Bulletin of the Seismological Society of America, Vol. 74, No. 5, pp , October 1984

Transcription

1 Bulletin of the Seismological Society of America, Vol. 74, No. 5, pp , October 1984 THE RELATIVE PERFORMANCE OF mb AND ALTERNATIVE MEASURES OF ELASTIC ENERGY IN ESTIMATING SOURCE SIZE AND EXPLOSION YIELD BY J. T. BULLITT AND V. F. CORMIER ABSTRACT A comparison has been made of the relative scatter of classical mb and alternative measures of P-wave energy from underground nuclear explosions at test sites in East Kazakh, USSR. The scatter of the energy measures is observed in teleseismic arrays of short-period Global Digital Seismic Network (GDSN) stations and the local broadband array at Graefenburg, Federal Republic of Germany. Four measures of A in Iog(A/T), spectral magnitudes, peak velocity, rms coda, and integrated velocity-squared are compared. The measures are constructed to be in equivalent units of the flux rate of radiated elastic energy. All measures are assumed to have the same slope in a linear regression of log(yield) versus log(measure). Three independent tests were made of the stability of the yield estimators: the scatter of the measures using: (1) Graefenburg array data; (2) GDSN data normalized to a reference station; and (3) GDSN data normalized to a reference event. The differences among the standard deviations are small (_-< 0.1 mb units), making it difficult using a small data base to conclude whether the performance of one estimator is significantly better than another. The relative order in the performance of the yield estimators, however, is preserved in each of the three tests. The coda measure is the most stable, followed by the spectral and time-domain A/T measures. The relations observed at Graefenburg between (1) the amplitude of direct P versus P coda, (2) the apparent azimuth of direct P, and (3) complexity, suggest that amplitude variations across an array are a product of scattering along the entire ray path as well as scattering, focusing, and defocusing localized in the lithosphere beneath the source and receiver sites. INTRODUCTION Remote seismic monitoring of a threshold nuclear test ban treaty relies on farfield measurements of radiated elastic energy to estimate the explosive yield of underground explosions. The effectiveness of a particular yield estimator can be assessed in terms of its stability; for a given event, a "good" estimator must give the same estimate of yield, after appropriate corrections, at all recording stations. In fact, all yield estimators exhibit instability, even after corrections for geometric spreading and known regional variations in mantle attenuation have been applied (e.g., North, 1977; Bache, 1982). The remaining scatter is usually attributed to the effects of complex structural heterogeneity beneath the source and receiver and along the propagation path (Haddon and Husebye, 1978; Chang and Von Seggern, 1980). As a result of scattering along the propagation path, a substantial fraction of the direct P-wave energy is lost to the coda. Estimates of body wave energy based on measurements made at a single point in the seismogram will therefore tend to underestimate the total energy associated with the P wave. Thus, it is not altogether surprising that there is often a large variation in reported body wave magnitudes, even for well-recorded events. For example, mb magnitudes of earthquakes and explosions recorded by stations in a large teleseismic network such as the WWSSN 1863

2 1864 J. T. BULLITT AND V. F. CORMIER often vary by as much as 0.5 magnitude units, even after correcting for the source radiation pattern (Blandford and Shumway, 1982). Stations in small seismic networks situated in regions of apparent geologic uniformity also exhibit surprisingly large variations in observed amplitudes due to scattering. For example, P-wave amplitude fluctuations of a factor of 3 or more are commonly observed across the small subarrays of the Montana LASA (Chang and yon Seggern, 1980). Correction for such amplitude variations is at best difficult without a detailed knowledge of the structure beneath the source and receiver sites. The use of broader time windows may in some cases help to overcome some of the inherent limitations of single-point time-domain yield estimators. For example, rms amplitudes of direct P waves and P coda are in some cases considerably more stable than single-point measures (e.g., Kraft, 1982). Frequency-domain measures (e.g., the mean spectral level in a narrow frequency band) can also perform better than single-point time domain measures (Shapira and Kulhanek, 1978; Kraft, 1982). Interference between P and pp in the time domain can affect all yield measures that rely on P-wave amplitudes (Marshall et al., 1979). In the frequency domain, pp contamination introduces spectral holes in the P-amplitude spectrum that may lead to inaccurate estimates of P spectral magnitude. One way to circumvent this problem is to apply a series of multiple narrow-band filters centered on frequencies in the range of interest. If the time resolution of the filters is made narrow enough, separate estimates can be made of the amplitude spectrum of each of the interfering signals. The variable-frequency magnitude (VFM) (Savino et al., 1980) takes advantage of this principle. In the case of explosions, however, for which pp-p seldom exceeds 1 sec, the narrow-band band-filter method cannot generally resolve P and pp separately and still maintain reasonable frequency resolution. Nevertheless, Bache et al. (1979) find that spectral magnitudes using the VFM method are generally more stable among an array of stations than are time domain amplitude measures. The advent of widespread digital recording now facilitates complete testing of all possible measures of P-wave energy for the relative sensitivity to, and variation resulting from, structural heterogeneity. In this paper, we present the results of an assessment of the stability of a variety of proposed alternative measures of body wave magnitude and radiated elastic energy. These measures were applied to data from explosions recorded by two networks: the broadband digital array at Graefenburg, Federal Republic of Germany and the GDSN network. GRAEFENBURG ARRAY The Graefenburg array consists of 10 vertical-component and 3 three-component seismometers arranged in a semicircular arc approximately 150 km long [see Figure 1, after Harjes and Seidl (1978)]. The instruments are Wielandt seismometers with an output designed to be fiat to ground velocity over the frequency band 0.05 to 5 Hz. The broadband nature of the seismometer output simplifies the testing of a variety of amplitude measures because instrument deconvolution is unnecessary. Summary of measures tested Table 1 summarizes the amplitude measures tested at Graefenburg. Except where noted, the time domain measures were applied to the broadband velocity seismograms. Measure 1 is the logarithm of the P-wave peak amplitude of the broadband velocity applied to each of four peak amplitudes (Figure 2a). The peaks are identified

3 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1865 as follows: zero to first peak (a); first peak to first trough (b); maximum peak-topeak amplitude in the first 5 sec (c); and maximum absolute amplitude in the first 5 sec (d). The "b" amplitude is frequently used in yield estimation as it is less influenced by pp than later peaks (Butler and Ruff, 1980). The "d" measure is commonly used in calculation of conventional mb; the absolute trace amplitude in the first 25 sec is recommended by IASPEI (1979) when reporting mb. N A Bayreuth Erlangen-~ NIJrnberg ~. OA2 OA~ o':,j O B3 B5 J Regensberg. C) c' C )c3,,0???? k m 3-Component Station OZ-Component Station FIG. 1. Map showing station locations at the Graefenburg Array, Federal Republic of Germany. Solid lines extending from the three-component stations point in the direction of apparent P-wave azimuth as inferred from three-component particle motion. Length of solid lines is proportional to peak P-wave amplitudes at the three-component stations. Dashed lines indicate back azimuth to the test site in East Kazakh. Measure 2 was applied to simulated narrow-band records obtained from the Graefenburg data by convolving the broadband velocity records with the response of a WWSSN short-period instrument. The peak amplitudes are the same as those used in measure 1. The period associated with each peak was measured and the measured amplitude corrected for the instrument response at this period. Peak

4 1866 J. T. BULLITT AND V. F. CORMIER TABLE 1 DESCRIPTION OF AMPLITUDE MEASURES TESTED IN THIS STUDY* Amplitude Measures Tested on GRF and GDSN Data Measure Type Time or Frequency Window 1 log(v) Peaks (Figure 2a) (a) zero to first peak (b) first peak to first trough (c) maximum peak-to-peak amplitude (d) maximum trace amplitude? 2 log(a/t) Peaks (Figure 2a) (a) zero to first peak (b) first peak to first trough (c) maximum peak-to-peak amplitude (d) maximum trace amplitude 3 log(rms velocity) 4 log(l)) (smoothed FFT) Time Windows (Figure 2b) (a) PtoP+5sec (b) P to P + 30 sec (c) P+5sectoP+35sec? (d) PtoP+60sec (e) P+5sectoP+65sec Frequency Bands (a) Hz? (b) Hz (c) Hz (d) Hz$ (e) Hz (f) Hz (g) Hz (h) Hz log(l~') (narrow-band filters) Frequency Bands (a) Hz (b) Hz (c) Hz (d) Hz$ (e) Hz (f) Hz$ (g) Hz (h) Hz * All measures shown were tested on the Graefenburg array data; measures marked with a single dagger were also tested on GDSN data.? Tested on GDSN data. :~ Best or worst frequency band; scatter shown in Figure 6. amplitudes and periods for measures I and 2 were determined using a semiautomated procedure. We define the rms amplitude of broadband velocity (measure 3) by 1 ft, t2 ]1/2 rms velocity = t2 - tl VZ(t) dtj, (I) where V is the broadband velocity, and tl and t2 are the start and end times, respectively, of the averaging window. The seismograms were high-pass filtered at

5 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1867 A J.. i t ~-1 Second >1 b B a c plo Seconds-I~ FIG. 2. Sample P waveform recorded at Graefenburg showing the portions of the waveform used in determination of time-domain peak amplitudes. (A) Peaks used in peak amplitude measures (measures 1 and 2). The peaks shown are (a) zero to first peak; (b) first peak to first trough; (c) maximum peakto-peak amplitude in first 5 sec; and (d) maximum trace amplitude in first 5 sec. (B) Time windows used in determination of rms velocity {measure 3). 0.3 Hz prior to the rms computation in order to reduce microseismic noise, rms amplitudes were computed for several time windows. These are described in Table 1 and shown in Figure 2b. Spectral magnitudes were computed from the mean spectral level of the P wave across a band of frequencies. Velocity amplitude spectra, v(f), were obtained either from a smoothed FFT (measure 4) or by the VFM method (Savino et al., 1980) (measure 5). In the VFM method, the seismogram at each station is narrow-band

6 1868 J. T. BULL1TT AND V. F. CORMIER filtered by multiplying the complex Fourier spectrum with a narrow Gaussian window. The filtered signal is then inverse-transformed along with the quadrature signal to produce the filtered analytic signal. The peak amplitude of the envelope of the filtered seismograms (the modulus of the analytic signal) over a constant narrow time interval is then computed at each frequency in the band. In both cases the mean spectral level, V, is given by -- ]C2~ 1 i V(/)I d/, (2) where i v(f) ] is either the modulus of the complex spectrum at frequency [, or the amplitude of the peak of the envelope of the waveform filtered at frequency [, and /1 and f2 are the lower and upper limits, respectively, of the averaging frequency band. To facilitate comparison with earlier work with classical mb's, we take the logarithm of each measure in units of nanometers/second. The scatter of each measure type is defined for a given explosion as the standard deviation across all array elements of this log quantity. In order to relate this scatter to the corresponding scatter in estimated explosive yield, we assume that each amplitude measure depends in a similar way on the yield. That is, we assume that the logarithm of any amplitude measure M~, can be related linearly to the logarithm of the explosive yield log M~ = ax + bxlog(y) (3) where a~ and bx are constants unique to the particular measure type M,. The instability (standard deviation, alogmx), of a particular measure is then given by O'logMx = b~a(log Y) (4) where a(log Y) is the associated standard deviation in the estimate of log Y. If the slope b~ were the same for each measure type, then the relative scatters of the different yield measures could be compared directly. In fact, the slope does vary according to the particular measure type, but remains close to unity for most measure types. When peak amplitude, energy integral, and spectral methods were applied to synthetic explosion seismograms, the constant was found to lie in the range 0.8 to 1.2. Tests using real data from the Graefenburg array show that the logarithms of any pair of measure types are linearly related with a slope near unity. Kraft (personal communication, 1983) reports similar values (0.6 to 1.2) of the slope for yield estimators applied to short-period WWSSN data from events at test sites in Nevada. In order to compare the relative performance of yield estimators, Kraft (1982) used a fixed-slope regression method, fixing the slope at 0.8 for all methods, as this constant value was suggested by the data. In this study we assume a constant slope bx for all yield measures. Even without assuming a particular value for bx, we can assess the relative performance of the measures as yield estimators by comparing the scatters of the logarithms of the various measures themselves. RESULTS The amplitude measures described previously were tested at Graefenburg using data from the underground nuclear explosion of 12 October 1980 which occurred at

7 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1869 the test site in East Kazakh, USSR, an angular distance of approximately 42 from Graefenburg. The ISC magnitude of this event is mb 5.9. Since distances from individual elements of the Graefenburg array to the East Kazakh test site (distance approximately 4600 km) vary by no more than approximately 50 km, distance corrections are unnecessary and are not applied to these data. Peak amplitudes range over a factor of 2.4 at Graefenburg, and measured values of classical mb range from approximately 5.7 to 6.1 across the array. These variations are consistent with those reported for LASA and other arrays of similar size (e.g., Aki, 1973; Shapira and Kulhanek, 1978; Chang and von Seggern, 1980). Measure 1--Peak amplitudes, broadband velocity records. The four peak amplitude X log(v) - broadband == 0.4 log(v) - high-pass filtered 4- log(a/t) - WWSSN simulation o X :> 0 c~ 0.2 "o = 10 c A & I I I I i I I i a b c d a" ~ c" d" Peak Type FIG. 3. Scatter of P-wave peak amplitudes (standard deviation of logarithm) at Graefenburg. The four peak amplitudes (a, b, c, and d) are the same as those in Figure 2a. (Left) Broadband velocity records. (Right) Simulated WWSSN records. measures shown in Figure 2a were applied to the broadband Graefenburg data. The results are presented in Figure 3. The scatter of the logarithms of the four peak amplitudes ranges from 0.12 log units (peak type "d") to 0.42 log units (peak type "a"). After high-pass filtering the broadband data to remove the microseismic noise, the measures show generally reduced scatter. The "a" measure applied to the filtered data performs about as well as the the "d" measure applied to the raw data. Measure 2--Peak amplitudes, simulated WWSSN records. For a narrow-band instrument, the division by T in A/T converts ground displacement obtained from an instrument-corrected A to ground velocity. Thus, the correction both for the shape of the amplitude response and for the period T can be avoided using broadband velocity data. To check if this procedure has any advantages over the conventional approach used on narrow-band instruments, a short-period WWSSN instrument response was convolved with the broadband records and A/T measurements made

8 1870 J. T. BULLITT AND V. F. CORMIER on the simulated WWSSN records. The scatter of the narrow-band measures of amplitude is shown in Figure 3. The measure of A or A/T exhibiting the least scatter in the unfiltered broadband and the narrow-band procedures is the "d" measure (the maximum absolute amplitude in the first five seconds). Because of the improved rejection of microseismic noise in the narrow-band records, however, the scatter of the peak amplitudes is more correctly compared with that of the highpass filtered broadband peak amplitudes. The scatter in both the "a" and "d" amplitude measures is worse for the narrow-band simulation than for the filtered broadband data, while the scatter in the "b" and "c" measures is slightly less. Worse scatter in the narrow-band simulation may be due both to the possibility of sampling spectral holes in the crustal transfer function and the large corrections for the shape of the response when the measured period is not near the center of the pass band. Note, however, that in this case the instrument response was specified and known exactly. The unknown variability of instrument responses over a worldwide network of poorly calibrated instruments can be expected to degrade the performance of conventional narrow-band mb measures. A fairer test would also include several events from different azimuths as well as several array sites. It should be noted that it is not strictly correct to make a direct comparison of corresponding peak amplitudes in narrow-band and broadband records. The phase response of the narrow-band instrument will alter the shape of the broadband P waveform when the narrow-band instrument response function is applied, so that a given peak in one record will not necessarily correspond with that in the other. Nevertheless, such comparisons are useful for identifying the most stable measures of radiated elastic energy. There is a strong correlation at Graefenburg between the apparent azimuth of arriving P waves and P-wave amplitudes. At each of the three-component stations (A1, B1, and C1 in Figure 1), P-wave azimuths and incidence angles were determined by finding the plane wave which best fits the observed P-wave particle motion. P waves recorded at station B1 appear to arrive from a direction some 10 to the south of P waves arriving at the other three-component stations. Station B1, along with its immediate neighbors, also exhibits the highest peak amplitudes recorded at Graefenburg. This is shown in Figure 1. Haddon and Husebye (1978) have interpreted such correlations at the NORSAR array in terms of focusing/defocusing due to the presence of lens-like heterogeneities beneath the array. It appears that similar focusing/defocusing effects are also responsible for much of the observed instability of amplitudes at Graefenburg. Measure 3--Coda amplitudes. The observed stability of coda amplitudes relative to direct waves (Aki and Chouet, 1975) suggests that an amplitude measure which includes the teleseismic P coda amplitude can be a useful yield estimator. If the P coda is generated as a result of scattering of incident P-wave energy by numerous heterogeneities beneath the receiver array, then coda energy should tend to be large at the expense of direct P energy. Yield estimators applied either to the first few cycles of the P wave or to the P coda will therefore tend to underestimate the total radiated energy. Estimators which include both direct P, and P coda should therefore be more stable across an array. Figure 4a shows the integral of squared velocity (the "energy integral") at each of the vertical component stations as it accumulates with time upon arrival of the P wave. In this figure, integration begins 5 sec before arrival of the P wave and extends well out into the coda. The integrals are characterized by a rapid accumulation of energy in the first few cycles of the P wave, which tapers off to a more gradual trend characteristic of the coda. At any

9 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1871 given time the scatter of this integral among stations is considerable (standard deviation = 0.23,og units at P + 30 sec). Although this scatter is due in large part to the scatter in the direct energy that accumulates in the first few seconds (standard deviation = 0.23 log units at P + 5 sec), some of the scatter is also due to variations in the coda level. This is evident in Figure 4b, which shows evaluation of the energy 8.9~ 7.99_ A "3 6.9a: t...,..._.., y-~'''-" =-z_:---: :'-:-- -:-- --= N E S. 90.: =: i= LU 3.90_: 2.9~ - I" /.;') _f_---i2t.zt s~ 9. _J IIII IIII IIII[I I I '"1",L... I"" I"' Time ($ec) -; ca 6.89_ sea: B = 4.ca: ~3 9~ == LU 2.9~ 1,9d 9, '"',""l'"l'"'... 1'"'31...,""1'"'1"'s1'','"' Time (sec) FIG. 4. Cumulative integral of squared velocity at each station at Graefenhurg. (A) Integration commencing 5 sec before the direct P arrival. (B) Integration commencing 5 sec after the direct P arrival. The largest contribution to the integral is due to the direct P wave, whose amplitudes vary widely across the array. Substantial scatter persists, however, when the direct P energy is excluded from the integration. integral beginning 5 sec after P onset. In this case, the signal consists entirely of scattered energy. The scatter of the integral is increased slightly in this case (standard deviation = 0.27 log units P + 35). The scatter of the logarithm of the rms amplitude is slightly smaller for time windows which include the direct P wave. In general, the scatter decreases as the

10 1872 J. T. BULLITT AND V. F. CORMIER time window is increased in duration. This is most likely due to the longer time windows capturing a larger fraction of the total energy associated with the P wave. As can be seen by comparing these figures, stations exhibiting large peak (direct P) amplitudes also exhibit high coda levels. The coda and the direct P thus appear to be focused/defocused in step. A significant fraction of the coda energy is therefore generated before the wave front encounters the focusing/defocusing structure beneath the array. The experimental error associated with the time-domain measures is quite small. Peak amplitudes were determined using a semiautomated peak-picking and interpolation algorithm. The results of this algorithm were always compared with the original seismograms to insure that the correct peaks had indeed been picked. Experimental errors introduced by interpolation between the data points surrounding a peak or on either side of a zero-crossing result in no more than a log unit variation in the standard deviation. In the rms coda measure, the principal source of experimental error is the slight variation in the position of the averaging window. An upper limit to the experimental error in the estimate of the scatter for this method is 0.01 log units. Measures 4 and 5--Frequency domain. Mean spectral levels of broadband velocity were computed for each of the vertical-component records at Graefenburg. At each station, a 6-sec time window beginning 1 sec before P onset was extracted, tapered, and Fourier transformed. The amplitude spectra were smoothed and the values over a chosen frequency band averaged as shown in equation (2). A variety of frequency bands were tested using this method (Table 1), including those suggested by Shapira and Kulhanek (1978) and Kraft (1982). Best results (i.e., least scatter) were obtained using the band 0.6 to 3.0 Hz, for which the scatter is 0.11 log units. The greatest scatter was found in the band 1.0 to 2.0 Hz (0.16 log units). Mean spectral levels were also computed using the VFM method of Savino et al. (1980). Figure 5 shows the envelopes of a suite of narrow-band filters applied to the data recorded at array element B3. The amplitude at a given frequency is taken as the amplitude of the peak nearest in time to the time of the first P-wave peak on the record filtered at 1.0 Hz. The least scatter using the VFM method (0.14 log units) was found in the band 0.33 to 3.0 Hz. The greatest scatter (0.17 log units) was found in the band 1.0 to 3.0 Hz. The scatter using this method is comparable to that using the conventional FFT and smoothing method described previously. The precision of these spectral estimates of amplitude scatter is limited by their relative insensitivity to the particular frequency band chosen. Small variations in the width of the frequency band and small variations in the position of the time window typically result in variations in the estimate of the scatter across the array amounting to 0.02 log units. This figure is interpreted as the experimental error associated with a given estimate of scatter. The observed scatter spans a range of no more than about 0.05 log units for all the frequency bands tested. This variation is almost within the range of the experimental error (+0.02). We therefore cannot conclude with confidence either that one spectral method performs significantly better than another or that one frequency band is significantly better than another. We conclude that the scatter calculated using either spectral method is about 0.15 log units, with an estimated error of log units. Summary of Graefenburg results The scatter of the amplitude measures tested at Graefenburg is summarized in Figure 6. The error bars show the estimated experimental errors associated with each measure type.

11 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1873 The coda rms measure performs slightly better than the peak amplitude measures when long (60 sec) time windows are used. Exclusion of the direct P wave from the averaging window in the rms coda measure increases the scatter slightly. Frequencydomain methods perform only about as well as the best of the peak-amplitude measures. At Graefenburg, the energy associated with the direct P wave, whether measured in terms of peak amplitude or of rms velocity in the first 5 sec, varies from station Frequency (Hz) a=lo I.. i... i i i i, I..... FIG. 5. Envelopes of narrow-band filtered seismogram from array element B3 (Graefenburg). Frequencies shown are the center frequencies of the filters. Filter width parameter is a = 10. The unfiltered broadband seismogram is shown at the bottom. sece I to station in the same way as the coda energy. In other words, stations with high peak amplitudes tend to exhibit large coda amplitudes, and vice-versa. This observation supports the interpretation that a large fraction of the coda is generated before the P wave encounters the lithosphere beneath the array. In this case, the direct P wave propagates upward to the structure beneath the array followed immediately by previously-generated coda energy. The P wave and coda energy are then focused and defocused in the same fashion by heterogeneities beneath the array. The relationship between direct and scattered P amplitudes is not, however,

12 1874 J. T. BULLITT AND V. F. CORMIER simply one-to-one. In general, the coda level tends to increase more rapidly than the peak amplitude. This is confirmed by the observed positive correlation at Graefenburg between the complexity (the reciprocal of the ratio of integrated amplitude in the first 5 sec to that in the next 30 sec; Douglas et al., 1973) and the rms coda amplitude. The often observed stability of P-coda amplitudes relative to direct P amplitudes has been interpreted in terms of multiple scattering by smallscale heterogeneities in the earth (e.g., Aki, 1973; Douglas et al., 1973). The P coda presumably becomes stable as a result of averaging over a large number of scattering paths (Aki, 1982). At Graefenburg, however, the coda appears not to be as "saturated" with scattered energy as would be expected for waves propagating over long i I i I i,i i ( i i i i 0.25 I Time Domain Frequency Domain I I I,,-,, G) 0 "~ 0.20 E c o c 0.15 o o= > GI lo 1o c 0.10.D 0.05 I I I I l J i I I I la lb lc ld 3a 3b 3c 3d 3e 40 4g 5d 5f Measure Type FIG. 6. Summary of relative performance of all measures tested at Graefenburg. Time-domain measures were applied to high-pass filtered records (cutoff frequency 0.3 Hz). For the two frequencydomain methods, scatters are shown only for the averaging windows that yielded the greatest and least scatter. scattering paths. Thus, some of the coda energy appears to have been generated along a relatively short path in the crust below the receiver. These features of the scattered P energy present in the Graefenburg records are highlighted in Figure 7. High-pass filtered broadband records from three stations are shown with their corresponding peak amplitudes, coda amplitudes (rms velocity in the 30-sec time window beginning 5 sec after P), and complexity. Stations B2 and B3 are separated by no more than 15 km, while station C2 is about 55 km to the south of the other two (see Figure 1). These seismograms are representative of the trend seen across the array: as peak amplitude increases, so does coda amplitude, but at a much faster rate. These observations suggest that while the P-coda amplitudes are slightly more

13 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1875 stable than direct P amplitudes, they may also be subject to the same focusing/ defocusing effects that affect direct P. Focusing/defocusing beneath the NORSAR array, however, seems to affect direct P more strongly than P coda, and P-coda amplitudes can be significantly more stable than direct P amplitudes there (Baumgardt, 1983; Ringdal, 1983). Stability of P coda relative to direct P is thus a regional effect which is not observed at all seismic arrays. At Graefenburg, then, we see evidence of scattering taking place at two sections along the source-receiver path: in the crust immediately beneath the receivers, and somewhere along the path extending from the source to the bottom of the crust beneath the array. It is not possible, however, to determine from these observations E32 ~1o Seconds FIG. 7. Seismograms from three stations in the Graefenburg array, showing the large variation of peak and coda amplitudes of the P wave. The numbers shown below each seismogram are, respectively, peak velocity, coda amplitude (rms velocity in the 30-sec time window beginning 5 sec after the P arrival), and complexity. Velocities are in units of nanometers/second. alone what relative proportions of the coda energy are generated near the source and along the teleseismic ray path (Dainty, personal communication, 1983). The observed instability of all yield measures tested at Graefenburg is strongly affected by three-dimensional structural heterogeneities beneath the array. GDSN NETWORK Guided by the results of the tests made on the Graefenburg data, we tested a subset of the Graefenburg yield measures on data from the GDSN (Global Digital Seismic Network). Short-period GDSN records of underground nuclear explosions at the Soviet test site in East Kazakh, USSR were deconvolved to remove the effect of the instrument response and converted to velocity records prior to all subsequent

14 1876 J. T. BULLITT AND V. F. CORMIER processing. All seismograms were high-pass filtered at 0.5 Hz to equalize the level of microseismic noise among stations of the network. P-wave amplitude measures ld, 3b, 3c, and 4a, (Table 1) were calculated for each seismogram. Data normalization Because the stations in the GDSN network span a wide range of distances from the test sites, corrections for distance and differential intrinsic attenuation must be applied prior to interpretation of the amplitude data. Still more important, however, is the effect of lateral variations in earth structure which will alter recorded P waveforms according to the particular path traveled by the rays. Thus, teleseismic arrays present a problem in comparing the variances of the different methods in equivalent yield units. Using digitized WWSSN data and published yields, Kraft (1982) established empirical relations between different magnitude measures and yields. Baumgardt (1983) established similar relations using NORSAR and SDSC data. Because the responses of the instruments in the GDSN network differ from those in these other networks, however, and because published yields are unavailable for the events used in this study, these empirical relations cannot generally be applied to, or determined for, our data. The relative performance of the various methods can, however, be compared by using to the following normalization procedure. Reference station (effects of varying source site). Consider a suite of N events at a particular test site each of which radiates P waves recorded at M stations. Let aii be the amplitude observed at station i for event j. We select one station to be a reference station (the oth station), and one event to be a reference event (the pth event). We can cancel variations in the measured amplitudes which are due to source size variation by normalizing each measurement, aii, to the measurement at a reference station aoi. That is, for each event divide the amplitude at the ith station by that at the reference station. The normalized amplitude is then a~ = aij (5) aoj where aoi denotes the amplitude measured at reference station o for event j. The average of the logarithm of this normalized measure over a suite of events of similar size at a test site is then, log(a ) -- log. (6) The corresponding standard deviation, a. is also estimated. (The dot notation, borrowed from Huitson (1966), denotes averaging over the index replaced by the dot). At a given station the normalized amplitudes will vary from one event to another as the source location moves around the test site. The standard deviation is a measure of this variation of source site at a given station and will, in general, differ from one amplitude measure to another. Thus, a comparison of the standard deviations can suggest which measures perform better at a given station. Note that the normalized amplitude is dimensionless. While we cannot compare these normalized amplitudes directly with the corresponding amplitudes obtained in the Graefenburg study, we can compare them among themselves to assess the relative performance of each measure.

15 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1877 Because the corner frequency of the far-field P-wave spectrum depends on source size, amplitudes do not increase uniformly over all frequencies as source size is increased. This normalization procedure is therefore strictly valid only for a set of events which are known a priori to have approximately equal yield. If events spanning a wide range of yield are used, the effects of the scaling of corner frequency as the inverse cube-root of yield (Mueller and Murphy, 1971) will introduce additional scatter to the yield measures. Reference event (effects of varying receiver site). For a given event this normalized quantity will vary from station to station as a result of geometric spreading and regional differences in attenuation. To cancel these effects of different ray paths, we can apply an alternative normalization by dividing the amplitudes measured at a given station by the amplitude measured at that station from a reference event. That is, with event p selected as the reference event, the normalized amplitude becomes,, _ ao aii- --. (7) The average of the logarithm of this measure over all stations is then evaluated for each event air 1 1 log(aijl. aqj = ~ ~ log(a~) = ~ ~ \aiv/ (8) The standard deviation, av.j, is then a measure of the stability of the particular yield estimator across the network of stations. The robustness of statistical estimates of amplitude means and variances generally increase as the sample size increases. Because of the sparseness of the GDSN network, however, it is difficult to find seismograms of a large number of events recorded at a large number of stations. In this study, 10 samples {events) from each of four stations were used in the reference station normalization; for the reference event normalization nine samples (stations) from each of six events were used. Only events within 0.3 mb units of mb 5.9 (ISC) were used. Both normalization procedures were used on the deconvolved GDSN records. Summary of GDSN results Reference station. The reference station normalization [equations (5) and (6)] was applied to the four selected amplitude measures at stations ANMO, CTAO, KAAO, and MAJO. The scatter of each measure was calculated for each station after averaging over a suite of 10 East Kazakh events. The scatter of the four measures for two reference stations (ANMO and MAJO) are shown in Figures 8 and 9. The uncertainty in the value of the scatter for a given measure is estimated from the experimental errors encountered in the Graefenburg study. We assume the experimental error in the estimate of the scatter of a given unnormalized measure is the same for both Graefenburg and GDSN data, as amplitudes were calculated using identical procedures. When the data are normalized in the case of GDSN data, however, both the numerator and denominator in the normalization contribute equally to the error, with the result that the error in the normalized amplitude is approximately ~f2 times that of each of the unnormalized amplitudes. We conclude that the uncertainties in our estimates of the scatters are approxi-

16 1878 J. T. BULLITT AND V. F. CORMIER 0.4 X Peak (ld) '~' RMS Coda (3c) + RMS Coda (3b) FFT ( Hz) Reference Station: ANMO > D Q 0.2 lo 0 "1o c t t 0.1 I I I CTAO KAAO MAJO Test Station FIG. 8. Relative performance of four amplitude measures tested on deconvolved SRO records of 10 East Kazakh explosions. Data normalized to reference station ANMO. See text for details of data normalization procedure. 0.4 X Peak (ld) h, RMS Coda (3c) + RMS Coda (3b) FFT ( Hz) Reference Station: MAJO T a "o 0~ '1o o~ I I I I I I ANMO CTAO KAAO Test Station FIG. 9. Same as Figure 8, but normalized to reference station MAJO.

17 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1879 mately for the rms coda measures, _0.01 for the peak amplitude measures, and for the spectral measures. These uncertainties are indicated in Figure 8 by the error bars. The two coda measures generally perform better than either the peak timedomain amplitude or the spectral magnitude. The difference between the four measures at station MAJO is considerably smaller than at the other stations. The behavior of the measures at MAJO may be anomalous because of the relatively complex waveform of East Kazakh events observed at this station. The complexity at MAJO may be a product of multipathing in the Japanese slab. At no station does 0.4 X Peak (ld) & RMS Coda (3c) -I- RMS Coda (3b) FFT ( Hz) Reference Event: >. "o '1o c O I I I I I Test Event FIG. 10. Relative performance of four amplitude measures tested on deconvolved SRO explosion records from nine stations. Data normalized to reference event 10. the spectral amplitude measure perform significantly better than the peak time domain measure. There is a suggestion that the coda measure performs better when the P wave is excluded from the average window, although this may not be significant. Reference event. Normalization of the data to a reference event [equations (7) and (8)] yields similar results. The normalized amplitudes were averaged over nine stations in the network and the standard deviations calculated. The results from two typical reference events (events 10 and 31) are shown in Figures 10 and 11. The error bars show the estimated experimental errors as previously described. Here, the pattern is more consistent: the two coda measures perform better than the other measures. The spectral magnitude usually performs better than the peak timedomain amplitude. Similar results were obtained with other events selected as reference events. The GDSN seismograms were high-pass filtered at 0.3 Hz to reduce the micro-

18 1880 J. T. BULLITT AND V. F. CORMIER seismic noise level. At some GDSN stations, however, considerable microseismic energy may be present at frequencies above 0.3 Hz. If a large amount of microseismic energy passes through the filter, the rms coda amplitude measure may exhibit spuriously small scatter, because the noise level may, in fact, be the most stable feature in the seismograms. In order to test whether the observed stability of the rms coda amplitudes was, in fact, an artifact of the high noise levels, the GDSN records were high-pass filtered again at 0.5 Hz, and the four amplitude measures recalculated. The resulting scatters are slightly different at all stations for each measure, but the relative performance of measure types is preserved: coda rms performs better than the peak amplitude or spectral methods, and the spectral method does not perform significantly better than the peak amplitude measure. 0.4 X Peak (ld) ARMS Coda (3c) 4- RMS Coda (3b) )E FFT ( Hz) Reference Event: > C~ "o 0.2 "o c /) 0.1! i I I to t3 t4 32 I 34 Test Event FIG. 11. Same as Figure 10, but normalized to re~rence event 31. CONCLUSIONS Digital broadband velocity seismograms facilitate computation of a wide range of physically meaningful measures of radiated elastic energy. Three independent tests of the stability of several estimators of yield were conducted using: (1) amplitudes from a local array at teleseismic distance; (2) amplitudes from a teleseismic network, normalized to a reference station; and (3) amplitudes from a teleseismic network, normalized to a reference event. In each case, spectrally averaged magnitudes perform only about as well as the best measure of amplitude in the time domain, the maximum peak or trough of broadband velocity in the first 5 sec. The rms amplitude of broadband velocity in a long time window in the P coda is slightly more stable than the other measures tested. These conclusions assume a constant slope, for all measures, in the log yield-log amplitude relations. The amplitude

19 ESTIMATING SOURCE SIZE AND EXPLOSION YIELD 1881 scatters must be adjusted by the corresponding slope factor in order to make direct comparisons of yield scatter. While comparisons of the stability of various yield estimators are much more difficult for a global array when yield data are unavailable, it is still possible to draw meaningful inferences of the relative performance of yield measures by normalizing the measures to reference stations and reference events. Across an array having an aperture of 100 km, or for an array of sources of the same dimension across a test site, all measures still exhibit scatter, including the best coda and spectral measures. The behavior of travel time, azimuth, and slowness anomalies observed at local arrays suggest that this scatter in amplitudes is due to focusing/ defocusing effects of three-dimensional structure beneath the source and receiver. For some source-receiver paths, focusing/defocusing can affect the coda level in the same way as it affects the amplitudes in the first several cycles. When the amplitude of the first several cycles is large or small, so is the coda amplitude, although the relationship is not one-to-one. This suggests that a significant fraction of the coda energy is generated by scattering along the ray path at points other than in the crust beneath the receiver. ACKNOWLEDGMENTS Tae Im assisted with the GDSN data analysis. The Graefenburg data were collected and supplied by George Choy. An anonymous reviewer made several helpful comments. This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract F C REFERENCES Aki, K. (1973). Scattering of P waves under the Montana LASA, J. Geophys. Res. 78, Aki, K. and B. Chouet (1975). Origin of coda waves: source, attenuation, and scattering effects, J. Geophys. Res. 80, Bache, T. C. (1982). Estimating the yield of underground nuclear explosions, Bull. Seism. Soc. Am. 72 (Part B), $131-$168. Bache, T. C., S. M. Day, and J. M. Savino (1979). Automated magnitude measures, earthquake source monitoring, VFM discriminant testing and summary of current research, SSS-R , S-cubed; La Jolla, California. Baumgardt, D. R. (1983). Teleseismic P-coda stability and coda magnitude yield estimation, SAS-TR , ENSCO Signal Analysis Systems Division, Springfield, Virginia. Blandford, R. R. and R. H. Shumway (1982). Magnitude-yield for nuclear explosions at the Nevada test site and Algeria: joint determination with station effects and with data containing clipped and lowmagnitude signals, SDAC-TR-81-16, Teledyne Geotech, Alexandria, Virginia. Butler, R, and L. Ruff (1980). Teleseismic short-period amplitudes: source and receiver variations, Bull. Seism. Soc. Am. 70, Chang, C. A. and D. H. yon Seggern (1980). A study of amplitude anomaly and mb bias at LASA subarrays, J. Geophys. Res. 85, Douglas, A., P. D. Marshall, P. G. Gibbs, J. B. Young, and C. Blarney (1973). P signal complexity reexamined, Geophys. J. Roy. Astr. Soc. 33, Haddon, R. A. W. and E. S. Husebye (1978). Joint interpretation of P-wave travel time and amplitude anomalies in terms of lithospheric heterogeneities, Geophys. J. R. Astr. Soc. 55, Harjes, H.-P. and D. Seidl (1978). Digital recording and analysis of broadband seismic data at the Graefenburg (GRF) array, J. Geophys. 44, Huitson, A. (1966). The Analysis of Variance, Charles Griffin and Co., London, England. International Association of Seismology and the Physics of the Earth's Interior (IASPEI) (1979). Commission on Practice, Canberra, Australia. Kraft, G. D. (1982). An evaluation of several time and frequency domain magnitudes for explosion yield estimation, (abstract) EOS, Trans. Am. Geophys. Union 63, Marshall, P. D., D. L. Springer, and H. C. Rodean (1979). Magnitude corrections for attenuation in the upper mantle, Geophys. J. Roy. Astr. Soc. 57,

20 1882 J. T. BULLITT AND V. F. CORMIER Mueller, R. A. and J. R. Murphy (1971). Seismic characteristics of underground nuclear detonations, Bull. Seism. Soc. Am. 61, North, R. G. {1977). Station magnitude bias--its determination, causes, and effects, Semiannual Technical Summary , MIT Lincoln Laboratory, Cambridge, Massachusetts. Ringdal, F. (1983). Magnitudes from P coda and Lg using NORSAR data, DARPA/AFOSR Seismic Research Symposium, May 1983, Rosario Resort, Eastsound, Washington. Savino, J. M., C. B. Archambeau, and J. F. Masso (1980). Discrimination results from the Priority 2 stations, SSS-R , S-cubed, La Jolla, California. Shapira, A. and O. Kulhanek (1978). Conventional and spectral short-period body-wave magnitudes, Bull. Seism. Soc. Am. 68, EARTH RESOURCES LABORATORY DEPARTMENT OF EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS Manuscript received 10 November 1984 The present address of J. T. Bullitt is: Terrametrics Research, 751 Main Street, Waltham, Massachusetts