is based on the assumption that the prediction errors are normally distributed, and one could obtain the values of P for other percentiles from a table of the nomal distribution function.
Because of the limited number of data points, however, the assumption o' nomality cannot be tested for the tail of the distribution and values of P 11
4 LLA e
greater than one should be used with caution. For a few rif the recent earth-quakes, geologic site data are not available at all sites (Tahle 2). A pre-liminary analysis using only the earthquakes for which site data are available indicated that the soil term is not statistically significant for peak accel-eration--a conclusion reached in earlier work -(Roore and others,1080)--and it is therefore not included. Equation (4) is illustrated in Figu*e 4 for the 60 and 84 percentiles.
It is of interest to note that the magnituue coef ficient is the same, to two decimal places, as that given by Donovan (1973).
The coefficient of P in equation (4) represents o, the standard error of y
an individual prediction, and is determined from a value of 0.?? for o, the g
standard deviation of the residuals from the regression described by ecuation (1) and a value of 0.13 for o, the standard deviation of the residuals from g
the regression described by equation (2). The value 0.26 obtained for c. compares well with the value 0.27 obtained by McGuire (1978) usinc a y
data set specially constructed to avoid bias in the estimate of residuals caused by multiple records from a single event or by multiple records from the same site of different events.
Residuals of the data with respect to equation (4) are plotted aaainst distance in Figure 5 with different syttols for three magnitude classes.
No obvious differences in trend are apparent among the three different magnitude classes, giving no support to the idea that the shape of the attenuation curves depends upon magnitude. Within 10 km the standard deviation appears to be less than the overall average; whether this is the result of the relatively few recordings from a small number of earthquakes or is a general phenomenon awaits further data.
To test further the concept of a magnitude-dependent shape for the attenuation curves, we retrated the analysis of the acceleration data usina a magnitude-dependent value ' f h_ given by o
12
l' I
l c
y exp(h [M - 6.0])
(5) h=h p
I where h1 a nd hp are detemined by minimizing the sum of squares of the residuals. The expression was written in tems of [M - 6.01 rather than simply M in order to reduce the correlation between h1 and h. We tested the 2
significance of the reduction in variance achieved by going to the magnitude-dependent h, using an approximate method described by Draper and Smith (1956) for multiple nonlinear regression problems. The reduction in variance is not si gnifica nt.
The distribution of the data set in distance, however, is such that this test is not definitive. The value of h_ has a large effect on the residuals only for values of d less than about 10 km.
Since d is greater than 10 km for most of the data set, changes in h bring relatively small chances in the total variance. A more sensitive test is providad by examining the residuals from equation (4) as a function of magnitude for stations with d less than or equal to 10 km (Figure 6).
If there is support in the data for a magnitude-dependent _h_, it should show as a magnitude dependence in these residuals. A least-squares straight line through the pnints in Figure 6 has a slope of -0.075, and the standard deviation of the sinpe is 0.042 A glance at the plot, however, shows that even this marginal relationship depends on a single earthquake, an aftershock of the 1979 Imperial Valley earthcuake, v.tich contributes all of the points plotted at M = 5.0.
If that earthouake is removed, the least-squares straight line through the remaining points has a slope whose value 's less than its standard deviation. From this we conclude that the cata do not support a magnitude-dependent h_.
A theoretical argument based on a stochastic source model predicts a slightly magnitude-dependent shape equivalent to choosing hp = 0.12 in eqration (5). The argument is detailed in the Appendix. The resulting prediction equation gives a value of the 50 percentile peak acceleration, for N = 7.7 and d = 0 only 16 percent less than that of equation (4). Even if we accepted the model without 13 i
I'-
4 reservation 'we would be disinclined to change the prediction equations for a dif ference so small. Lacking an adequate basis in the data or in theory for choosing between a magnitude-independent and magnitude-dependent shape for the attenuation curve, we have adopted the magnitude-independent shape because it requires fewer parameters.
in order to demonstrate the sensitivity of the prediction equations to the presence c' particular earth::uakes in the data set we recorputed t he pre-diction equations repeatedly, each time excluding a dif ferent one (or in some cases two) of the earthquakes. This process was carried out for all of tha earthquakes that contribute a significant fraction of the data sat.
The results are given in Table 3, which shows the parameters of the pradiction equations and the predicted 50 percentile values of peak acceleration at d = 0 for M = 6.5 and 7.7.
In order to show the effect of h on the residuals, prediction ecuations were developed for four different values of h bracketing the value detemined by least s qua res. Residuals against these equations are shown in Figure 7.
The value of the distance coefficient b_ determined by least souares is also shown for each value of h, illustrating the coupling between these two parameters.
The aj values resulting from the regression of peak velocity data usina equation (1) are pintted against P in Ficure 8.
As with peak acceleration earthquakes represented in the data set by only one record are shown by diamonds and are excluded in fitting the straight line.
It is apparent that the exclusion of these events has a relatively small effect in detemining the line but a rather large effect on the standard deviation of points about the line. The coefficient of the second-degree tem of the polynomial fitted to the pluses in Figure 8 is statistically significant and leads to a curve concave upwards.
In view of the small number of points we have suppressed the second-degree term. The prediction equation for peak horizontal velocity is la
log V = -0.67 + 0.489 M - log r - 0.nn256r + 0.175 + 0.22P r = (d2 + 4.0 )1/2 5.3 1 P f 7.4 (6) 2 where d and S are as defined in equation (1) and P as defined in equation (4).
Equation (6) is illustrated in Figure 0 The soil term in equation (6) is statistically significant at the 0A percent -level in etntrast to the cese of peak acceleration where it is not i
si gnificant. Similar resuus have been reported by poke and others (1072),
Trifunac (1976), and Boore and others (1978,1980).
It seems likely that some sort of amplification mechanisms are operating on the longer periods that are dominant on velocity records and that for the shorter periods dominant on the acceleration records these mechanisms are counterbalanced by anelastic attenuation.
It is important to note that the determination of the soil effect is dominated by data from southern California where the thickness of low-Q naterial near the surface is typically large. Net ampli#ication of peak acceleration at soil sites nay occur for some other distributions of 0.
The coef ficient of P in equation (6) is o, the standard error of an y
individual prediction, and it reflects a value of 0.20 for s, the standard deviation of the residuals of the regression of equation (1), and a value o#
O.10 for a, the standard deviation of the residu?.ls of the regression of equation (2). As with peak acceleration the value of 0.22 for o, compares reasonably well with McGuire's (1978) value of 0.28.
Residuals of the peak velocity data with respect to equation (6) are plotted against distance in Figure 10 for the three different magnitude classes. As with peak acceleration there are no differences in trend amona the different magnitude classes that would support a magnitude-dependent shape for the attenuation curves. As with peak acceleration we further test the idea of a magnitude-dependent shape by plotting the residuals from equation 15
(6) as a function of magnitude for stations with d less than or equal to 10.0 km (Figure 11). The slope of the least-squares straight line through the points is smaller than its standard error.
The sensit' ity of the prediction equations to particular earthauakes in the data set was axanined by repeating the computations, each tire excludirq a I
dif ferent one of the earthquakes. The results are given in Table a.
In Figure 12 are sbown the residuals of peak borizontal velocitv for four dif ferent values of h bracketino the value determined by least squares. Also shown is the value of the distance coefficient b detemined by least squares for each value of h.
DISCUS SI 0f,'
The prediction equations are presented in terms of moment magnitude for convenience and for ease of comparison with other studies. Seismic moment,
however, is the fundamental parameter, and we believe it desirable to repeat the prediction eauations, expressed directly in tems of moment.
{
l og A = -3.6o + 0.166 log Mo - log r - 0.00255r + 0.26r r = (d2 + 7.3 )1/2 23.5 1 log Mo 1 27.6 2
1og V = -5.90 + 0.3261og M - 1 og r - 0.00256r + 0.175 + 0.22P l
e 2
r = (d2 + 4.0 )1/2 24.0 1 1og Mo 1 27.2 (Po ent in dyne cm)
The prediction equations are constrained by data at soil sites over the whole distance range of interest for M less than or equal to 6.5, the value for the Imperial Valley. earthquake. The data set contains no recordings at rock sites with d less than 8 km for earthquakes with M greater than 6.0, and caution is indicated in applying the equations to rock sites at shorter distances for earthquakes of larger magnitudes.
Some indication of the applicability of the equations under those conditions can be obtained by 16
6 comparing the predicted and observed values, given in Table 5, for the Pacoima Dam record of the San Fernando earthquake (d = 0.0 km, M = 6.6).
The Pacoima Dam-site is a rock site, but the record was excluded from the data set used in the regression analysis because it was recorded on a dam abutment.
The observed values are higher than the predicted values for both acceleration and velocity, but the difference is less than the standard error of prediction (c ) for velocity and also for acceleration if the observed acceleration is y
corrected for topographic amplification (Poore,1073).
For distances less than 40 km from earthquakes with r greater than 6.6 the prediction equations are not constrained by data, and the results should be t eated with caution. An indication of the applicability o' the equation for acceleration in that range of magnitude and distance can be had by comparing predicted and observed values, given in Table 5, for the Tabas, Iran, and Gazli, USSD records. These records were not included in the data set because they did not originate in western North America.
We do not propose use of the prediction equations beyond the magnitude limits of the data set, 7.7 for peak acceleration and 7.4 for peak velocity, but we do note that Figures 3 and 8 show no tendency for either peak acceleration or peak velocity to saturate with magnitude. We do not believe that a valid basis now exists for specifying the behavior of peak acceleration and velocity at magnitudes beyond the limits of our data set. Alt ho igh it might be argued that peak acceleration and peak velocity should saturate for the same reason that the body-wave magnitude scale saturates, we are not aware of any careful analysis supporting this argument. We consider the c'Jestion open. The recent demonstration by Scholz (1981) that mean slip in large earthquakes correlates linearly with fault length will certainly have important bearing on these questions.
17
6-The prediction equations predict peak velocities greater than 200 cm/sec for R greater than or equal to 7.0 at close distances. No values that hioh have ever been observed but we know of no physical reason why they could not occur. At soil sites in an earthquake of M greater than 6.5, the finite strength of the soil might limit the peak acceleration to values smaller than those given by the prediction equations, but determining what that lirit would be would require adequate jjl situ determination of the dynamic soil prope rt ies.
On the basic of fewer available data, Trifunac (lo76) made estimates comparable to ours for the peak velocity at small distances # rom eartFcuakes of magnitude 7.n and above. Kanamori (1078) gave an estimate o' 20n cm/sec for the peak velocity at 10 kn from an earthquake like Kern County (P = 7.a),
a value somewhat greater than ours (Figure 6). Both -Trifunac (19761 and Ka namori (1978) erployed the attenuation curve used for local magnitude determinations in southern California. That curve is only weakly constrained by data at short distances. Recent data, especially from the 1979 Imperial Valley earthquake, enable us to develop more closely constrained curves for both acceleration and velocity.
1 The attenuation relationships developed by Campbell (1981; Carrbell and otSers,1080) for peak horizontal acceleration are compared in Figure 13 with our results.
His definition of peak horizontal acceleration differed #r om ours in that he used the mean of the two components rather than the larger of the two. To compensate for this we have raised his curves in Figure 13 by 13 percent, a value determined by him. He selected magnitudes to be consistent with a moment-magnitude scale, essentially PL for F < 6 and Ms>6.
His measure of distance was "thi
- .artest distance from the site to the rupture zone", whereas our measure is the shortest distance to the surface projection 18
i I
of the rupture. This will make no difference for the large magnitude events, which typically break the surface, but the dif ference may be significant for the smaller events in which the rupture zone may be at significant depth below the surface. His curve for magnitude 5.5 is cut off at 5 km in Figure 13 because at smaller distances the difference in definition of distance invalidates the comparison. He included only data with distances less than 50 km, which severely limits the number of data points included from bigher maga.itude events.
The differences shown on Figure 13 are small compared to statistical prediction uncertainty. The most conspicuous difference is the chance in shape with magnitude shown by his curves, which may be in part due to the dif ferent definition of distance. All things considered we view the relative agreement between the two sets of curves n more significant than the dif ferences.
It suggests that the results of both studies are insensitive to rather large variations in method and assumptions.
It is of some interest to consider the physical interpretation of the parameters in the attenuation relationship.
If the values agree with what we would expect from cth, considerations, we gain more confidence that the model, though oversimplified, is appropriate. The value detemined for the attenuation coefficient in the relationship for peak acceleration corresponds to a Q of 700 for an assumed frequency of 4 Hz and 350 for a frequency of 2 Hz. The latter value is probably the more appropriate one to consider because the distant records with frequencies closer to ? Hz than 4 Hz dominate in the determination of the attenuation coefficient. The va'ae of the attenuation coefficient in the relationship for peak velocity correspond to a Q of 180 for an assumed frequency of 1 Hz. These r) values lie in the range 19
a generally considered appropriate on the basis of other data and increase our confidence in the nodel. The smiller value for velocity than for acceleration is consistent with the frequency dependence of Q described by Aki (1480). but in view of the oversimplified character of the model we dn not propose tHs as evidence for a frequency-dependent O.
The values of 7.3 and 4.0 km for h in the relationships for paal acceleration and peak velocity seem reasonable in the sense that they lie in the range of one quarter to one half of the thickness of the seismogenic zone in California, where most of the data were recorded. Why the value is less for velocity than for acceleration is not clear.
It might be argued that the larger value of _h_ for peak acceleration represents a limitation in acceleration near the source by the limited strength of the near-surface material s.
If that were the case, however, one would expect the cttenuation curve for earthauakes of magnitude less than 6 to differ in shape from thtt of i
earthquakes greater than 6.
Figures 5 and 6 show no evidence of this.
Another possibilicy relates to directivity. The effect of directivity would be to increase the peak velocity preferentially at sites near the fault. 'his effect woul/ 5e reflected in a smaller value for h.
Directivity would be expected to have a similar effect on peak acceleration (Bonre and Jnyner, j
1978; Boore and Porcella,1980), but one might speculate that local variations l
in the direction of rupture propagation or scattering and lateral refractinn might in some way reduce the effect of directivity upon the higher frequency waves dominant in the acceleration record.
The magnitude coefficient in the relationship for peak acceleration is 0.25 and has a standard error of 0.04.
It thus differs by little more than one standard error from the value 0.30, which corresponds to the scaling of 5
peak acceleration as M derived theoretically by Hanks and McGuire (10P1) by 20
treating the acceleration record as a stochastic process. The magnitude coefficient for peat velocity is 0.49 with a standard error of 0.06.
It lies within one standard error of the value 0.5, which corresponds to the scaling of peak velocity as Mf/
appropriate for a deterministic rupture propanating outward from a point (Boatwright,1980; oral communication,1081; McGarr, 1981).
It seems quite reasonable that the acceleration should lonk like a stochastic process and the velocity like a deterministic process.
ACKNOWL EDF, MENT S I
Unpublished strong-motion data were generously supplied to us by the California Division of Fines and Geology, by J. N. Rrune on behalf of the University of California at San Diego and the liniversidad Nacional Autonoma de Mexico and by Kinemetrics Inc. and the Shell Oil Co.
We benefited sinnifi-cantly from discussion with T. C. Hanks.
J. Boatwricht a C. Rujahn critically reviewed the manuscript and made a number of valuable sugges-t io ns. We are indebted to K. W. Campbell for extended helpful discussions.
APPENDIX The theoretical arguments for a magnitude dependent shape, referred to in the text, are based on consideration of the scaling of peak acceleration with magnitude at close and far distances, and follow from an extension of the reasoning given in Hanks and McGuire (1981). Their stochastic source model predicts that the acceleration time hist y is to a good approximation a finite-duration sample of band-limited white, Gaussian noise. Using a resul.
from Vanmarcke and Lai (1980), Hanks and McGuire (1981) give the following expression for the peak acceleration at a site whose distance to the source is large compared to the source dimensions 21
s f
\\1lE 2So
^ ax * #ms( ", T
/
I) m g
where A is the root-mean-square acceleration, S is the duration of the m3 o
acceleration tire history, and T is the predominant period of the o
acceleration.
By the Hanks and McGuire source theory A scales as F and, given m3 the moment-magnitude relation of equation (3), log A is therehy ms proportional to moment magnitude with a coef ficient of 0.25.
Using their scaling of S in terms of moment and assuming T eauals 0.2 sec, the logarithm o
o of
\\III f
2Sg P\\;n _ 'o. /
is approxinately proportional to momerit magnitude in the range between 6.5 and 7.5 with a coefficient of 0.05.
Combining the two factors gives a magnitude coefficient of 0.30 for log (ex.
( As stated in the text this compares with our value of 0.25, which has a standard deviation of 0.04 The difference is only slightly greater than the standard deviation.)
Further considerations are needed for the magnitude scaling close to the source. At snall distance from a large source only a restricted portion of
- the source has an opportunity to generate the peak accelerations.- In other words the ef fective duration S is fixed even as moment magnitude increases.
o Furthemore since the predominant period T in Hanks and McGuire's analysis is o
independent oT magnitude, the bracketed tem in equation (A1) will also be magnitude independent. A at small distance should then scale with Tnax magnitude in the same way as Am3, provided that A is measured over the ms 22
O restricted portion of the record that corresponds to the effective duration.
But A measured over a fixed interval should scale with magnitude in the rms same way as A over the whole record scales at distant stations. The rms dif ference in magnitude coefficient between near and disi. ant stations is just the quantity
. )1/2
[
. 2Sg l og 2tn T
N which we have found to be 0.05 in the maanitude range 6.5 to 7.5.
Ry choosing hp = 0.12 in our equations we can force the 0.05 difference in maanitude coef ficient between near and distant stations.
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32
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Table 1.
Continued Date (GMI)
M Month Day Year Sources Bear Valley, California 5.3 5.1 2
24 72 Bolt and Miller (1975);
Ellsworth (1975); Johnson and ticEvilly (1974).
Sitka, Alaska 7.7 7
30 72 Page and Gawihrop (1973); Page (oral cmnun., 1976); Purcaru and Berckhemer ( 1978).
Managua, Nicaragua (6.2) 6.2 12 23 72 Jennings and Kanamori ( 7979);-
Plafker and Brown (1973*; Ward and others (1973); Kn ton and
.llansen A. (1973); U.S. Dept. of Commerce (1973).
g Point Muau, California 5.6 6.0 2
21 73 Ellsworth and others (1973);
Boore and Stierman (1976);
Stierman and Ellsworth (1976).
Hollister, California (5.2) 5.2 l'
28 74 Cloud and Stitier (1976);
W.II.K. Lee (written commun.,
1976).
Oroville, California 6,0 5.7 75 fogleman and others (1977);
Bufe and others (1976); Lahr and others (1976); Langston and Butler (1976); llart and others (1977).
Santa Barbara, California 5.1 5.1 8
13 78 Wallace and llelmherger (1979);
Lee ad others (1978).
St. Elias, Alaska 7.6 2
28-79 liasegawa and others (1980);
C. D. Stephens (written commun., 1979); J. Boatwright (oral commun., 1979).
- -..l
Table 1.
Continued Date (6MI)
M Month Day Year Sources Coyote Lake, California 5.8 5.9 8
6 79 Uhrhanener (1980); Lee and others (1979).
Imperial Valley, California 6.5 6.6 10 15 79 Kanamori (oral consnun., 1981);
C. E. Johnson (oral coninun.,
1979); Boore and Porcella (1981).
Imperial Valley, California (5.0) 5.0 10 15 79 C. E. Johnson (oral consnun.,
aftershock 1979).
Livermore Valley, California 5.8 5.5 1
24 80 Bolt and others (1981); R. A.
Uhrhanoner (oral conunun., 1981);
J. Boatwright (oral consnun.,
g 1980).
Livermore Valley, Calif ornia 5.5 5.6 1
27 80 Bolt and others (1981); R. A.
Uhrhanener (oral conrnun., 1981);
J. Boatwright (oral coninun.,
1980); Lockerham and others (1980).
Horse Canyon, California (5.3) 5.3 2
25 80 L. K. Hutton (written commun.,
1980).
-I no i
et l
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1 898371 0201 1
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t 1
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1 1 1 1 1 1 1 1 1 t
S a
t a
D no i
8 t
0 6
o 4
9 M
9 1
1 g
2 n
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y 5
i o
k e
9 7
6 a
r a
l 1
5 6
t t
u l
9 9
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q a
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t o
t n
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t Table 2.
(continued)
Peak Peak-Horizontal fior i zo n't.*1 Distance Acceleration Velocity Site-j Earthquake Station km g
cm/sec Condition Borrego Mountain 1968 130 187.0 0.010 soil (continued) 475 197.0 0.010 soil 269 203.0 0.006 soi1 135 211.0 0.013 soil Santa Rosa 1969 1093 62.0 0.005 soil first event Santa Rosa 1969 1093 62.0 0.003 soil second event Lytle Creek 1970 111 19.0 0.086 5.6 rock 116 21.0 0.179 rock 290 13.0 0.205 9.6 soil tj 112 22.0 0.073 soil 113 29.0 0.045 soil San Fernando 1971 128 17.0 0.374 14.6
' rot.k 126 19.6 0.200 8.6 rock 127 20.2 0.147 4.8 rock 141 21.1 0.188 20.5 rock 266 21.9 0.204 11.6 rock 110 24.2 0.335 27.8 rock 1027 66.0 0.057 2.8 rock 111 87.0 0.021 rock 125 23.4 0.152 18.0 soil 135 24.6 0.217 21.1 soil 475 25.7 0.114 14.3 soil 262 28.6 0.150 14.2 soil 269 37.4 0.148 5.4 soil 1052 46.7 0.112 8.5 soil 411 56.9 0.043 5.0 soil 290 60.7 0.057 3.8 soil 130 61.4 0.030 10.4 soil-
Table 2.
(continued)
Peak Peak Horizontal Horizontal 1
Distance Acceleration velocity Site Earthquake' Station km g
cm/sec Sondition San Fernando 1971 272 62.0 0.027 7.3 soil (continued) 1096 64.0 0.028 1.4 soil 1102 82.0 0.034 2.5 soil 112 88.0 0.030 soil 113 91.0 0.039 soil Eear Valley 1972 1028 31.0 0.030 soil Sitka 1972 2714 45.0 0.110 rock 2708 145.0 0.010 rock 2715 300.0 0.010 soil Managua 1972 3501 5.0 0.390 soil 8!
Point Mugu 1973 655 50.0 0.031 rock 272 16.0 0.130 soil Hollister 1974 1032 17.0 0.011 rock 1377 8.0 0.120 soil 1028 10.0 0.170 soil 1250 10.0 0.14 0 soil Oroville 1975 1051 8.0 0.110 5.0 rock 1293 32.0 0.040 rock 1291 30.0 0.070 soil 1292 31.0 0.080 soil Santa Barbara 1978 283 2.9 0.210 885 3.2 0.390 Goleta substation 2 7.6 0.280 St. Elias 1979 2734 25.4 0.160 Munday Creek 3-32.9 0.064 2728 92.2 0.090
4
._=
Table 2.
(centinued)
Peak Peak Horizontal liorizontal
~
Distance Acceleration Velocity
. Site j
Earthquake Station '
km g
cm/sec Condition-Coyote I.ake 1979 1413 1.2 0.420 43.8 rock:
1445 1.6 0.230 20.5 rock-1408 9.1 0.130 10.3 rock 1411 3.7.
0.260 32.2 soil 1410 5.3 0.270 29.4' soil 1409 7.4 0.260 31.9 soil 1377 17.9 0.110 soit 1492 19.2 0.120 soil-1251 23.4 0.038 soil 1422 30.0 0.044 soil 1376 38.9 0.046 soil Imperial Valley 1979 Cerro Prieto4 23.5 0.170 rock 286 26.0 0.210 9.0 rock
~
Meloland Overpass 5 0.5 0.320 soil w
5028 0.6 0.520 110.0 soil 942 1.3 0.720 110.0 soil 4
1.4 0.320 soil Aeropuerto 5054 2.6 0.810 44.0 soil 958 3.8 0.640 53.0 soil 952 4.0 0.560 87.0 soil 5165 5.1 0.510 68.0 soil 117 6.2 0.400 soil 955 6.8 0.610 78.0 soil 5055 7.5 0.260 48.0 soil Imperial Co. Center 5 7.6 0.240 soil Mexicali SAliOP4 8.4 0.460 soil 5060 8.5 0.220 37.0 soil 412 8.5 0.230 44.0 soil 5053 10.6 0.280 19.0 soil 5058 12.6 0.380 39.0 soil 5057 12.7 0.270 46.0
- soil Cucapah4 12,9 0.310 soil 5051 14.0 0.200 17.0 soil
t Table 2.
(continued) i Peak
' Peak llorizontal Horizontal Distance Acceleration Velncity Site j
Earthquake Station km e
cm/sec Condition Imperial Valley 1979 Westmoreland5 15.0 0.110 seit j
(continued) 5115 16.0 0.430 31.0 scil l
Chihuahua 4 17.7 0.270 soil l
931 18.0 0.150 19.0 soil l
5056 22.0 0.150 15.0 soil
)
5059 22.0 0.150 15.0 soil 5061 23.0 0.130 15.0 soil 4
23.2 0.190 soil l
Compuertas 5062 29.0 0.130 soil l
5052 32.0 0.066 soil Delta 4 32.7 0.350 soil 724 36.0 0.100 soil Victoria 4 43.5 0.160 soil 5066 49.0 0.140 soil
$5 5050 60.0 0.049 soil 2316 64.0 0.034 soil Imperial Val ~Iey 1979 5055 7.5 0.264 aftershock 942 8.8 0.263 i
5028 8.9 0.230 l
5165 9.4 0.147 952 9.7 0.286 958 9.7 0.157 955 10.5 0.237 117 10.5 0.133 412 12.0 0.055 5053 12.2 0.097 5054 12.8 0.129 5058 14.6 0.192 5057 14.9 0.147 5115 17.6 0.154 5056 23.9 0.060 5060 25.0 0.057
4 Table 2.
(continued)
Peak Peak-Horizowtal Horizontal Distence Acceleration Velocity Site j
Earthquake Station km 9
cm/sec Condition Livermore Valley 1980 1030 10.8 0.120 January 24 1418 15.7 0.154 1383 16.7 0.052 1308 20.8 0.045 1298 28.5 0.086 1299 33.1 0.056 1219 40.3 0.065 Livermore Valley 1980 Fagundes Ranch 5 4.0 0.259 January 27 Morgan Terrac= Park 5 10.1 0.267 1030 11.1 0.071 1418 17.7 0.275 1383 22.5 0.058
'S Antioch Contra Lomab 26.5 0.026 1299 29.0 0.039 1308 30.9 0.112
{
1219 37.8 0.065 1456 48.3 0.026 Horse Canyon 1980 5045 5.8 0.123 5044 12.0 0.133 5160 12.1 0.073 5043 20.5 0.097 5047 20.5 0.096 C168 25.3 0.230 5068 35.9 0.082 C118 36.1 0.110 5042 36.3 0.110 5067 38.5 0.094 5049 41.4 0.040 C204 43.6 0.050 5070 44.4 0.022 C266 46.1 0.070
Table 2.
(continued)
Peak Peak florizontal linrizontal Distance Acceleration Velocity Site j
Earthquake Station km g
cm/sec Condition Horse Canyon 1980 C203 47.1 0.080 (continued) 5069 47.7 0.033 5073 49.2 0.017 5072 53.1 0.022 l
IStationi numbers pr'eceded by the letter C are those assigned by the California Division of Mines and Geology. Other numbers are those assigned by the U.S. Geological Survey (1977; the stations not necessarily being U.S.G.S. stations).
25tation operated by the Southern California Edison Company.
3 Station operated by the Shell Oil Company.
4 g
Station operated by the Universidad Nacional Autonoma de Mexico and the University of California at San Diego.
5 Station operated by the California Division of Mines and Geology.
l i
Table 3.
The effects of removing individual earthquakes from the data set for peak horf zontal acceleration 50 percentile Peak Ma gni tude Distance Horfrontal Acceleration (g)
Constant Term Coefficient h
Coefficient M = 6.5 M = 7. 7 Data set a
B (Tm) b d = 0.0 d = 0.0 y
All earthquakes
-1.02 0.249 7.3
-0.00255 0.52 1.04 San Fernando earthquake omitted
-0.97 0.240 1.3
-0.00241 0.51 0.99 Parkfleid earthquake omitted
-0.87 0.223 3.0
-0.00210 0.46 0.R5 Kern Co.
earthquake omitted
-0.91 0.232 7.6
-0.00294 0.5n 0.94 Coyote Lake earthquake omitted
-0.97 0.244
- 7. 8
-0.00257 0.51 0.99 197? Impertal Valley mainshock and g
aftershock omitted
-1.21 0.275 5.6
-0.00255 0.65 1.40 i
Borrego Mountaf n earthquake omitted
-0.97 0.240 7.3
-0.00247 0.51 0.99 Liversere Valley j
earthquakes omitted
-0.99 0.246 7.3
-0.00257 0.53 1.05 g
Horse Canyon earthquake omitted
-1.11 0.262 6.7
-0.00254 0.56 1.16 O
l
.-. +...
Table 4.
The effects of removing Individual earthquakes from the data set for peak horf rontal veloctty 50 percentile Peak Sfte Ibrirontal Velocity (cm/sec)
Magnitude 01 stance
[ffect M = 6.5 M = 7.4 Constant Tem Coef ficient h
Coefficient Coef ficiant d = 0.0 d = 0.0 Data 3et a
8 (Fm) b c
S=1 5-1 All earthquakes
-0.67 0.4R9 4.0
-0.00756 p.17 116 371 San Fernando earthquake cultted
-0.55 0.465 3R
-n.n0150 n.19 119 313 Parkfleid earthquake omitted
-0.62 0.4R3 4.3
-0.n0253 0.17 111 3n?
Rern Co.
g earthquake omitted 0.17 n.359 4.7 0.n031R n.17 97 704 Coyote Lake earthquake omitted
-0.60 0.4RI 3.9
-0.0074A 0.15 119 171 1979 Imperial Valley earthquake cultted
-0.74 0.501 3.4
-0.00750 0.17 140 396 I
'M1
Table 5.
Comparison of values given by the prediction equation with values for selected strong motion records not in the data set.
d Record M
(km)
Observed Value Predicted Value Pacolma Dam Abutwnt, San Fernarvio [arthquake (Boore and others,1978) 6.6 0.0 reak horizontal acceleration 1.25 g 0.5% a Peak horizontal acceleratton corrected for effect of topography (Roore, 1973) n.73 q Peak horf rontal velocity ill cm/sec M cm/see Ko-akyr site, Carit, llSSR, earthquake (Campbell,10P1) 7.0 3.5 0.Rl q 0,f;7 q Tabas, Iran (Campbell,19R1) 7.7 3.0 0.M q 0.95 g
Figure 1.
Distribution in M and d of the data set for peak horizont al acceleration (small symbols). The large rynbols show other data points which are compared with the results of the prediction equation in Table 5.
s l
46
b I
i o
o 0
o o
o o g$
o 00 2
g8 o
o o
e$
e o
r o
0 M
8 o*
o 3
8 8
- N@d o
o o oo 3 o
> z
~
D o
o o
C o
F p
o o
M J
O g-o a
o b
o 8
I
^
I
~
V m
e o
W l
l
i O
Figure 2.
Distribution in fr ard d of the data set for peak horizontal velocity.
1 47
' " ~
~-,,.4 li.8 l-l r4
.e 1
o 4
8 o
0 o
I o9 Y
o 8
o o
o O
2W
~
o o
o o o
0 Z
o o
o C
g k
o
(/)
~
4 O
o o
o 2
o M
I l
o-e m
W e
c h
Figurs3.
. Values 'of at for peak horizontal. acceleration from the regression analysis of equation (1) plotted agaiest moment magnitude.
Diamond symbols are earthquakes represented by only one accelera-tion value; those events were not used in detemining the-strainht.
line.
t i
't i.
e 48 r
I I
L_
1, m
J_
_.2.
a 4
p4 Y
9 e
9 4.0
-s 3.0._
l 2.0 i
+
1.0
+
~~+ $
+
+ +
o l
0.0
+o o
2
- 1.0 i.
5.0 6.0 7.0 8.0 M
l l
F%.T i
L
Figure 4.
Predicted values of peak horizontal acceleration for 50 and 84 percentfie as functions of distance and moment magnitude.
i k
i 49
il 3I
,lg)!
l i
T:._
T_-
'5 i
~-.
50505 7 7 6 6'5 i
e 0
5 0
=
0 l
i 1 M
s i
a s
i e
i i
M K
i i
e 0E i
l i
1 i
C s
NA n
i T
E S
L i
I i
I T
D i
NE C
R q
l I
i E
e P
i n
i j
t i
T-r5 8
T:._.
T_-
75 i
05 5
e i
77'665 i
0 5
0
=
l0 i1 M
i n
i n
i i
M i
i x
i 0E i
l 1 C i
n i
NA e
i T
E i
i L
i S
I e
I T
i D
N i
E C
R l
1 E
e P
n n
i i
0
?-
r5 i
5 0
l D
o.
1 o
g 0.
zg,HxTJNoug 1Es fN,._$I 1
1 iT..
l1 l
,l1ll
Figure 5.
Residuals of peak horizontal acceleration with respect to equation (4) plotted against distance, i
1 50
e isi 4 & 5 6
6 644 4 4 4 4
m i
xx"K DC X
x x
_s a gx, -
x g-x x me o
a PMfe ggy O Y
o xx vp
.D r
o x x
o w~
5 o
x j
a g#
ew qg' x 0
s z
n.
cr o
g xC?
(/)
X Q
o o o N.
x
~
w o
_ eN N V V V8 g
22 2 x
g
_ VI VI VI m
- ooo
- o e s' "oXC f??t ?
t t?f ? ? f f
o o
n o
o 038d/S80 NDDB ZIB0H 4
e r
R.r 3
J Figure 6.
Residuals of peak horizontal acceleration with respect to equation (4) plotted against M for stations wi h d less than or eoual to t
10.0 km.
3 t
1 51 l
l 9
66i ai i 4 a
lii6 6 6
.4 i
cI e
O O
+r R
O o
o s'
a O2l o e <,.
r o
o>
9 o
e om o>
o oo coo j L P.,,,,,,
j 9
9 o
o 038d/S80 N339 ZIBOH 7
I
- v
\\
Figure 7.
Re duals of peak acceleration with respect to prediction equations developed usina the indicated values of h.
Sy201s defined as in Figure 5.
i 52
...i...
.a...
646 4 i i.
6 44 i 4 4.
g m
m G
G x,,x xx>x
@ C
% C x x x
x x x
O @x A S D
g
@x gi x,o:
w e
E 5
x
<4 P x
x #7 o
D Cb j
cb c
9&W@p P S hC' c
t 5
AyD x
o o
D o
y &
va e9 x
o x h<
o
,- df 9 8[ c7 x*o cY o
Cf*o, xo C
x e*#cb s-
,-r x
ce"3{%o b C
C o
=
.o cg ci 7 x
W x
i 9o e
x q
o xcp q
x
,xxc>
, u e
c:
o o
x s
x s
7 to
_ E E
o o
- o x
0 o
CO o
O ro6 7
T D
7 C
~~
- g t
- o i
n n u
=
- o n x
7
- a n x
-, o x
- ' t t e a
t tt?
- f t
ttt, t,
e t
.!t
't t
C.
C.
~.
o.
C.
o o
o o
iii....
iaa6 6 6 i 6
i 4..
'~
CD CD 1
m 3
E Q
9rr x
xx,
%C
%C x
x x
x x x
x
{* #
g'
- A
_d~
g xx xx x
0 O
% vw o
c-
% xw o
d5 og, p odo c4 edc._o J
GoWx c g;x
& gg x&
~
x D
O o
y?
o rw 2 o
y &
o x f
~
o SI[,,"
x*U 9[
0, x EO C
v o
o y-o C
-r 3 E y
c@,
dx C, o cp c M
I O
2 dO
]
nxc xwo o
o "j
m x
W
~
o o
o o
U m
x
_I N
N v
Z N
([
,E o o
(
Eo o
x x
s o
o (f)
- O. 6
=
- c6
~~
': T I
- Lt.:
i C
- n n x
x
- n.o x
,n ffit 9 f f
9 ftt ? e f f f
fff f f f f
f fff ! t f f
f a
o e
o o
o 03Bd/S80 NDOW ZIBOH hi. 7 g
)
Figure 8.
Values of ai for peak horizontal velocity from the regression analysis of equation (1) plotted against moment magnitude.
Diamond symbols are earthquakes represented by only one velocity value; those events were not used in deterrining the straight line.
l l
53 f
5.....
e 4.0
+
3.0.
o
++
2.0
+
o o
1.0 0.0
- 1.0 5.0 6.0 7.0 8.0 M
0 I
Figure 9.
Predicted values of peak horizontal velocity for 50 and P.4 parcentile as functions of distance, moment magnitude, and geologic site conditions.
54
1 50 PERCENTILE 8tl PERCENTILE
- g.,
,,,,i.,
.., v, p
..xix.....;
~~
r
- ~~~s N
N N (300.0 x
g
\\
\\ N i
N E
~-
- n N
~
x\\x x
N \\ N N o
-Q h
x N \\g u____.__~
x NN x
N NNs\\
N s
x\\x N \\ s N N NN N
N N
s 3
\\
N\\\\ \\
x\\ x\\ \\ x\\
x
\\\\\\ \\
T T
N
\\ N'\\\\
to o r N
\\
o gj N
N\\\\ \\
g\\ \\g\\\\
\\ NN\\
x\\ Ng\\
N \\ g \\ \\g x\\ g 7.5 -
j N
\\
\\g
\\ \\
\\x\\ g \\.5 -
N \\ g\\.0 -
\\
7
\\
7 o
D! i.o
\\
7.0,
\\\\
6.5-r
\\ x \\.5 :
\\\\
m s
6 o
6
\\ \\
.0 :-
I
}
- rock
'\\
reck g
.0 -
\\ 5.5.
6 soil 5.5 -
- - soil M=5.0 M=5.0 iiiiiil i i i i iiil i i i i iiiil ii iniini i i i i iiil isinul i
ie 0.I e ii 1
to 100 1
10 100 DISTRNCE e KM DISTRNCE. kM b
o i
\\
{
l Figure 10. Residuals of peak horizontal velocity with respect to equation (6) plotted against distance.
55
l V
j l
t i
i i
i i
4 4
a 8
~
O x
2 x
x
{x x x
~
- O r
x x
y g
x x
- x x
x xe g
x o LAj i
a 7
u i
e z
x c
w I
~
O O v OX (0
was C
V V VI i
- 222 o
vi vi vi c
e
_ 00 0 oss x
ox0 I'
fff f f i f
f tIf t 9 9 g 9
e o
d A
03Bd/S80 73A ZIB0H l
,8" 8
h a
o
o Figure 11. Residuals of peak horizontal velocity with respect to equation (6) plotted against M for stations with d less than or equal to 10.0 kn, 56
s e
e e
i6i 6 6 i 6
i li; e s 6 6 a
i O
+t k
,a O
O O=
O w
a2e oNNo h o
c o
o e
oaoo O
O fff f f f I
f ff I f f f f
f C
O O
q
~
O 038d/S80 13A ZIB0H 4
. Il
I o
Figure 12. Residuals of peak velocity with respect to prediction equations
(
developed using the indicated values of h.
Sydels defined as 1n Figure 10, 57
10.0 i iisiig iisii; i i i i i 10.0 i i
- i iisiig i i sig i i..
i i i i i. il i
_ii...;
_ h = 1.0 km
- h=5.0km
- b = - O.00153
- b = - 0.00286 x
x x
O x
x
.O x
X x
N
?n x R
m x On N
Q x
x 1.0 x
8" x
1.0 5
{
5
- N b
Dxx gxn 5
g Ex
- x o 4 **
o x x 0
0 x
x x
x x
~.
x x
x x
O x
0 x x
x x
W x
0:
Q.
e i sial e e i i i n iiil i i i e i i i e e
a i 0.1 1 ieist!
N M
0.1 ieiniil nieanal sasial i e O
10.0 i iiiiii iiiii; i;
i i i i i 10.0 i
i i i i
i i iiiii;
_ i i iiiig i i iiiii i i g
_ i i i iii; w
- h = 7.0 k m
_ h = 3.0 km N
b = - O.00224
~ b = - 0.00 34 2 x
gr 0
x 0
x x
O o
x x
x N
I 0x g
x x
x
'D x 0x m
gx x
M 1.0 m m ax 1.0 n
e x,
- g o
x x
v
- W g x x x
0 m
Oxx x
x x xx x
og o g,,
x g
x x
x x
xx x
x x
x M
x x
e m issil s e n sil siniil i i i e > >
i i i iiil
. i iiil 0.1 i i i iiil i i i i i i i i 0.1 i
i i 1
10 100 1
10 100 DISTANCE
. xn DISTANCE, xM B
u
..Q Figure 13. Comparison of attenuation curves for peak horizontal acceleration by Campbell (1980) (dashed lines) with the 50 percentile curves from this report (solid lines). Campbell's curves are raised by 13 percent. to compensate for the fact that he defined peak horizontal-acceleration as the mean of the two components rather than the larger one as we riid.
.l i
d
...l sa
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