a comparison of regional-phase amplitude ratio measurement...

Bulletin of the Seismological Society of America, VoL 87, No. 6, pp. 1613-1621, December 1997

A Comparison of Regional-Phase Amplitude Ratio

Measurement Techniques by Arthur J. Rodgers, Thorne Lay, William R. Walter, and Kevin M. Mayeda

Abstract We compare several procedures for measuring regional-phase amplitude ratios commonly used in discrimination studies. Amplitude measurements are made on both raw velocity-proportional broadband seismograms and instrument-deconvolved displacement seismograms in the time and frequency domains. Pn/Lg and Pg/Lg ratios are measured on vertical-component waveforms for regional earthquakes observed at the Global Seismic Network (GSN) station ABKT (Alibek, Turkmen- istan). Time-domain amplitude measurements are made on narrow-band filtered waveforms using signal energy measures given by the absolute mean, rms, and envelope mean, and peak measures given by the absolute maximum and envelope maximum. Frequency-domain measurements are made by computing the logl0-mean amplitude within a narrow band from the broadband spectrum of each windowed phase.

Time-domain amplitude ratios for raw velocity and instrument-deconvolved displacement seismograms are very similar (linear correlations >-0.97), indicating that the instrument response does not affect the time-domain amplitude ratio measurements for the broadband GSN data at the frequencies studied (0.75 to 9.0 Hz). Time- domain amplitude ratios made using the energy or peak measures are well correlated among themselves (linear correlations >-0.97). However, the energy and peak measures are slightly less well correlated with each other (linear correlations between 0.87 and 0.99). For the time-domain measures, the correlations generally degrade, and the scatter increases for the higher-frequency bands. Time- and frequency-domain measurements are well correlated for the lowest-frequency band (0.75 to 1.5 Hz). However, as the frequency band increases, the correlations decrease and the slopes deviate from 1.0. Time-domain amplitude ratios (for both Pn/Lg and Pg/Lg) are consistently larger than the frequency-domain amplitude ratios. Investigation of the frequency spectra of broadband and narrow-band filtered phases revealed that significant energy from outside the passband, particularly from lower frequencies, possibly biases the time-domain measurements. Log averaging the spectral amplitudes in a given passband before forming the amplitude ratios does not bias the measurements to the low end of passband. Better agreement between time- and frequency-domain measurements is found when linear averaging of the spectrum is used. These observations suggest that with care, time- and frequency-domain measures can be made to agree. We suggest that log-averaged frequency measures look promising for discriminant measures because (1) frequency-domain measurements offer complete control of the frequencies that contribute to the measurement, and (2) log averaging of the spectra does not overweigh spectral amplitudes associated with lower frequencies within the passband. However, because we consider only earthquake data, we cannot evaluate the discrimination performance of the various measurement techniques.

Introduction

Regional broadband seismic data have proven to be ef- fective for discriminating explosions from earthquakes. Dis- crimination at regional distance is especially critical for

smaller e v e n t s (m b <= 4.5) as these events may not be de- tected and discriminated teleseismically (Blandford, 1981; Pomeroy et al., 1982). Amplitude and spectral ratios of re-

1613

1614 A.J. Rodgers, T. Lay, W. R. Walter, and K. M. Mayeda

gional phases, particularly Pn, Pg, and L g at frequencies greater than about 3.0 Hz, have been shown to separate explosion and earthquake populations in many cases (e.g., Baumgardt and Young, 1990; Kim et al., 1993; Walter et

al., 1995; Taylor, 1996; Hartse et al., 1997). Complicating the situation, however, are path effects. Regional variations in geologic, tectonic, and topographic structure lead to great variability in regional-phase amplitudes. Furthermore, re- cordings of regional events can be noisy due to poor signal excitation and attenuation, especially at high frequencies and distances greater than several hundred kilometers. Nonethe- less, measurements of regional-phase amplitude ratios can provide a valuable tool for identifying small seismic events under the Comprehensive Test Ban Treaty (CTBT) provided that variations in earthquake-generated regional phases are determined for each monitoring station and region. Efforts are under way to map variations in regional-phase amplitude ratios and to understand the path effects in support of CTBT monitoring.

Complicating comparison of various P / S discrimination

results is the fact that regional-phase amplitude measurements have been made in a number of ways, including techniques operating in either the time or frequency domains. Time-domain measures include peak amplitude measures, rms amplitudes, and envelope measures on instrument-corrected or uncorrected data, for various instrument or filter band responses. Some examples include peak amplitude measurements on uncorrected WWSSN short-period or filtered data by Murphy and Bennett (1982), Bennett and Mur- phy (1986), and Taylor et al. (1989). Rms and envelope measures on data filtered to various passbands were favored by Banmgardt and Young (1990), Zhang and Lay (1994), and Hartse et al. (1997). Frequency-domain methods in- volving spectral amplitudes are generally derived from data that have been cut and tapered with various types of func- tions and then fast-Fourier transformed. Again, the data may or may not have been corrected for instrument response. In the frequency domain, the division of uncorrected spectra mathematically cancels out the effects of the instrument response, so deconvolution of the instrument response is less

1000 2000 4000 8000 Elevation (m).

~0 o 40 ° 45 ° 50 ° 5 5 ° 6 0 ° 6 5 °

5ff

~ o

So

45 °

40"

So

..... ~i:!ii~i~! ~

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•

~ ~ X Kazahh Platform "

!~l~%~ii ~ • ABKT

Ardbian Shield ........... ;~ii!Jiiiii!~iiii!:ill j p

30 ° 35 o

45° 50 ° 55 ° 60" 65° 70"

Figure 1. Map of earthquakes (circles) used in this study recorded at the GSN station ABKT (triangle). Topographic relief is plotted and indicated by the scale. Major tectonic units are labeled.

75 °

A Comparison of Regional-Phase Amplitude Ratio Measurement Techniques 1615

of an issue. Examples of frequency-domain-based studies include Kim et al. (1993), Walter et al. (1995), and Taylor (1996). In order to compare these and other studies, it is important to know what differences are introduced by em- ploying different methodologies. Furthermore, as research- ers contribute regional discriminant calibrations to U.S. and international agencies, efforts to understand and possibly standardize data-processing procedures will advance opera- tions. The true test of a measurement technique is to evaluate how well it discriminates. If one technique shows superior separation of earthquake and explosion populations, then it is clearly the technique to employ. Because we consider only earthquakes, we cannot address this issue.

In this article, we investigate several procedures making regionai-phase amplitude ratio measurements. Pn/Lg and Pg/Lg amplitude ratios are computed using both time- and frequency-domain methods on raw velocity and instrument- deconvolved displacement seismograms. Results are compared, and the causes of differences in the measurements are investigated.

Regional Earthquake Data at A B K T

The data used in this study were recorded at the Global Seismic Network (GSN) station ABKT in Alibek, Turkmen- istan. This station employs a Streckeisen STS-2 broadband seismometer with flat velocity response from approximately 0.01 to 10 Hz (sample rate = 20/sec). We collected waveform data recorded at ABKT for earthquakes in the region reported by the National Earthquake Information Service- Preliminary Determination of Epicenters (NEIS-PDE) for the years 1994 and 1995. The selected data had reported depths less than 50 km, and body-wave magnitudes, m b, were greater than or equal to 4.0. The events, paths, and region studied are shown in Figure 1.

All waveform data were previewed, and a Pn arrival was picked. Data with clearly low signal-to-noise ratio were discarded. For this study, only the vertical component was considered. The instrument response was removed, and the data were integrated to displacement. Regional phases were isolated with the following group-velocity windows: Pn 8.0 to 6.2 km/sec, Pg 6.2 to 5.0 km/sec, andLg 3.6 to 3.0 km/sec. In order to reduce possible biases due to poor event locations and timing errors, all group velocity windows were shifted such that Pn arrives at 7.9 km/sec. These shifts were typi- cally less than + 10 sec. Noise was sampled in a 35-sec window ending 5 sec before the Pn arrival. Figure 2 shows an example of the phase windowing.

Propagation of regional phases in this region is strongly influenced by the complex topographic and tectonic structure. High elevations of the Turkish-Iranian plateau are associated with recent volcanic activity and low sub-Moho P- wave velocities (Hearn and Ni, 1994). Regions of low Pn velocities are strongly correlated with a zone of inefficient Sn propagation (Kadinsky-Cade et at., 1981; Rodgers et al., 1997). Low Q within the crust of the Iranian plateau leads

ABKI.BHZ 1994 54 11 54 rob= 5.3 Distance= 823 km Filtered 0.75-9.0 Hz

50 100 150 200 250 500 550 400 Time After Event, seconds

Figure 2. Recording of an eastern Iran earthquake at ABKT showing the windowing of the noise, Pn, Pg, and Lg phases. Group velocity marks are shown (km/sec) and the trace was passband filtered (0.75 to 9.0 Hz).

to inefficient Lg propagation (Nuttli, 1980; Wu et al., 1996). The topographic relief associated with the boundaries of the Turkish-Iranian plateau has been shown to weaken and/or block propagation of the Lg phase (Kadinsky-Cade et at., 1981; Rodgers et al., 1997). Figure 3 illustrates the variability in Pg and Lg propagation for the region. Pg/Lg amplitude ratios were made as described below using the time- domain rms amplitudes in four frequency bands. The Pg/Lg ratio for each path is plotted and symbol coded. Note that the Pn to pre-Pn amplitude ratio (signal-to-noise) cutoff is 2:1 and that many data for paths crossing the Iranian plateau that survive this criterion for lower frequencies (0.75 to 1.5 Hz) fail at high frequencies (6.0 to 9.0 Hz). This suggests that attenuation is higher in the Iranian lithosphere relative to the Kazahk Platform. For the lowest-frequency band, 0.75 to 1.5 Hz, paths crossing the Iranian Plateau generally show weak Lg (Pg/Lg = 1.0), whereas paths crossing the Kazahk Platform (with similar distances to ABKT) show strong Lg (Pg/Lg <-_ 0.5).

The complicated regional-phase behavior of this region makes it well suited for evaluating regional-phase measurement techniques because wide ranges of Pn/Lg and Pg/Lg ratios are observed. However, for monitoring purposes, azimuthal variations in regional-phase amplitude ratios com- plicate the use of a single distance correction. Investigation of the azimuthal dependence of regional-phase propagation at this station and distance corrections will be presented in a future study.

Time-Domain Measu remen t s - -Methodo logy

Time-domain measurements of phase amplitudes were made by narrow-band filtering the waveforms using a 4-


ABKT Pg/Lg A?mPeli2d2R2tiLs : P g / L : p : ; 5 L ' : : ? f f i 0 c , ie? : in termedia te

P n / n o i s e > 2.0 o P g / L g > 1.0, Lg weak

30° 0 ° $0° 13 ° S 30° ° ~O° °

0.75-1.5 Hz 1.5-3.0 Hz

S 30° ° N° ° 30° ° za°

so° , 0 ° 50 ° 6 ° ° 70° , 0 ° 50° 60 ° 7°°

3.0-6.0 Hz 6.0-9.0 Hz

Figure 3. Map of Pg/Lg ratios for each frequency band. Data are plotted at the event location and are shown with different symbols (key upper right).

pole, 2-pass Butterworth filter (bands: 0.75 to 1.5, 1.5 to 3.0, 3.0 to 6.0, 6.0 to 9.0 Hz). Pn, Pg , and L g phases were isolated as described earlier. For each windowed, de-meaned phase, s(t) , we measured the absolute mean (L1 norm):

abs. mean = ll(t), where l l ( t ) = Is(t)l; (1)

the rms (L2 norm):

rms = + [s(t)2]1/2; (2)

thus, envelope mean:

env. mean = e(t), where e(t) = Is(t) 2 + H[s(t)]2] 1/2 (3)

an d H[s( t)] is the Hilbert transform; the absolute maximum, abs. max. = max[1 l(t)]; and the envelope maximum, env. max. = max[e(0]. The absolute mean, rms, and envelope mean are measures of the average energy in the window, whereas the absolute maximum and envelope maximum are

measures of the peak energy. Time-domain measurements for each phase must be made on filtered waveforms for each passband separately.

T i m e - D o m a i n M e a s u r e m e n t s - - R e s u l t s

The waveform data at ABKT were recorded as digital counts proportional to ground velocity. After deconvolution of the instrument response and integration, the trace repre- sents true ground displacement. Comparisons of the P n / L g

amplitude ratios measured in the time domain from raw velocity and instrument-deconvolved displacement seismograms are shown in Figure 4. Rms amplitudes were used, and the ratio of the P n amplitude to the pre-Pn noise amplitude was required to be 2.0 or greater. The comparison is shown for the same four frequency bands as Figure 3. The individual l o g l o [ P n / L g ] ratios are plotted as circles and are fit to a straight line. Also shown in each panel are the number of points, linear correlation, standard deviation about the best-fit straight line, and the slope of the fit. The raw velocity


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i . . . . i . . . .

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Figure 4. Comparison of Pn/Lg amplitude ratios (rms amplitude in the time domain) for raw velocity and instrument-deconvolved displacement for the four passbands. The pre-Pn noise to Pn amplitude ratio was required to be greater than or equal to 2.0. The data (circles) were fit to the straight (solid) line. Standard deviation (l-a) in the fit are shown as dotted lines. The passband, number of data, n, linear correlation, r, standard deviation about the best-fitting straight line, sd, and the slope of the fit, k, are shown.

and instrument-deconvolved displacement give very similar Pn/Lg amplitude ratios. The slopes and linear correlations are all close to 1.0. As noted above, the number of data surviving the signal-to-noise criterion rapidly decreases as the frequency passband is increased. Also note that the lower Pn/Lg ratios (loglo[Pn/Lg] --< 0.0) are preferentially discarded due to the signal-to-noise criteria as mentioned above.

Comparison of the various time-domain measurements for Pn/Lg and Pg/Lg are complied in Tables 1 and 2, re- spectively. Some time-domain measurements give very con- sistent results. The absolute and envelope measurements, both mean and maximum, are particularly strongly related. The rms (energy measure) and the absolute maximum (peak measure) are not correlated as well as the other pairs shown. The standard deviation generally increases and the linear correlation decreases as frequency increases.

F requency-Domain M e a s u r e m e n t s - - M e t h o d o l o g y

Frequency-domain measurements were made by windowing the noise and each phase as described earlier, de- meaning and applying a 5% cosine taper to the trace, then computing the frequency spectrum for a broad frequency range (0.03 to 9.99 Hz) by fast-Fourier transform (FFT). The

frequency spectrum was resampled evenly in log frequency, smoothed, and stored. Then the log~o-mean spectral amplitude was computed for the same frequency bands considered above (0.75 to 1.5, 1.5 to 3.0, 3.0 to 6.0, and 6.0 to 9.0 Hz). Only frequencies within the passband were used to compute the logw-mean spectral amplitude of each phase. An im- mediate advantage of frequency-domain techniques is that the broadband spectra of each phase need only be calculated once, and the operation of computing the logl0-mean spectral amplitude within a passband is extremely fast. Another advantage of frequency-domain techniques is that the instrument response and source-time function become multipli- cative factors instead of convolutions with the Greens function. This means that the frequency-domain instrument and source-time effects explicitly cancel in P/S ratios. Thus, frequency-domain P/S ratios do not depend on instrument type or magnitude.

Compar ing Time- and Frequency-Domain Measurements

Comparison of the time- and frequency-domain Pg/Lg- phase amplitude ratios is shown in Figure 5. Statistics for comparison of time- and frequency-domain Pn/Lg and Pg/Lg amplitude ratios are compiled in Tables 1 and 2, re-


ABKT Pg/Lg chan: BHZ, Pn/pre-Pn noise > 2.0

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, , . i . . . . i . . . . E . . . . i . . . . t . . . . -1.0 -0.5 0.0 0.5 1.0 1.5

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1.5 I I ' ' l . . . . r . . . . i . . . . i . . . . i . . . . ABKT 6.0-9.0 H z

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. . . . ~ . . . . i . . . . P i l l ¸1 . . . . t . . . . ] 1.5 ABKT |

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Logl0[Pg/Lg] time domain, rms

Figure 5. Comparison of Pg/Lg amplitude ratios measured in the time (instrument-deconvolved displacement, rms) and frequency domains, similar to Figure 4.

spectively. Time-domain measurements were made on instrument-deconvolved displacement data using the rms measurement. For the lowest frequency band (0.75 to 1.5 Hz), the measurements compare quite favorably, although they are more scattered than most of the time-domain comparisons. However, as the passband frequencies increase, the correlations decrease, the slope deviates from 1.0, and the data become more scattered. Scatter is partly due to signal to noise. The linear correlation decreases to 0.59 for the highest frequency band. We found that increasing the signal- to-noise criteria reduced the standard deviations, but the linear correlation and slope were largely unaffected, and the number of data was strongly reduced. Similar behavior of the correlation coefficient and slope were found for Pn/Lg (Table 1).

The trend of the slopes in Figure 5 indicates that the time-domain measurements of Pg/Lg are consistently larger than the frequency-domain measurements for the higher passbands. Insight into possible causes of this disagreement can be seen by plotting the frequency spectra of the broadband and narrow-band filtered data, shown in Figure 6. This was done for the seismogram shown in Figure 2. The noise and Pn, Pg, and Lg phases were windowed as described earlier. Then the broadband (0.5 to 9.99 Hz) and narrow- band filtered (0.75 to 1.5, 1.5 to 3.0, 3.0 to 6.0, and 6.0 to

9.0 Hz, 2-, 4-, and 8-pole, 2-pass Butterworth filter) spectra were computed by FFT. Within the 0.75 to 1.5, 1.5 to 3.0, and 3.0 to 6.0 Hz passbands, the spectra of the filtered data compare quite well with the broadband spectra. However, significant energy from outside the passband, particularly at frequencies below the passband, contributes to the filtered spectra. The time-domain filtering is equivalent to multipli- cation in the frequency domain of a symmetric Butterworth filter with the regional-phase spectrum, which drops off rapidly with increasing frequency. The resulting spectrum is skewed to lower frequencies. Increasing the number of poles strongly reduces the energy from outside the passband, while maintaining excellent agreement to the broadband spectrum within the passband. We found that the relationship of the time-domain measurements to the frequency-domain measurements was generally similar to that shown in Figure 5, regardless of how many poles were used for the time-domain measurements. This suggests that energy from outside the passband is not the primary cause of the disagreement between the time- and frequency-domain measurements, although the spectral contamination seen in Figure 6 is dis- turbing.

For the highest frequency band (6.0 to 9.0 Hz), note that the broadband spectral amplitudes in Figure 6 begin to increase around 9.0 Hz. This results from deconvolution of the


Table 1

Pn/Lg Ampli tude R a t i o s - - C o m p a r i s o n

Frequency Band 6.0-9.0

Measures Number Lin. Corr. Stand. Dev. Slope

Raw vel. vs. deconed dis. 109 0.997 0.019 0.997 Abs. mean vs. rms 109 0.977 0.052 1.032 Abs. mean vs. env. mean 109 1.000 0.002 1.001 Rms vs. env. mean 109 0.977 0.049 0.926 Abs max. vs. env. max. 109 0.998 0.019 0.996 Rms vs. abs. max. 109 0.910 0.127 1.150 Rms vs. freq. log 109 0.657 0.192 0.687 Rms vs. freq. lin. 119 0.789 0.204 0.990

Frequency Band 3.0-6.0 Hz


Raw vel. vs. deconed dis. 162 0.978 0.047 0.973 Abs. mean vs. rms 161 0.990 0.032 1.006 Abs. mean vs. env. mean 161 1.000 0.002 0.999 Rms vs. env. mean 161 0.990 0.031 0.974 Abs. max. vs. env. max. 161 0.997 0.021 0.984 Rms vs. abs. max. 161 0.931 0.095 1.060 Rms vs. freq. log 162 0.883 0.107 0.880 Rms vs. freq. lin. 182 0.955 0.065 0.927


• Measures Number Lin. Corr. Stand. Dev. Slope





Comparison of Pn/Lg, amplitude ratio measurement techniques for four frequency bands. Measurements, described in the text, are absolute mean (abs. mean); rms (rms); envelope mean (env. mean); absolute maximum (abs. max.); envelope maximum (env. max.); loglo-mean frequency spectral amplitude (freq. log); and linear-mean frequency spectral amplitude (freq. lin.). Raw velocity (raw vel.) and instmment-deconvolved displacement (deconed dis.) were compared using the rms.

i n s t r u m e n t r e s p o n s e . T h e an t i a l i a s ing fil ter s tar ts ro l l i ng o f f

at a r o u n d 6.0 Hz . W h e n the o b s e r v e d spec t r a are d iv ided b y

th i s r e s p o n s e a n d the n o i s e f loor is r e ached , the r e s u l t i n g

s p e c t r u m is g rea t ly ampl i f ied . C l ea r l y there are s ign i f i can t

d i f f e r e n c e s b e t w e e n the b r o a d b a n d and f i l tered spec t r a fo r

the h i g h end o f th is h i g h e s t p a s s b a n d . T h e n o i s e s p e c t r u m

Table 2

Pg/Lg Amplitude R a t i o s - - C o m p a r i s o n


Measure Number Lin. Corr. Stand. Dev. Slope

Raw. vel. vs. deconed dis. 109 0.997 0.016 0.988 Abs. mean vs. rms 109 0.972 0.046 1.021 Abs. mean vs. env. mean 109 1.000 0.002 1.000 Rms vs. env. mean 109 0.971 0.044 0.923 Abs. max. vs. env. max. 109 0.997 0.020 0.989 Rms vs. abs. max. 109 0.875 0.120 1.127 Rms vs. freq. log 109 0.590 0.157 0.591 Rms vs. freq. lin. 119 0.714 0.171 0.888



Raw vel. vs. deconed dis. 162 0.971 0.038 0.975 Abs. mean vs. rms 161 0.982 0.030 1.035 Abs. mean vs. env. mean 161 1.000 0.002 0.999 Rms vs. env. mean 161 0.982 0.029 0.931 Abs. max. vs. env. max. 161 0.993 0.024 0.984 Rms vs. abs. max. 161 0.909 0.083 1.134 Rms vs. freq. log 162 0.798 0.096 0.804 Rms. vs. freq. lin. 182 0.892 0.071 0.871






Raw vel. vs. deconed dis. 251 0.994 0.029 0,977 Abs. mean vs. rms 251 0.996 0.026 0,995 Abs. mean vs. env. mean 251 1.000 0.001 1,000 Rms vs. env. mean 251 0.996 0.026 0.996 Abs. max. vs. env. max 251 0.999 0.012 1.001 Rms vs. abs. max. 251 0.961 0.081 1.009 Rms vs. freq. log 251 0.967 0.073 1.006 Rms vs. freq. lin. 254 0.980 0.055 0.996

Comparison of Pg/Lg measures, similar to Table 1.

is a l so s h o w n in each pane l o f F i g u r e 6 as the do t t ed b l a c k

line. F o r the Lg p h a s e , n o i s e a n d s igna l spe c t r a m e r g e fo r

the l o w e n d o f th is h i g h e s t p a s s b a n d . T h e s i g n a l - t o - n o i s e

cr i ter ia is app l i ed to the Pn and p r e - P n t i m e w i n d o w s . F o r

the ca se s h o w n , the Lg/pre-Pn a m p l i t u d e ra t io w o u l d p r o b -

ab ly fai l to be g rea t e r t han 2.0, a l t h o u g h Pn and Pg w o u l d

p r o b a b l y pass . Pn, Pg, Sn, a n d Lg s i g n a l - t o - n o i s e ra t io at-

t r ibu tes fo r th is s t a t ion wi l l be d i s c u s s e d f u r t h e r in a f u tu r e

art icle.

W e be l i eve that the m a i n c a u s e o f d i s a g r e e m e n t b e t w e e n

the t i m e and f r e q u e n c y - d o m a i n m e a s u r e m e n t s in F i g u r e 5 is


Pn Spectra 8-poles Pg Spectra 8-poles

-'~-z+~ ~"-4 - -2 ~.-~,..j + -

- 4 7 . - - ' . . . , , . , + - 4 - +-

_6!u ~,4,', I J 4 , -'J--" - -6 .-L_ I 2 3 4 5 6 7 8 9 I0 I 2 3 4 5 6 7 8 9 10

Lg Spectra 8-poles

6 1 2 3 4 5 6 7 8 9 1 0

Pn Spectra 4-poles Pg Spectra 4-poles 2 , I | I + + i c ' v r - ~ - - r - 2cril---]-T--r-T-r-V~ ~ - r - -

+ _ , +

'::'- +- -2 r+ ' L "~ - o + "t#, I ~,_ I_ "',£"-".~+. +- -4 .,r,~ + ':+--,'-. =

4 i / f I , ~ _ , _ _ ~, , ~ _6!~ ' ~- ,..+ _ I 2 3 4 5 6 7 8 9 10 2 3 4 5 £ 0

Lg Spectra 4-poles 2r-r T- . . ~, ~ .

i _

-6 ( --%- 1 2 3 4 5 6 7 8 9 10

Pn Spectra 2-poles

~ 0

~ - 2

-6 1 2 3F4q5ncy , l~z 9 10

Pg Spectra 2-poles

F,'I I I , ! ,.I 6 2 3 4 5 6 l~z 8 9 i0

Frequency,

Lg Spectra 2-poles 2°~J~ ....... q -~ -~+q-" - -q-~-r-~Fr[l

-6 2 3-.4 ~ 6 8 ~requency, l~z 9 10

Figure 6. Comparison of Pn, Pg, and Lg spectra for broadband (black solid) and narrow-band filtered data (red 0.75 to 1.5 Hz, green 1.5 to 3.0 Hz, blue 3.0 to 6.0 Hz, yellow 6.0 to 9.0 Hz) for the seismogram shown in Figure 2. Spectra are shown for each phase for 2-, 4-, and 8-pole, 2-pass Butterworth filters. The noise spectra for each case are shown as dotted black lines.

due to log averaging of the spectra. The spectra for all phases fall off very rapidly within the band 1.0 to 10 Hz. Averaging the log10 amplitude of the spectrum does not weigh the amplitudes associated with frequencies near the low end of the passband as heavily as does linear averaging of the spectra. Time-domain amplitude measurements weigh each frequency equally and are thus biased toward the relatively larger-amplitude energy at the low end of each passband. To illustrate this point, we computed linear averages of the spectral amplitude of each phase and formed the amplitude ratios PnlLg and Pg/Lg. These measurements were more strongly correlated with the time-domain (rms) measurements, and the slopes of the scatter plots were closer to 1.0. Results are compiled in Tables 1 and 2. Linear and log averaging of a spectrum should yield converging results as the passband is narrowed. Remaining disagreement between the time and linearly averaged frequency-domain measurements for the highest passband is possibly due to poor Lg signal to noise as described previously.

Discussion

In this study, we present comparisons of regional-phase amplitude ratio measurement techniques. Regional-phase ratios (Pn/Lg and Pg/Lg) for the area studied show large vari- ation, and thus results for this region should be applicable to other regions. Various time-domain measurements, particularly energy measures, agree very well with each other (linear correlations between 0.97 and 0.99). Absolute and envelope mean and maxima agree nearly perfectly. Energy and peak measures do not compare as favorably with each other, but they are still rather well correlated (linear correlations between 0.88 and 0.99). For some cases, peak measures in the time domain may discriminate better than energy measures. This could be due to the impulsive nature of P waves from explosions. The population studied in this article are all earthquakes, thus investigation of discriminant performance was not possible.

Time-domain (rms) and frequency-domain measure-


ments compared favorably for the lowest frequency band,

but the linear correlation decreased as the passband in-

creased. More importantly, however, is that the time-domain Pn/Lg and Pg/Lg amplitude ratios were consistently higher than the log-averaged frequency-domain ratios and that the disagreement increased as the passband increased. A major

disadvantage of t ime-domain measurements is revealed in

Figure 6. Time-domain filtering does not offer as much con-

trol over the frequencies that contribute to the measurement. Clearly significant energy from frequencies below the pass-

band contributes to the time-domain measurements, particularly for the 2-pole, 2-pass filter. Frequency-domain mea-

surements of regional-phase amplitudes and amplitude ratios are not contaminated by energy from outside the passband

of interest, and they allow log averaging. These are clear

advantages over time-domain measurements. For the highest

frequency band (6.0 to 9.0 Hz), significant differences between the broadband and filtered spectra (Fig. 6) result from

deconvolution of the instrument response. This probably contributes to the disagreement seen for this passband in Figure 5 and Tables 1 and 2.

Linear averaging of the spectral amplitude brings the time- and frequency-domain measurements into much better

agreement. Log averaging provides a more robust estimate

of the energy within a given passband because the regional-

phase spectra vary by several orders of magnitude within the band of interest (0.5 to 10.0 Hz). Time-domain measure-

ments weigh all frequencies within the band equally and are

thus biased by the large spectral amplitudes associated with the low end of the passband. This bias may be reduced by

considering narrower bands. Because the broadband spectra need only be calculated and stored once, the frequency-do-

main measurements are more efficient. Log averages of the spectral amplitude within any band can be easily computed

from the broadband spectra, instead of having to read the data, bandpass filter, and then compute the amplitude. How-

ever, these differences in efficiency are minor given modern

computational power. It remains to be determined if one

measurement technique discriminates earthquakes and explosions better than another.

A c k n o w l e d g m e n t s

Comments by Mark Fisk and an anonymous reviewer improved the origi- nal version of this article. Raw waveform data were obtained from the Incorporated Research Institutions for Seismology-Data Management Cen- ter (IRIS-DMC). Parts of the analysis were done using the Datascope Seis- mic Data Application package obtained from the University of Colorado, Joint Seismic Program Center and the Seismic Analysis Code (SAC2000) developed at Lawrence Livermore National Laboratory. This is LLNL jour- nal contribution UCRL-JC-127080. Research was performed under the aus- pices of the U.S. Department of Energy by the Lawrence Livermore Na- tional Laboratory under Contract W-7405-ENG-48. This is Institute of Tectonics Contribution #321, and this research was supported in part by Phillips Laboratory Contract F19628-95-K-0014.

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Lawrence Livermore National Laboratory Geophysics and Global Security Division L-205, P.O. Box 808 Livermore, California 94551

(A.J.R., W.R.W., K.M.M.)

Earth Sciences Department and Institute of Tectonics University of California Earth and Marine Sciences Building Santa Cruz, California 95064

(T.L.)

Manuscript received 14 April 1997.

a comparison of regional-phase amplitude ratio measurement...

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