BY KIN-YIP CHUN, GORDON F. WEST, RICHARD J. KOKOSKI, AND. CLAIRE SAMSON. ABSTRACT. Spectral amplitudes of regionally recorded Lg waves are ...
Bulletinofthe SeismologicalSocietyofAmerica,Vol.77, No. 2,pp. 398-419,April1987
A NOVEL T E C H N I Q U E FOR MEASURING Lg A T T E N U A T I O N - RESULTS FROM E A S T E R N CANADA B E T W E E N 1 TO 10 HZ BY KIN-YIP CHUN, GORDON F. WEST, RICHARD J. KOKOSKI, AND CLAIRE SAMSON
ABSTRACT Spectral amplitudes of regionally recorded Lg waves are studied in detail between 0.6 and 10 Hz, using vertical-component, velocity seismograms of the Eastern Canada Telemetered Network stations and a supplementary Seismic Research Observatory-type station at Glen Almond (GAC), Quebec. We find that the site responses vary among these stations by more than a factor of 3 within the frequency range of interest. Furthermore, they are found to be strongly frequency dependent. Consequently, it is essential that they be taken into consideration in studies of Lg wave attenuation and Lg source spectra of regionally recorded seismic events. We present a new method of measuring interstation surface wave attenuation, which is closely related to the conventional two-station method. While retaining all the desirable features of the conventional two-station method, the new technique, which we will call the "reversed two-station method," allows simple, direct (one-parameter) determination of the Lg wave attenuation from sparse spectral data in a manner unaffected by station site effects and associated instrument error. The reversed two-station method is successfully tested over weakly attenuating, short (53 to 210 km) interstation paths in eastern Canada, a difficult experimental condition by normal standards. The Lg attenuation coefficient (0.6 to 10 Hz) in eastern Canada is found to be frequency dependent and of the form ~ ( f ) = 0,0008 f081 km-l, At higher frequencies, the Lg attenuation appears to be essentially frequency independent. This latter finding is preliminarily interpreted as evidence that regionally recorded Lg waves in the Canadian Shield are, as in the case of Lg waves propagating through the structurally complex Appalachian Province, contaminated by the high-frequency coda of Sn waves. The Lg contamination over the shield paths becomes severe starting at 14 Hz, twice the frequency above which the Lg signal propagating over the Appalachian Province becomes completely dominated by non-Lg arrivals.
INTRODUCTION Seismologist's interest in the attenuation of short-period Lg wave motions has been growing at a remarkable rate over more than a decade, following the publication of the widely referenced article by Nuttli (1973), who proposed using l-Hz Lg amplitude to estimate m~ values of eastern North American earthquakes too small to be recorded teleseismically. Ground acceleration associated with Lg wave attenuation is of relevance in engineering design (Cornell et al., 1979), particularly in stable shield areas where Lg is often the most prominent seismic phase seen on regional seismograms (Hasegawa, 1985). Much of the more recent progress in observational and theoretical studies of Lg wave propagation has been strongly motivated by its potential value in seismic verification research (Blandford and Hartenberger, 1978; Pomeroy and Nowak, 1978, 1979; Pomeroy, 1979, 1980; Bache et al., 1980; Barker et al., 1980; Nuttli, 1981; Pomeroy et al., 1982; Baumgardt, 1986). For example Nuttli (1986) has attempted to use 1-Hz Lg amplitude as a yield estimator of underground nuclear explosions at the Nevada Nuclear Test Site. In 398
MEASURING Lg ATTENUATION RESULTS FROM EASTERN CANADA
399
their study of earthquakes and underground nuclear explosions occurring in the Nevada Nuclear Test Site region, Murphy and Bennett (1982) found that the ratio of average Lg spectral amplitude level in the 0.5- to 1.0-Hz passband to that in the 2.0- to 4.0-Hz passband is a useful discriminant of the two populations when the events being studied have mb above 4.3. It is well known that the Lg amplitude is complicated by station site effects, which are in general strongly frequency dependent (e.g., Campillo et al., 1985). The station site effects, difficult to model directly and generally totally neglected in the previously published Lg attenuation studies, are compounded by the problem of instrument response uncertainty. Furthermore, source radiation pattern effects can cause wide variation in Lg amplitude depending on the focal mechanism of the event used (Herrmann and Kijko, I983). The cumulative error arising from neglecting to correct for the above factors has especially adverse consequences when scarcity of the Lg amplitude data does not permit a meaningful, independent assessment of the reliability of the Lg attenuation measurements. In nuclear test ban verification research in which the absolute spectral amplitude and the spectral content of the recorded seismic waves form the fundamental data pair from which critical determinations (nuclear explosion yield and seismic source type) are to be made, an accurate knowledge of the seismic wave attenuation characteristics is indispensable. The objectives of this paper are: (1) to introduce a simple but reliable method for measuring the frequency-dependent attenuation of high-frequency surface waves, such as Lg waves; and (2) to obtain an improved knowledge of the Lg attenuation characteristics in the Grenville Province, a stable shield region in eastern Canada. SEISMIC DATA
Table 1 lists the 21 earthquakes, two possible mineblasts, and one rockburst selected for this study. The magnitude of these events, as determined by the Geophysics Division, Geological Society of Canada (GSC), Ottawa (formerly the Earth Physics Branch, Department of Energy, Mines and Resources of Canada), ranges from 2.2 to 5.3. The recording stations shown in Figure 1 are part of the Eastern Canada Telemetered Network (ECTN), supplemented by a Seismic Research Observatory type station at Glen Almond (GAC), Quebec. The lines connecting the stations represent the eight interstation paths over which the Lg attenuation has been measured in this study. GAC is the only location where threecomponent recordings are available, and the data gathered at this station are routinely incorporated into the ECTN acquisition system. All analyses are based on short-period, vertical-component velocity recordings. The ECTN stations have a sampling rate of 60/sec (corresponding to a Nyquist frequency of 30 Hz) and a minimum detectable ground velocity of 10 nm/sec. The dynamic range of 96 and 108 dB, respectively, at the stations deploying Mark I and Mark II outstation packages (see Figures 1 and 2). The sampling rate at GAC is half that of the ECTN stations, giving a Nyquist frequency of 15 Hz. Figure 2 shows the velocity responses of all three types of recording instruments mentioned above. More detailed station information can be found in Canadian Seismograph Operations (1983). The epicentral distances considered range from 90 to 867 km; the interstation path lengths from 53 to 210 km. The Lg record window has been selected in two ways: (1) fixed time length (FTL); and (2) fixed minimum group velocity (FMGV). In the first case, we follow Hasegawa (1985) and Shin and Herrmann (1986), and
400
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON TABLE 1 EASTERN CANADA EARTHQUAKES Event No. 1 2 3 4 5 6 7 8 9 10 11 12t 13 14 15 16 17t 185 19 20 21 22 23 24
Date 30 July 1979 3 Apr. 1980 23 May 1980 31 July 1980 28 Sept. 1980 28 Oct. 1981 23 June 1982 13 Aug. 1982 3 Sept. 1982 1 Dec. 1982 29 May 1983 4 July 1983 7 Oct. 1983 7 Oct. 1983 30 Oct. 1983 1 Nov. 1983 21 Dec. 1983 20 June 1984 14 Apr. 1985 16 May 1985 16 Aug. 1985 24 Aug. 1985 10 Nov. 1985 31 Jan. 1986
OriginTime (Hr Min Sec) 00 16 08 10 03 19 00 01 23 22 05 12 10 10 12 10 15 14 03 13 22 06 14 16
13 57 39 10 41 56 22 06 14 52 45 54 18 39 14 16 04 12 44 39 48 04 21 46
48 24 44 04 12 14 00 40 03 24 49 08 46 39 15 52 44 27 40 07 37 02 28 44
Latitude Longitude Magnitude* (°N) {°W) 47.92 48.77 44.89 49.90 43.44 49.83 47.39 46.66 45.69 43.63 44.48 46.74 43.94 43.95 44.14 45.67 45.21 46.58 42.96 46.80 49.30 45.67 46.50 41.76
74.35 67.95 74.54 82.04 79.75 65.25 76.95 78.61 76.61 71.58 70.41 72.57 74.26 74.26 74.34 73.90 73.96 80.80 80.03 75.90 67.67 76.64 75.78 81.11
2.6 mN 4.0 m N 2.5 m N 3.0 m N 2.2 ML 3.9 m g 3.5 mN 4.3 m N 3.7 m N 3.0 mN 4.1 mN 2.6 m N 5.1 mb 3.5 mb 2.8 mN 3.4 m N 3.0 m N 3.4 m N 3.1 m N 3.2 m N 3.1 m N 3.1 m N 2.5 m N 5.3 mN
* m N = magnitude based on L g amplitude; ML = local magnitude.
t Possible blast. $ Rock burst.
FIG. 1. GAC and E C T N stations selected for attenuation study of vertical-component L g waves. The lines connecting the station pairs are the path segments along which the L g attenuation measurements are taken.
401
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use a 17.07-sec-long window, beginning 0.85 sec earlier than the Lg onset times, as picked by the GSC. The extra lead time provides the needed space for a 5 per cent Hanning tapering, which is also applied at the end of each windowed record. Only those GSC-picked onset times which correspond to group velocities within the range 3.40 to 3.76 km/sec are considered. For the ECTN sampling rate of 60/sec, this window consists of 1024 samples; for the GAC records, it consists of 512 samples. The average group velocity inferred from the selected onset times is 3.61 + 0.07 km/sec. For the FMGV windowing, the same starting points are selected but the ending points for all records correspond to a fixed 2.60 km/sec group velocity. Unlike in long-period surface wave attenuation studies, the FMGV windowing procedure does not strictly fix the upper group velocity limit. We feel that fixing the starting point individually, according to a carefully picked Lg onset time of each record, optimizes the signal to noise ratio. This practice of positioning the window according to the picked "arrival" time, rather than according to the expected travel time, is common in spectral analysis of body wave phases. Our group velocity range (---3.61 to 2.6 km/sec) is closely compatible with those considered by others (Murphy and Bennett, 1982; Campillo et aI., 1985). After removal of the mean and trend, the FMGV windowed seismograms are each padded with zeros to the next nearest power of 2 to allow the application of the Fast Fourier Transform algorithm. The purpose of experimenting with two windowing types, both of which have been used in previous Lg attenuation studies, is to determine if the measured Lg attenuation coefficient is affected by the windowing procedures. A representative sample of the short-period, vertical-component velocity seismograms selected for analysis in this study is shown in Figure 3a. In Figure 3b are shown some examples of the signal and noise velocity spectra (0.6 to 10 Hz). The signal spectra are computed from FMGV windowed records. In each case, the individual noise spectrum is computed from a time window preceding the Pn arrival and having the same length as that of the signal record.
402
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FIG. 3. Examples of the vertical-component velocity seismograms (a) selected for this study. Records are arranged in order of increasing epicentral distance (top to bottom). Arrival times of the Pn phase (first short vertical bars appearing at the left side) are aligned for ease of display. Where Sn arrival time has been picked, it is indicated by a vertical arrow. The second short vertical bar marks the onset time of the Lg waves. All time picks were made by the GSC. (b) Representative examples of the signal and noise spectra calculated from selected Lg records (see text for more detail). Event numbers refer to those listed in Table 1.
MEASURING
Lg ATTENUATION RESULTS FROM EASTERN CANADA
403
Herrmann and Wang (1985) and Shin and Herrmann (1986) have shown evidence suggesting that Lg waves which propagate across the structurally complex Appalachian Province are contaminated by high-frequency (>7 Hz) Sn coda waves. It is not certain, however, that the same phenomenon would occur over pure Canadian Shield paths. Hasegawa (personal communication) suggests that excessive scattering of Sn waves over the Appalachian path segments may be the cause of the Lg contamination. As a necessary precaution, we have also examined individual noise spectra computed from a time window immediately preceding the Lg onset time. Comparisons between the noise spectra computed in this manner and their corresponding signal spectra fail to reveal convincing evidence of Sn contamination at least up to 10 Hz. The noise and the signal spectra do tend to take similar forms, eventually, but only starting at a frequency roughly twice as great as the (7-Hz) frequency above which Lg contamination by the Sn coda becomes a problem over the Appalachian paths. The source selection criteria are controlled by the source-receiver geometrical considerations. The selection details are discussed in the following section. In all, 52 seismograms have been selected for the analysis. We will initially focus our attention on the analysis of the propagation characteristics of the low-frequency (0.6 to 10 Hz) Lg waves. The results pertaining to the attenuation characteristics of higher frequency seismic waves contained in the Lg wave train will be presented in a later section. CONVENTIONAL AND REVERSED TwO-STATION METHODS (RTSM) We denote by F the displacement spectral amplitude of the Lg wave. F can be expressed in the form
F(/, d) = S ( f ) R ( [ , O)G(d)r(f, d ) I ( f ) S S ( f ) ,
(i)
where [ denotes the frequency, d the epicentral distance, 0 the station azimuth, and S (f) = the source excitation function, R(f, 0) = the source radiation pattern, G(d) = the Lg geometrical spreading function (e.g., Hasegawa, 1985) G(d) = d -°5,
(2)
F (/, d) = the anelastic attenuation function which can be written as F(/, d) = e -~d
(3)
~f is the attenuation coefficient, Q the dimensionless quality factor,
where 7 = ~
and U is the group velocity, I ( f ) = the assumed instrument response, S S ( f ) = the station site response--assumed to be independent of azimuth. This function also incorporates any frequency-dependent instrument miscalibration, which is the ratio of the actual instrument response to that assumed. Surface wave attenuation data can be obtained using the two-station method (TSM), in which analysis is restricted to records from seismic sources whose
404
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON
epicenters lie within a few degrees of the great-circle path connecting two receivers. The ratio of the surface wave amplitude measured at station 2 (the distant receiver) to that at station 1 (the nearer receiver) is F(/:, d2) _ G (de)I2 (/)SS2 (/) e_.~(i)a, F(f~ dl) G(dl)Ii([)SS~(/)
(4)
where the indices 1 and 2 refer to station 1 and station 2, respectively, and A is the interstation distance. The azimuthal amplitude variation over a few degrees is assumed to be negligible. Since the velocity spectrum computed from a particular seismogram is 2~[ times the displacement spectrum, the displacement spectral ratio on the left-hand side of equation (4) can be replaced by the corresponding velocity spectral ratio. Unless otherwise specified, velocity spectra are used in subsequent equations, since we shall deal only with spectral ratios rather than the spectral amplitudes themselves. Equation 4 can easily be solved to yield ~ (/), provided one makes the common assumptions that the ratio SS2 (f)/SS1 ( f ) = 1 and that the instrument responses /1 ([) and/2 ([) are perfectly known so that they can be corrected for. Recent studies show, however, that for both the body P waves and for the Lg waves, the station site effects can vary greatly even among closely spaced receivers and that they are in general strongly frequency dependent (Tucker et al., 1984; King and Tucker, 1984; Tucker and King, 1984; Campillo et al., 1985). The instrument uncertainty can also be a significant source of systematic error at infrequently calibrated stations, or if the interstation paths are short and only weakly attenuating, the latter being the case in this study. Our data set consists of 27 distinct (one-way) interstation passages (Table 2) over eight distinct interstation paths (Figure 1). An examination of equation (4) reveals that the ratio S S 2 ( f ) / S S I ( [ ) will be exactly reversed if the roles of the two stations are interchanged. This simple observation leads to the formulation of the R T S M method, as illustrated in Figure 4. Clearly, we now require a pair of sources whose epicenters lie within a few degrees of the great-circle path connecting the two receivers which are located between them. As illustrated in Figure 4, when we multiply the two spectral ratios obtained through repeat application of the T S M [equation (4)], using one seismic source at a time, the result is
PR (/) = G~e -2"y(I)'~,
(5)
from which one obtains, after simple rearrangement, ( / ) = log10Gp - logloPR 2A logloe
(6)
where the new notations, PR, Gp, and A are explained below. PR([) =PR([, dl ...... dl,/ar, d2..... d2.tar) is the product of the two spectral ratios. The subscripts 1 and 2 here refer to the seismic sources 1 and 2 on opposite sides of the interstation path segment. For each source, the subscript near refers to the closer station, far the more distant station, and A is the interstation distance (see Figure 4).
MEASURING
Lg
ATTENUATION
RESULTS
FROM
EASTERN
CANADA
405
TABLE 2 STATION PAIRS* Event No.
Epicentral Distance (km)
Station
Azimuth
(°)
Interstation Distance
(km) 1 2 2 3 4 5 6 7 8 9 10 11 12 13 14 14 15 16 17 18 19 19 20 21 22 23 24
Near
Far
Near
Far
Near
Far
MIQ GNT MNT MNT MIQ FHO LPQ OTT CKO GAC WBO MNT GRQ WBO WBO WBO WBO GNT OTT GAC CKO WBO OTT GAC GAC GAC MNT
FHO MNT GAC GNT FHO MIQ GNT WBO OTT MNT GAC GAC CKO OTT OTT GAC OTT LPQ CKO WBO GRQ GAC WBO WBO MNT WBO GNT
212 427 563 99 599 360 447 241 116 88 332 278 252 143 142 142 121 141 139 423 395 444 160 711 91 92 733
309 563 664 235 660 442 656 296 265 234 386 422 385 199 198 217 177 352 286 464 523 474 209 749 236 171 867
216 233 232 46 129 50 234 156 129 89 299 295 268 326 326 326 322 56 279 101 30 58 175 239 87 165 53
208 232 242 45 136 41 237 153 121 94 308 291 259 325 325 334 322 57 289 110 38 48 166 233 93 167 51
97 136 101 136 61 82 209 55 149 146 54 144 133 56 56 75 56 211 147 41 128 30 49 38 145 79 134
* N o t e t h a t t h e r e are 27 s t a t i o n pairs.
Gp = (dl,iard2,rar/ dl ..... d2 . . . . . )--0.5 is the "generalized" geometrical spreading function associated with the product PR. The subscript p refers to the fact that the G here is associated with the product of two quantities (spectral ratios). For each source, the interstation distance is the difference in epicentral distance of the two recording stations, not the true distance between the two stations. Obviously, the A, as appearing in equation (6), is simply the mean of the two effective interstation distances associated with the two sources and two receivers. The form of equation (6) is extremely simple: it contains neither station site responses nor instrument responses, both having been cancelled during the multiplication of the spectral ratios. With the RTSM method, the task of determining the frequency-dependent Lg attenuation now reduces to straightforward arithmetical operations. The set of two passages, one "forward" and one "reverse," is termed one combination for convenience. For each combination, there is associated with it a set of four seismograms. The pair of seismic records produced by a source located to one side of the receivers can be used repeatedly in conjunction with the pairs of records generated along the "reverse" passage by sources located to the other side of the receiver pair. In other words, to form a new combination, we have the options of replacing either
406
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON
Reversed Two-Station Method
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FIG. 4. Schematic drawing illustrating the RTSM of measuring the interstation surface wave attenuation. First, we obtain two spectral ratios through separate applications of the conventional TSM ]equation (4) in the text], using one seismic source at a time. The attenuation coefficient ~ can be directly calculated from the product of these two ratios (PR) and the known epicentral distances.
one or both sources by other appropriately selected one(s). With the stated redundance, we are able to form 25 combinations (Table 3) out of the 27 one-way interstation passages (Table 2) which have been selected with the RTSM method in mind. In the present study, each individual source is selected in such a way that the source-station azimuths involving the selected station pair do not differ by more than 10 °. The allowed source-station azimuthal difference between the selected pair of stations is kept small to help minimize the radiation pattern effects. Table 2 gives, for each event selected, information on the epicentral distances of the recording station pair, the source-station azimuth, and the interstation distance. In Table 3 is shown detailed information on the 25 combinations and their associated interstation passages. OBSERVED
Lg
ATTENUATION
Unsmoothed velocity spectra are used to obtain ~ ( f ) via equations (4) and (6), corresponding to the TSM and the RTSM methods, respectively. Unlike all other known methods (including TSM), as summarized by Yacoub and Mitchell (1977), the RTSM method eliminates the need for linear or nonlinear least-squares determinations of several unknowns (e.g., % the station site responses, and possibly the source spectrum and the source mechanism), thereby avoiding propagation of error among them. Except for the RTSM, all other methods for measuring regional surface wave attenuation require explicit instrument corrections, which in general are not perfectly known. Instrument uncertainties may not appear very important until one realizes that the interstation path lengths dealt with in this study are short (53 to 210 km) and that the 1-Hz Lg amplitude reduction due to anelastic attenuation (including scattering) can be as small as 4 per cent. In each case (TSM or RTSM), the ~ (f) obtained is smoothed once with a simple running average over a frequerLcy interval 5f = __+0.234 Hz. Figure 5 (a and b) shows the Lg "y(f) results obtained using the TSM method, assuming, following common
MEASURING
Lg ATTENUATION RESULTS FROM EASTERN CANADA
407
TABLE 3 COMBINATIONS Combination
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Stations
Events
WBO (3)-GAC (3)
10-18 10-21 10-23 14-18 14-21 14-23 19-18 19-23 13-7 13-20 14-7 14-20 15-7 15-20 2-9 2-22 11-9 11-22 3-2 24-2 5-i 5-4 6-16 8-17 12-19
WBO (3)-OTT (2)
M N T (2)-GAC (2)
MNT (2)-GNT (i) FHO (1)-MIQ (2)
LPQ (1)-GNT (1) CKO (1)-OTT (1) GRQ (1)-CKO (1)
AverageInterstation Distance (km)
53
54
134
147 80
210 148 130
The number in parentheses indicates how many times each station has been the closest to the source. This indicates that, for each of the eight interstation paths, the number of "forward" and "reverse" paths are approximately balanced.
practice, that the station site effects can be neglected (i.e., the ratio SS2 (f)/SSI(f) appearing in equation (4) is taken to be unity]. The results in Figure 5a are derived from the FTL windowed records, the results in Figure 5b from the FMGV windowed records. The corresponding RTSM results are displayed in Figures 5c and 5d, respectively. In all cases, the 7 ( f ) observations are plotted at 162 frequency points equally spaced between 0.6 and 10 Hz. The attenuation data displayed in Figure 5 (a and b) are from 27 individual interstation passages. Both show a discernible average trend. The scatter, however, is very large and is apparently erratic in nature, suggesting that drawing inferences based on few observations can be a risky proposition. In contrast, the RTSM results show a much smaller scatter which, significantly, does not display a detectable increase with frequency. On average, the scatter shown in the TSM results (Figure 5, a and b) is approximately twice as large as that shown in the RTSM results (Figure 5, c and d). The differences are particularly conspicuous between 5 and 10 Hz. This dramatic difference in the magnitude of the scatter of the ~ measurements suggests that the station site effects are very important and that, to a first approximation, they are indeed independent of azimuth throughout the entire frequency band of interest, as assumed. In both cases (TSM and RTSM), the results from the FTL windowed records tend to be more diffuse than the results from the corresponding FMGV windowed records. We interpret this as an indication that
408
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FIG. 5. Observed Lg a t t e n u a t i o n 7 ( f ) . T S M results from F T L windowed records (a); T S M results from F M G V windowed records (b); R T S M results from F T L windowed records (c); R T S M results from F M G V windowed records (d). T h e T S M results are obtained from 27 individual i n t e r s t a t i o n passages; t h e R T S M results are obtained from t h e 25 c o m b i n a t i o n s w h i c h are formed from t h e s a m e 27 passages. T h e R T S M m e t h o d effectively removes t h e station site effects which cause t h e large fluctuations seen in t h e T S M results (a a n d b).
the spectral amplitudes of the Lg waves are better estimated using the group velocity window than using the FTL window• Relative to those estimated at nearer stations, the spectral amplitudes calculated from the FTL windowed records of more distant stations tend to be underestimated, biasing the attenuation upwards. Since the amount of the amplitude underestimation depends on the epicentral distance, but not directly on the interstation path length, per se, it results in the estimated 3' being biased by a variable amount depending on how far, or how close, a particular interstation path segment is to the source involved. This variable positive bias is expected to produce a larger scatter in the 3' measurements. As will be shown later, the larger scatter in the measured ~, values (Figure 5, a and c) is indeed accompanied by a noticeable increase (over the results from the FMGV windowed records) in the measured 3' values themselves. Examination of our individual interstation results reveals that the wide fluctuations seen in Figure 5 (a and b) are in fact not random: for a given interstation path, the Lg attenuation determined depends systematically on the Lg wave propagation direction. To further explore the influence of the station site effects, we present our averaged ~/observations for each interstation path. Figure 6 shows the TSM results (dashed and dotted curves) and the RTSM results (solid curve). The results being displayed are derived from the FMGV windowed records only. Since the results from the FTL windowed records show similar appearances, path by path, they are not plotted• For convenience, with each of the eight pairs of station codes appearing at the top of the plots, the left one is referred to as station 1 and the right one as station 2. With this clarification, the dashed (topmost) curve corresponds to the case in which the Lg waves propagate in the direction pointing from station 1 to station 2; the dotted curve corresponds to the case in which the waves
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MNT-GAC
1,,$ ~, :U
0.02 -
.-...
409
Lg ATTENUATION RESULTS FROM EASTERN CANADA
I _
I
I
I, 57:,o-4
3.51 x 10-3' 1 2.25x10-3
CKO-OTT
GRQ-CKO
J
0 (.9
FHO-MIQ
LPN-GNT
0.02 _1
• ~
~i ; '~' ': t 'i~ •f ~ P
-0.02
1.54
5 . 9 3 x 10-3 2.72 x 10-5
I
0
5
I0
0
5
~
3.82 xlO-3 3 8 3 x I0 -3
x 10 -5
5.04 x I0-3 I0
0
5
- 3 . 6 0 x 10-3 4.56 x I0 -3
I0
I
I
0
5
10
FREQUENCY (Hz) FIG. 6. Average interstation Lg wave attenuation coefficient. Only the observations made from the F M G V windowed records are shown. For each station pair, the dashed curve corresponds to TSM results
obtained when the Lg waves propagate in the direction pointing from the first to the second station--in order of their appearances (e.g., from WBO to GAC). The dotted curve corresponds to the TSM results obtained when the wave propagation direction is reversed; the solid curve corresponds to the R T S M results. Note the very strong directional dependence of the TSM results.
propagate in the opposite direction. Each of the three curves represents the average of all available measurements of the same type for the particular interstation path (Figure 1). Note the persistent, and sometimes very large, separation between the dashed and the dotted curves. Where large separation occurs between the TSM results (the dashed and the dotted curves), the station site response ratio SSe (f)/ SSI(f) [see equation (4)] is much below 1; where the two curves approach each other this ratio is close to 1. The first (upper) number appearing near the bottom of the plots is the average 1' in the frequency range 0.6 to 10 Hz; the second (lower) number is the rms difference between the dashed and the dotted curves, computed over the same frequency range. The relative size difference between the two numbers gives a measure of the degree of influence the site effects have upon the 1' estimated using the TSM. For example, when the lower number is comparable to, or greater than the upper number, it indicates that the TSM results are strongly dependent on whether the Lg waves propagate in the direction pointing from station 1 to station 2, or vice versa. Since the GAC and the ECTN station instruments are very well calibrated (North, personal communication), we can reasonably assume that the instrument errors are negligible in comparison with the local geological site effects. Therefore, the examples shown in Figure 6 can be construed as evidence that geological site effects are far from being negligible, as is implicitly assumed in previous studies of Lg wave attenuation. As shown in Figure 6, the site effects may contribute to an error in */as large as 300 per cent, depending on the station sites involved. In some regard, the attenuation measurement problem arising from the station site effects is analogous to the complication in refraction seismology, which arises from the presence of dipping interfaces beneath the survey area. Unless a
410
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON
profile is reversed, neither the Lg 7, nor the refraction travel-time data, can be interpreted without a great deal of reservation. As far as Lg attenuation measurement is concerned, the site effects become less important if the path length increases. In other words, one may exercise the option of sacrificing spatial resolution in exchange for reduced ~ uncertainty. In reality, because the signal strength decreases with increasing distance, the ~ measurement is additionally complicated by low signal to noise ratio. Both the magnitude and the station-specific nature of the site effects point to the difficulties in using any existing attenuation measurement methods that are ineffective in removing the site effects. This is because permanent seismographic network stations, such as the ECTN stations, are often sited with known, or perceived, regional seismicity patterns in mind. As a result, the wave propagation paths linking the sources and the receivers are not randomly distributed. Relying on having the site effects averaging themselves out can lead to a large dispersion among published attenuation measurements obtained in the same general region. Having demonstrated how much the station site effects affect the Lg attenuation measurement, we shall, from now on, present and discuss only the R T S M results. That is, unless otherwise specified, all subsequent mentions of the Lg attenuation measurements refer to the R T S M results. FREQUENCY DEPENDENCE OF
Previous Lg studies in central and eastern North America indicate that ~ and Q are frequency dependent, and are both of the form a/n, where a and fl are two constants. The work by Herrmann and Kijko (1983) indicates that for the central and north-central United States, 7 = 0.001/0.7 kin-1. In the central United States, Lg wave coda analysis by Singh (1981) gives Q = 1000 fo.2 between 0.5 and 3.5 Hz; time domain analysis by Dwyer et al. (1983) suggests Q = Qof °4°±°1~, where Qo is the value of Q at 1 Hz. More recently, Hasegawa (1985), using acceleration spectral amplitudes measured from more than 400 Lg records from the ECTN network, concluded that ~ = 0.001 [0.8 km-1 in the Canadian Shield. To obtain the frequency dependence of the Lg ~ for the region of interest, we first compute, for each of the eight interstation paths, the average of all available measurements made on records windowed in the same manner (FTL or FMGV). The average Lg "y from the eight interstation paths are superposed and shown in Figure 7. Figure 7a shows the results derived from the FTL windowed records; Figure 7b shows the results derived from the FMGV records. The lengths of the eight interstation path segments range from 53 to 210 km. Because the attenuation measurements are less well determined along the shorter paths than along the longer paths, it is appropriate to weight them accordingly. We adopt a simple weighting scheme such that the weights assigned to the measured values are directly proportional to the interstation path length. The weighted regional Lg attenuation observations thus obtained are plotted in Figure 8 as dotted curves. Figure 8a shows the results derived from the F T L windowed records; Figure 8b shows those from the FMGV windowed records. We separately fit the two data sets, using, in each case, the functional form ~/([) = aft,
(7)
where a and fi are constants to be determined. The maximum-likelihood solutions (James and Roos, 1975), shown as solid curves in Figure 8, are discussed below.
MEASURING Lg ATTENUATION RESULTS FROM EASTERN CANADA
411
(a) 0.04
....
...."
,""".
.....
.~.....
~. :
:
~
.
~
-~ ...
~
.-.'..,,:~:~z' ~
~
0,00 ...-..
'E - 0 . 0 4 I
t.d
I
I
I
I
lag
o
(D
I---
"'
0.04
(b)
t
...:::
~:: . . . . . . . . . . . . .
"" . . . .
.- b:.'::2~
IIll["il::.I' ,~:[:::,:'!:[[}ii,ihli,*Illl[li[lll;~ll",il[}~l~-I
0.00
-0.04 [
I
]
[
]
0
2
4
6
8
A ~
10
FREQUENCY (Hz)
FIG. 7. Interstation Lg attenuation observations from the study region. In this figure, each plot contains average interstation observations from all eight interstation path segments (Figure 1). RTSM results from FTL windowed records are shown in (a); RTSM results from FMGV windowed records are shown in (b).
The calculated ~ derived from the FTL windowed records is 3' = (1.11 -+ 0.10) X 10-3[ 0.74-0.05
(8a)
and the calculated ~ derived from the FMGV windowed records is "y ---- (0.81 "+" 0 . 0 8 ) X l O - 3 f °'s1-+0"05
(8b)
Examination of the above relations reveals that, the calculated values (solid curve in Figure 9) are larger when the FTL windowing procedure is applied than when the FMGV procedure is applied. This is illustrated in Figure 9. In conjunction with the previous discussions on the effects of the windowing procedures upon the variability (scatter) of the measured Lg attenuation, we conclude that this disparity arises from the fact that at greater epicentral distances, the FTL window of 17.07 sec in length becomes increasingly deficient, as it allows more and more Lg energy to be excluded from the record sections used for the analysis, biasing the ~ upwards. Lengthening the FTL window will, on the other hand, inadvertently result in a reduction of the signal to noise ratio at relatively close stations because of the inclusion of extra noise as well as low-frequency energies of fundamental-mode surface waves. The absolute magnitude of the bias is shown in Figure 9 to increase monotonically with frequency. On a percentage basis, however, the largest bias occurs at 1 Hz (36 per cent), the reference frequency in Nuttli's (1973) original
412
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON 0.010
(Q)
0.005
. ..,,,"
0.000
y = I. I x 10-3f ° - ' 4
-0.005
'E LE bJ 0 0
la.J
t--
-0.010
I
0.010
I
I
I
I
(b)
O.0 05 _J 0.000
y=8. I x 10-4 fO.81
-0.005
-0.010
0
I
I
I
I
1
2
4
6
8
I0
FREQUENCY (Hz) FIG. 8. Frequency dependence of observed Lg attenuation coefficient. Dotted curves represent the weighted regional observed data; solid curves represent the calculated maximum-likelihood fits (see text for details). RTSM results derived from FTL windowed records are shown in (a); RTSM results derived from FMGV windowed records are shown in (b). Note that the vertical scale is different from that used in Figures 5 and 7.
definition of Lg magnitude for earthquakes occurring in eastern North America. It is interesting to point out the Lg attenuation estimation is rather insensitive to the exact position of a fixed group velocity window. For example, in their crustal attenuation study in central France, Campillo et El. (1985) find that the Lg quality factors (and hence -y) estimated using three different group velocity windows (2.3 to 2.6, 2.6 to 3.1, and 3.1 to 3.6 km/sec) are essentially identical. This suggests that gradually "compressing" the group velocity window with increasing epicentral distance, an inevitable consequence of the FTL windowing procedure, will bias the Lg attenuation upwards, as asserted. With the above remarks, we conclude that application of the R T S M to seismograms windowed according to the FMGV produces the most reliable results. That is, we consider equation (8b) to be the one which best expresses the frequency dependence of the Lg attenuation coefficient in eastern Canada.
Lg WAVE ATTENUATION BETWEEN 10 AND 20 Hz Figure 10 shows several examples of the Lg signal and noise spectra between 10 and 20 Hz, computed from FMGV windowed records as described earlier. Because of its lower digital sampling rate (30 samples/sec), all records from GAC station are excluded here, leaving 13 available combinations (see Table 3) for analysis of the attenuation behavior of the high-frequency Lg waves. We apply the R T S M method to the FMGV windowed records, and the results are plotted in Figure lla. The F T L
MEASURING
•006
Lg A T T E N U A T I O N
RESULTS
FROM
EASTERN
_--~ FTL WINDOWED
413
CANADA
J
'lE
,,m .004 o
hl
J
.002
.O00r
I
I
2
0
I
4
6
I
8
I0
FREQUENCY (Hz) FIG. 9. Maximum-likelihood fits to the weighted regional Lg attenuation data (from Figure 8). The
differences between them illustrate the effects due to the two different record windowing procedures (FTL and FMGV).
103 - Event No. 15 Station : WBO
~
9
12 GR(
10I
I
i
a)
i h
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i
n-laJ 13_ 0")
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2
19 CKO
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-I I0
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,,I I0
,I'I~,
,
,I iO
I0
2'0
IO
FREQUENCY
(Hz)
2O
I I0
, 2O
Fro. 10. Representative noise and Lg signal spectra (10 to 20 Hz) computed from among the selected ECTN records (Table 2). Typically, the signal amplitude is 20 to 40 dB above the noise amplitude. w i n d o w i n g p r o c e d u r e a n d t h e T S M a t t e n u a t i o n m e a s u r e m e n t are n o t r e p e a t e d here in light of the discussions p r e s e n t e d in t h e p r e c e d i n g section. I n Figure 11b, we show the w e i g h t e d regional Lg ~ ( d o t t e d curve), c o m p u t e d u s i n g e x a c t l y t h e s a m e p r o c e d u r e s as described in t h e p r e c e d i n g section. T o facilitate direct c o m p a r i s o n s , Figure 11a uses t h e s a m e vertical scale as Figure 5; Figure 11b uses t h e s a m e vertical scale as Figure 8.
414
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON
(a) 0.04
~-.- , , . . , . . : . . ~
..,,.
...-:
.-.,~-.
.~ G-"'e-:-
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.,....
0.00
'E
-0.04
v
I
I..E w 0 o
I
I
I
I 18
I 20
Z
I.-
_J
0.015
(b)
0.010
0.005
0.000
Y= 4.1 x 103f °'m
- O, 005 I0
I 12
I 14
I 16
FREQUENCY (Hz) Fro. 11. Observed Lg attenuation coefficient (10 to 20 Hz) derived from FMGV windowed ECTN records using RTSM method (a). This is the high-frequency extension of the ~ data shown in Figure 5d, except no interstation paths involving GAC station are included in the analysis. (b) The weighted regional Lg attenuation data (dotted), the maximum-likelihood fit (solid curve) to the observed data, and the values predicted by equation (8b) (dashed curve). See text for the weighting scheme.
The solid curve in Figure l l b represents, as before, the maximum-likelihood solution fitting the observed attenuation data. The calculated frequency-dependent Lg attenuation coefficient is of the form 3~ = (4.14 _ 0.74) X 10-3/°15-+°°7.
(9)
The calculated ~/ is proportional to /0.15. This frequency dependence departs markedly from those obtained earlier (/o.74-o.sl) for Lg waves in the 0.6- to 10-Hz frequency range. We preliminarily interpret this to indicate that the Lg waves recorded regionally in the Canadian Shield are also contaminated, at a significant level, by the high-frequency coda of the seismic phase Sn. Shin and Herrmann (1986), using data generated by the 1982 Miramichi earthquake and recorded at WBO, with the wave path crossing in part the Appalachian Province and in part the Canadian Shield, have shown evidence that the Lg signal at frequencies above 7 Hz is completely dominated by Sn and, to a lesser extent, Pn coda waves. Figure
MEASURING Lg ATTENUATION RESULTS FROM EASTERN CANADA
415
11b clearly shows that, starting only at a frequency around 14 Hz, does the apparent Lg Q implied by equation (9) (solid curve) deviate noticeably from what one would obtain by extrapolating the results (dashed curve) determined at frequencies below 10 Hz [equation (Sb)]. Taken together, the above discussion indicates that although the Lg signal contamination by non-Lg energies is a general phenomenon in eastern Canada, Sn scattering within the Appalachian Province may be a prime source of Lg contamination between 7 and 14 Hz. SITE EFFECTS (0.6 TO 10 Hz) It is interesting to note that the station site response ratio can be calculated rather simply from any combination of seismograms suitable for the application of the RTSM method. The RTSM method is based upon the observation that the multiplication of two spectral ratios [equation (4)] derived from a "forward" and a "reverse" surface wave passage results in 3` being the sole unknown parameter to be determined from the observed spectral amplitudes [equation (6)]. However, instead of the multiplication, the division of one ratio by another results in the station site response ratio SS2 ( [ ) / S S 1 ( f ) being the sole unknown parameter to be determined from the observed data. From equation (4) and Figure 4, we have
(12([)~ 2 (SS2([)~2 e -'~(i)D,
R R ( f ) = Gr \ i - - - ~ l
\SS,(/)]
(10)
R R ( f ) = (F([, dldar)/F(dl . . . . ))/(F(d2,1ar)/F(d2 ..... )) is the ratio of the two spectral ratios. As before, the subscripts 1 and 2 here refer to the seismic sources 1 and 2 on opposite sides of the station pair. For each source, the subscript near refers to the closer station (station 1) and far the more distant station (station 2). Gr = ( dl,[ard2 . . . . / dl . . . . . d2,[ar ) -0"5 is the "generalized" geometrical spreading function associated with the function RR. The subscripts 1 and 2 here refer to the seismic sources 1 and 2. D = (dldar - d~..... ) - (d2dar - d2. . . . . ) is the difference in the effective interstation distance associated with the "forward" and the "reverse" passages. In our case, D is always small because the sources have been selected to lie close to the great-circle path which contains the line segment connecting the two stations. Because D and 3` are both small, the anelastic attenuation factor in equation (10) is nearly equal to unity, this means that the station site response ratios can be determined even if we only had very approximate knowledge of 3` to calculate this factor. In the actual calculations, we use the frequencydependent 3' expressed in equation (8b). Equation (10) can be rearranged so that the station site response ratio is expressed in terms of all other known quantities. The site response ratios for the eight station pairs are shown in Figure 12. The solid curves are derived from the F T L windowed records; the dashed curves are derived from the FMGV windowed records. For each station pair indicated in the plots, the numerator in the ratio is the station site response of the station appearing on the left-hand side of the given pair. For example, relative to GAC, WBO has a station site response (at 8 Hz) which is nearly 3 times as large. Let us suppose we have Lg waves propagating in the
416
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON WBO - OTT
WBO- GAC,
MNT - GAC
MNT- GNT
4.0
J
2.0 1.0 0
~
f,
0.5
c~
I
w o3 z o n 50
LPQ-GNT
FHO- MIQ
GR(,- CKO
CKO - OTT
4.0
%
I.- 2.0 1.0 0.5
0
I 5
I0
0
I 5
I0
0
5
I0
L~
L
0
5
t0
FREQUENCY ( H z )
FIG. 12. Station site response ratios. For each station pair, the ratio is the station site response of the first station over t h a t of the second s t a t i o n - - i n order of their appearances (e.g., the site response of WBO over that of GAC). Solid curves are derived from F T L windowed records; dashed curves from the FMGV windowed records.
direction pointing from WBO to GAC, then the attenuation coefficient obtained from the application of the conventional T S M will be a gross overestimation. This is apparent in Figure 6. To appreciate the significance of these ratios from yet another perspective, it is interesting to point out that the mean of our eight interstation path lengths is about 120 km and that the Lg amplitude reduction rate due to anelastic attenuation (including scattering) over this distance range is less than 10 per cent at 1 Hz and is no more than 50 per cent at the highest frequency (10 Hz). The variability of the frequency-dependent station site response, as demonstrated here, must have profound implications in earthquake/explosion discrimination studies as well as in earthquake source parameter determinations (e.g., characteristic source dimension, seismic moment, stress drop, etc.). DISCUSSION
Based on a linear regressional analysis of Fourier amplitude spectra of ground acceleration of Lg waves propagating across the same general region covered in this study, Hasegawa (1985) suggests that the frequency dependence of the Lg attenuation coefficient is of the form: ~/= 0.001 f0.79. Hasegawa's work involves the use of more than 400 Lg records, a very large dataset by normal standards. The spatial attenuation coefficient of vertical-component Lg waves derived in this study [equation (8b)] is noticeably smaller than is predicted by Hasegawa's expression, up to 10 Hz. The discrepancy between the two sets of results is in part due to fundamental differences in the methodologies adopted by Hasegawa and by us. There are two other factors which we must consider. First, we find that the difference in the record windowing procedure contributes significantly to the above discrepancy. Compared
MEASURING Lg ATTENUATION RESULTS FROM EASTERN CANADA
417
to the Lg attenuation coefficient measured from the records windowed according to a fixed, 17.07-sec-long time duration, the value measured from the records windowed between the group velocity limits 2.6 and 3.61 km/sec is smaller throughout the frequency range (0.6 to 10 Hz) of interest (see Figure 9). Second, the regions being studied are not exactly the same: ours is a subregion amounting, in areal size, to only a fraction of Hasegawa's. It is interesting to note that, for the same general region (but different station localities), time domain measurements of ~ (14 samples) by H o m e r et al. (1978) indicate ~ (1 Hz) = 0.0006 _+ 0.0002 km -1. The reason for the apparent discrepancy between our frequency domain results and their time domain results cannot be ascertained because of their small sample size and the fact that none of their 14 Lg paths are reversed. We present our Lg attenuation results in terms of average regional values for the Canadian Shield, in adherence to the traditional practice, and for facilitating intercomparisons with the published results from the same general region. However, for specific applications requiring high spatial resolution, such as in seismic verification studies and in certain earthquake engineering investigations, the RTSM method provides by far the greatest reliability among known Lg attenuation measurement methods. As an added advantage, it requires very little seismic data: for an interstation path segment measuring 100 km long, it generally requires no more than two to three combinations of data since, from our experience, the results are highly repeatable. An alternative way to express seismic wave attenuation is in terms of Q, the quality factor [see equation (3)]. The form is
Q(f) = Qo/~.
(11)
Taking the group velocity U to be 3.5 km/sec, the value assumed by Hasegawa (1985), we calculate, from equation (8b), Q0 to be 1100 and ~ to be 0.19. Because Singh and Herrmann (1983) have shown that the Q of Lg waves and the Q of seismic coda waves are correlated, their work on the regionalization of crustal coda Q implies that our Qo and fl values characterize the Grenville Province (Figure 1) of eastern Canada to be among the most stable continental regions in North America. CONCLUSIONS We have presented a new methodology for determining surface wave attenuation as a function of frequency. Formulated to remove station site effects, the RTSM has been shown to be a very robust means of extracting the attenuation coefficient of high frequency Lg, a wave type of considerable importance in yield estimation of underground nuclear explosions, in discrimination between natural earthquakes and underground nuclear explosions, in the studies of source parameters of the earthquakes occurring in continental shield regions, and in earthquake engineering applications. The method is especially suitable for detailed (small-scale) mapping of the Lg wave attenuation at nuclear test sites because only a few carefully aligned stations and chemical explosions will suffice to obtain the required measurements for a given site. For the Grenville Province of eastern Canada, the Lg attenuation coefficient is frequency dependent, and in the frequency range of 0.6 to 10 Hz, it has the form: "y(f) = 0.0008 fo.sl km-i. In terms of Q, the dimensionless quality factor, the
418
K.-Y. CHUN, G. F. WEST, R. J. KOKOSKI, AND C. SAMSON
equivalent form is Q ( f ) = 1100 [o.19. At frequencies above 10 Hz, the apparent Lg attenuation is distinctly different, indicating that contamination by the Sn coda can be severe enough to produce obviously spurious results. ACKNOWLEDGMENTS It is our pleasure to record our gratitude to M. Berry, P. Basham, and R. North without whose generous, unselfish cooperation this research would not have been possible; to O. W. Nuttli and R. B. Herrmann for reviewing the paper; and to D. M. Boore for comments which led to a substantial gain in clarity of the presentation. We thank the Geophysics Division of the Geological Survey of Canada for unlimited access to its entire data archives. The Lawrence Livermore National Laboratory of the University of California provided us with the Seismic Analysis Code (SAC), a software package which saved us considerable data processing time. We are very grateful to Derek York for his encouragement and for his Toronto Globe and Mail article (February 24, 1986), which explained to the general public the connection between our seismic sleuth work and nuclear test ban treaty verification. This work was supported by the Arms Control and Disarmament Division, Department of External Affairs, Government of Canada, under DSS Contract 06ST.08011-5-0015.
REFERENCES Bache, T. C., H. Swanger, and B. Shkoller (1980). Synthesis of Lg in eastern United States crustal models, with frequency dependent Q, Report No. SSS-R-81-4668, Systems, Science and Software, La Jolla, California. Barker, B. W., Z. A. Der, and C. P. Mrazek (1980). The effect of crustal structure on the regional phases Pg and Lg at NTS, in Studies of Seismic Wave Characteristics at Regional Distances, TeledyneGeotech Report AL-80-1, Teledyne-Geotech, Alexandria, Virginia. Baumgardt, D. R. (1986). Source characterization of yield estimation from Lg and P-coda measurements, DARPA/AFGL Seismic Research Symposium, 6-8 May, 1986, U.S. Air Force Academy, Colorado Springs, Colorado. Blandford, R. R. and R. H. Hartenberger (1978). Regional discrimination between earthquakes and explosions (abstract), EOS, Trans. Am. Geophys. Union 59, 1140. Campillo, M., J.-L. Plantet, and M. Bouchon (1985). Frequency-dependent attenuation in the crust beneath central France from Lg waves: data analysis and numerical modeling, Bull. Seism. Soc. Am. 75, 1395-1412. Canadian Seismographic Operations (1983). Earth Physics Branch, Department of Energy, Mines and Resources Canada (compiled by Shannon, W. E., D. R. J. Schieman, R. J. Halliday, and P. S. Munro), Ottawa, Canada. Cornell, C. A., H. Banon, and A. F. Shakal (1979). Seismic motion and response prediction alternatives, Earth Eng. Struct. Dyn. 7, 295-315. Dwyer, J. J., R. B. Herrmann, and O. W. Nuttli (1983). Spatial attenuation of the Lg wave in central United States, Bull. Seism. Soc. Am. 73,781-796. Hasegawa, H. S. (1985). Attenuation of Lg waves in the Canadian Shield, Bull. Seism. Soc. Am. 75, 1569-1582. Herrmann, R. B. and A. Kijko (1983). Modeling some empirical vertical component Lg relations, Bull. Seism. Soc. Am. 73, 157-171. Herrmann, R. B. and C.Y. Wang (1985). Fundamental studies on Lg-coda and coda excitation, DARPA/ AFGL Seismic Research Symposium, 6-8 May, 1985, U.S. Air Force Academy, Colorado Springs, Colorado. Horner, R. B., A. E. Stevens, H. S. Hasegawa, and G. LeBlanc {1978). Focal parameters of the July 12, 1975, Maniwaki, Quebec, earthquake--An example of intraplate seismicity in eastern Canada, Bull. Seism. Soc. Am. 68, 619-640. James, F. and M. Roos (1975). Minuit--A system for function minimization and analysis of the parameter errors and correlations, Computer Physics Communications 10, 343-367. King, J. L. and B. E. Tucker (1984). Observed variations of earthquake motion across a sediment-filled valley, Bull. Seism. Soc. Am. 74, 137-152. Murphy, J. R. and T. J. Bennett (1982). A discrimination analysis of short-period regional seismic data recorded at Tonto Forest Observatory, Bull. Seism. Soc. Am. 72, 1351-1366. Nuttli, O. W. (1973). Seismic wave attenuation and magnitude relations for eastern North America, J. Geophys. Res. 78,876-885.
MEASURING
Lg ATTENUATION RESULTS FROM EASTERN CANADA
419
Nuttli, O. W. (1981). On the attenuation of Lg waves in western and central Asia and their use as a discriminant earthquakes and explosions, Bull. Seism. Soc. Am. 71,249-262. Nuttli, O. W. (1986). Yield estimation of Nevada Test Site explosions obtained from seismic Lg waves, J. Geophys. Res. 91, 2137-2151. Pomeroy, P. W. (1979). Regional seismic wave propagation, Semi-Annual Technical Report, No. 3, Rondout Associates, Inc., Stone Ridge, New York. Pomeroy, P. W. (1980). Regional seismic wave propagation, Semi-Annual Technical Report, No. 4, Rondout Associates, Inc., Stone Ridge, New York. Pomeroy, P. W. and T. A. Nowak, Jr. (1978). An investigation of seismic wave propagation in western USSR, Semi-Annual Technical Report No. 1, 15 December 1977-30 June 1978, Rondout Associates, Inc., Stone Ridge, New York. Pomeroy, P. W. and T. A. Nowak, Jr. {1979). An investigation of seismic wave propagation in western USSR, Semi-Annual Technical Report No. 2, Rondout Associates, Inc., Stone Ridge, New York. Pomeroy, P. W., W. J. Best, and T. V. McEvilly (1982). Test ban treaty verification with regional data-A review, Bull. Seism. Soc. Am. 72, $89-S129. Shin, T.-C. and R. B. Herrmann (1986). Lg attenuation and source studies using 1982 Miramichi data, Bull. Seism. Soc. Am. 77, 384-397. Singh, S. (1981). Regionalization of crustal Q in the continental United States, Ph.D. Dissertation, Saint Louis University, St. Louis, Missouri. Singh, S. and R. B. Herrmann (1983). Regionalization of crustal coda Q in the continantal United States, J. Geophys. Res. 88,527-538. Tucker, B. E. and J. L. King (1984). Dependence of sediment-filled valley response on input amplitude and valley properties, Bull. Seism. Soc. Am. 74, 153-166. Tucker, B. E., J. L. King, D. Hatzfeld, and I. L. Nersesov (1984). Observations of hard-rock effects, Bull. Seism. Soc. Am. 74, 121-136. Yacoub, N. K. and B. J. Mitchell {1977). Attenuation of Rayleigh-wave amplitude across Eurasia, Bull. Seism. Soc. Am. 67, 751-769. GEOPHYSICS DIVISION DEPARTMENT OF PHYSICS UNIVERSITYOF TORONTO TORONTO, ONTARIO, CANADAM5B 1A7 Manuscript received 16 September 1986
