FIRE and MUD Contents

Worldwide Observation of Bichromatic Long-Period Rayleigh Waves Excited During the June 15, 1991, Eruption of Mount Pinatubo

By W. Zürn¹ and R. Widmer²

¹Black Forest Observatory Schiltach, Heubach 206, D-77709 Wolfach, Germany.

²Geophysical Institute, Karlsruhe University, Hertzstr. 16, D-76187 Karlsruhe, Germany.

ABSTRACT

During the climactic phase of the June 15, 1991, Mount Pinatubo eruption, an essentially bichromatic signal with frequencies of 3.68 and 4.44 millihertz was recorded on gravimeters and very long period (VLP) seismometers worldwide. The narrow-band nature of this signal distinguishes these recordings from the usual broadband signal recorded after large earthquakes. Group velocity estimates and particle motions show that the signals propagate as Rayleigh waves. The bichromatic spectra, which had not been recognized during previous plinian eruptions, can be explained only by source models that provide for harmonic forcing of the solid Earth. In this article we summarize the results of the data analysis and focus on the constraints the signals place on models of the source. Two models suggest that the eruption excites atmospheric oscillations that have vanishing horizontal wavenumber and that these oscillations, by exerting a harmonic pressure on the surface of the Earth, are responsible for the bichromatic Rayleigh waves. In order to account for the observed phase coherence of the signal over many hours, one of the models invokes positive feedback between the atmospheric resonances and the plume. Atmospheric oscillations that are associated with severe convective storms have bichromatic spectra very similar to seismic spectra from the Mount Pinatubo eruption, a fact that corroborates both tentative source models.

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THE SEISMIC SIGNALS FROM MOUNT PINATUBO

A new powerful source of low-frequency seismic energy has been detected independently by two research teams on the occasion of the climactic eruption of Mount Pinatubo on June 15, 1991 (Kanamori and Mori, 1992; Widmer and Zürn, 1992a,b). The seismic signal from the climactic phase of the eruption that was recorded at teleseismic distances (>20° away) is dominated by a long-lasting (>6 h) narrow-band signal with peaks at 3.68 and 4.44 mHz. These oscillations last from 0700 to 2000 G.m.t. on June 15, 1991 (local time, 1500 on June 15, 1991, to 0400 on June 16). Figure 1 shows the data from the very long period, high-gain channel of the vertical component seismometer (STS-1; Wielandt and Streckeisen, 1982) of station HRV at Cambridge, Mass., from this day. Other records can be found in figures 1, 3, 4, and 7 of Kanamori and Mori (1992) and in figure 1 of Widmer and Zürn (1992a). Essentially all modern vertical long-period seismographs, including superconducting gravimeters at Miami and Strassbourg, observed these oscillations. At 0059 G.m.t. an M_s 6.1 earthquake occurred in the Caucasus followed immediately by an M_s 6.3 earthquake in the South Sandwich Islands at 0113 G.m.t. On the low-pass filtered seismograms, Rayleigh wave trains up to R₄ of the latter event can be identified before the onset of the Pinatubo signal. Between 0113 and 2300 G.m.t. on June 15 (between 0913 local time on June 15 and 0700 on June 16) no earthquake larger than M_s 5.5 occurred worldwide. However, 36 events with the epicenter located on Luzon Island and magnitudes less than M_s 5.5 are listed in the catalog Preliminary Determination of Earthquake Epicenters (USGS, 1991) in this time period, demonstrating the crisis. The higher frequency signals between 1100 and 1200 G.m.t. are body and Rayleigh waves from the largest of these events. Since there is no sharp onset to the low-frequency signal arriving at approximately 0700 G.m.t., the standard techniques for locating earthquakes could not be used. Although we had immediately suspected that the signal was linked to the eruption of Mount Pinatubo, we had to use a cross-correlation method to confirm this source. All available seismograms were cross-correlated with the vertical seismogram from station KMI (Kunming, China), and from the lags determined from these correlograms a group velocity of 3.78 km/s was estimated, which corresponds to the group velocity of Rayleigh waves with the periods of the bichromatic signal (see fig. 2 of Widmer and Zürn, 1992a). We also find that the horizontal particle motion at the closest station (KMI) lines up with the direction to Pinatubo and thereby provides a second piece of evidence for the Rayleigh wave hypothesis. KMI was the only station where these signals were clearly visible on the horizontal components. This is presumably because of the generally much higher noise level on horizontal component recordings. Unfortunately no long-period records from the immediate vicinity of the volcano are available to study the ground motion in the source region in more detail.

Figure 1. The 24-h record from the IRIS (Incorporated Research Institutions for Seismology) station HRV at Cambridge, Mass., for June 15, 1991. Superimposed on the tides are the first two earthquakes (0059 G.m.t. and 0113 G.m.t.) followed by the signal from Mount Pinatubo (0700 G.m.t. or 1500 Philippine time). Philippine local time is 8 h ahead of G.m.t. In the upper panel the signal from the Pinatubo eruption is shown at higher resolution. The peak amplitude of the signal is approximately 0.5 gals.

Figure 2 shows the amplitude spectra of the 42 best vertical component VLP recordings from the global networks. The time period spans from 0600 to 1400 G.m.t. (1400 to 2200 local time) and the time series were Hanning tapered to reduce spectral leakage. The spectra are essentially bichromatic with two sharp peaks at 3.68 and 4.44 mHz (see also fig. 2 of Kanamori and Mori, 1992, and fig. 3 of Widmer and Zürn, 1992a). When Rayleigh waves travel around the Earth more than once, destructive and constructive interference produces spectra with discrete resonance peaks at the periods of the spheroidal free oscillations of the Earth. The amplitude pattern among the emerging peaks depends on the source mechanism and on epicentral distance. In figure 2 we see a strong variation from station to station in the relative amplitudes of the three fundamental spheroidal modes in the 4.44 mHz band. Because we know both the location of the source (Pinatubo) and the coordinates of the stations, we can use this amplitude variation to learn about the characteristics of the source. In order to test the model of an isotropically radiating source, we calculated spherical earth Green's functions for a vertical force couple acting at Pinatubo. A comparison with the observed spectra shows good agreement in the relative amplitudes of the three modes in the 4.44-mHz band and thereby confirms our hypothesis. We do not make use of the phase spectrum, because we lack a model of the time dependence of the source. Using a traveling wave analysis, Kanamori and Mori (1992) have determined the phase arrival times that are also found to be consistent with an isotropically radiating source. Figure 3 shows a world map with the location of the seismic stations that contributed to figure 2 spectra and demonstrates the global nature of the low-frequency observations discussed here. Table 1 lists the station codes, networks, station coordinates, and the azimuths and epicentral distances away from Pinatubo.

Figure 2. Linear amplitude spectra for the main eruption of Mount Pinatubo (0600 to 1400 G.m.t.). The 42 records are vertical components, taken from regional and global digital seismograph networks. Two resonances at 3.68 and 4.44 mHz are visible on all spectra. Because the time period contains recurring Rayleigh waves up to at least R₅, we can resolve individual fundamental spheroidal modes‹-that is, the peaks of the resonance around 4.44 mHz are ₀S₃₆-₀S₃₈. The spectra are normalized to have the same maximum amplitude, and the station codes are given at the right margin. The spectra are arranged so that the azimuth from Pinatubo increases from top to bottom (see also table 1). Note the similarity between stations KMI and KMY. These two stations are separated by only 2.8 km.

Figure 3. Molweide projection of the world with the locations of the seismic observatories that recorded the bichromatic signal that originated from Mount Pinatubo. The distribution of the stations demonstrates the global nature of the signal. The minor arcs connecting Pinatubo with the different stations are plotted to indicate the azimuthal coverage of the source (see table 1).

Table 1. Seismic stations that recorded the low-frequency signals from the Mount Pinatubo eruption.

[Listed are station code, and geographic coordinates of the stations, as well as the distance and azimuth from Mount Pinatubo. The entries are sorted according to the azimuth from Mount Pinatubo as in fig. 2]

The Pinatubo source has excited the elasto-gravitational spheroidal fundamental modes ₀S₂₈ and the triplet ₀S₃₆, ₀S₃₇, and ₀S₃₈. Thus, the source spectrum encompasses three fundamental spheroidal modes near 4.44 mHz and only one at 3.7 mHz. Considering that the fundamental spheroidal modes between 3 and 10 mHz are spaced at regular 100-Hz (0.1-mHz) intervals, the above observation shows that the source spectrum is narrower at 3.7 mHz than at 4.44 mHz. From the spectral stack in figure 4 it is clear that, additionally, Pinatubo emitted low-frequency seismic energy up to 7.2 mHz; so the bichromatism is not perfect.

Figure 4. Stack of the 42 spectra shown in figure 2. The spectra were normalized to unit maximum amplitude prior to summation. Several secondary resonances are visible between 4.5 and 7.2 mHz. At 7.4 mHz there seems to be a cutoff frequency beyond which no low-frequency seismic energy was transmitted. We also note the pronounced asymmetry of the resonance peak at 3.7 mHz. This asymmetry is expected if the 3.7 mHz resonance is the high-end cutoff frequency for freely propagating gravity waves as postulated by Kanamori and Mori (1992).

We see two reasons that the 36 events on Luzon mentioned above cannot be responsible for the observed long-period signal. First, if they were normal earthquakes, they were not energetic enough. The second reason, which also applies to "slow" and "silent" earthquakes (Beroza and Jordan, 1990), is that a seismic source that is localized in space and time possesses a broad frequency and wavenumber spectrum; hence, a broad spectrum of free oscillations is excited. One remaining possibility for the production of a narrow-band spectrum is a periodic occurrence of point sources with time. The listed earthquakes in the time period of our observations did not show such a periodicity but occurred in a random sequence.

We studied the phase coherence of the signals by using a version of a well-known method called "summation dial" by Bartels (1938) and "phasor walkout" by Rydelek and Sacks (1988). It is also similar to "complex demodulation" described by Bolt and Brillinger (1979). The contributions of successive samples in a time series to its Fourier transform at a given test frequency are added graphically in the complex domain ("phasor walk"). The final value is the complex Fourier coefficient of the whole series. In the idealized case of a time series consisting of a single sine wave the phasor walk consists of a straight line if the test frequency is equal to the signal frequency. If the test frequency is moved away from the frequency of the signal, the phasor walk shows more and more curvature. If multiple reexcitations of the harmonic signal under investigation occur without phase locking, the phasor walk will consist of several straight segments with sharp angles between them. If there is no harmonic signal detectable at this frequency, the plot looks like a random walk in two dimensions.

Figures 5A and 5B show these walkouts for the stations ALE (4.440 mHz) and BFO (3.723 mHz), respectively. These are examples in which the amplitude spectra consist of large isolated peaks and no leakage effects occur from neighboring peaks. The steady, linear growth of the phasor demonstrates that the source radiated in phase for at least 8 h. When the peak at 4.44 mHz (₀S₃₇) is smaller than its neighbors, ₀S₃₆ and ₀S₃₈, this is a sign for destructive interference between the different Rayleigh wave trains. This interference can be observed in the phasor walks, and it makes the picture more complicated. Another complication could arise due to air waves, which might be present in the later parts of the seismograms of the closest stations (see below). From figures 2 and 4 we can also identify resonances at frequencies up to 7.3 mHz, and the phasor walkouts for the frequencies 6.156 and 7.270 mHz at station HRV are shown in figures 5C and 5D. The steady, nearly linear growth indicates that these secondary resonances remained phase coherent for at least 6 h.

Figure 5. A, Phasor walkout for the 4.440 mHz spectral line at the International Deployment of Accelerometers (IDA) station at Alert, Canada (ALE). The steady growth of the Fourier coefficient with time demonstrates the phase coherence of the signal. The time period analyzed spans from 0600 to 1400 G.m.t. (1400 to 2200 local time). B, Phasor walkout for the 3.723-mHz spectral line at the Black Forest Observatory (BFO), Germany for the same time window as in figure 5A. C, Phasor walkout for the 6.156-mHz spectral line at station HRV. The relatively large lateral excursions in this phasor walk are caused by the high-amplitude signal at 3.7 and 4.4 mHz in the analyzed seismogram. However, the overall linear evolution of the phasor walk indicates that at least some of the secondary peaks in figure 4 correspond to phase-coherent resonances (see also fig. 5D). D, Phasor walkout for the 7.270-mHz spectral line at station HRV. Pinatubo radiated coherently at this frequency from at least 0800 to 1400 G.m.t. (1600 to 2200 local time).

OTHER OBSERVATIONS

BAROGRAMS FOR MOUNT PINATUBO

Kanamori and Mori (1992, fig. 6) and Oswalt and others (this volume) show the microbarogram from Clark Air Base, located about 21 km from the volcano. This record shows pressure pulses from individual explosions as well as continuous oscillations with peak amplitudes of about 300 Pa during the climactic phase of the eruption. Unfortunately, the time resolution is not good enough to determine the periods of these oscillations. Digital air-pressure records with 0.1-Pa resolution from Piñon Flat Observatory (station PFO) in southern California and the Black Forest Observatory (station BFO) in southwestern Germany did not show any unambiguous signals from this eruption.

Tahira and others (this volume), however, report acoustic-gravity waves with a dominant frequency at 1 mHz and a clear, isolated resonance at 4.4 mHz. This observation was made at several observatories in Japan so that the phase speed and direction of propagation could be determined and the source traced back to Pinatubo. Thirty-five hours after the onset of the climactic eruption of Pinatubo, a second disturbance was observed and identified as the airwave, A2, that traveled in the opposite direction from Pinatubo to Japan. The spectra of the direct air wave, A1, show no indication of a resonance at 3.7 mHz, while in the case of El Chichón, the 3.7-mHz signal was well observable in the late-arriving air wave. (See fig. 6 of Widmer and Zürn, 1992a.)

INFRARED SATELLITE IMAGE OF PINATUBO'S ERUPTION CLOUD

In infrared images from the NOAA-10 polar orbiting weather satellite taken on June 15 (Lynch and Stephens, this volume), numerous faint concentric bands can be distinguished in the eruption cloud from Mount Pinatubo. These images provide further evidence for narrow-band, low-frequency atmospheric oscillations.

SEARCH FOR PINATUBO-TYPE SEISMIC SIGNALS FROM OTHER ERUPTIONS

We searched the digital VLP seismic data sets for other Pinatubo-type signals--that is, quasi-harmonic wave trains of long duration. For recent eruptions of Bezymianny (Kamtchatka, February 11, 1979), Mount St. Helens (May 18, 1980), Galunggung (Java, 1982), Colo (Sulawesi, July 28, 1983), Mount Etna (Sicily, September 24, 1986), Redoubt (Alaska, December 15, 1989, January 8, 1990, April 21, 1990), Avachinsky (Kamtchatka, January 13, 1991), and Mount Spurr (Alaska, August 18, 1992), this kind of wave was not observed in the seismic records. However, our search was successful in the case of El Chichón (southern Mexico).

The El Chichón eruption of April 4, 1982, excited Rayleigh and air waves visible on the records from the digital global seismic networks (figs. 4, 5, and 6 of Widmer and Zürn, 1992a). Again, the spectrum turned out to be bichromatic, with frequencies of 3.70 and 5.14 mHz. The lower frequency is nearly the same as for Pinatubo, while the higher one is significantly different. Due to the relatively short duration of the signal in this case (approximately 1 h) we can distinguish two clear phases in the record section (fig. 4 of Widmer and Zürn, 1992a) of the El Chichón eruption: one with a group velocity of 3.7 km/s and the other with 300 m/s. Both have the same frequency contents. On the basis of their group velocity, the two wave groups were identified as Rayleigh and air waves. (In the case of Pinatubo the air-wave arrival, if it exists, is masked by the late-arriving Rayleigh waves.)

KRAKATOA (1883), TUNGUSKA (1908), MOUNT ST. HELENS (1980), AND ATMOSPHERIC NUCLEAR EXPLOSIONS

No VLP seismograms are available for the great Krakatoa explosion on August 27, 1883, or the Tunguska meteorite impact on June 30, 1908. However, these events were recorded on microbarographs worldwide and led to several theoretical investigations of the propagation of pulses in the atmosphere. From the published records one can clearly see that these signals were not of the Pinatubo or El Chichón type but consisted of a short, dispersed wave train with a broad spectrum (Pekeris, 1939, 1948). For the case of Krakatoa, however, Kanamori and others (1992) identified atmospheric pressure oscillations with periods of about 300 s (~3.3 mHz) in a barogram from Batavia (Java) about 200 km from Krakatoa. The period cannot be measured accurately because of lacking resolution. Short, dispersive wave trains were also typical for barograms and seismograms from atmospheric nuclear explosions, well documented in the literature (for example, Gossard and Hooke, 1975). Again, the observations were made in the farfield of the events.

When Mount St. Helens exploded on May 18, 1980, modern digital long-period seismographs recorded seismic body waves and dispersive Rayleigh wave trains very similar to the ones observed after earthquakes. Kanamori and Given (1982) and Kanamori and others (1984) analyzed these records to determine the source mechanism of the event. Pinatubo-like resonant behavior was not observed by these authors then. In addition to the Rayleigh waves dispersive air wave-trains with speeds around 300 m/s, very similar to air waves from atmospheric nuclear explosions, were observed worldwide on barographs, seismographs and gravimeters (Bolt and Tanimoto, 1981; Müller and Zürn, 1983). Recently, Kanamori and others (1992) claimed the observation of an atmospheric oscillation with a 300 s period (~3.3 mHz) on a digital long-period vertical seismograph at station LON, Longmire, Washington State, only 67 km from Mount St. Helens. As in the case of Krakatoa, these oscillations were only observed fairly close to the volcano.

CONVECTIVE STORMS

In the literature of atmospheric acoustic-gravity waves, we find one set of observations that appears very closely related to the bichromatic signal observed during the Pinatubo and El Chichón eruptions. Georges (1973) reports in a study of infrasound emitted from severe convective storms that ionosounders, which use radio waves to map the position of reflective horizons in the ionosphere, find bichromatic waves with frequencies of 3.7 and 4.8 mHz above convective storms. Georges also finds that the line at 3.7 mHz remains unchanged from storm to storm, whereas the higher frequency mode at 4.8 mHz varies by an appreciable (but unspecified) amount from event to event. Analysis of the ionosounder observations also shows that these waves travel in vertical direction and only exist above severe convective storms. Barograms from the vicinity of the storms are not bichromatic but show rather broad spectral features. It appears that the bichromatic oscillations in the ionosphere do not propagate very far away from their source. Considering that the lower frequency reported by Georges (1973) coincides nicely with the lower frequencies observed on seismographs for Pinatubo and El Chichón and that Georges' higher frequency is between the two higher frequencies observed for the two volcanoes, we conjecture that the bichromatism of Pinatubo, El Chichón, and severe convective storms has the same physical explanation.

JUNE 10, 1991

On June 10, 1991, between 1500 and 1800 G.m.t. a clear oscillation with a frequency of 3.7 to 3.8 mHz was observed at the Black Forest Observatory, at the Geoscope station SSB (near Lyon, southern France), and at MedNet station BNI (Italy, close to French border) on vertical seismographs. All our attempts to trace this signal to the then-active volcanoes Mount Pinatubo or Mount Unzen (Japan) failed. The signal was not as large at station BFO as the signal on June 15, 1991, but it was clearly above the noise level. No signal could be seen on the records of other European stations (for example MedNet stations besides BNI: ESK, GRF, KEV, KONO) or any other station of the global networks. Volcanoes being ruled out, we turned to meteorological possibilities, but we have not yet identified the source.

SOURCE MECHANISM

Periodic phenomena associated with volcanoes and geysers are well known. Examples are harmonic tremor (around 1 Hz), geyser repose periods (Old Faithful, Yellowstone), periodic modulations of seismic shock activity (see Martinelli, 1991), and periodic temperature variations in eruption clouds and pulsating or periodic eruptions (mentioned in Williams and McBirney, 1979). The periods corresponding to the above phenomena range from seconds to many hours. Another interesting periodic phenomenon was found by Woods and Caulfield (1992) in laboratory simulations of eruption mechanisms, where, under certain conditions, periodic release of buoyant parcels (called "thermals" by these authors) of material was observed.

However, a comparison of the observed resonance frequencies for Pinatubo and El Chichón with cutoff frequencies found in dispersion calculations for a stratified atmosphere (Harkrider, 1964) led Kanamori and Mori (1992) to suggest that these are free oscillations of the atmosphere excited by the eruption. According to their analysis, the pressure variations observed at Clark Air Base are large enough to explain the observed seismic amplitudes when a source area of radius 37 km is assumed. Underlying this analysis is the assumption that the periods of these pressure variations are the same as in the seismic records. The validity of this assumption may be questioned on the basis of figure 10 of Tahira and others (this volume), who show microbarograph power spectra of acoustic-gravity waves recorded at five different sites in Japan. The energy associated with the 4.4-mHz resonance in these spectra accounts for only approximately 15 percent of the total energy between 0.2 and 10 mHz. Because we do not know how the different spectral components decay with the propagation distance, we can only speculate about the spectrum of the atmospheric pressure variations in the vicinity of Pinatubo. The energy at 3.7 mHz produced at the source was effectively radiated as Rayleigh waves and not as air waves, while the reverse situation is true for the energy around 1 mHz. Most likely the cause for this lies with the energy distribution with height at the source for the different frequency bands.

We, too, favor an explanation where the frequencies are determined by the atmosphere and not by any oscillating phenomena inside the volcanoes. It would be very hard to explain the almost identical frequency of 3.7 mHz for Pinatubo, El Chichón, and the convective storms. However, in order to explain the phase coherence of the source, one has to assume that the oscillator was either only excited once or that reexcitation occurred periodically, perfectly in phase with itself. Single excitation can be ruled out because of the long duration of the climactic phases of the two eruptions. To assume that the reexcitation of the atmospheric oscillations occurred with perfect phase coherence is considered highly unlikely, unless the reexcitation is strongly influenced by the atmospheric oscillations themselves. We therefore propose a source model with positive feedback between the atmospheric free modes and the eruption process or the plume.

Much work has been done on the theory describing the propagation of acoustic-gravity waves in the atmosphere--for example Pekeris (1939, 1948), Lamb (1945), Harkrider (1964), Yeh and Liu (1974), and Francis (1975). From the dispersion relation for the simplistic case of an isothermal atmosphere overlying a rigid halfspace, one finds that three types of waves can exist: (1) the Lamb waves, propagating along the rigid surface, (2) acoustic waves, and (3) gravity waves. The frequency wavenumber domain in this case is split in two regions where freely propagating waves can exist: acoustic waves with frequencies above the acoustic cutoff frequency and gravity waves with frequencies below the Brunt-Väisälä frequency. At the cutoff frequencies, the horizontal wavenumbers (k_H) of the two types of waves vanish, and, thus, the direction of propagation at these frequencies is vertical. This implies that the long-term response in the nearfield of an impulsive source will consist only of a narrow-band signal with all energy concentrated at one or both cutoff frequencies. Energy at other frequencies has a finite horizontal wavenumber and will therefore propagate away from the source region. Numerical values of these cutoff frequencies for acoustic and acoustic-gravity branches for simple atmospheres correspond approximately to the two frequencies observed for the two eruptions, but it is very likely that the atmospheres over violently erupting volcanoes are not this simple. The same certainly applies to severe storms, possibly in a different way.

It is clear that atmospheric modes that strongly excite Rayleigh waves cannot be modes that have vanishing pressure amplitudes at the Earth's surface. From plots of the eigenfunctions given by Francis (1975), it appears that the fundamental gravity mode near its cutoff frequency has very small amplitude at ground level, and all its energy is concentrated around the thermopause at 200 km in altitude. This corroborates the interpretation of Chimonas and Peltier (1974), who suggest that the bichromatic spectra are due to the fundamental and first higher acoustic modes for k_H=0.

A more detailed theoretical investigation of the bichromatic spectrum observed in the ionosphere above severe convective storms was done by Jones and Georges (1976), who compute the transfer function for vertically propagating (k_H=0) acoustic waves between the altitudes of 10 and 300 km. They find three effects that shape the transfer function. At the low-frequency end, the transfer function is bounded by the acoustic cutoff frequency; at frequencies higher than 6 mHz, the transfer function rapidly rolls off due to absorption in the thermosphere; between these two frequencies, the spectrum is modulated by acoustic resonances due to the temperature stratification. The frequencies for these resonances are 3.7, 4.6, 5.3, and 6.6 mHz. From the vertical distribution of the displacement amplitudes, Jones and Georges (1976) identify the three higher frequencies as second-, third-, and fourth-order acoustic resonances between the ground and the base of the thermosphere. The lowest frequency resonance at 3.7 mHz occurs as a result of trapping in the temperature maximum at 50 km in altitude. Jones and Georges also find that the frequencies of the three higher resonances are a strong function of the temperature structure in the thermosphere (above 100 km in altitude) but that the frequency of the 3.7-mHz resonance is controlled by the mesospheric temperature profile. While the work of Jones and Georges (1976) is the most detailed theoretical investigation of the bichromatic ionospheric signal that we know of, it is not entirely evident how these results relate to the bichromatic seismic signal observed during the Pinatubo eruption. More work is needed in this field.

If we model the eruption as the superposition of a random sequence of individual explosions, we could obtain the farfield response (assuming linearity) by a convolution of the source time history and the Green's function of the earth-atmosphere system. The Green's function, however, is essentially what was recorded after the atmospheric nuclear explosions conducted around 1960. They have a very broad frequency content similar to the farfield signals from the very short (<4 min) climactic phase of the eruption of Mount St. Helens, the Tunguska event, and the eruption of Krakatoa.

In our source model, the volcanic eruption column and the surrounding atmosphere constitute a self-excited oscillator. This oscillator generates Rayleigh waves by periodically pushing on the surface of the Earth, and it generates Lamb waves (or higher modes) by periodically pushing on the neighboring atmosphere (El Chichón). We propose that the type of atmospheric oscillations that participate in the feedback correspond to waves with vanishing horizontal wavenumber (k_H=0), which are traveling vertically, up and down between the ground and the thermopause (at approximately 120 km altitude). These obviously do not propagate away from the source region. The bichromatic spectra now lead to an interpretation as the cutoff frequencies for the acoustic and gravity waves or for the fundamental and first higher acoustic mode, as suggested by Chimonas and Peltier (1974) and Jones and Georges (1976).

To explain why in the case of Mount St. Helens, Krakatoa, and the severe convective storms, the 3.7-mHz signal can be observed only in the nearfield, we propose that in these cases the vertically propagating waves were directly observed, while in the case of the air waves from El Chichón, the local resonances coupled with the Lamb waves, which then propagated around the globe. If this is correct, we would also expect to see these waves in the case of Pinatubo. As indicated previously, the suspected arrival of the bichromatic air wave is masked by late-arriving Rayleigh waves, and the only observation of the narrowband air waves emitted from Pinatubo that we know of was made with microbarographs in Japan.

A highly speculative physical model that can lead to positive feedback may consist of the following two elements:

1. The rising and expansion of the plume excites a broad spectrum of acoustic and gravity waves. The response of the atmosphere over the volcano, however, is dominated by the k_H=0 components of the atmospheric transfer function. This is the forcing of the atmosphere by the plume. (Note that waves for which the horizontal wave number is k_H>0 leave the source region laterally and hence cannot interact with the plume or participate in a feedback mechanism.)
2. If we assume that the atmosphere surrounding the plume undergoes harmonic pressure fluctuations, and if we further assume that the plume has a different compressibility than the surrounding atmosphere, then the plume will experience a harmonically varying buoyancy force. This will lead to a harmonic modulation in the rise and expansion of the plume. Such a harmonically forced plume will preferentially excite acoustic and gravity waves at the forcing frequency and can lead to positive feedback. This is the forcing of the plume by the atmosphere.

Of course, the phase of the feedback signal must be right for such a mechanism to work, but possibly this is a self-organized process. Thus, the atmosphere-plume system constitutes a self-excited oscillator, which then radiates seismic and air waves. The energy for this radiation must be provided by the volcano, of course. Presently, the evidence that Kanamori and Mori (1992) and we have collected is  circumstantial, and our mechanisms need further verification.

In conclusion, we point out that the bichromatic character of the Pinatubo and El Chichón signals is unique to these two eruptions. The observations we have presented cannot have been caused by a small number of very large explosions. A very strong oscillator was excited by the eruption that radiated the signals observed in the ground and the atmosphere. Explosions could be superimposed on this process but certainly did not dominate the farfield signals.

ACKNOWLEDGMENTS

We thank the operators of the global (IDA, IRIS, Geoscope) and regional (CDSN, MedNet) digital seismic networks for providing excellent low-frequency seismic data, NOAA for making available the infrared satellite image, T.M. Georges for sending us reprints and helping with the literature search, M. Tahira for an early version of his manuscript, D. Seidl for helpful comments, and K.H. Glassmeier for looking at magnetograms and for his interest. J. Mori and C. Newhall are gratefully acknowledged for constructive reviews. The figures were drafted with the programs PLOTXY by Robert Parker, and GMT by Paul Wessel and Walter Smith, and we would like to thank them for sharing these programs. This research was supported by Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 108: "Stress and Stress Release in the Lithosphere," Project D9. R. Widmer was partially supported through a fellowship from the Swiss Academy of Sciences.

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