ML20011A425
| ML20011A425 | |
| Person / Time | |
|---|---|
| Site: | Summer  |
| Issue date: | 10/31/1981 |
| From: | SOUTH CAROLINA ELECTRIC & GAS CO. |
| To: | |
| Shared Package | |
| ML20011A422 | List: |
| References | |
| NUDOCS 8110130333 | |
| Download: ML20011A425 (21) | |
Text
- - n g h t .
1 J
l APPLICANT EVALUATION JOYNER - FLETCHER REPORT i
VIRGIL C. SUMMER NUCLEAR STATION DOCKET No. 50/395 SOUTH CAROLINA ELECTRIC & GAS COMPANY OCTOBER - 1981 i
t
~8110130333 811001 PDR ADOCK 05000395 A PDR
ek o .
APPLICANT EVALUATION OF JOYNER AND FLETCHER REPORT ON VIRGIL C. SUMMER NUCLEAR STATION SEISMICITY STUDIES Joyner and Fletcher have reviewed the " Supplemental Seismologic Investigation" Report, the Safety Evaluation Report, and Section 361 of the Final Safety Analysis Report for *.he Virgil C. Summer Nuc3 ear Station. Their response is contained in a memorandum to Morris dated September 9, 1981. Joyner acJ Fletcher apparently have not read tran-scripts of ACRS subcommittee meetings or of ASLB hearings to date. The issues raised by Joyner and Fletcher are caused by misinformation or misinterpretation (indeed, Joyner and Fletcher state that, " . . . we did not have sufficient time for a thorough review ..."), and deserve a direct response by the Applicant to clarify the record. The form of this rerponse follows the issues raised by Joyner and Fletcher, in order.
MAXIMUM MAGNITUDE OF THE RESERVOIR-INDUCED EARTHQUAKES Joyner and . Fletcher give values ranging from 30 to 44 bars for the August 27, 1978 earthquake. Joyner and Fletcher give threi methods by which they have calculated these values: rms accelerations, numerical integration of the squared spectrum, and a " straightforward application of the Bruna model," but no formulas or parameter values are given.
Although it is not clear from Joyner and Fletcher's report, the major difference between their estimates of stress drop for the 1978 earthquake and those of the Applicant is the assumption of the highest frequency that can be recorded and documented in the digitization process (Flet-cher, personal communication 1981). Since stress drop is an important parameter, and one which has been the subject of some debate, this point I
l deserves further elaboration.
The peak accelerations recorded on an accelerometer during an l earthquake c;e a function of the highest frequency which the instrument and record processing procedure can transmit, a2nong other factors. For records obtained very close to sources of nigh frequency energy (e.g.,
l rock bursts), accelerations can be almost arbitrarily high if the in-strument and processing procedures are adequate to transmit the high l
l I
y i
4 , frequencies of motion at which high accelerations occur. McGarr et al.
(1981) documented accelerations as high as 12g during mine tremors in South Africa, where the magnitudes were less than 1.5 and source-to-site distances were several hundred meters. These peak accelerations occurred at frequencies of several hundred hz, and the instruments were specially designed to record ground motion at these high frequencies.
Typical strong motion instruments, including the one installed at Jenkinsville, have a natural oscillation frequency of 25 hz, meaning that the instrument itself tends to damp out motion at higher frequen-cies. Joyner and Fletcher have taken 25 hz as the upper limit of motion that can be recorded. However, accelerographs can easily record fre-quencies higher than their natural frequency. The upper solid curve in Figure i shows the response of an accelerograph with natural frequency of 25 hz and damping 0.6 of critical (the characteristics of the SMA-1 accelerograph at Jenkinsville, according to Brady et al., 1981) plotted as a function of frequency. Not only can the accelerograph itself record frequencies higher than 25 hz, but standard record processing procedures (including those used by Brady in the above reference) " correct" for the ins trurtent 1esponse, effectively by dividing the recorded ground motion at each frequency by the ordinate on Figure 1. This effect can be signifi~ cant: the peak aceleration of c'ie "2nd af tershoci." record, 90*
component, documented by Brady et al. (1981), increases 35 percent due to
- instrument correction procedures.
Furthermore, the Jenkinsville data indicate that frequencies higher l
than 25 hz have been recorded. Brady et al (1981) find that, "... these i
(Jenkinsville) records have frequencies as high as 25 and 30 hz." A perusal of the Brady et al. (1981) document shows that the August 27, 1978 record, 90* component, has a peak accelerction with a 33 hz fre-quency, and the "2nd af tershock" recor d , 90* component , has a peak acceleration with a 40 hz frequency.
That there is substantial energy in the ;round motion recorded at Jenkinsville can also be inferred from the plots of response spectra
. . ~. -. . - . _ _ . _ _ . . _ _ . . . _ _ _ _ _ _ _ _
. C)-
provided by Brady et al. (1981), one of which (August 27, 1978 earthquake 90* component) is reproduced here as Figure 2. Although spectra are only plotted down to a period of 0.04 seconds (up to a frequency of 25 hr), it is evident that there is no decrease of energy near 25 hz, and it is safe to assume that the spectra, if plotted at higher frequencies, would continue horizontally to frequencies as high as 35 or 40 hz, and this would indicate ground motions at those frequencies.
The Applicant has used an upper frequency of 40 hz to accurately characterize these records, making it clear that it is the record cor-rected for instrument response and digitized at 500 points per second to which this upper bound applies. The choice of upper bound f affects estimates of stress drop ao in the following way:
a0 =C "res (1)
(fu - f o)1/2 9here a is the root-mean-square acceleration from the record and f is the corner frequency (see the Appendix for a derivation of this).
Both the Applicant and Joyner and Fletcher have used a lower bound frequency f of about 10 hz (the issue of corner frequency is addressed in detail below). Therefore, for the same observation u a , the choice of f = 25 hz leads Joyner and Fletcher to an estimate of Ao which is high relative to f = 40 hz, by the factor:
no (J & F) ,
(40-10)1 2 = 1.4 (2) no (Applicant)
(25-10)1/2 This explains why Joyner and Fletcher obtain 60 = 35 bars for the August August 27, 1978 earthquake, and the Applicant obtains no = 25 bars.
a.
Joymr and Fletcher have used an upper-bound frequency equal to the nominal frequency of the instrument; the Applicant has accounted for the higher frequencies evident in the strong motion record.
As a separate issue, Joyner and Fletcher assert that the Appli-cant did not correctly account for the corner frequency in making esti-mates of ao . While this is implied by the equations in section 361 of the FSAR, which Joyner and Fletcher reviewed , the effect of corner frequency was examined and found not critical by the Applicant. The Appendix to this report derives the theory with which the effect of corner frequency can be included in estimating aa; estimates using this theory were presented to the ACRS seismic subcommittee on February 26, 1911. Table 1 reproduces the data presented at that meeting, which is a matter of public record. Using the appropriate corner frequency f, the ctress drops derived for the August 27, 1978 earthquake are o
still on the order of 20 bars. Thus it is the Applicant's pocition that 25 bars is an appropricte and conservative stress drop to use for characterizing earthquakes at Monticello Reservoir for the purposes of estimating strong ground motion characteristics.
Joyner and Fletcher have reviewed the Applicant's arguments on stress barriers, stress heterogeneities, and material properties defining maximum rupture dimensions, and find these arguments "... unconvin-cing." It is not clear what alternative physical explanation Joyner and Fletcher have for the observations that have been made, not- why they do not accept the Applicant's explanations. In any case, Joyner and Flet-cher base their estimate of the maximum rupture dimension and of the associated magnitude on the spatial extent of observed seismicity, without consideratioa of whether the seismicity " lines up" or indicates any through going structure (in fact it does not). Such an analysis is unsupported by obse rvatons anywhere in the world, to the Applicant's knowledge, i.e., chere is no location where swarm-like seismicity has indicaten the size of a later, larger earthquake. Frequently in seis-mology she locations of af ter-shocks are used to infer the dimensions of a mcin shock (even this has been suggested as giving a conservatively
. ~ .
o large estimate of the main shock area). This is a far different pro-cedure from using the location of diffuse seismicity to infer a main shock area. What has frequently been done by investigators is to use the length of an identified fault to estimate a maximum magnitude, and here only one-half of the entire fault length is presumed to rupture. Thus Joyner and Fletcher's procedure is without validity in terms of world-wide empirical observations, does not constitute an accepted method, and has not had the benefit of peer review.
In calculating the magnitude associated with source radii of 1 and 1.4 km, Joyner and Fletcher have used a stress drop of 40 bars.
Since magnitude is proportional to th'e logarithm of stress drop in this calculation, this leads to Joyner and Fletcher magnitude estimates that are only marginally higher ( ,0.1 magnitude units) than those supplied by the Applicant at the request of NRC.
The experience of induced earthquakes at Denver is entirely ir-relevant to the issues at Monticello. The Denver earthquakes were caused by cyclical' fluid inj ection in deep wells; the correlation of l earthquakes with inj ection is a point made by the reference cited by
! Joyner and Fletcher (Healy et al., 1968). Thus at Denver the causatiire mechanism was cyclical. At Monticello there has been a one time change
~
l in water elevation; during operatiors, lake fluctuations will not cxceed about 2 meters total rerge. Thus the causative mechanisms of the two phenomena are fundamentally different, and to suggest that the experience at one site would or should guide us at the other is inapposite.
GROUND MOTION ESTIMATES The first difference (concerning digitization rnte) mentioned oy Joyner and Fletcher between their and the Applicant's ground motion f analysis is not a difference at all. In 1980 the Applicant used the records digitized at 100 points per second to estimate stress drop during the August 27, 1978 event, because at that tied (when the relevant parts of Section 361 of the FSAR were prepared), these were the only data l available. In February 1981 the digitizations at 500 points per second l
l
4 were made available by USGS (Brady et al., 1981) and the Applicant confirmed that its analysis was appropriate for the higher digitization rste. Table I reproduces data presented at the February 26, 1981 ACRS subcommittee .neeting which shows ground W ion e nimates made by the Applicant which are in agreevnent with Montic611s earthquake records digitized at 500 points per second. Thus the Applicaat can and h as explained the factor-of-two differeu e in pesk accelerations due to digitization race.
Where the Applicant's procedure does differ from that of Joyner and Fletcher is in the implied digitization rate associated with the peak acceleration used to enaracterize ground motion for seismic analysis of the facility. To determine the appropriate digitization rate, one must consider how the peak acceleration is to be used to generate response spectra for structural analysis. Thas the structural engineering consid-erations cannot "... be kept scparate fron the seissological analysis,"
as Joyner 6nd Fletcher wish.
The manner in which response spectra are derived for the seismic design and analysis of nuclear facilities is straightforward: (1) an expected peak acceleration is selected corresponding to a largest ground motion anticipated, (2) an effective acceleration is calculated from the peak acceleration, and (3) a response spectrum is scaled to that effective acceleration. For the Virgil C. Summer facility, step (2) hau <:onservatively been ignored, i.e., peak acceleration has been ,
assumed to equal effective acceleration. For tectonic earthquakes, a broad-banded spectrum is used to represent the wide frequency content of the motion. For reservoir-induced eart_hquakes at Monticello, the __
important eventa will occur close to the facility; in this case, appro-s . . _ . _ _ _ _ _ . _ . _ _ . -
3 priate high frequency spectra have been developed as suggested by Regulatory Guide 1.60. This development is documented in Section.361 of the FSAR ,
For the high frequencies of interest, it is the high frequency components of the structure which are of concern. These frequencies lie
4
~7-in what is of ten termed the " acceleration-amplification" portion of the spectrum, that is, amplitudes of response are most sensitive to the peak acceleratior 'f the input motion, rather than by the peak ve.ocity or peak dis;.lacement.
The mathematical representation of this two-step procedure to calculate high frequency w uctural response is as follows:
a =a x (3) res p a p
where a is the structural response in terms of maximum response acceleration, and a a peak ground acceleration (step (1) above). The r:7.to on the right-hand-side is step (3) above, the " acceleration ampli-rication factor" used ts determine both standard spectral shapes (e.g.,
Regulatory Guide 1.60) and the spectral shapes used on this project to represent reservoir-fnduced earthquaker.
It should be ev!??7.t that the peak acceleration estimated for the .
earthquakes of concern (the first '2 " on the right-hand-side of p
equation (3)) should be determined in a consistent manner with the value of a used to calculate the acceleration amplification factor. This p
implies, among other things, that records processed in the same manner should be used to calculate a p and the ratio ares /ap . In determining the appro p p te ratio of a /a p for near-source, hard rock sites, records digitized at 50 points per second (Johnson, personal communica-tion, 1981) were used. It follows cut peak accelerations for rertwoir-nduced earthquakes should be estimated for a digitized record at 50 points per second, not for some other digitization rate.
The Applicant has estimated values of a in an appropriate and consistent way. The effect of digitization sc 50 pointa per second was accounted for by using. an upper frequency f of 20 hr. for the es' '2tes of peak acceleration. For comparison, f = 40 hz is appropriate tc estimate peak accleration i roe. a 200 points-per-second record. This is illustrated in Table 1, as described above.
I. ,
1 Joyner and Fletcher's procedure c rJ - uses the peak accelerations of the 500 points-per-second digitized record, and makes no attempt to f
j account for other digitizing rates used in scaling response spectra.
Under this procedure, if the instr %ents of McGarr et al. (19E1) had recorded the August 27, 1978 esrthquake with frequencies up to several hundred hz, and a peak acceleration of several g had been obtained, this
! high acceleration would be scaled up to estimate peak acceleration during aM "
4.5 earthquake. Such an extreme hypothetical example illus-trates why, in addition to other considerations such as effective peak acceleration, instrument characteristics, record processing and correc-tion ' procedures , and response spectrum scaling methods must he incorpo-rated into the estimates of peak acceleration, as the Applicant has done.
In summary, the theory to estimate peak accelerations ased by the I Applicant is consistent with instrumental observations at Jenkinsville, with digitized versions of ebse observations made by USGS, and with the way in which response spectra sho tid br. w ied. Further. this methodology h r calculating reservoir-induced earthquake response opsetra is consisteni with the methodology recommended for tectonic earthquakes (Regulatory C,uide 1.60). The implications by Joyner and Fletcher 'that
- (a) the' Applicant has not accounted for strong-motion records at Monti-cello digitized at 500 points per second, and ();) the peak accelerations i from these records are tha only data on which seismic evaluations should be made, are erroneous, and do not account for the way peak accelerations are used to evaluate structures.
t j The second difference mentioned by Joyner and Fletcher is in the area of saturailon of ground motion with distance. Joyner and Fletceer imply Gat the Applicant has changed its position on this issue, but this fs decidedly not the cass, and Joyner and Fletcher's confusion apparently
~
comes from misreading the re:ord. 7's Applicant's position is illus-trated in Figurc 3. At a distance T. < 4r, the use of a point-a .ur e model "... is not strictly applicable; these values (calculated at these distances) are therefore conservative." This is stated in Applicant's Tabl. 361.17.4-2. This is shown in Figure 3 as point A, where the solid line deviates from the dotted line. At closer distances , ". .. extrapo-lation of the far-field model to a source-to-site distance of one source
_ _ _ . ~ - - - - - - _ _ . _ _ _ _ _ _ _ _ _ _ . - _ . _ _ . _ _ _ _ _ _ _ _ , , _ _ _ _ _ _ _ _ . - _ _ - - ~ - - . ~ _ _ _ . - - _ _ _ _ -
o diameter (R-2r) gives a reasonable approximation to the saturation level." This is stated in Appendix XI of the Supplemental Seismological Investigation Report. M s statement != illustrated in Figure 3 as point B, where the dotted lanc and dashed lin, cross. Whether or not Joyner and Fletcher agree with thesa Statements ; they are consistent, and the Applicant has not, introd 2ce.(d ) distance saturation in a slightly different way in Appendix XI ...," as Joyner and Fletcher state.
The Applicant agrees with Joyner and Fletcher's statement that,
"... the assumption that the saturation level corresponds to the value computed at at-y fixed me:tiple of the source radius leads to the un-palitable (sic) conclusion that the saturation level decreascs with magnitude." In fact the Applicant noted this effect in Appendix XI of the Supplemental Seismologic Investigation: "... earthquakes of M = 5.0 and 5.5 would have f aulting diameters of 3.6 and 6.3 km, respectively. A blind application of the distance limits discussed above (R=7r) yield peak accelerations of 0.17g and 0.13g, 'respectively. This does not imply that saturated peak accelerations decrease with magnitude; rather, other factors are important." Among these is the observation that smaller magnitude (( i 5) earthquakes are not gaerally itnown to rupts.re the carth's surface, partice.larly in the Eastern U.S. Thus it is unlikely that a site on the earth's surface would ever be in the near-
~
fiel:1, at R=2r, from such m .' vent. Use of the R=2r distance saturation limit is thus conservative roc .:och earthquakes.
The Applicant notes that Joyner and Fletcher do not propose any alternative to choosing saturation distance by scaling by source cize.
l Further, Joyner and Fletcher's mention of R=r as the saturation distance appears to be motivated more by where ground motions are anticipated to decrease from any saturation level (point C on Figure 3) than what distance is appropriate to extrapolate point source models.
1 The peak acceleration values listed in Joyner and Fletcher's Table 1
~
are calculated by the following equation:
l a (H) = a p(2.8) 10 25(M-2.8) g l
l
~
-10e where a (M) is the predicted peak acceleration for magnitude M and a (2.8) is the larp r of the two horizontal peak accelerations re-corded during the August 27 1978 earthquake (0.26g). Implicit in equation (4) is the use of a source-to-site distance of 0.7 km for all earthquakes. It is appropriate to make several comments on this method-ology.
- 1. The Applicant knows of no other majet facility where the profce d peak acceleraions for seismic analysis are based on a single component of one ground motion record, and use such a simple realing relation as equation (4). The physical para-meters which are associated with reservoir-induced earthquakes at Monticello are not addressed adequately.
- 2. The values from Joyner r.nd Fletcher are derived from an in-strumental frequency peak acceleration not ap,ropriate for scaling response spectra.
- 3. Joyner and Fletcher's Table 1 is critically dependent on the
, distance between the August 27, 1978 event and the Jenkinsville accelerometer, which was a random occurrence. Suppose this distance had been twice as far. and had caused 0 Mg at the accelerometer; would they' recommend valuet belf n large as those in Table 17 In effect Joyner and Fletcher have estab-lished ground motion saturation levels and distances on the basis of a single chance occurrence.
- 4. Joyner and Fletcher present no observed data in the mar.ntude and distance range of Table 1 to support their estimates.
- 5. There is no method suggested by Joyner and Fletcher to limi1 the magnitudes for which peak acceleratincs can be calculated by equation (4).
The Joyner and Fletcher method of scaling peak ground acceleration (a ) and velocity (v ) with magnitude (M) can also be written:
log 10 *p = -1. 85 + 0.25 M (O log 10 #p = -1.038 + 0.50 M (6) where a p
in eqaation (5) is in enits of gravity and v p is in cm/sec.
f
. 7t is instructive to compare these results, by extrapolation, cith those given by Joyner and Boore (1981). This is an appropriate comparison because the magnitude coefficients 0.25 and 0.50 in enuations (5) and (6) were taken by Joyner and Fletcher from Joyner ad Swre (1981). For the case where the distance to the surface projection of the fault rupture is zero, Joyner and Boore (1981) obtain log 10 *p
= .902 + 0.26 M (7) log 10 *p
= . 82 + 0.489 M (8)
Equations (7) and (8) are supported by near-field dets for earthquakes in the magnitude range 5.0 to 6.5.
- Equations (5) through (8) are av uated in Table 2 for various magnitudes. Results of extrapolation are indicated by asterisks. The results of Joyner and Fletcher are not similar to those of Joyner and Boore (1981). For ma, Mitt.de 6.5, equations (5) and (6) yield peak ground acceleration and velcaity greater than have ever been measured for naturally-occurring or reservoir-induced earthquakes. For all magni-tudes, the results of Joyner and Fletcher greatly exceed those of Joyner and Boore (1981).
There are several reasons for this difference. The Joyner and Fletcher equations are based only on a single horizontal component of one earthquake record. The peak acceleration and velocity of this horizontal d
component occurred during a very high frequency pulse (and should not be used to scale response spectra, as discussed above). Further, the motion recorded at Monticello Dam is undoubtedly amplified over free-field concitions due to the topographic effects (the instrument sits on an earth dam abutment). The Joyner and .Boore (1981) equations are based on a large number of earthquake records from California, including near-field records, and reflect free-field conditions. Thus they are more appropriate to estimate peak accelerations and velocities for important facilities such as nuclear power plants.
-_-.-____---a
SUMMARY
Joyner and Fletcher's review of Virgil C. Summer Nuclear Station seismicity studies is based, in part on a misinterpretation of certain documents and, oc : haps in part, on not having had access to complete transcripts of 4'1S subcommittee meetings and ASLB hearings. Two con-cerns of Joyner and Fletcher, the effect of corner frequency on the
, stress drop estimate for the August 27, 1978 earthquake, and the digi-tization of the record from that event at 500 points per second, are not h issues at all. The Applicant has analyzed tath in detail, and its recom-mendations incorporate those analyses. The estimates of maximum magnitude made by Joyner and Fletcher are based on the area of observed seismicity; such a method is not valid in the seismic design of important facilitit . .
The third area of Joyner and Fletcher's concern, ground motion saturation, involves significant interpretation and judgment, and da Applicant has acknowledged this. Joyner and Fletcher offer no alternative methods to deter- "
mine the distance srithin which ground motion amplitudes are saturated, except to use the distan:e between the source and recording site for the August 27, 1978 event, a chance occurrence. Further, Joyner and Fletcher use a single component peak acceleration from that event's record to scale peak accelerataan and make recommendations. Suen a procedure is without precedent. It takes no account of important parameters such as ,
earthquake stress drop, distance to larger events, instrument and record )
. processing procedures, and scaling of response spectra from the predicted <
peak accelerations. Joyner and Fletcher state that the methods of Newmark and Hall (1969) can be used to compute response spectra given its estimates of peak acceleration (and velocity), but the broad-band ampli-fication facters of Newmark and Hall (1969) would be wholly in3ppropriate for what Joyner and Fletcher admit would be high frequency motions. l'his illustrates a position which the Applicant has taken since the begin-ning: the estimates of peak acceleration must be made in light of the overall design problem and local conditions at the facility.
l REFERENCES Brady, A.G., P.N. Mork, and J.P. Fletcher (1981), " Processed Accelero-grams from Monticello Dam Jenkinsville, South Carolina 27 August 1978, and from Later Shocks", USGS Open-File Report 81-448, March, 35 pp.
Healy, J.H., W.W. Rubey, D.T. Griggs, and C.B. Raleigh (1968), "The Denver Earthquakes," Science, vol. 161, pp. 1301-1310.
Hudson, D.E. (1979), " Reading and Interpreting Strong Motion Accelero-
. grams", Earthquake Eng. Res. Inst. Monograph, 112 pp.
Joyner, W.B., and D.M. Boore (1981), " Peak Horizontal Acceleration and Velocity from Strong Motion Records including Records from the 1979 Imperial Valley Earthquake," Bull. Seis. Soc. Am., vol. 71, Dec. (in press).
McGarr, A.R., W.E. Green and S.M. Spot tiswoode (1981), " Strong Ground Motion of Mine tremors: Some implications for near-source ground motion parameters", Bull. Seis. Soc. Am., vol. 71, pp. 295-319.
McGuire, R.K. and T.C. Hanks (1980), "RMS Accelerations and Spectral
- Amplitudes of Strong Ground Motion During the San Fernando Earth-quake", Bull . Seis . So. Am. , vol 70, pp. 1907-1919.
Newmark, N.M., and W.J. Hall (1969), " Seismic Design Criteria for Nuclear Reactor Facilities", Proceedings, 4th World Conference on Earthquake Engineering, Santiago, Chile.
l
. APPENDIX Derivation of a f r case where lower bound is finite:
rms
(.85) exp(- * ) fgf a(f) =<
(.85)
PRS exp (- vfR QS f>f where symbols are as defined in Section 361 of the FSAR.
T 2rf d
a lal dt a la (w)l du
,=Td 1
- d 1
J o o
'2xf, 2sf }
= c j expf-2wfR) f dw + exp-2rfR)dwI ,
wT ! \ 98 # I l 98 # l d o o 2rf, aor where c= (.85) Rb an 2sf = w Neglecting, conservatively, the first integral, 2rf
~ ~ "
2 2 a
= c - g exp[ wR) wT - R \ Q8 4 d
2wf 9
= c ,8 Q "'o -
exp u f
wT R "
expf90\ / \ 90 /-
d so that a - (.85)(.37) ao 2Qr exp -
/-2rf R o -exp 2rfuRII!2
)
ras OR
- 90 98 ! -
--m - y-, _ ,, ,,-.,--,9_ - , , - ,- --
9-----y ,
..,,,,-.-m - , , - , . , , , -
g -+ - ,7, epu,, . - - , - - - - , -
For f small and f large, the above is the same as equation (9) in McGuire and Hanks (1980). For f non-negligible and f non-infinite, and for typical values of R, Q, and 8:
4 2wf R u < 0.1 QS so:
(f" -f) !
a
= (.85)(.37) ao /2Qr 2wR pRl .5 V2.34 ,
QS J
If ao is being estimated from recorded a ,, the above equation can be inverted to give:
ao -
OR a rms 4wRr (f" -f) ~~!
(.85)(.37) 2.34 8 .
f
TABLE I DATA AND ESTIMATES ON MONTICELLO EARTilQUAKES PRESENTED TO ACRS SUBCOMMITTEE ON FEBRUARY 26, 1981 event APEAK, f( a ., KM DEPTH, KM R,KM Fu,Hz A 7, BAR S ARMS,CM/SEC2 CM/SEC2 AUGUST 27, 1978 2.8 0.66 0.1 0.67 40 22 104 221 1023 UTC OBSERVATIONS: 108 225 AucuST 27, 1978 2.8 0.66 0.1 0.67 20 17 53 96 1023 UTC OBSERVATIONS: --
93 OCTOBER 27, 1978 2.7 1.03 0.2 1.05 40 65 106 182 072E UTC (?)
OBSERVAT10f!S: 100 185 OCTOBER 27, 1978 2.8 0.15 0.5 0.52 40 11 77 173 OBSERVATI0f!S: 83 169 e
Q
o ._ __
TABt.E 2 Comparison between Joyner and Fletcher Memorandum and Joyner and Boore (1981)
Moment Joyner and Fletcher Joyner and Boore Magnitude - - '
(g) Eq. (1) Eq. (2) Eq. (3) Eq..(4)
PGA PGV PGA PGV (g) (cm/sec) (g) (cm/sec) 2.8 0.26 2.3 .06* 1.2*
4.ia 0.73* 18.3* .17* 9.3*
5.0 0 92* 29.0* .22 14.5 5.5 1.23* 51.5* .29 25.5 6.0 1.64* 91.6* 39 44.8
. 6.5 2.19* 162.8* .52 78.7 i 7.0 2.91* 289.6* .69* 138.3*
7.5 3.89* 514.9* .92* 242.8*
l l
1
- Extrapolated l
l t
i
~
i l
i t .. , .-. ,__ . . . - , . . _ . . _ _ ,._. , .~._-. , _ . . , . _ . , . . , _ . , . _ _ _ . - _ _ _ . . - . . . . . _ . _ . . _ _ _ . . _
2 l4 O_
H 4 ,
" PERFECT" ACCELEROGRAPH x -
W w I.O ---
O ACCELEROGRAPH
< 0*8 .
FREOUENCY w = 25 CPS DAMPlNG ( n = 0.6 CRITICAL E O.6 -
W b O.4 - -
E w n= 7.15 CPS;(=l.0 D O .2 -
N N w ' ' '
g O # :
O 5 10 15 20 25 30 FREQUENCY-CPS l
l FIGURE 1 TYPICAL ACCELEROGRAPH RESPONSE AS A FUNCTION OF FREQUENCY
( AFTER HUDSON, 1979) 1 . . . , .. . . . . . . -. .. - -- .
i (135? 'IV 13 ACVHS E313Y) IN3NodWoD o06
'3XYnbh1HV3 846T isnDaV LZ Eol VH133dS 3SNodS3H l
Z 3E00I3 l
SGNC03S-00183d lv8niVN 03dWYONn oz ot r z i ro zo !o to o
&RY,&WQ&&R? '
A'XV^
N/NKX/N/\ /NKX/N/N /NK AxXxy^ AX M; x '" l x / x<x x x / xxx x.x / .xxx
./ A/r / // v // N *'.*
x.- X X X l
\ \ /' \ '
\ 3 i
N / /6 N /N / . N / l X
N \ . /\
X
\ / - /\\
X
. \ m .
m 1
MXMd MXWN NX4- E Nx /NKX/N/N/NKxA /N/WKe
/ xxx x x< xxxv x / xxx ~
/' v .'
//i N 4 v /r // N =
X# NV X N X m N m N Ww1 < N .* 2 x / ,
/ N / / s g g N \ . 4N. \ . h. A MXWA
\/NKX/\
MiXX/A M M)r
/N /NKXA /N /NX>d 3
a x / xx x x '
x / xxx x x/ xx x- coo os
/ ,// / ,/g N,r //y.g X X X X
\ N N \/ occ o 73 7-7 ,7 - \ 7; X
\X%. / A_ Fd X
/\ \
MXMd MXWh MXN N/NKXA/N/NXWN /N/NKXe x /ixx x x x / xxN x x/ :xx s .
Zh o 05 2 =N 01 Zh 00- *t- 6 83 SS oNYS ON!dWYG lV011180 IN3083d 02 Ot*S*2*C 030 06'010 C20! 82/12/6'15300 N33 Oll20!1NOW V8133dS 3SNCdS3h l
EYTRAPOLATION OF PolNT SOURCE MODEL 9 t .,
. h SATtMATION LEVEL
- 7 t y e
w
~...
4 MEDIAN PEAK ACCELERATL .,
v
- E t -
/@
8 i i i r 2r 4r ;
LOG R (SOURCE-TO-SITE DISTANCE)
FIGURE 3 I
CONCEPTUAL REPRESENTATION OF MEDIAN PEAK ACCELERATION VERSUS DISTANCE
, , , , _ __ a