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Bulletin of the Seismological Society of America, Vol. 77, No. 4, pp. 1252-1273, August 1987

ANALYSIS OF NEAR-SOURCE CONTRIBUTIONS TO EARLY P-WAVE CODA FOR UNDERGROUND EXPLOSIONS. II. FREQUENCY

DEPENDENCE

BY THORNE LAY

ABSTRACT

An analysis of dispersion in more than 1600 teleseismic short-period P waves from 46 underground explosions has established that near-source effects are responsible for systematic frequency-dependent variations observed in the first 15 sec of the P signals. Explosions from the Nevada, Amchitka, and Novaya Zemlya test sites exhibit a common magnitude dependence of the dispersive behavior, with smaller events having relatively enriched low-frequency (0.4 to 0.8 Hz) energy in the coda. For the Nevada and Amchitka sites, the larger events have relatively enhanced high-frequency (0.8 to 1.1 Hz) energy in the coda as well, which may actually be a consequence of diminished high-frequency content of the direct arrivals. The dispersive behavior also correlates well with known source depths for the Nevada Test Site and Amchitka events, and with estimated pP delay times for the Novaya Zemlya events, indicating that burial depth and/or explosion size are important factors. Pahute Mesa tests show a secondary dependence on position in the site, with centrally located events having stronger dispersion, as well as more pronounced slowly varying azimuthal patterns in the frequency dependence. Stations at azimuths to the north-northeast from the Mesa have particularly strong dispersion for centrally located events. The spatial and azimuthal variations for Pahute Mesa events do not appear to be the result of aftershock radiation, as suggested by Douglas (1984), but instead are associated with frequency-dependent defocusing and scattering from a high-velocity structure beneath the test site. Some of the dispersion from Novaya Zemlya events appears to result from deep path properties; however, the strong magnitude/depth dependence for all of the test sites indicates that very near-source conditions have the strongest influence on the frequency dependence. A likely explanation for the dispersive behavior is a combination of relatively enhanced surface wave excitation and scattering for shallower events, and frequency- dependent defocusing for sites overlying anomalous high-velocity structures, as is the case for both Pahute Mesa and Amchitka.

INTRODUCTION

Numerous studies of both earthquake and underground explosion signals have established that frequency-dependent variations of the energy flux in teleseismic short-period P waves are very common. There is a general association between observations of delayed high-frequency energy, diminished first arrival amplitudes, and higher waveform complexity (i.e., higher relative coda levels) (e.g., Douglas et al., 1973; Aki, 1982). Attempts to explain this behavior have invoked the notions of greater variability of direct arrivals stemming from their restricted path coverage, and greater stability of coda due to intrinsic averaging over numerous paths for the many arrivals in the coda. The direct arrivals are thus more strongly influenced by propagation effects involving spatial variations in absorption, multipath interference, or focusing and defocusing, all of which may be frequency-dependent processes. It is also now recognized that elastic wave propagation through a medium with random heterogeneity results in scattering and apparent attenuation, which in turn

1252

NEAR-SOURCE CONTRIBUTIONS TO EARLY P-WAVE CODA 1253

can result in P coda having higher frequency content than the direct P arrivals (Frankel and Clayton, 1984; McLaughlin and Anderson, 1985).

Several recent investigations of nuclear explosion signals have indicated that propagation effects deep in the heterogeneous earth are not the only causes of frequency-dependent variations in teleseismic signals; near-source effects are also important. Gupta et al. (1985) found that slopes of spectral ratios of direct P / P coda increase with the velocity of the source medium. Events in lower velocity media tend to have relatively enhanced long-period content in the early portions of the signals. This behavior was attributed to coupling effects and source velocity dependence of the excitation of high-frequency fundamental mode Rayleigh waves that convert to P waves by scattering from near-source heterogeneities and arrive in the P coda. Douglas (1984) analyzed a pair of teleseismic short-period P waves from two Nevada Test Site (NTS) events separated by 30 km (PILEDRIVER and GREELEY), and observed relatively enhanced high-frequency content in the coda of one event (GREELEY). On the basis of similarity of the paths to the station (EKA, Scotland) and observed differences in the frequency content of the direct arrivals at a regional station, Douglas concluded that anomalous absorption or defocusing was not responsible for the waveform differences. He then proposed that high-frequency radiation from aftershocks was responsible for the GREELEY observation, concluding that the aftershocks have higher corner frequencies than the explosion.

In this study, we adopt the same general procedure followed by Douglas (1984), involving comparison of frequency-dependent variations in teleseismic signals from nearby events, but we apply it to a much larger data set of 1620 signals. A large, well-distributed station set is used for suites of events in several different test sites in order to isolate and discriminate between near-source contributions to the frequency-dependent behavior. The data set used is the same as was analyzed by Lay and Welc (1987) (hereinafter referred to as Paper 1), who determined near- source contributions to frequency-independent waveform complexity measurements. The analysis described below strongly supports the observations of Douglas (1984) and Gupta et al. (1985), further establishing the importance of near-source contributions to the frequency dependence of the teleseismic signals. However, it is also shown that aftershock radiation is probably not the explanation for the observations of Douglas (1984), with a combination of intrinsic magnitude/depth- dependent variations and frequency-dependent defocusing and scattering from known velocity heterogeneity under NTS being a more likely explanation.

DATA ANALYSIS

Reliable interpretation of frequency-dependent variations in teleseismic signals like those observed by Douglas (1984) requires that we isolate and distinguish between various possible near-source contributions to the signals. It is plausible that, for underground explosions, frequency-dependent near-source processes may involve systematic variations with explosion size, source medium properties, or burial depth. There may also be systematic variations with source position resulting from scattering processes linked to particular structures. Finally, the near-source contributions may be unique to a particular event, as in the case of an aftershock sequence or anomalous spalling effects, either of which would have distinct characteristics from event to event. All of these possibilities must be addressed when comparing events such as PILEDRIVER and GREELEY, which have very different

1254 THORNE LAY

first-cycle magnitudes, mb ab, of 5.41 and 6.09, respectively, were detonated at different depths in different rock types (granite versus tuff), and were located 30 km apart in diverse geological structures (Climax Stock versus Pahute Mesa).

A data intensive approach to isolating the near-source frequency-dependent contributions is adopted in this study. By analyzing a large number of recordings for each event, and a large number of events for several test sites, we can establish the relative importance of the various possible near-source effects, as well as providing a basis for recognizing variations that are unique to individual events. The basic procedure followed is similar to that in Paper 1, with event to event comparisons at common stations being used to eliminate receiver and deep path effects. The data are also inspected for slowly varying azimuthal and ray parameter trends and intrinsic magnitude and depth dependence that may be diagnostic of particular near-source phenomena. The data set assembled in Paper 1, which is the only sufficiently large data set available for this purpose, is analyzed for frequency- dependent effects in this study. The data are digitized WWSSN and Canadian Seismic Network recordings of 28 NTS events, 3 Amchitka events, and 15 Novaya Zemlya events. Twenty-five of the NTS events were from Pahute Mesa, with additional events FAULTLESS (Hot Creek Valley), COMMODORE (Yucca Flat), and PILEDRIVER (Climax Stock) being analyzed. Eleven of the Novaya Zemlya events are from the northern subsite and 4 are from the southern subsite. Table 1 lists all of the events used and mb ~ values determined in Paper 1.

The data processing performed was based on the procedure introduced by Douglas (1984). The short-period instrument response was deconvolved from each recording, with the variations between the Canadian Seismic Network instruments being accounted for, and a sequence of third-order Butterworth bandpass filters was applied to the ground motion. The filtered traces, with passbands of 0.4 to 0.8, 0.8 to 1.1, and 1.1 to 1.5 Hz, were then analyzed to determine the temporal variations of energy flux in each passband. Figure 1 illustrates this procedure for three teleseismic P-wave recordings of event GREELEY. Station ESK is the WWSSN station nearest to station EKA (analyzed by Douglas, 1984), and a clear relative enrichment of the high-frequency content of the early P-wave coda (defined to be the interval from 5 to 15 sec after the first P arrival) is apparent. The filtered ESK traces closely resemble those for EKA (Figure 2; Douglas, 1984), establishing that the hand-digitized analog recordings have sufficient bandwidth and reliability to process in this manner. Note that the BOG recording has a very similar frequency dependence to that at ESK, while the record at ATL does not have significant relative enrichment of the high-frequency content of the coda. The azimuths of the three stations are indicated with respect to the strike-slip tectonic release P-wave radiation pattern known to be appropriate for GREELEY (Lay et al., 1984b; Wallace et al., 1985). ESK and BOG are located at azimuths where tectonic release radiation should be strong, while ATL locates along a radiation node. The observations suggest the possibility that azimuthal patterns in the frequency-dependent variations may establish whether aftershock radiation is responsible. It is also important to note that ESK and BOG have lower first arrival magnitudes than ATL. This is another example of the correlation between relatively low direct P-wave amplitudes and apparently enhanced high-frequency content of the coda. Lacking a precise knowledge of the source spectrum and attenuation along each path, it is difficult to establish whether the direct P waveforms at ESK and BOG are depleted in high- frequency content, or whether the subsequent coda is enriched in high-frequency content. The greater amplitude variations of the direct arrivals with respect to the

NEAR-SOURCE CONTRIBUTIONS TO EARLY P-WAVE CODA

TABLE 1

MAGNITUDES AND DISPERSION MEASUREMENTS FOR UNDERGROUND EXPLOSIONS

1255

Event mbab C(o.8~1.1) - C(0,4~.8) C(LI-LS) - - C(0,4-0.8) C(LI-I,6) -- C(0.$-L1) No. o f (sec) (sec) (sec) Observations

A L M E N D R O B E N H A M B O X C A R C A M E M B E R T C H E S H I R E COLBY E S T U A R Y F O N T I N A G R E E L E Y H A L F B E A K H A N D L E Y I N L E T J O R U M K A S S E R I M A S T M U E N S T E R P I P K I N P O O L P U R S E R I C K E Y S C O T C H SLED S T I L T O N S T I N G E R TYBO C O M M O D O R E P I L E D R I V E R F A U L T L E S S

C A N N I K I N L O N G S H O T M I L R O W

10/27/66 10/21/67 11/07/68 10/14/69 10/14/70 09/27/71 08/28/72 09/12/73 08/29/74 08/23/75 10/21/75

09/27/73 10/27/73 11/02/74 10/18/75

Nevada T e s t Site Even t s

5.96 1.25 _+ 0.22 1.02 _+ 0.25 -0 .23 - 0.29 33 6.16 1.74 + 0.29 1.74 + 0.30 0.00 __- 0.18 31 6.12 1.69 ± 0.24 1.52 ± 0.40 -0 .17 ± 0.32 40 6.06 1.79 ± 0.25 1.10 ± 0.31 - 0 . 6 9 ± 0.31 36 5.76 0.68 ± 0.33 0.15 _+ 0.36 -0 .53 ± 0.25 33 6.23 1.71 ± 0.32 1.31 ± 0.25 - 0 . 4 0 _+ 0.33 32 5.70 1.00 ± 0.27 0.61 ± 0.33 - 0 . 3 9 _ 0.29 30 6.19 1.28 ± 0.30 0.98 ± 0.25 - 0 . 3 0 ± 0.29 35 6.09 1.69 ± 0.23 1.73 ± 0.27 0.04 ± 0.27 50 5.81 0.24 + 0.20 0.88 ± 0.36 0.64 _ 0.33 37 6.34 1.87 ± 0.20 1.84 ± 0.23 -0 .02 ± 0.20 33 5.71 0.91 ± 0.29 1.06 ± 0.36 0.15 ± 0.44 33 6.16 1.70 ± 0.25 1.44 ± 0.19 - 0 . 2 6 ± 0.32 43 6.15 1.60 ± 0.27 1.88 ± 0.34 0.29 ± 0.30 33 5.81 0.39 ± 0.30 1.41 ± 0.33 1.03 ± 0.35 47 6.11 1.22 ± 0.26 0.81 ± 0.22 -0 .41 ± 0.25 33 5.31 -0 .05 ± 0.38 1.17 ± 0.31 1.23 ± 0.25 37 5.78 0.43 ± 0.25 0.48 ± 0.20 0.05 + 0.21 29 5.51 0.32 ± 0.24 0.98 ± 0.32 0.66 ± 0.24 42 5.56 - 0 . 2 9 ± 0.24 0.69 ± 0.39 0.98 + 0.37 30 5.39 0.61 ± 0.20 0.78 ± 0.32 0.18 ± 0.30 38 5.75 0.28 ± 0.22 1.36 ± 0.24 1.08 ± 0.18 41 5.59 0.15 + 0.24 1.33 ± 0.32 1.18 ± 0.23 44 5.35 -0 .42 _ 0.21 0.31 _ 0.31 0.73 + 0.19 37 5.81 0.65 ± 0.24 1.38 ± 0.27 0.73 ± 0.30 43 5.66 0.96 ± 0.23 0.38 ± 0.26 - 0 . 5 8 + 0.32 49 5.41 -0 .63 ± 0.38 -0 .37 + 0.35 0.26 + 0.24 29 6.18 0.97 ± 0.18 2.38 ± 0.29 1.41 ± 0.27 53

Amchi tka Even t s

6.73 0.84 ± 0.12 0.18 ± 0.20 -0 .67 _ 0.16 30 5.47 - 0 . 8 6 ± 0.16 -1 .09 ± 0.21 -0 .23 ± 0.20 38 6.27 -0 .01 ± 0.17 0.71 ± 0.22 0.72 ± 0.17 42

Nor t he rn Novaya Zemlya Even t s

6.38 0.45 ± 0.13 0.61 ± 0.16 0.16 ± 0.15 43 5.65 -0 .47 ± 0.15 -0 .92 ±. 0.17 -0 .45 ± 0.13 53 5.83 - 0 . 3 6 ± 0.15 - 0 . 2 9 ± 0.15 0.07 ± 0.10 61 5.97 - 0 . 1 5 ± 0.16 - 0 . 2 6 ± 0.18 -0 .11 ± 0.11 48 6.73 - 0 . 1 4 ± 0.23 0.11 ± 0.24 0.25 ± 0.17 28 6.53 0.32 ± 0.20 0.17 ± 0.20 -0 .15 ± 0.15 27 6.25 0.27 ± 0.17 0.36 ± 0.19 0.09 ± 0.13 31 6.84 0.76 ± 0.22 0.89 ± 0.28 0.13 ± 0.17 15 6.39 0.08 ± 0.21 0.33 ± 0.27 0.25 • 0.23 19 6.38 0.20 ± 0.19 0.09 ± 0.26 -0 .11 ± 0.15 27 6.35 0.05 ± 0.18 0.37 ± 0.22 0.32 ± 0.18 25

Sou the rn Novaya Zemlya Even t s

5.52 - 1 . 2 7 ± 0.23 -1 .52 ± 0.27 - 0 . 2 4 + 0.12 43 6.98 -0 .02 ± 0.23 0.69 ± 0.40 0.71 + 0.47 5 6.72 0.61 ± 0.23 0.61 ± 0.32 0.00 + 0.21 16 6.47 0.63 ± 0.19 0.64 ± 0.27 0.01 _-+ 0.19 20

1256 THORNE LAY

ESK AT L BOG A mgb°~'8~ 6.3~ /i 6.~8

~ ~ (0.4- 0.8hz) (0.4-0.8 hz) ~ ~ " ~ / / " B O G I TL

sec I - - I 0 lo

FIG. 1. Short-period P-waves from event GREELEY at three WWSSN stations (top row) and corresponding signals after deconvolution of the instrument responses and bandpass filtering with the indicated passbands (middle and bottom rows). The analytic envelopes of the filtered traces are shown as well. The azimuths of the three stations with respect to the tectonic release P-wave radiation pattern for GREELEY are shown on the right.

coda that are generally observed for the NTS data (Paper 1) do suggest that the former interpretation is correct.

It is of obvious importance to establish whether the variations in frequency content apparent in Figure 1 are due to source, path, or receiver effects. The contribution of deep path and receiver effects can be appraised by comparing signals at a given station for events in close proximity to each other, although the exact meaning of "close" is not well defined. Figure 2 shows the squared analytic envelopes of ESK recordings for several NTS events after deconvolving the instrument response and bandpass filtering the ground motion with low-frequency (0.4 to 0.8 Hz) and high-frequency (1.1 to 1.5 Hz) passbands. With the exception of PILE- DRIVER, the events are all from Pahute Mesa and locate within 12 km of the GREELEY shotpoint. Event KASSERI was detonated within 2 km of GREELEY, so the paths are most similar for that pair. There are significant variations in the temporal distribution of energy in both passbands, with a clear tendency for smaller magnitude events to have a greater proportion of long-period energy in the early P coda. The high-frequency variations are more erratic, although there is a general tendency for larger events to have relatively enriched high-frequency content in the coda. Note that few, if any, systematic features common to all of the traces can be identified, indicating that common paths or receiver effects are less important than near-source effects. The lack of late, high-frequency arrivals at ESK for PILE- DRIVER is consistent with the EKA waveform analyzed by Douglas (1984).

The comparison between KASSERI and GREELEY in Figure 2 is particularly interesting because KASSERI produced less total tectonic release. Douglas (1984) suggested that early aftershock radiation affecting the short-period P coda may directly correspond to the overall tectonic release radiation observed in long-period signals. Using the long-period seismic moments for the nonisotropic radiation determined by Wallace et al. (1985) and the relative explosion strength estimates determined by Lay (1985), the relative F-factor (ratio of tectonic release/explosion moments) for GREELEY is 1.7 times greater than for KASSERI. KASSERI does, in fact, have less high-frequency content in the coda than GREELEY, suggesting a correlation. However, event JORUM has significant late high-frequency enhance-


ESK FONTINA /~0"4-0.8hz) //~ (1.1-1-5 hz)

JORUM

KASSER! ~ / ~ 6.14 A

BOXCAR / ~

6.12

GREELEY 6.09

ALMENDRO 5.96

5.78 / ~

PURSE . ~ 5.51 _/~-~_

5.31 __A/~ j , ,

PILEDRIVER ~ ~ ~ , 5.41

f I 0 sec 10

FIG. 2. Squared signal envelopes for bandpass-filtered and deconvolved recordings at station ESK for several NTS events. All of the events except PILEDRIVER are from Pahute Mesa.

ment, but the F-factor is seven times lower than for GREELEY. It is clearly necessary to analyze more than one station to establish whether aftershock radiation is present.

The normalized signal envelopes shown in Figure 2 are smooth functions that contain all of the information about the temporal energy flux in each trace. In order to characterize the average properties of each passband, it is useful to stack the area-normalized squared envelopes for all stations recording a particular event. For our large data set, this results in smooth event-averaged envelopes for each passband, examples of which are shown in Figure 3. These evelope stacks clearly

1 2 5 8 THORNE LAY

a) Pahute Mesa c) NNovaya Zemlya (0.4-0.8 hz) (0.8-1.1 hz) (0.4- 0.8hz) (0.8-1.1 hz)

m~)b=5.75/ ~ 5.65 /

5.96 ] ~ 5.83 ] ~

6.16 J ~ "--. 6.38 ] k / / ~

b) Amchi tka o'---~c--~o d) S. Novaya Zemlya LONGSHOT/~

MtLROW / ' ~ 6.27 )

CANNIKIN/~ 6.73 / ~

9127/73/'~ 5.52 ]

10/'8/75 /~k 6.47 )' ~ _

11/02/74/~ / ~ - ~ _ ~ 6.72 /

FIG. 3. Traces obtained by stacking the area-normalized squared envelopes of the deconvolved and filtered recordings for all stations for a given event. Representative events from four different test sites are shown.

illustrate how we can characterize event to event variations in frequency-dependent energy distribution, which can then be related to source parameters such as magnitude, burial depth, or tectonic release F-factor. Note that the Pahute Mesa events in Figure 3 tend to have quite variable high-frequency energy distributions relative to events at the other sites. There is also a subtle systematic tendency for the events outside of Pahute Mesa to have slightly higher levels in the coda for the long-period stacks.

While the stacking procedure used in Figure 3 is useful for visually characterizing the frequency-dependent behavior, it is necessary to adopt a parametric waveform measurement in order to systematically analyze the information in all 1620 waveforms, each of which is deconvolved and filtered in three separate passbands. For each filtered trace, the energy temporal centroid of the first 15 sec of the squared analytic envelope was computed by

15 15

C(Bp,= f s2(t)tdt/ f s2(t)dt 0 0

where s(t) is the signal envelope, and (Bp) indicates the passband of the filtered signal. A useful property of the centroid parameter is that the centroid of the stack of the area-normalized envelopes is the same as the average of the centroids of the separate envelopes. The differences in the centroid measurements between each passband provide measures of the "dispersion" of each waveform, in the sense of different temporal distribution of the frequency content. For each event, the centroid differences were summed and event corrections were applied. The event corrections, which account for pP interference effects and were always very small, were obtained by applying the data analysis to synthetic P waveforms computed using the complete explosion source models obtained by relative waveform analysis for events at Amchitka (Lay et al., 1984a), NTS (Lay, 1985), and Novaya Zemlya (Burger et al., 1986b). For each test site, the centroid differences at each station were averaged to established corrections for common path and receiver contributions. These station


corrections were applied to the Amchitka and Novaya Zemlya data in computing the event averages to reduce any bias due to systematic patterns common to all of the events in each site. For Pahute Mesa, the station averages showed no systematic patterns, reflecting the signal variability observed in Figure 2; so rather than apply station corrections, the centroid differences were azimuthally averaged with 7.5 ° azimuth window when computing the event mean. The resulting event-averaged dispersion measurements, along with the standard error and number of observations for each estimate, are listed in Table 1. Similar event-averages were computed for the centroid measurements for each passband, with event and station corrections being applied in every case, along with additional azimuthal averaging for the Pahute Mesa and Amchitka sites. The next two sections will establish the patterns in both the event-averaged measurements and the individual event observations, and their relation to near-source processes.

RESULTS FOR NTS EVENTS

Following the same procedure used in Paper 1, the event-averaged centroid differences between each passband for the NTS events (Table 1) were compared to various known source parameters. Some of the comparisons for the 25 Pahute Mesa events are shown in Figure 4. The dispersion measurements are plotted as functions of mb ab, source depth, radial distance from the center of the test site (37.28°N, 116.425°W), and tectonic release relative F-factor. The centroid differences exhibit a clear magnitude dependence, which is particularly interesting because the average event complexity measurements in Paper I had no such dependence. Larger positive values indicate a higher proportion of high-frequency energy later in the signal for each case. Given that these measurements have been averaged over all stations for

g

~3 L ' , , - - -

o.o81

3 i , , I ' ' ' I

~ 11 , , i J

50 58 6.6 0.5 1.0 1.5 0 8 16 0 3 6 m'l~b Depth, km Distance,km F-factor

FIG. 4. The variation of event-averaged dispersion measurements for Pahute Mesa tests with source parameters mb ~, burial depth, radial distance from the center of the test site, and tectonic release relative F-factor. The correlation coefficient, CC, and a variance-weighted regression line are shown for each case. The error bars are standard error of the mean centroid difference.

1 2 6 0 T H O R N E LAY

each event, the t rends are quite robust, and the application of source or receiver corrections, or azimuthal averaging, have almost no affect on the relative variations. The larger (and deeper} events show systematic shifts between the centroids of the high- and low-frequency passbands, with the strongest and most consis tent shifts being between the 0.8- to 1.1- and 0.4- to 0.8-Hz passbands. The highest f requency passband (1.1 to 1.5 Hz) shows less variat ion relative to the low-frequency passband, indicating an interest ing band-l imited behavior of the dispersion. Th e regression lines for the comparisons with correlat ion coefficients greater than 0.8 are given in Table 2. In addition to the strong magni tude /dep th dependence, the Pahu te Mesa events show a weaker correlat ion with radial distance from the center of the site. This secondary spatial dependence, which is part ial ly due to a magnitude-distance correlation, may be related to the spatial pa t te rn apparent in the complexi ty measurements analyzed in Paper 1. Note tha t relative tectonic release size does not have a significant effect on the event-averaged centroid differences, which argues against the idea tha t late high-frequency radiat ion from aftershocks produces these pat terns.

The magnitude dependence in Figure 4 could result f rom anomalous behavior of ei ther the high- or low-frequency passbands. In order to establish which variat ions are responsible, the event-averaged centroid measurements in each passband were directly tested for dependence on the various source parameters . Figure 5 shows the results for the 0.4- to 0.8- and 0.8- to 1.1-Hz passbands. These measurements are significantly more likely to be contamina ted by s tar t t ime misal ignments and source function variat ions than the centroid differences, but the level of scat ter proved sufficiently low to provide useful results. The application of stat ion corrections in these calculations zero-means the overall da ta set, bu t larger positive values always indicate later centroid times. It is clear tha t the strong magnitude dependence observed for the centroid differences is the result of systematically later centroids for smaller events for the low-frequency passband, and systematically later centroids for the larger events for the high-frequency passband. Th e variat ions with magnitude in the 1.1- to 1.5-Hz passband are relatively flat compared to those shown in

TABLE 2

VARIANCE-WEIGHTED REGRESSION OF DISPERSION MEASUREMENTS AND EVENT PARAMETERS

Dispersion Measurements (sec) Event Parameter Slope Intercept

Pahute Mesa

C ( o . ~ l . l ) - C(0 .4~) .8 ) mb ~ 2.15 __ 0.23 -11.73 -+ 1.37 C(0.8-1.1) - C(0.4-0.8) Depth (km) 2.52 -+ 0.29 -1.61 __ 0.29

Amchitka

C(o.s-l.1) - C(o.4~.s) mb ~ 1.35 _+ 0.21 -8.30 -- 1.28 C(o.s-l.1) - C(o.4~.8) Depth (km) 1.56 ± 0.05 -1.94 _+ 0.07 C(o.s-l.1) - C(o.4~.s) P velocity (km/sec) 1.71 _+ 0.01 -7.17 _+ 0.02

Northern Novaya Zemlya

C(1.1_1.5) - - C(0.4~0.8) m b ab 1.21 - 0.25 -7.45 ± 1.59 C(1.1 1.5) - C(o.4-o.s) p P - P (sec) 6.86 _+ 1.51 -4.44 ± 1.00 C(1.1_1.5) - - C(0.4~0.8) p P / P 4.36 ± 1.01 -4.39 ± 1.04

Southern Novaya Zemlya

C(L1-1.5) -- C(o.4-o.s) rnb ~ 1.73 _ 0.39 --10.93 _ 2.50 C(1.1-1.5) - C(o.~L1) p P - P (see) 5.79 ± 1.12 -3.35 ± 0.67 C(1.1-1.5) - C(o.s-l.1) p P / P 1.98 ± 1.92 -2.08 ± 2.02


1 . 2 , , , , ,

1.21 , , , I I - °~ , °4 , , I

1.2 . . . . . .

5D 5 ~ b 6.6 0.5 1D 1,5 0 8 16 D e p t h . k m D i s t a n c e , k m

FIG. 5. The variation of event-averaged centroid measurements for two different passbands for Pahute Mesa events with source parameters rnb ~, burial depth, and radial distance from the center of the test site. The correlation coefficient, CC, and a variance-weighted regression line are shown for each case. The error bars are standard error of the mean centroid.

Figure 5, accounting for the band-limiting behavior in Figure 4. These competing trends provide an explanation for the absence of any strong magnitude dependence in the frequency-independent complexity measurements in Paper 1. The low- frequency passband appears to be slightly more strongly influenced by explosion size than by burial depth and is not strongly influenced by position in the site. The two most overburied events, SCOTCH and CHESHIRE, deviate from the depth regression line, but lie directly along the magnitude trend. In order to verify that this magnitude dependence is not simply a signal to noise level effect, the noise correction procedure used in Paper 1, which involves removing an rms noise level before calculating the centroids, was performed for several large and small events. While the long-period passband for the smaller events was more strongly affected by noise contamination than any other measurement, the size of the bias appears to be negligible relative to the strong trends in Figures 4 and 5. The high-frequency passband in Figure 5 shows a somewhat greater dependence on depth than on magnitude, although the most deeply buried event, MUENSTER, deviates from the general trend. The high-frequency passband also shows a clear dependence on position in the site, which is directly responsible for the corresponding dependence in the centroid differences in Figure 4. None of the three passbands has a significant variation with F-factor, further establishing that tectonic release is not a controlling factor.

Having established that there are significant magnitude, burial depth, and source location influences on the event-averaged frequency-dependent measurements, the individual event observations can be inspected for systematic patterns that may further constrain the near-source processes that are responsible. The individual station centroid differences between the 0.8- to 1.1- and 0.4- to 0.8-Hz passbands for several NTS events are shown in Figure 6. The plus symbols indicate stations with relatively enriched high-frequency content in the coda. The magnitude dependence of the average dispersion is readily apparent, with the large events (GREELEY, JORUM, KASSERI, and FAULTLESS) clearly having positive average centroid differences. Note that PILEDRIVER, which is a very low magnitude event, has a similar distribution of centroid differences to the small Pahute Mesa

1262 THORNE LAY

GREELEY JORUM KASSERI PILEDRIVER

PIPKIN STILTON TYBO FAULTLESS

C(0,8-1.1 hz) -- C(oA-O.8hz) + sec <~ 2.5 -2.5 - , 5,"0

FIG. 6. Equal-area projections of the observed centroid differences between the 0.8- to 1.1- and 0.4- to 0.8-Hz passbands for several NTS events. Plus symbols indicate relatively enriched high-frequency content late in the signals. The perimeter of each projection corresponds to a take-off angle of 22.5" for a source velocity of 3.5 km/sec. Note that the larger magnitude events {Table 1) have positive average residuals and coherent azimuthal patterns.

events P IPKIN and STILTON. These smaller events have a near-zero average difference and lack any slowly varying patterns. The large Pahute Mesa events exhibit a strong concentration of large centroid differences at azimuths toward the north-northeast. Inspection of azimuthal patterns in the short- and long-period centroid measurements separately established that these azimuthal patterns are principally due to patterns in the high-frequency passband. Stations ESK and EKA, which have an azimuth near 33 ° , lie within this cluster of observations. It is well- established that teleseismic P waves recorded at azimuths to the north-northeast from Pahute Mesa have anomalously low amplitudes and early arrival times (Lay et al., 1984b; Lynnes and Lay, 1987; Paper 1). Defocusing by high-velocity structures in both the uppermost mantle and at greater depths beneath the source region is believed to be responsible for the latter patterns (Lynnes and Lay, 1987; Paper 1), and it is important to establish whether the azimuthal patterns in Figure 6 are associated with this process or with an independent phenomenon such as aftershock radiation. Note that while there is substantial variability in the overall patterns in Figure 6, there are some stable path or receiver effects common to all of the events, notably at southeastern azimuths. In order to appraise the near-source effects, we need to suppress the path variations and isolate any slowly varying, near-source components in the patterns.

Figure 7 presents a procedure for isolating the long-wavelength azimuthal components in the dispersion measurements for each event. For all 25 Pahute Mesa events, curves with the form Asin[2(0 - 0o)] or Asin[4(0 - 00)] were regressed to the zero-meaned centroid differences for each passband. The statistical significance of each regression was appraised with the F-test used in previous studies (Lay et al., 1984b; Paper 1). The data for events COLBY and FONTINA shown in Figure 7 have the strongest slowly varying patterns, with statistically significant (at the 99 per cent confidence level) sin(20) and sin(40) components for the C(o.s-l.1) - C(o.4-o.s)

NEAR-SOURCE

COLBY ~ . . . . . ,.,,,~,~

"C(o _1.1)o k" >-1 C(o.,.o.s),S

- 5 0 . . . . . . . . . . . . .

, , , , , : 1 C'°"-°'s)'S t . ." " ' :. :

• .SO I I I I I I I I I I I I I

CONTRIBUTIONS TO EARLY P-WAVE CODA

FONTINA

l I I I I@ I I I I 1 fill

1263

GREELEY

I I I I I I I I I I I

MUENSTER I I ] I I I I I I

I I I I I I I I I

~ l o l • • cola e~

s.ol , , . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

" 5 , 0 ' i i I i i i I l l I l I

-180 -90 0 90 180 -180 -90 0 90 180 -180 -gO 0 90 180 -180 -90 0 90 180

AZIMUTH, deg FIG. 7. Azimuthal pat terns of the centroid difference measurements for four Pahute Mesa events of

comparable magnitude. A best-fit sin(20) curve obtained by regression is shown for each case in order to emphasize the slowly varying components of the azimuthal patterns.

differences. Application of station corrections slightly reduces these patterns, but the sine curve regressions are still highly significant. For the same centroid differences, the only other events with significant (at the 95 per cent level) sin(20) components are JORUM, M U E N S T E R (Figure 7), CHESHIRE, PIPKIN, and SLED. These events have a wide range of magnitudes, burial depths, and F-factors. Many events, such as GREELEY (Figure 7), do not have a simple long-wavelength component, although substantial variations in the dispersion measurements are apparent. The events with the strongest azimuthal patterns, COLBY and FON- TINA, have F-factors of 0.79 and 2.39, respectively, compared to the larger values for GREELEY {3.44) and M U E N S T E R (3.40). Figure 7 shows that the azimuthal pattern for MUENSTER is rotated by almost 90 ° relative to those for the other events. It is known that the tectonic release orientations for the Pahute Mesa events do not vary by more than 25 ° in strike (Wallace et al., 1985).

In order to establish the spatial variations in the dispersion measurements, Figure 8 shows a map indicating both the relative size of the event-averaged centroid shifts between the 0.8- to 1.1- and 0.4- to 0.8-Hz passbands and the characteristics of the azimuthal pattern in the centroid differences for each event. The length of each arrow is proportional to the amplitude, A, of the sin(20) regression to the centroid differences, and the direction is that of a northerly maximum in the regression curve. The average centroid shifts are largest for events in the central part of the Mesa, although reference to Table 1 confirms the greater importance of the event sizes. While only seven of the events have statistically significant sin(20) components, as mentioned above, the arrows do indicate the approximate direction of the maximum centroid differences in each case. Note that very nearby event pairs (such as SLED and ALMENDRO, POOL and RICKEY, GREELEY and KASSERI, BENHAM and TYBO, and PURSE and FONTINA) tend to have similar azimuths of greatest dispersion. This indicates some very near-source control on the patterns, although the event pairs CAMEMBERT and SCOTCH, and COLBY and JORUM are exceptions to this consistency.

Similar maps of the characteristics of azimuthal amplitude patterns for Pahute

1264 THORNE LAY

Mesa events (Lay et al., 1984b; Paper 1) show more regular behavior than the patterns in the centroid differences, but there is substantial correspondence between the dispersion patterns in Figure 7 and azimuthal patterns in waveform complexity (Figure 8, Paper 1). In both cases, events in the west-central part of the Mesa have the strongest patterns, and these events also have similar variations in azimuthal orientation. To corroborate this correlation, the individual centroid differences C(o.8-1.1) - C(0.4-o.s) were compared to the complexity measurements based on the ratio of rms amplitudes in the time intervals from 5 to 15 and 0 to 5 sec after the P arrival, log(rms~-15/rms°-5), from Paper 1. Figure 9 shows the resulting correlations for events FONTINA and COLBY, both of which have a moderate correlation between relatively enhanced coda amplitudes and relatively delayed high-frequency energy. The correlation coefficients for all of the other Pahute Mesa events were lower than those in Figure 9. Comparison of the same two measurements for all 25 Pahute Mesa events simultaneously (844 values) gave correlation coefficients of 0.19 without removing the event-averaged dispersion values, and 0.20 after removing

37.40 °

37.32"

N

37.24 °

37.16'

I I I I I I I Pahute Mesa #AST -~

STILTON, 4b@$TING[R |

T~ ,~EELE ~ HALFBEAR BOXCAR @ ~ CAM(H~RT vIdU[NSTER

pUI~SE4)~ONTINA KA, SSERI ~SGOTCH POOL -1 P.~,P SLEO. %EY /

,,x,,$ %~,E *,,.~0

I I I I I I

I I I I I I

¢ • ,S

ZX 1.o + -1.0

I I I I I I 116,60 ° t l 6 . S O " 1 1 6 . 4 0 ° 1 1 6 . 3 0 1 1 1 6 . 6 0 ° 116 ,50 e 1 1 6 , 4 0 ° r l 6 . 3 0 °

w w

FIG. 8. Maps of the Pahute Mesa test site indicating the event locations (/eft) and characteristics of the individual event centroid differences between the 0.8- to 1.1- and 0.4- to 0.8-Hz passbands (right). The event-averaged centroid shifts (Table 1) are indicated on the right, with the size of the triangle being proportional to the relative delay of high-frequency energy. The arrows indicate the direction and amplitude of a northerly maximum in the sin(20) curves regressed to the individual event measurements, as in Figure 7. Thus, the azimuths indicated by the arrows correspond to the directions with strongest dispersion.

0.5 F O N T I N A

U3

%

u~ O9 0 cc v o o~ 0

_J

-0,5 -5.0

I • • = • •

C C - 0 . 5 5 8

C O L B Y

• m ~ • •

~ , " " C C = ( ~ 4 8 4

5£) - ~ 0 0 5 .0

L~ C(0.8_1.1)-0(0,4.0.8), s FIG. 9. Correlation plots between dispersion and waveform complexity measurements for two Pahute

Mesa events. In each case, the measurements have been zero-meaned. These two events have the strongest correlation between these parameters as well as the strongest azimuthal patterns in each parameter.


the averages. A correlation coefficient of -0.17 was obtained using all of the dispersion measurement and individual relative amplitude measurements given by log(tins °-5) anomalies, indicating that larger direct arrivals have a weak tendency to have less delayed high-frequency content in the coda. The evidence discussed in Paper 1 that favors an explanation of the complexity variations by near-source preferential focusing and defocusing of the direct arrivals relative to the coda can also be used to argue that the frequency-dependent azimuthal variations have a similar origin, requiring a dispersive defocusing effect.

RESULTS FOR THE AMCHITKA AND NOVAYA ZEMLYA TEST SITES

The three Amchitka tests exhibit a frequency-dependent behavior that is very similar to that of the Pahute Mesa events. Figure 10 shows that the event-averaged centroid differences (Table 1) between the 0.8- to 1.1-Hz and the 0.4- to 0.8-Hz passbands increase systematically with magnitude, burial depth, and source medium P velocity. The regression lines for these three comparisons are given in Table 2. The highest frequency passband (1.1 to 1.5 Hz) shows less systematic variations relative to the lower frequency bands, just as for the Pahute Mesa events. Consid- eration of the magnitude dependence of the event-averaged centroid measurements in each passband, shown in Figure 11, indicates that the trends in Figure 10 are

15 . &

O 0

d

O0

m 0

0 -1.1 1.5

d

O 0 I

I

c2 0

-1.5 1.5

O 0

"2

c~

-1.~

f CC=0.989

I i I

0.789 i i i

/= i i i

i i i

+

-0.159 i i i

-0.336 i I L

i i i

i i i

-0.309 h i I

5.4 m61b~ 6.80A 1.2 20 3.4 4.2 5.0 Depth, km P Velocity, km/s

FIG. 10. The variation of event-averaged dispersion measurements for the three Amchitka events with source parameters mb ~, burial depth, and shot point P velocity. The correlation coefficient, CC, and a variance-weighted regression line are shown for each case. The error bars are standard error of the mean centroid difference.

1 2 6 6 T H O R N E LAY

again the result of a combination of relatively enhanced long-period content in the coda of the 0.4- to 0.8-Hz passband for smaller events, and enhanced high-frequency content of the coda for the 0.8- to 1.1-Hz passband for larger events. Given the strong correlation found with the different source parameters, and the limited numbers of events, it is not possible to identify which source parameter most directly controls the overall behavior. The individual centroid measurements and centroid differences were inspected for azimuthal patterns, with no significant slowly varying patterns being detected. The station averages do not show any systematic azimuthal patterns either, indicating that the dispersion characteristics are predominantly influenced by the very near-source environment.

As in Paper 1, the Novaya Zemlya data from the two subsites were analyzed separately because of the known strong intersite variations in amplitude patterns and tectonic release orientation (Burger et al., 1986a, b). The Northern test site was found to have significant slowly varying azimuthal patterns in the station-averaged centroid differences. A statistically significant (at the 99 per cent confidence level) sin(20) azimuthal component is apparent in the path-averaged centroid differences between the 0.8- to 1.1- and 0.4- to 0.8-Hz passbands, as shown in Figure 12. An azimuthal pattern with similar orientation is also apparent for the centroid differences between the 1.1- to 1.5- and 0.4- to 0.8-Hz passbands, although the sin(28)

, ,

0

CC=-0.990

5.4 6.1 m~ b

, ,

~ 0 d

0

6 . 8

0.889

-1 54 6.!a b 6.8

m b FIG. 11. T h e var ia t ion of even t - ave raged cen t ro id m e a s u r e m e n t s for two d i f fe ren t p a s s b a n d s for the

A m c h i t k a even t s wi th mb ~. T h e cor re la t ion coeff ic ients , CC, a n d a va r i ance -we igh ted regress ion l ine are shown for each case. T h e e r ror ba rs are s t a n d a r d e r ror o f t h e m e a n cen t ro id di f ference.

5 e"

0 - 5

E I I I I ~ I I I I I [ I I I I 1 1 I [ I i I

- . " " , . . - 1 " . . ." - • ,~I ee eo e ° - -

. . .

___[ I I I I I i I I I I b I I I I I ~ I I I I I I_

"~ -180 -90 0 90 180-180 -90 0 90 180 AZIMUTH,deg

FIG. 12. Az imutha l va r ia t ion of p a t h - a v e r a g e d d i spe rs ion anomal i e s for t he N o r t h e r n Novaya Zemlya t es t site. A bes t - f i t sin(20) regress ion curve is s h o w n for each d i spe rs ion m e a s u r e m e n t .


component has a lower (95 per cent) confidence level. The slowly varying component is indicative of a regional effect, which is probably a propagation effect given that it is common to all of the events. The tectonic release F-factors for the Northern Novaya Zemlya events vary by a factor of 3 (Burger et al., 1986a), so it is unlikely that the common pattern results from either tectonic release or aftershock radiation. After the station averages were applied as path corrections to the individual event data, none of the 11 events were found to have statistically significant (at the 99 per cent confidence level) residual sin(20) or sin(4#) azimuthal patterns. Given the oblique normal faulting orientation of the tectonic release for these events (Burger et al., 1986a), aftershock radiation would not be expected to produce a simple sinusoidal variation, but the low F-factors involved also indicate that any tectonic release radiation should be even smaller than for Pahute Mesa.

The event-averaged dispersion measurements for the Nothern test site (Table 1) proved to have systematic magnitude dependence as well as trends with the p P parameters determined by relative waveform analysis (Burger et al., 1986b), as shown in Figure 13. The second largest event (14 October 1970) deviates from the magnitude trend, but not from the trend with p P delay for the C(0.s-l.1) - C(0.4-0.s) and C~1.1-1.5) - C(0.4-0.s) differences. Note that the average centroid differences increase systematically from the 0.8- to 1.1- to the 1.1- to 1.5-Hz passbands, which was not

1.5 U}

oo d ,4 d

O O

? co

0 -12 1.5

d

0 0

¢Y -1.5 1.5

&

0 0

"T

c~ -1.~

5.4

CC=0 .767

= = i

/ 0 .834

= i =

0 . 795

i i i _

0 . 838

i i

0 . 741

= i i 0 . 674

J i =

0 . 493

i i

0 . 543 0 .589 0 .579 - 0 .187

. . . . . . . . . . ().9 ' 6.2 7.0 Q5 0.7 -0.9 0.6 1.0 1.4 0.3 1.5 m~ b pP-P, s IpPVIPI F-factor

FIG. 13. The variation of event-averaged dispersion measurements for the Novaya Zemlya events ~b with source parameters mb , p P - P lag time, p P relative amplitude, and tectonic release relative. F-

factor. The correlation coefficient, CC, and a variance-weighted regression line are shown for each case. The error bars are standard error of the mean centroid difference.

1268 THORNE LAY

observed for the Pahute Mesa and Amchitka data. The correlation with pP delay time indicates a source depth dependence; however, the significance of the correlation with pP relative amplitude is less obvious. The pP amplitude estimates were derived under the assumption that only P and pP arrivals contribute to the relative waveform differences between events (Burger et al., 1986b}, and it is possible that spall phases or crustal reverberations contaminate the pP estimates. The correlation detected here, with larger apparent pP amplitudes being associated with relatively delayed high-frequency centroids, suggests that frequency-dependent spall effects actually do bias the amplitudes. The correlations with tectonic release F-factor in Figure 13 are stronger than for any of the other test sites investigated, but these are still subdued relative to the magnitude and depth dependence, particularly for the differences between the 1.1- to 1.5- and 0.4- to 0.8-Hz passbands, which have the strongest variations. The regression lines for the comparisons in Figure 14 with correlation coefficients greater than 0.8 are given in Table 2.

The Northern Novaya Zemlya dispersion patterns are not the result of a combination of high- and low-frequency variations, as was the case for the Pahute Mesa and Amchitka sites. Instead, the systematics in the centroid differences are simply the result of enhancement of the coda energy for the lower frequency passband, as shown in Figure 14. The 0.8- to 1.1-Hz passband has decreasing centroid times for larger events, as was also the case for the 1.1- to 1.5-Hz passband. The strong magnitude dependence of complexity measurements for these events found in Paper 1 appears to result from this systematic dispersive behavior. The behavior of the 14 October 1970 event is clearly associated with the low-frequency passband, but this event alone does not suffice to resolve whether explosion size or burial depth has a greater influence on the frequency-dependent variations. The common azimuthal

1.2

oO

?o

o

-1.2 1.2

~ NNZ

C C = - ~ i i K___

r , , NNZ

. 5 - - - r , ,

- 0.942 .1.5 . . . . . . . . . 1.5r

~, SNZ

-0.406

T= o

- 0 . 819

-1.2 ' ' -0.691

i • i

ol Y

-0.395 -0.824 1.51 J _ ~ ......... ~_ . . . .

5 , 4 ~ 2 b ~ , 0 0 . 5 0 , 7 0 9 5 . 2 6 2 7 , 2 0 , 4 0 , 6 0 . 8 d4gb pP-P, s pP-P, s

FIG. 14. The variation of event-averaged centroid measurements for two different passbands for Northern Novaya Zemlya (NNZ) and Southern Novaya Zemlya (SNZ) events with mb ~ and p P - P lag time. The correlation coefficient, CC, and a variance-weighted regression line are shown for each case. The error bars are standard error of the mean centroid difference.

NEAR-SOURCE CONTRIBUTIONS TO EARLY P-WAVE CODA 1 2 6 9

pattern in the station averages for these events is also principally the result of variations in the low-frequency band.

The event-averaged centroids for the 0.4- to 0.8- and 0.8- to 1.1-Hz passbands for the four Southern Novaya Zemlya events, which are shown in Figure 14, have magnitude dependence as well. The general trends are similar to those for the Northern events, but the scatter is greater. The increase in scatter may partially be the result of the small number of observations (five) available for the largest magnitude event, as well as the fact that the event of 18 October 1975 was a complex double explosion (Burger et al., 1986b). The event-averaged centroid differences (Table 1) are plotted in Figure 15, with the magnitude dependence having the strongest correlations. Table 2 gives the regression lines for the comparisons with correlation coefficients greater than 0.8. Note that the lowest magnitude event has an estimated pP delay time as late as for events that are an order of magnitude larger, which indicates either deep overburial or emplacement in a different source medium. Whatever the actual explanation, the correlations between pP delay time and the dispersion measurements are diminished relative to the magnitude dependence for all but the highest frequency case. No slowly varying azimuthal patterns were apparent in either the individual event observations or in the station-averaged measurements for the Southern test site.

1.6

qo

-1.q 1.6

U'J

~1.6 1.6

¢o

~ 0 I A tq. V

T-=

-1 . ( 5.2

0 , 7 8 3 L

, o:ogs

~ 0.445

0 . 9 6 5

t i i

O.7 pP-P, s

~ - 0 1 4 5 6

0 . 0 8 7

= m

0 . 8 2 0 = =

0.9 0.6 1.0 0 . 4 2 1

t i t

1.4 Q3 0'.9 1.5 IPPI/IPI F-factor

FIG. 15. The variation of event-averaged dispersion measurements for Southern Novaya Zemlya ~b events with source parameters, mb, p P - P lag time, pP relative amplitude, and tectonic release relative

F-factor. The correlation coefficient, CC, and a variance-weighted line are shown for each case. The error bars are standard error of the mean centroid difference.

1270 THORNE LAY

DISCUSSION

The preceding data analysis has established that the near-source contributions to frequency-dependent variations in teleseismic short-period P waves from underground explosions are of first-order importance. The systematic nature of these contributions has not been well-appreciated in previous investigations. There are, of course, additional frequency-dependent effects in the data produced by scattering and attenuation processes associated with deep structure and near-receiver complexity, which would be best isolated using array analysis (e.g., Dainty, 1985); however, such distant processes cannot explain the trends determined in the previous sections. Several of the fundamental assumptions {that a priori appear quite reasonable) adopted by Douglas (1984) in his interpretation of the EKA waveforms from GREELEY and PILEDRIVER have been demonstrated to be invalid as a result of the near-source contributions. First of all, there is a strong magnitude and/or source depth influence on the frequency-dependent energy flux in the teleseismic P waves that has no obvious relationship to aftershock radiation. Next, systematic spatial variations in the frequency-dependent behavior are apparent for events separated by much less distance than GREELEY and PILEDRIVER, as is well-known to be the case for amplitude measurements. Finally, the differences in frequency-dependent behavior between the test sites analyzed in this study suggest the possibility that source media play an important role in the dispersive processes, as is also indicated by the observations of Gupta et al. {1985).

All of the test sites analyzed in this paper have relatively enhanced long-period content in the early P coda for smaller, less deeply buried events (Figures 5, 11, and 14). There is a weak indication that explosion size plays a greater role than burial depth in this behavior for the Pahute Mesa events, while the opposite may be true for the Northern Novaya Zemlya events. This general magnitude/depth dependence, along with the evidence that long-period content of the early P signal is enhanced for events in media with lower source region P velocity (Gupta et al., 1985), can be qualitatively attributed to greater fundamental mode Rayleigh-wave excitation and attendant scattering to P waves for shallower events, as suggested by Gupta et al. (1985). The amplitude, R, of the fundamental mode Rayleigh wave for an explosion source with source function S([) at depth, d, in a homogeneous half-space with compressional velocity, ~, is given by (e.g., Hudson and Douglas, 1975)

R = C S ( f ) fl.~ lO-2.18(2d/~)f/rO.5pa3.5

where a Poisson's ratio of 0.25 is assumed, p is density, r is the epicentral distance, and C is a constant. This equation indicates that a medium with a lower velocity will excite larger Rayleigh waves with relatively depleted high-frequency content. In general, to the degree that the near-source environment can be characterized as a half-space, the relative excitation of the near-field Rayleigh waves should decrease with increasing burial depth, yielding less available surface-wave energy that can scatter from crustal heterogeneity to arrive in the teleseismic P-wave coda. Numer- ical calculations of such a depth-dependent process for realistic source velocity structures will be presented in a future study. The general notion that surface-wave scattering produces a significant component of the teleseismic P-wave coda has frequently been advanced (e.g., Greenfield, 1971), but the frequency-dependent consequences of such scattering have not received detailed consideration.

The tendency for the larger Pahute Mesa and Amchitka events to have relatively enhanced high-frequency energy in the coda (Figures 5 and 11) requires an inde-


pendent explanation. Neither the event-averaged characteristics nor the azimuthal variations of this behavior have any apparent relation to the tectonic release radiation measured in long-period signals. Furthermore, the large events in Pahute Mesa have very similar patterns of the dispersion, for which any explanation in terms of coincidental timing of aftershock sequences is highly unlikely. This behavior may be partially the result of pP interference effects being more pronounced early in the signal, with destructive interference of high-frequency energy leading to centroid shifts between passbands. The early coda, partially comprised of energy radiated horizontally from the source, should be relatively free of such frequency-dependent interference effects, leading to relatively enriched high-frequency content. However, the presence of azimuthal patterns in the dispersion (Figure 6) and the correspondence with magnitude and travel-time anomalies suggest that an additional propagation effect is involved. It is well-established that both Amchitka and Pahute Mesa are located in regions with strong upper mantle velocity heterogeneity, which is the cause of strong azimuthal patterns in direct amplitudes and waveforIn complexity (Paper 1). The Amchitka site overlies the subducting Aleutian slab, while a high-velocity root to the caldera system beneath Pahute Mesa extends into the upper mantle (Spence, 1974; Minster et al., 1981; Taylor, 1983). For the Pahute Mesa data, a correlation was found between the spatial and azimuthal variations of the frequency-dependent centroid shifts and waveform complexity measurements, which suggests that the former are also related to defocusing effects. While specific, three-dimensional scattering calculations have not yet been performed, it is reasonable to postulate that frequency-dependent defocusing from the upper mantle heterogeneity is at least partially responsible for the dispersion. For Pahute Mesa events, the magnitude dependence may arise as a consequence of the spatial systematics, with larger events being more centrally located in the site, which in turn enhances the effects of the defocusing structure. It is likely that deeper burial results in greater coupling of high-frequency energy into the P wave field in general, but it is probably depletion of the high-frequency content of the defocused direct arrivals which accounts for the azimuthal patterns in the high-frequency content. The band-limited nature of the defocusing effects for both Pahute Mesa and Amchitka events may help to constrain the spatial velocity gradients that are responsible.

It is important to recognize the presence of frequency-dependent variations in the direct P waves and P coda resulting from near-source effects when analyzing the signals to determine source functions or attenuation operators. Usually, the possibility of any magnitude dependence has been ignored in such analyses. Some of the discrepancies between time domain and frequency domain attenuation determinations may be the result of biases in the data sets due to use of different time windows of the P arrival, as has also been suggested by McLaughlin and Anderson (1985). It remains to be established whether these frequency-dependent effects can be used to retrieve useful properties of the source region, such as near- surface velocity gradients, as well as whether or not earthquake signals have corresponding variations. It is particularly clear that interpretation of small sets of observations must be performed cautiously, even when the comparisons appear to involve "reasonable" assumptions.

CONCLUSIONS

Analysis of frequency-dependent variations in teleseismic P waves from underground explosions has demonstrated that near-source effects play a major role in

1272 THORNE LAY

determining the energy flux in different frequency bands. Using a large data set to establish event to event systematics and individual event azimuthal patterns, both explosion size-related and spatial effects have been isolated. Smaller events, which are usually buried at shallower depths, exhibit relatively enriched long-period content of the P-wave coda for distinct test sites in Nevada, Amehitka, and Novaya Zemlya. This is probably the result of enhanced surface wave excitation and subsequent scattering for the shallower events. For the Amchitka and Pahute Mesa test sites, which overlie strong upper mantle velocity heterogeneities, there is a tendency for larger events to have relatively enhanced high-frequency content of the P coda with substantial azimuthal variations. This appears to result from a frequency-dependent defocusing effect that depletes the high-frequency content of the direct arrivals. Neither tectonic release nor aftershock radiation appear to be significant in the frequency-dependent variations.

ACKNOWLEDGMENTS

Chris Lynnes and W. Scott Phillips provided constructive comments on the manuscript. Joan Welc assisted with the data processing, and almost all of the seismograms were digitized by Cindy Arvesen. This research was supported by the Sloan Foundation, a Shell Faculty Career Initiation Grant, and the Advanced Research Projects Agency of the Department of Defense, and was monitored by the Air Force Office of Scientific Research under Contract FI9628-85-K-0030.

REFERENCES

Aki, K. (1982). Scattering and attenuation, Bull. Seism. Soc. Am. 72, $319-$330. Burger, R. W., T. Lay, T. C. Wallace, and L. J. Burdick {1986a). Evidence of tectonic release in long

period S waves from underground nuclear explosions at the Novaya Zemlya test sites, Bull. Seism. Soc. Am. 76, 733-755.

Burger, R. W., T. Lay, and L. J. Burdick (1986b). Estimating the relative yields of Novaya Zemlya tests by waveform intercorrelation, Geophys. J. 87,775-800.

Dainty, A. M. (1985). Coda observed at NORSAR and NORESS, Final Technical Report, AFGL-TR- 85-0199, Hanscom Air Force Base, Massachusetts, 73 pp.

Douglas, A. (1984). Teleseismic observations of aftershocks immediately following an underground explosion, Geophys. J. 77,503-515.

Douglas, A., P. D. Marshall, P. G. Gibbs, J. B. Young, and C. Blarney (1973). P signal complexity reexamined, Geophys. J. 33,195-221.

Frankel, A. and R. W. Clayton (1984}. A finite-difference simulation of wave propagation in two- dimensional random media, Bull. Seism. Soc. Am. 74, 2167-2186.

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DEPARTMENT OF GEOLOGICAL SCIENCES UNIVERSITY OF MICHIGAN 1006 C. C. LITTLE BUILDING ANN ARBOR, MlCHIGAN 48109

Manuscript received 19 October 1986

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