Journal of Geophysical Research: Atmospheres

Infrasound from earthquakes

Authors


Abstract

[1] Infrasonic signals have been observed from 31 earthquakes by arrays of microphones operated by the Los Alamos National Laboratory between 1983 and 2003. The properties of the signals are presented. Signal amplitudes corrected for propagation and distance show a relation with seismic magnitude. The variance in the relation is understood primarily in terms of the uncertainties or errors in the ground motion, deduced from an independent data set, and the stratospheric winds, which strongly influence signal propagation. Signal durations can extend over many minutes. A relation is found between signal duration and magnitude. To understand this, we propose a model in which regions distant from the epicenter are excited by seismic surface waves. The surface motion of these regions, in turn, produces signals which precede or follow the signals from the epicenter. Analysis failed to detect signals from 56 earthquakes during the observation period. Predicted signal-to-noise ratios for these earthquakes indicated that the signals would have been too weak for detection.

1. Background and Introduction

[2] Very low frequency sound, or infrasound, from earthquakes has been reported previously by numerous authors. Several of the reports concern detection of ground-coupled effects in which local seismic waves generate infrasound. These include Grover and Marshall [1968] for an earthquake near the coast of Honshu, Grover [1977] for earthquakes in Italy and China and Cook [1971] for a Montana earthquake. Direct atmospheric path signals from the epicenter and surrounding region have been reported by others. Examples are Benioff and Gutenberg [1939] and Benioff et al. [1951] for California earthquakes. Young and Greene [1982], among others, reported the complex signals from a very large earthquake in Alaska. Le Pichon et al. [2002] reported both types of arrivals from an earthquake in Peru. Olson et al. [2003] discuss signals from a recent large earthquake in Alaska. Le Pichon et al. [2003] discuss infrasound from a very large earthquake in China. Mutschlecner et al. [1985] have described observations of the Coalinga, California, earthquake; Mutschlecner and Whitaker [1994] have also reported on the Northridge, California, earthquake.

[3] An earthquake generates atmospheric infrasound by the low-frequency oscillation of the earth's surface near the epicenter and surrounding regions. The waves then travel through the atmosphere where they are refracted by the effects of the variations of sound and wind velocities with height. In a ray-acoustic interpretation the waves are ducted back toward Earth from regions near 50 km in altitude and return to Earth at distances of about 200 to 250 km from the source. The waves are efficiently reflected from the surface and may be transmitted by multiple “bounces” to more distant regions. For example, infrasound detected by us from Mexican earthquakes would have made about 10 bounces to reach the detectors. Figure 1 shows the source regions schematically. Two possible mechanisms are indicated: (1) Near the epicenter (EC) the infrasound is generated by the local ground motion (body waves or Rayleigh waves), and (2) in regions far from the epicenter infrasound may be generated in the interaction of surface waves with topographic features, such as mountains, by a diffraction process. The region with radius RL is discussed in section 8. Infrasonic waves may also be refracted from the thermospheric region near 110 km, but our findings are that these signals are generally much weaker than the stratospheric signals. An additional mode for transmission can be a near surface wave, which travels by means of seismic and acoustic coupling. The detections reported here are from waves refracted from stratospheric heights, consistent with observed travel times (with one exception).

Figure 1.

Schematic diagram of the infrasound-producing region surrounding the epicenter (EC) of an earthquake. In the model the limit of production is set at a radius RL. Epicenter region infrasound production is shown along with production by the interaction of surface motion with local terrain features.

[4] Figure 2 gives an example of a portion of a wave train from an earthquake on 22 February 2002, near Mexicale, California, showing four sensor channels at an array in Los Alamos at a distance of 915 km. Notice the strong correlation among the channels. In this instance the signal was seen for about 10 min.

Figure 2.

An example waveform (raw voltage versus time) for an earthquake signal with four channels of data in the peak region. The sample is for an earthquake of 22 February 2002. The horizontal lines on the first channel illustrate the technique used to measure amplitude.

2. Data Sources

[5] The data used here consist of observations over the interval from 1983 through 2003 but with an emphasis on the period through 1992. A total of 31 earthquakes was observed of which 13 were detected by two or more infrasound stations for a total of 47 signals. All but nine of the earthquakes were in California. The most distant earthquake, in Alaska, was at a distance of about 4100 km and the closest, in New Mexico, at about 165 km. Table 1 lists the observed earthquakes indicating date, day of year (DOY), origin time, location, seismic magnitude, latitude and longitude, and hypocenter depth. All data were obtained from the National Earthquake Information Center. Magnitudes were placed on a common ML scale by the use of transformations given by Utsu [2003] with additional information given in the review by Lay and Wallace [1995].

Table 1. Earthquakes Detected
EarthquakeDay of YearDateEvent Time, UTLocationMLLatitude, degLongitude, degDepth, km
13073 Nov. 20022212:41Mount McKinley, Alaska7.563.52−147.444
25322 Feb. 20021932:41Mexicale, Calif.5.832.38−115.3510
35928 Feb. 20011854:32Puget Sound, Wash.6.647.15−122.7351
428916 Oct. 19990946:44Hector, Calif.7.034.59−116.276
51717 Jan. 19941230:55Northridge, Calif.6.634.21−118.5418.4
62762 Oct. 19920719:57Lucerne, Calif.4.434.6−116.643
718028 June 19921505:31Bear Mountain, Calif.6.534.2−116.835
817928 June 19911443:55Pasadena, Calif.6.134.26−118.0111
929724 Oct. 19900615:21Yosemite, Calif.5.738.05−119.1612
1010818 April 19901353:51Watsonville, Calif.5.636.92−121.685
115928 Feb. 19902343:36Claremont, Calif.6.234.14−117.75
121616 Jan. 19902008:22Humbolt, Calif.5.840.23−124.142
131515 Jan. 19900529:03California-Nevada5.037.99−118.215
1433329 Nov. 19890654:38Isleta, N. M.4.734.46−106.8913
153030 Jan. 19890406:23Salina, Utah5.038.82−111.6124
161919 Jan. 19890653:29Malibu, Calif.5.433.92−118.6312
1735116 Dec. 19880553:05Banning, Calif.5.233.98−116.688
183383 Dec. 19881138:26Pasadena, Calif.5.034.15−118.1313
192828 Jan. 19880254:02Brawley, Calif.4.732.91−115.686
202525 Jan. 19881317:51Baja5.231.74−115.845
2132824 Nov. 19870154:14El Centro, Calif.6.533.08−115.784
2232824 Nov. 19871315:56El Centro, Calif.6.733.01−115.842
2332824 Nov. 19870215:26Salton, Calif.4.433.25−115.625
242741 Oct. 19871442:20Whittier, Calif.6.134.08−118.0810
2520221 July 19861442:26Bishop, Calif.6.537.5−118.49
2612030 April 19860707:18Mexico City, Mexico6.718.4−102.4726
2726421 Sept. 19850137:14Mexico City, Mexico7.117.8−101.6530
2826219 Sept. 19851317:47Mexico City, Mexico7.318.19−102.5327
2932823 Nov. 19841808:25Bishop, Calif.6.237.48−118.6515
3032823 Nov. 19841912:34Bishop, Calif.5.537.44−118.640
311232 May 19832342:38Coalinga, Calif.6.736.22−120.3210

[6] The data were measured at arrays operated by the Los Alamos National Laboratory (LANL) at Los Alamos, New Mexico (LA); St. George, Utah (SG); and Mercury, Nevada (NTS). An additional, non-LANL, array at Lac du Bonnet, Canada (LdB), provided one additional detection but no amplitude information. This four-element array, with 2 km aperture, uses the MB2000 microbarograph and is IS10 in the International Monitoring System of the Comprehensive Test Ban Treaty Organization. Over half of the detections were made by the SG array. The arrays have four very low frequency sensitive microphones spaced at distances of about 100 m from a central point and covering an overall size of about 300 m. The microphones are Globe 100C for the earlier observations and Chaparral Physics Model II for the later ones. Mutschlecner and Whitaker [1997] have provided a discussion of the operation and physics for microphones of this type. Wind noise reducers consisting of porous hoses are attached to each microphone in a radial pattern with a diameter of about 30 m. For some of the earliest observations the noise reducers were PVC pipes with multiple hypodermic-type ports. Two of the earthquakes were observed at a prototype array at Los Alamos (DLIAR) with a larger overall diameter of 1.2 km. Data sampling rates were 20 samples/s except for the prototype array at 10 samples/s. The frequency band pass is about 0.1 to 10 Hz, except for DLIAR with 0.1 to 4 Hz.

3. Signal Processing

[7] Data from each array were processed by Fourier domain correlation beam formers. Many of the data from the period 1983–1992 were processed with an array signal processing algorithm originally due to Young and Hoyle [1975]. This correlation beam former used frequency slowness variables rather than frequency wave number. After about 1999, data were processed with a newer implementation of the Young and Hoyle processor. The algorithm was made part of the Matseis waveform/time series software by researchers at the Sandia National Laboratory. This version, Infra-Tool, uses a graphical user interface and can be linked to some other Matseis routines. Time windows were generally 20 s with 50% overlap. The most frequent noise sources were local winds or microbaroms (sea storm-generated infrasound), which typically have a peak power near 0.2 Hz. The frequency passband used for most analysis was 0.5 to 3.0 Hz to reduce the effects of the microbaroms and local wind noise while still including most of the earthquake signal. In a few cases this passband was altered to give a greater signal-to-noise ratio (SNR).

[8] The results of the processing are (1) average pairwise channel cross correlations, (2) azimuth of the peak power activity, (3) trace velocity, (4) frequency of the peak power determined from a power spectrum, and (5) power. The windows of peak power and peak correlation often coincide; however, they may differ by one or two processing intervals. An example of the results is given in Figure 3 for the earthquake signal shown in Figure 2 during a portion of the time surrounding the peak signal. The earthquake data are in the region from 2020 to 2030 UT. The later periods of constant azimuth are probably not related to the earthquake event.

Figure 3.

Results from the automated processing of earthquake data. (top to bottom) The results are averaged correlation among the channels, trace velocity, azimuth, and signal amplitude in volts. The earthquake signal is the high-correlation region from 2020 UT to 2030 UT. The later high-correlation features are probably not earthquake related.

[9] For the purposes of this study infrasonic detection of an earthquake has, during the peak signal period, the following characteristics: (1) high correlation among the channels as compared to the nearby background, (2) an azimuth close to that predicted along a great circle path from the station to the epicenter (typically within 5° or less), (3) a trace velocity in the range of that expected for stratospheric return signals, and (4) an arrival time close to that predicted for a stratospheric return (typically having an average velocity along the surface great circle path of about 290 m/s which we have observed for numerous infrasonic signals). Trace velocity is the horizontal component of the phase velocity for the signal across an array and is usually in the range of 350 to 450 m/s.

[10] For 23 detections the local seismic arrival was observed through its effects on the microphones. In these cases the pressure signal is presumed to be generated by the vertical motion of the microphone as the seismic wave passes and by local seismoacoustic coupling. Typically, these signals have a travel velocity of about 3 km/s corresponding to seismic S waves. For nine of the detections P wave transits were observed with velocities of about 5 km/s. Bedard [1971] has discussed the effect of seismic waves on microphones. These ground wave signals are not discussed in the present work, where we concentrated on atmospheric signals.

[11] Peak-to-peak amplitudes were determined as averages over major features in an interval of about 5 to 10 s in the peak correlation and power window, coming from the epicenter region. See Figure 2 for an example. The results were averaged over all microphone channels. Amplitudes were converted from microphone output voltage to pressure in microbars (1 μbar = 0.1 Pascal) using calibrations determined for each microphone at reasonably frequent intervals. The calibrations have an estimated accuracy of 15% and average about 0.18 V/μbar. Noel and Whitaker [1991] showed that noise reducers of the type described here reduce the signal amplitude from an open microphone by a factor of 0.87. This correction has not been applied here. Signal durations were determined as the time interval during which signal characteristics were reasonably close to the accepted parameters described earlier. Durations can range up to many minutes in length and will be discussed in section 8.

[12] The observed amplitudes, Ao, have been normalized for the effects of distance and stratospheric wind by the use of

equation image

where An is the normalized amplitude, R is the great circle distance to the epicenter, Rs is an arbitrary standard distance, and Vd is the stratospheric wind component directed from source to array; s and k are empirical parameters. Mutschlecner et al. [1999] discuss the background for this normalization process and determinations for s and k. On the basis of the analysis of signals from numerous atmospheric nuclear explosions and large high-explosive tests we have adopted s = 1.45 and k = 0.018 s/m; Rs = 1000 km which is approximately the average of the distances.

[13] Stratospheric wind data are needed to normalize the signals as indicated in equation (1). These data were taken from National Climate Data Center records of high-altitude winds observed by rocketsonde flights. Rocketsonde stations included Point Mugu, California; White Sands, New Mexico; Wallops Island, Virginia; and Cape Canaveral, Florida. We employed data from all stations, which were available and close to the required date but emphasized data from Point Mugu and White Sands for the California earthquakes. Zonal and meridional components of the wind were averaged from the records for altitudes between 45 and 55 km. This procedure is in agreement with the protocol used for the Stratospheric Circulation Index described by Webb [1966] and closely represents the region of the stratosphere involved in the return of signals to Earth where the wind velocity is critical.

[14] Because wind data for a specific earthquake date were usually not available, data were interpolated for the zonal and meridional components from nearby dates. Typically, the time interval used for the interpolations was about 1 week. The average interval between the required date and the nearest rocketsonde observation was about 2 days. We estimate the internal accuracy of this procedure to be about 8 m/s. Depending upon the time of year, the observational accuracy of the wind data is about 15 m/s. Stratospheric winds show the greatest variability from about November through January. For the most recent earthquakes (1999–2003) rocketsonde observations were not available. For these, statistical models for the zonal and meridional winds were used. These models are given by Mutschlecner et al. [1999].

4. Data Set

[15] Table 2 contains the observational data for each detection. For each signal we determined an average travel velocity defined as the great circle distance to the epicenter divided by the signal travel time (peak signal time minus the earthquake origin time). Subjective estimates of quality were given for each signal from A (excellent) to D (poor); 24% of the signals are of A quality, 36% are of B quality, 38% are of C quality, and 2% are of D quality.

Table 2. Infrasound Signal Parametersa
EarthquakeArrayR, kmA, μbarAn, μbarAZobs, degDel Az, degCCFmax, HzDur, minVtrav, m/s
  • a

    Abbreviations are as follows: R, distance; A, amplitude; An, normalized amplitude; AZobs, observed azimuth, Del Az, azimuth deviation; CC, correlation at peak signal, Fmax, frequency at peak signal, and Vtrav, average travel velocity.

1DLI41390.903.03335.64.60.84-15312
1SG37190.581.85334.31.10.94-23313
1NTS36580.280.89336.82.20.77-24302
2LA915.41.300.18245−2.50.941.0611.8279
2DLI915.41.040.14246−1.50.721.069.8279
3LdB1978--268−2.50.63-18.6299
4DLI9001.410.26264−10.720.6519298
4LA912.81.370.26262−20.871.3537301
4NTS235.82.790.211881.20.910.5325312
5SG5439.520.722403.50.970.5327278
6SG3820.150.022303.70.941.273.7302
7SG4270.460.402251.20.790.6318226
8SG5020.540.912362.40.900.6022283
9SG4983.150.25278−7.70.990.6426291
9LA11600.600.16286−0.20.870.5710300
10SG7160.270.09270−1.60.890.785.5301
11SG4881.020.062365.70.950.6918.8289
12SG9810.720.193005.40.871.108286
13SG4190.280.022914.70.940.807.5274
14LA1650.650.01196−20.902.382279
15SG2671.040.44454.50.881.325.8298
16SG5700.550.032361.70.840.847275
17SG4370.260.012254.70.681.046288
18SG5180.200.012395.60.60-4.5295
19SG4940.760.0820740.882.464.8283
19LA9280.690.1025200.820.509292
20LA9910.470.07243−2.10.750.5810304
20SG6220.440.07198−1.80.690.505310
21LA9201.260.0725410.871.0612.2297
21SG4793.880.252072.20.950.6912.5288
22SG4898.540.572071.90.961.4129282
22LA9284.960.292541.20.940.6232289
23SG4501.90.122072.70.670.563295
23LA9191.500.08252−10.730.534286
24LA11030.650.4926200.760.6021287
24NTS3721.100.182206.30.801.0012.5300
24SG5211.000.252363.80.920.5328298
25SG4270.250.59278−0.70.610.6518224
26SG23150.130.41150−0.50.810.6011314
27LA20580.521.581660.10.930.1333282
27SG2433--1534.90.760.327297
28SG23560.702.11149−0.80.910.3223282
28LA20011.403.18164−4.40.840.2925290
29SG4354.760.082780.90.980.9715.5283
30SG4402.120.042780.70.861.7012290
31LA12550.901.692782.10.840.3633288
31SG6051.741.02270.46.80.950.4527271

[16] Table 2 contains, in order, earthquake number, array, distance, amplitude, normalized amplitude, observed azimuth (clockwise from north), azimuth deviation, correlation at peak signal, frequency at peak signal, duration, and average travel velocity. The earthquake corresponding to each detection is keyed to Table 1. In Figure 4 the characteristics of the population are shown including magnitude (ML), distance (R), duration (Dur), and peak power frequency (Fmax). Earthquakes in these data range in magnitude from 4.4 to 7.5. However, aftershocks from the Northridge earthquake, while not included here, were detected down to magnitude 3.5. The signal durations range from a few minutes to as long as 42 min. The peak power average frequency is about 0.8 Hz. However, it must be remembered that for most detections the low band-pass frequency was 0.5 Hz. Figure 4e also shows the deviations between the azimuths at peak correlation and the predicted azimuths to the epicenters. The standard deviation for the azimuth departures (at peak correlation) is 3.0°. This amount is caused primarily by a combination of the discretization used in the slowness plane giving uncertainty of about 2° and the aperture of the arrays, coupled with SNR values, which results in uncertainty of about 1°. Thus many of the deviations cannot be attributed to source effects. On the other hand, some of the larger deviations may be caused by a combination of propagation and source effects.

Figure 4.

Histograms showing the characteristics of the data set: (a) the distribution of seismic magnitudes, (b) the distribution of distances from the epicenter to receiver, (c) the signal durations, (d) the frequencies at peak signal, and (e) the azimuth deviations (observed-predicted).

[17] Correlation analyses were made for pairs of the various variables. One, for Fmax versus hypocenter depth, is shown in Figure 5 and indicates a possible relation, with the deeper earthquakes showing the lowest frequencies. This relation will require further study using appropriate seismic data.

Figure 5.

Signal peak frequency at peak signal time versus hypocenter depth.

5. Amplitude-Magnitude Relation

[18] It is anticipated that there is a relation between normalized infrasonic amplitude and seismic magnitude since magnitude is related to ground motion strength which, in turn, drives the infrasound generation. In Figure 6 the log of the normalized amplitudes, log(An), is plotted versus ML. The least squares fit to these data is

equation image

While a correlation is indeed indicated, it is not very strong. Table 3 contains the fit values. In an effort to strengthen the relation we employed only the data with the best determinations of stratospheric wind. This improved the fit only slightly. Similarly restricting the data to those with A or B amplitude quality produced only a modest change. These efforts suggest that the cause of the large dispersion in the fit is not related primarily to the wind data or amplitude data quality. We return to this question in section 7.

Figure 6.

Log of amplitudes of peak signal normalized for distance and wind effects versus seismic magnitude. A least squares fit is shown.

Table 3. Comparison of Observed and Predicted Relations for Amplitude and Duration
 ObservedPredicted
  • a

    Value is for simulation.

  • b

    Value is for ground motion only.

Log(An) versus ML
Slope0.57 ± 0.070.56
σ(log(An))0.410.37a
R20.600.70
 
Log(Dur) Versus ML
Slope0.30 ± 0.170.37
σ(log(Dur))0.170.14b
R20.72-

[19] About half of the amplitude determinations used unfiltered (UF) channel plots and half filtered (F) channel plots with a 0.5 to 3.0 Hz passband in most cases. The later were used in the instances where significant background noise was present. The possible effects on amplitude of using the F channel plots were examined. A small bias was found in the sense of larger amplitudes for the UF values compared to the F values. However, the effect of this bias on the quality of the correlations was negligibly small.

6. Ground Motion Effects

[20] In order to understand details of the generation of infrasound from earthquakes it is essential to examine ground motion characteristics. The physics for generation of overpressure p(H, t) above a moving surface at time t, and slant height, H, was given by Rayleigh [1945] and involves an integration of the acceleration of the surface over the area in motion. Thus the infrasound overpressure is related to the acceleration (or velocity) of the surface.

[21] An extensive survey of earthquake strong ground motion compiled by Shakel and Bernreuter [1980] was used; the data are primarily from earthquakes in California. The set includes 40 events and covers distances from epicenters of about 1 to 20 km. One event had sufficient data over a range of distances to allow us to derive a putative distance scaling relation for Vv (cm/s), vertical velocity. This relation was used to scale all the data to 1 km. Figure 7 shows the relation between log(Vv) and ML. The least squares fit to these data is

equation image

The variances for vertical velocity and vertical acceleration are nearly identical. It is expected that the dependence of normalized infrasound amplitude on magnitude will be determined by the relation of velocity or acceleration to magnitude. Ground motion parameterizations given by Abrahamson and Silva [1997] and by Bolt and Abrahamson [2003] were also used in this study. They give somewhat different results from those of equation (3) because they apply to larger distances and reflect observed changes in slope.

Figure 7.

Log of vertical ground motion scaled to 1 km versus seismic magnitude. A least squares fit is shown.

7. Uncertainties and Error Analysis

[22] The large variance found in the fit for log AnML in Figure 6 was investigated with respect to the estimated uncertainties or errors, which enter into this relation. Table 4 gives our estimates of the standard deviations of each variable. The estimate for σ (log(Vv)) comes from the fit in Figure 7. Table 4 also gives an estimate of the percentage effect on log(An) by the uncertainty in each variable or parameter. The value used for stratospheric wind uncertainty (15 m/s) may be an underestimate for some events because wind variability can be very large at some times of the year. In addition, wind profiles often show complex structure, which can influence propagation.

Table 4. Contributions to Signal Uncertainties
SourceσestEstimated Contribution to σ(log(An)), %
k0.002 s/m10
Vd15 m/s40
s0.208
Log(R)0.0041
Log(Ao)0.046
Log(VV)0.2335

[23] To better understand the effect of the uncertainties, statistical simulations were performed in which each of the parameters or variables was allowed to vary independently and randomly about its central value with a Gaussian distribution based upon the standard deviation of that quantity as given in Table 4. The simulations proceeded as follows. For each of the observations a value of log(Vv) is assigned according to the observed magnitude using equation (3). Then a simulated “raw” amplitude, log(Aos), is determined by

equation image

where the bracketed quantities indicate randomization as described above. EA is the simulated observational error in log(Aos). The resulting simulated “raw” amplitudes are then normalized as usual by

equation image

and a least squares fit of these values was made to the corresponding values of ML as in the case of the actual data. Fifty realizations of the process were performed and average values for the fits were determined. Table 3 compares the simulation values with the observed values of the relation given by equation (2). We conclude that the slope and variance of the fit of normalized amplitude versus magnitude can be understood in terms of uncertainties of the underlying variables with the predominant effect from the ground motion and the wind velocity uncertainties.

[24] Signals were detected for nine of the earthquakes at both the SG and the LA arrays. Within each pair the values of ML, ground motion and upper altitude wind structure are, of course, identical for both arrays. This permits a further analysis of the effect of uncertainties for the subset. The RMS difference between log (An) for the nine pairs was 0.24 which can be roughly compared with the value of σ(log (An)) = 0.41 found in Figure 6. The significantly lower value for the pairs presumably reflects the facts that (1) there are no ground motion variations within a pair and (2) wind variations play a secondary role since only the relatively small azimuth differences to the epicenters from each array will have effects on the directed wind component.

[25] A statistical simulation was performed which took into account the secondary effects of wind correction, parameter uncertainties, and pressure measurement uncertainties through a randomizing process similar to that described for the general fit analysis. The result from 20 simulations was an RMS for the differences in log(An) of 0.18 which can be compared with the observed RMS for the pairs of 0.24. This close agreement again helps to confirm the strong importance of the ground motion variance and the wind variance in controlling the fit of the observations seen in Figure 6.

8. Signal Durations

[26] Figure 8 shows the relation between the log of the duration, Dur, (in minutes) and ML for all signals. The least squares fit to the data is

equation image
Figure 8.

Log of the signal durations versus seismic magnitude. Predicted durations are shown for limiting surface accelerations of 10 cm/s2 (curve A) and 20 cm/s2 (curve B).

[27] Duration appears to correlate with magnitude although the scatter is large. Since earthquake ground motion near the epicenters is relatively brief, typically a minute or less, a cause for the long durations must be sought elsewhere. One possible cause is signal lengthening during atmospheric propagation by a multipath process. Signal wave trains may contain thermospheric or tropospheric components in addition to the primary stratospheric signals. However, our investigation suggests that these contributions will be minor compared to stratospheric signals and will influence only portions of the wave trains. Our experience with large signals from high explosive tests is that their durations are, on average, considerably smaller than those from earthquakes. The mean value for earthquakes is about twice that from explosive tests. Hence we look to possible earthquake-specific causes. We propose a simple model in which seismic surface motion moving outward from the epicenter continues to generate infrasonic signal contributions to large distances. Regions closer to an array than the epicenter will generate signal prior to the peak signal and regions farther than the epicenter will generate late components to the signal. Interestingly, Benioff and Gutenberg [1939] proposed a similar concept much earlier. Cook [1971] has discussed the physics of infrasound signal generation by diffraction at the surface for such waves. Topographic features such as mountains play a role in the character of the diffraction. Deviations from epicenter azimuths seen during the course of the signal durations average about ±5°; for some signals the deviations are considerably larger. These are presumed to be caused by the mechanism proposed here. Note that these are not the deviations discussed for Figure 4e, which are specific to the peak signals assumed to be from epicenter regions.

[28] From this simple model the duration is predicted as

equation image

where RL is a limiting distance from the epicenter for generation of observable infrasound and vt is the average travel velocity of atmospheric signals along the great circle path (about 290 m/s). The seismic surface wave velocity does not influence the duration.

[29] Combining equations (6) and (7) results in a relation between RL and ML:

equation image

The ground motion at RL as a function of magnitude can now be examined. The peak acceleration relations to magnitude of Abrahamson and Silva [1997] for rock and soil and of Bolt and Abrahamson [2003] were used. For any given relation, such as that for rock, peak acceleration values over the broad magnitude range of 5 to 8 change by only a factor of 1.4 or less at the corresponding values of RL. Typical peak accelerations are in the range of about 10 to 20 cm/s2. Figure 8 shows the durations predicted by the Abrahamson and Silva relations for rock at limiting peak accelerations of 10 and 20 cm/s2 as examples. These predictions bracket the observations rather well and help to validate the proposed model. It appears then that a minimum peak surface acceleration threshold exists for atmospheric signal generation. The current work suggests a value between 10 and 20 cm/s2. The relation in equation (8) places the limiting radius, RL, near the upper limit of rupture distances as a function of magnitude given by Abrahamson and Silva [1997].

[30] A more detailed analysis of durations will require that the durations be corrected for the effects of multipath. Observation of surface explosions over a wide range of energies and distances give durations from this cause of from less than a minute to well over 10 min. However, the explosion signals are of much higher amplitude than those of earthquakes; hence, duration physics may not be comparable. A trial correction with a 30% reduction of the observed earthquake durations shows that the agreement with the acceleration predictions is still acceptable. It is also probable that there are effects on duration by the ambient background noise levels and by effects of stratospheric winds. These effects are not found in the data, probably because ground motion variance dominates.

[31] The dispersion in the fit given in equation (6) results from (1) the variability in RL which, in turn, results from the dispersion in acceleration or velocity for a given magnitude and distance, and (2) the variability in the signal multiple propagation paths. An estimate can be given of the effect of the first cause based upon the dispersions found in the data of Shakel and Bernreuter [1980] and the slopes seen in the acceleration-distance relation. Table 3 contains the observed and model predicted fits for the duration-magnitude relation. From the close agreements, we conclude that the proposed model for duration is reasonable and that effective signal generation stops at distances from the epicenter with nearly the same acceleration regardless of earthquake magnitude.

9. Nondetections

[32] In addition to the infrasound detections described here, signal from 56 earthquakes were searched for but not found; 32 of these were located in California. In 14 instances two or more arrays (LA, SG, NTS) were employed for a total of 71 nondetections (NDs). For several of the NDs the causes are rather obvious: The epicenters are at very large distances, or there was very high wind noise. It is useful, however, to examine these NDs for the possibility that there are earthquakes that are intrinsically poor infrasound sources in spite of having strong parameters such as magnitude.

[33] Predictions were made of the SNR for these NDs. The procedure was as follows for each case: (1) From equation (2) the log of normalized amplitude, log(An), was predicted for the corresponding magnitude. (2) The directed wind velocity, Vd, was obtained using the wind models referenced previously. (3) The predicted “raw” amplitude, log(Aos), was obtained from equation (1). (4) Power, Pos, corresponding to the predicted Aos was obtained from

equation image

where Pos is in V2 and Aos is in μbar; the empirical constant results from a fit of log (Po) to log (Ao) of miscellaneous observations. (5) The SNR, Pos/Pn, was computed using the observed background noise, Pn, in the vicinity of the expected signal time.

[34] Figure 9 shows the resulting log SNR values versus magnitude. Infrasound signals with SNR <1 would generally not be detectable. Figure 9 shows that all but one of these earthquakes are predicted to be below the detection threshold. The lack of NDs with SNR >1 indicates that, at least in this sample, there are no cases for which there is a suggestion of poor infrasound-generating earthquakes.

Figure 9.

Log of the predicted signal-to-noise ratios (SNR) versus seismic magnitude for earthquakes without infrasonic detections.

10. Conclusions and Future Work

[35] In this study the data cover a fairly wide range of earthquake magnitudes and of distances. Within this population a relation has been found between normalized amplitude and seismic magnitude. A large variance is seen in the relation; the explanation for this is apparent in the effect of the variance of surface motion as a function of magnitude and in the inherent uncertainties in the stratospheric winds. The observed slope of the log (An) − ML relation very closely matches that predicted on the basis of ground motion.

[36] A relation was also found for signal duration as a function of magnitude. A tentative explanation for this relation is found in a simple model having source regions extended from the epicenter by seismic surface waves. Ground motion data suggest that the extended source size may be restricted to a radius at which the peak vertical acceleration reaches a limiting value for effective infrasound generation. The distance for this limiting acceleration is, in turn, controlled by magnitude.

[37] The lower frequency limit of 0.5 Hz used here will, of course, influence the results of the paper. Data at frequencies below this limit may have somewhat different results. In particular, the influence of surface waves in mountain regions could be different at lower frequencies. However, as already stated the ability to observe effectively at lower frequencies is often limited by noise considerations.

[38] A possible relation was found between peak frequency of signal and hypocenter depth. This relation might find explanation in a connection between ground motion characteristics and source depth but this will require further analysis and data. A number of earthquakes were not detected in the study. Predicted signal powers ratioed to the observed noise powers gave SNR values which show that there is no expectation that these earthquakes could have been detected.

[39] The putative relations of normalized signal amplitude and duration to magnitude permit the prediction of earthquake infrasonic signal detections at an array. There is, however, a caveat since, in this study, 71% of the earthquakes were in California. However, the non-California earthquakes do appear to conform to the same relations.

[40] There is a rich potential for future research in this field. The use of earthquake parameterizations beyond magnitude may be able to enhance the understanding of signal characteristics such as amplitude, duration and frequency for individual cases. Modeling of the source generation and acoustic propagation by appropriate hydrodynamic calculations should be pursued. In particular, the use of surface motion data in the extended region of an earthquake from strong motion stations would be valuable and could help to explain duration characteristics. Work taking into account the effects of local surface characteristics on signals has been pursued by Le Pichon et al. [2002].

[41] Full use of infrasonic data requires good quality profiles of stratospheric structure and winds. Few rocketsonde observations are now made. Fortunately, there is an effort in the modeling of the atmospheric structure and winds which has the potential of providing the required information. Drob et al. [2003] have described a methodology for this information.

[42] A growing global network of infrasound arrays of the International Monitoring System (IMS) offers the possibility of detection of infrasound from earthquakes globally with possible multiarray detections for many. Future use of the IMS could rapidly expand the database of detections and correspondingly provide a greater source for analysis.

[43] An interesting possibility for the future is the incorporation of infrasonic with seismic methods for earthquake analysis. Infrasound signals from extended, and possibly unmonitored, regions away from an epicenter could provide important data on surface motions.

Acknowledgments

[44] We wish to acknowledge the support of the U.S. Department of Energy for this work. We are grateful to Masha Davidson, Susan Noll and the late Susan Bunker for their careful work in the processing of the data. Dan Cooper did the artwork for Figure 1. We thank all the referees for their useful comments.

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