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Evolution of the December 14, 1989 precursory long-period event swarm at Redoubt Volcano, Alaska
Journal of Volcanology and Geothermal Research 109 (2001) 133±148 www.elsevier.com/locate/jvolgeores
Evolution of the December 14, 1989 precursory long-period event swarm at Redoubt Volcano, Alaska C.D. Stephens*, B.A. Chouet US Geological Survey, 345 Middle®eld Road, M/S 977, Menlo Park, CA 94025, USA Received 30 July 1998; revised 18 January 2000; accepted 2 February 2000
Abstract The intermittency pattern and evolution in waveforms of long-period (LP) seismic events during the intense, 23-h swarm that preceded the December 14, 1989 eruption of Redoubt volcano are investigated. Utilizing cross correlation to exploit the high degree of similarity among waveforms, a substantially more complete event catalog is generated than was available from near realtime detection based on short-term/long-term amplitude ratios, which was saturated by the high rate of activity. The temporal magnitude distribution of the predominant LP events is found to have an unusual banded structure in which the average magnitude of each band slowly increases and then decreases through time. A bifurcation that appears in the uppermost band shortly after the peak in magnitudes is characterized by a quasi-periodicity in intermittency and magnitude that is reminiscent of one of the classic routes to chaotic behavior in some non-linear systems. The waveforms of the predominant events evolve slowly but unsteadily through time. These gradual changes appear to result from variations in the relative amplitudes of spectral peaks that remain stable in frequency, which suggests that they are due to differential excitation of a single, resonant source. Two other previously unrecognized, repetitive waveforms are also identi®ed, but the signals from these secondary events are not clearly recorded at distances beyond the closest station. Similarities among the spectra of the predominant and secondary events suggest that the signals from these events also could represent different modes of exciting the same source. Signi®cant changes in the rates and the sizes of the largest of these secondary events appear to coincide with the peak in the size distribution of the predominant LPs. At least some of the non-repetitive LP waveforms in the swarm appear to be the result of the superposition of signals from the rapid repetition of predominant LP source, thus placing a constraint on the repeat time of the triggering mechanism for this source. A lone hybrid event, which has a waveform character intermediate between the predominant LP events and high-frequency volcano-tectonic events, was also identi®ed in the swarm; the occurrence of this event provides important evidence that the low-frequency character of the LP events is a source rather than a path or site effect. q 2001 Elsevier Science B.V. All rights reserved. Keywords: volcano; long-period earthquakes; precursors; swarms; Redoubt
1. Introduction
* Corresponding author. Tel.: 11-650-329-4752; fax: 11-650329-5163. E-mail addresses: [email protected] (C.D. Stephens), [email protected] (B.A. Chouet).
The eruption of Redoubt volcano (Fig. 1) on December 14, 1989 was preceded by an intense swarm of long-period (LP) seismic events of about 23 h duration (Power et al., 1994). Most of these events have remarkably similar waveforms with dominant frequencies near 2 Hz (Fig. 2), and span at
0377-0273/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0377-027 3(00)00308-5
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Fig. 1. Seismograph stations on or near Redoubt Volcano that were operating during the December 14 swarm. Redoubt is an andesitic volcano situated near the eastern end of the Aleutian volcanic arc about 175 km southwest of Anchorage (inset; the northeast-trending Aleutian trench is located just off the southeast edge of the map area).
least two orders of magnitude ranging up to M1.6. Near the onset of the swarm the incidence rate of LPs was about once per minute, but as the swarm progressed their rate continually increased until at least 5 h prior to the eruption, at which time the seismic signals from individual events began to overlap and produce nearly continuous tremor. Throughout the interval of tremor the average spectral signature has dominant peaks matching those in the spectra of the earlier LP events (Stephens et al., 1994), which suggests that the source processes of LP events and tremor are genetically linked (e.g. Latter, 1979; Seidl, 1981; Fehler, 1983; Malone, 1983; Koyanagi et al. 1987; Hurst, 1992; Chouet, 1992). Chouet et al. (1994) modeled the seismic signals from the LP events in this swarm as the resonant vibrations of a single, magmatic ¯uid-®lled crack induced by unsteady ¯uid ¯ow. Their proposed triggering mechanism is the interaction between the crack walls and a shock wave that developed in the ¯uid as the ¯ow became supersonic downstream from a constriction in the crack. In this model, the ¯ux of
magmatic ¯uids through the crack is controlled by the pressure differential between a sealed, shallow hydrothermal system above the crack and an underlying magmatic reservoir (Fig. 3). Temporal variations in the size of the largest LP events and the average rate of seismic energy release, both of which peaked between 10 and 12 h before the eruption (Lahr et al., 1994), were interpreted by Chouet et al. (1994) as re¯ecting changes in the pressure differential between these two systems. Since the origin of the LP events likely originates in the dynamics of magmatic ¯uids, we were motivated to investigate whether some aspects of the swarm, in particular the intermittency of the LP events and the transition to tremor, re¯ect behaviors characteristic of non-linear systems. For example, one of the classic routes to chaotic behavior in non-linear systems driven by a time-varying forcing function is through a cascade of period-doubling sequences in intermittency (e.g. Moon, 1987). Evidence for chaotic behavior has been reported in the pattern of eruptions of the hydrothermal system at Old Faithful (Nicholl et
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al., 1994), and such behaviors are expected on the basis of theoretical models of ¯uid ¯ow in volcanic systems (e.g. Julian, 1994). In order to study the intermittent behavior of the LP swarm at Redoubt it was ®rst necessary to obtain a more complete record of events than was available from automatic, near real-time detection based on short-term/long-term amplitude ratios (e.g. Power et al., 1994) because this technique was desensitized by the high rate of activity. Taking advantage of the similarity among the waveforms, we employed cross correlation (e.g. Aster and Scott, 1993) to identify events in continuous recordings of the swarm. The event catalog we obtained is estimated to be nearly complete for events larger than about magnitude 0.5. While patterns such as period-doubling sequences in intermittency were not clearly evident, other important features were discovered that provide important constraints on the source mechanism of the LP events. 2. Event detection and classi®cation 2.1. Predominant events Event detection was based on locating peaks in the linear correlation function between a reference event and the time series of the swarm. Initially the record from station NCT was selected for processing because nearly all of the LP events recorded on-scale (the highest amplitudes of only a few of the largest events slightly exceeded the clipping level), and because the signal did not gain-range 1 throughout the swarm. Correlation parameters, selected on an empirical basis, include a correlation window length of 10 sÐ intermediate to the signal durations of the largest events (about 30 s) and the shortest time intervals between discrete smaller eventsÐand a minimum peak correlation coef®cient of 0.68 to declare a 1 Automatic gain-reduction by a factor of 10 occurs in the VCO of some seismic stations when the signal exceeds twice the clipping level (Rogers et al., 1980). Once triggered, gain-ranging persists for a minimum of 6 s and until the signal no longer exceeds clipping for at least 6 s. Although gain-ranging transitions are instantaneous with respect to the digitizing interval, signi®cant distortion of the signal in the form of spurious, high-frequency pulses is often observed in the interval between the time that the signal ®rst clips and the activation of gain-ranging, and is thought to be due to the discriminator losing lock.
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detection. In general, the correlation function in the neighborhood of similar events is oscillatory about a central peak, with side lobes at intervals roughly commensurate with the dominant period in the waveforms. To ensure that detection is based on relatively sharp peaks in the correlation function, the amplitudes of peaks adjacent to and of the same polarity as the central maximum were required to be less than 0.707 times the amplitude of the central peak. The relative sizes of the events were determined from the average absolute amplitude of the signal in the correlation window. This parameter was found to be more reliable and more consistent between stations than magnitudes determined from maximum peak-totrough amplitude and period measurements. Under the assumption that the waveforms scale linearly with event size, the magnitudes are then proportional to the log of the average signal amplitude, which are calibrated to local magnitude, M, using a set of located events for which magnitudes are determined from maximum-amplitude/period measurements (e.g. Eaton et al., 1970). After the ®rst pass of event detection, it was noted that the peak values of the correlation coef®cients gradually but continually decreased with increasing time separation from the reference event (Fig. 4a), even for events of comparable size and high signalto-noise ratios. This systematic variation suggested that the waveforms were gradually evolving. A similar result was observed using different reference events that occurred later in the swarm (Fig. 4b, c). To account for this evolution in the waveforms, the detection algorithm was designed to update the reference event whenever a new event with a correlation coef®cient at or above a designated threshold was detected (Fig. 4d). The revised reference event is formed by stacking two waveforms in the time domain: the ®rst is a normalized version of the current reference event scaled by a factor of 0.9, and the second is a normalized version of the newly detected event scaled by a factor of 0.1. A measure of the rate at which the waveforms evolve is obtained by correlating each new reference event with the initial reference event (Fig. 4e, f). The increased sensitivity of the detection algorithm is indicated by both the generally higher correlation coef®cients for all events and the greater number of events detected. The smallest events of this type detected at NCT
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Fig. 2. (a) Waveforms of a typical predominant LP (M 1.5) that occurred at 04:18, and stacked waveforms for LP1 and LP2 events recorded at the stations RDN, RED, NCT and RDT. The signals from LP1 and LP2 events cannot be discerned at stations more distant than RDN unless the signal-to-noise ratio is enhanced by stacking in the time domain. Accordingly, events with correlation coef®cients of 0.9 and larger at RDN were used to generate the stacked waveforms, and include 89 events of LP1 and 65 events of LP2. All of the waveforms for the 04:18 event and all of the RDN traces are aligned by the P-wave onsets, which can be clearly read. For each of the other stations, where the P-wave onsets are less certain, both stacked traces are aligned by the same offset as the 04:18 event relative to RDN. For the 04:18 event the signal at RDN is clipped during much of the ®rst 1 s following the P-wave arrival before gain-ranging begins, and clipping at RED produced a single spike about 4 s after the P-wave and several spikes in the last 1.5 s of the trace. (b) Normalized velocity spectra corresponding to the waveforms in (a).
were about M 0.2 (Fig. 5). However, the detection and completeness levels are not uniform through time due to changes in the signal-to-noise ratio which, in general, is a function of both amplitude and frequency. For example, as the activity rate increased the effective background noise level was also elevatedÐparticularly at frequencies near the dominant peak in the waveform spectraÐdue to the fact
that inter-event times approached the coda duration of individual events. Under the assumption that the general shape of the spectra of the background noise remains stable, an approximate measure of the temporal variation in background noise level was obtained by computing the median of the absolute values of the signal within 5-min intervals (Fig. 6). In general, events could be detected only if their size,
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Fig. 2. (continued)
expressed as the mean absolute amplitude of the signal in the correlation window, exceeded this threshold. Smaller events also typically have lower correlation coef®cients, but this appears to be due to a lower signal-to-noise ratio rather than a signi®cant difference in waveform shape (Fig. 7). This detection method clearly fails in cases where there is signi®cant interference between two or more events within the correlation window. Such instances are not easily recognized by other than a visual inspection of the seismograms, and thus their impact on the completeness of the catalog is dif®cult to quan-
tify. While the likelihood of such occurrences was greater later in the swarm when the rate of activity was highest, cases of overlapping events were identi®ed throughout the swarm (e.g. Fig. 8). We estimate that relatively few events of about M 0.5 and larger were undetected due to overlapping events, and that the ®nal catalog is nearly complete at this level prior to about 14 h UT (all absolute times in this paper are in UT). Fortuitously, at the closest station RDN many events with magnitudes at or below the detection threshold at NCT generally have much higher
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Fig. 3. Schematic model of (a) magmatic ¯uid ¯ow and (b) temporal pressure distribution prior to the December 14 eruption of Redoubt (from Chouet, 1996). The LP source is a crack connecting a perched magma chamber with volatiles at pressure Pm to a shallower hydrothermal reservoir at lower pressure Ph. This system is sealed by the dome emplaced at the end of the previous eruption in 1966. Prior to the initial eruption the pressure differential across the crack, which controls the rate of ¯uid ¯ux, varies through time due to differing rates of pressurization in the magma chamber and the hydrothermal system.
signal-to-noise ratios and are also relatively free of distortions from clipping and gain-ranging which affected larger events. Thus, many additional events ranging to as small as 20.5 and a few as large as about 0.9 were detected by applying waveform correlation to the record from this station (Fig. 5). That relatively few of these additional events have magnitudes above about 0.5 is consistent with the inferred completeness level for events detected at NCT. However, it is apparent from the temporal distribution of magnitudes that the detection threshold at RDN began to increase much earlier than at NCT, and by about 11 h UT the detection level is about the same at these two stations. 2.2. Secondary events At RDN, many events were identi®ed that correlate poorly (i.e. corr. coeff. , 0.69) with the predominant waveform type and are too small to be readily discerned at more distant stations. The waveforms of these events are also dominated by low frequencies near 2 Hz. By visual inspection, many of the secondary events were found to be characterized by one of two distinct repetitive waveforms (Fig. 2). Catalogs of these two event families, termed LP1 and LP2, were
generated using correlation detection with an evolving reference event. For LP1 events a correlation window length of only 4 s was used because in the seismograms it was observed that LP1 events occasionally, but not systematically, preceded larger predominanttype events by several or more seconds and could be readily distinguished on the basis of the distinct 5 Hz energy in the ®rst few seconds of the waveform. For LP2 events, a correlation window length of 7 s was used mainly because most of the energy was contained in this duration of signal. However, because the amplitudes in the ®rst 1 s of the LP2 signals typically have a low signal-to-noise ratio, it was necessary to stack the signals from 20 selected events to produce a reliable initial reference waveform for detecting these events. LP1 events were present throughout the swarm (Fig. 9). The sizes of the largest LP1 events remained at about the same level until about 9 h UT, at which point they began to increase slowly until the time of the eruption. LP1 events were detected frequently in the last few hours before the eruption when the predominant event type could no longer be detected. However, the relative enhancement in the detection of LP1 events during this interval is probably due to
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Fig. 4. Correlation coef®cients for the predominant LP waveform. (a±c) Coef®cients for 1095 events commonly detected using three different ®xed reference events. In each case, the time of the reference event is indicated by a `V' at the top of the plot. (d) Coef®cients for 1449 events detected using a reference event that was allowed to evolve (see text). For 65% of these events the correlation coef®cient is 0.9 or larger. Note that in general the correlation is much better throughout the swarm than for any case using a ®xed reference. (e) Coef®cient of the evolving reference event at NCT with respect to the starting reference event. The reference event was updated whenever the coef®cient of a newly detected event was 0.95 or larger (see text), which occurred for 664 events. (f) Coef®cient of the evolving reference event at RDN. The correlation threshold for updating the reference event was also 0.95, but only 82 events met this criteria, largely because signal distortions from clipping and gain-ranging contributed to generally lower correlation coef®cients. Note the similar trends in the plots for NCT and RDN.
the shorter correlation window emphasizing the characteristic higher-frequency onset of these waveforms. LP2 events, on the other hand, were nearly absent prior to about 9 h UT, but once active, both the rate and the size of the largest of these
events increased continually until the time of the eruption. Although the waveforms for some discrete longperiod events appear to be unique, in at least one case the waveform can be closely approximated by
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Fig. 5. Magnitude distribution through time for 1877 predominant-type LPs. Circles indicate 1448 events detected at NCT, of which 1201 were also detected at RDN, and crosses indicate 429 events detected only at RDN. Gray curve below is a normalized plot of seismic energy release, as measured by the sum of the squared signal amplitude in 10-min intervals. The interval labeled `Continuous Tremor' was characterized by inter-event times that were generally shorter than the coda durations of individual events, so that event detection was hindered by low signal-tonoise. The arrow at 11:44 indicates the approximate time interval shown in Fig. 11. There are two brief (15 and 10 m) intervals of missing or discontinuous data starting at 23:24 on December 13 and 04:48 on December 14. At the upper right, the cumulative (heavy solid curve) and interval (shaded bars) numbers of events are shown as a function of magnitude. Note the signi®cant departure from a linear distribution in the cumulative magnitude frequency distribution above the estimated magnitude completeness threshold of 0.5, and the large dip in the interval distribution centered near M 1.2.
Fig. 6. Relationship between event signal amplitude (circles), as measured by the absolute amplitude within the correlation window, and background noise (solid curves), which is approximated by the median of the absolute amplitude within 5-min intervals. Amplitude is measured in digital counts. For both NCT (a) and RDN (b) relatively few events were detected with signal amplitudes below the median signal amplitude, so the latter can be used to estimate the magnitude detection threshold. While the magnitude detection threshold at NCT increased only slightly throughout the swarm, the threshold increased by about 0.5 magnitude units at RDN, with the most rapid increase occurring between about 9 and 12 h. The apparent low density of events in the amplitude range of about 2.8±3 at RDN is an artifact caused by partial clipping of the signals; for larger events that triggered gain-ranging, the fraction of clipped signal during an event was much smaller.
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Fig. 7. Correlation coef®cient as a function of synthetically reconstructed signal-to-noise ratio. The signal at NCT from a relative large event (M 1.5) that occurred near 7 h was used as a reference. Noise from four different inter-event periods was in turn added to successively smaller versions of this signal, and in each case the summed signal was correlated against the original reference signal. Signal-to-noise is the ratio of the average absolute amplitude of the derived signal to the median of the absolute amplitude of the noise segment. The dashed line indicates the assumed detection threshold.
a linear superposition of two predominant waveforms offset in time by 0.27 s (Fig. 8). This observation is important because it provides a possible constraint on the maximum duration of the triggering mechanism. The inferred time offset between the events is comparable to the pressure pulse of 0.5 s duration used by Chouet et al. (1994) to model the dominant LP source. Similarly, some of the other apparently unique waveforms in the swarm may represent the superposition of seismic waves events that occurred close in time. The shortest interval suggested by these instances is on the order of 0.06 s. 2.3. Hybrid event The precursory swarm on December 14 was devoid of volcano-tectonic (VT) earthquakes (Stephens et al., 1994), even though such events were common after the ®rst eruption and include locations near the LP source (Power et al., 1994; Lahr et al., 1994). VTs are distinguished from LPs by a broader-band spectral signature enriched in higher frequencies, and are thought to be caused by brittle failure in rock. However, one event which is apparently a unique occurrence in the entire swarm on December 14 has a waveform which is very similar at low frequencies (below about 5 Hz) to that of the predominant LP type, but is distinguished by an unusually high-
Fig. 8. (Top) Seismograms showing one of the non-repetitive waveforms in the swarm (observed waveform) that correlated poorly with the predominant waveform (master) but closely corresponds to the linear superposition (synthetic) of time-shifted versions of the dominant waveform. (Bottom) Spectra of the three waveforms normalized in the 3±4 Hz interval. Note that peaks in all of the spectra occur at the same frequencies, but the peak near 2 Hz which dominates the master event is suppressed in the synthetic by destructive interference due to the offset between the summed traces.
frequency (near 10 Hz) onset and a clear compressive ®rst motion at RDN (Fig. 10). The similarity of these waveforms at low frequencies suggests that the two events had nearby origins (within about 150 m), although a precise relative location could not be determined because the higher-frequency event was recorded clearly only at RDN. The crack thickness (less than about 20 cm) for the LP source modeled by Chouet et al. (1994) is very small compared to the wavelength (about 500 m) of the seismic waves in the high-frequency onset of the hybrid event, so it is unlikely that attenuation effects in the source region can account for the observed difference in frequency content. Similar events with waveform characteristics intermediate to VTs and LPs, termed hybrids by Lahr et al. (1994), occurred frequently after the initial eruption and were located to within a few hundred meters
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of the predominant LP source of the December 14 swarm. These later hybrid events are thought to involve coupled volumetric and double-couple sources, and represent the interaction between brittle rock failure and resonance of a ¯uid-®lled crack. Thus, the observed differences in frequency content and ®rst motion at the beginning of the signal at RDN for the hybrid event on December 14 are interpreted as source rather than path effects.
3. Discussion 3.1. Magnitude distribution
Fig. 9. Magnitude distribution of LP1 (a) and LP2 (b) events. Note that the magnitudes of the largest events of either type are at or near the detection threshold for NCT (e.g. Fig. 6). Because of the relatively small sizes of these events and the shorter correlation windows (4 s for LP1 and 7 s for LP2) used to detect them, only those events with correlation coef®cients of 0.8 and larger are included. The apparent upper limit of about M 0.3 for LP2 events after 16 h is due in part to clipping of the signal.
Fig. 10. Seismogram and spectrum for the M 0.0 hybrid event at 08:01 (thin lines), and for an M 0.5 predominant-type LP that occurred about 21 s earlier (heavy lines). These two signals are remarkably similar except for the high-frequency onset of the hybrid event, which is re¯ected in a small peak at 10 Hz in the spectrum, and its clear compressive ®rst motion, which is opposite to that of the LP (unclear at this scale).
Based on a relatively small set of detected events, Lahr et al. (1994) noted an unusual bi-modal distribution in the frequency±magnitude relationship of the LP events. The frequency distribution of the more complete catalog of events presented here (Fig. 5, upper right) is consistent with this earlier observation and contrasts sharply with the typical linear Guternberg±Richter relationship found for VT earthquakes during the eruption sequence (Lahr et al., 1994). Viewed as a function of time and with a more complete record of events, the magnitude distribution reveals a striking multi-banded structure (Fig. 5). Similar, but less pronounced banding is apparent in the temporal distribution of magnitudes of LP events that preceded the May 18, 1980 eruption of Mount St Helens (e.g. Figs. 4 and 5 in Qamar et al., 1983). At Redoubt, the banding appears most distinct between about 6 and 10 h UT on December 14, when the largest LPs occur and the rate of seismic energy release is highest (we note that the principal features of this distribution persist even when events with correlation coef®cients less than 0.9 are excluded). Within at least the uppermost band the average magnitude initially increases, but at a gradually diminishing rate, until about 10 h before the eruption, and then decreases at an accelerating rate until at least a few hours before the eruption when discrete events can no longer be identi®ed. This unusual timefrequency distribution of events in the precursory LP swarm is consistent with the inference that the source process for these events is not controlled by brittle-elastic behavior. Shortly after the peak in magnitudes, at about 9 h
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Fig. 11. Example of intermittency of predominant LPs during a 5-m interval. The onset of each event is indicated by a `V' symbol with the magnitude above. Note the fairly regular pattern of alternating large and small magnitude and inter-event times.
UT, the uppermost band appears to bifurcate. Over the next 3 h the average magnitude in both branches decreases, but more rapidly within the lower branch so that it eventually appears to merge into the next lower band (Fig. 5). During this time period, the recurrence of LPs is characterized by intervals within which events from the upper and lower bands occur alternately in time, and the larger events repeat, to within a few seconds, about every minute (e.g. Fig. 11). These patterns, which persist up to several tens of minutes, are reminiscent of quasi-periodic behavior that precedes transitions to chaos in some non-linear systems (Moon, 1987). A second but less distinct bifurcation of the upper branch develops shortly after 12 h. 3.2. Evolution of the predominant LP source Progressive changes in the waveforms of the predominant LP events are evident at both NCT and RDN (Fig. 12). This evolution tends to occur gradually but at a variable rate, with the most rapid changes occurring between about 6 and 8 h UT at both stations, in approximately the same time interval that the largest LPs occur. Chouet et al. (1994) suggested that the size of the LPs is controlled by the pressure differential driving magmatic ¯uids through the crack. If source
properties otherwise remained stable through time, then the waveforms of comparable-sized events occurring before and after the peak in magnitudes would be expected to have generally similar shapes. Instead, the continuing divergence of the waveform shapes, relative to initial reference event, after the peak in magnitude (e.g. Fig. 4e) indicates that other properties of the source must also be continually changing through time. An important constraint on possible causes for the evolution in waveforms comes from the spectra of the LP events, in which the position of the peaks remain stable through time (Fig. 13). If these peaks correspond to resonant modes the source, then this observation implies that the geometry of the source and the bulk properties of any ¯uids within it must have remained relatively ®xed through time. Thus, temporal variations in the relative amplitudes of the peaks (for example, compare the peaks at 2.0 and 2.2 Hz in Fig. 13) can account for most of the temporal variations in the waveforms. Such amplitude variations could be produced either by altering the spectral content of the triggering mechanism or by relative spatial offsets between triggers acting on a single crack. We note that the generally high values of the correlation coef®cients among the predominant LP
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waveforms result mainly from similarities in the relatively high-amplitude, long-period components of the signals near 2 Hz, which contain most of the energy in the signals. At these longer periods, signi®cant changes in waveform shape tend to develop gradually during the swarm. At higher frequencies, however, and particularly within the emergent onsets of the waveforms, much greater variability is evident
Fig. 13. Normalized velocity spectra for the LP events of Fig. 12 recorded at NCT. Note the stability in the positions of peaks in the spectra through time as the relative amplitudes of these peaks change.
among events, even for those that occur nearby in time (Fig. 14). The greater variability observed at higher frequencies it attributed to differences in the space±time characteristics of the source triggering mechanism, whereas the long-period component of the signals is controlled by the resonant modes of the ¯uid-®lled crack that presumably change less rapidly through time. Fig. 12. Representative seismograms from successive hours of the swarm illustrating the evolution of the predominant LP waveforms at NCT (a) and RDN (b). The events all have magnitudes in the range 1.3±1.4 and have correlation coef®cients of 0.99 at NCT. Traces are normalized and aligned at 0 s by the detection times at NCT. Note the difference in time scale for the two stations. The signals at RDN begin clipping about 0.25 s after the P-wave onset, and gain-ranging occurs about 1 s into the record, as indicated by the square-wave pulses superimposed on the traces about 4 s into the record (3 s after gain-ranging begins); the RDN traces have not been corrected for gain-ranging so that the P-wave onsets can be more clearly observed.
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Fig. 14. Details of the P-wave onsets for two large LP events separated in time by about 90 s. For each station, the upper trace corresponds to an M 1.38 LP at 10:02:15 UT, and the lower trace to an M 1.45 LP at 10:03:45 UT. The traces are aligned in time by ®rst cross correlating the initial 1 s of the signals at NCT and then applying a constant offset in time to the traces for each of the other stations. Amplitudes are normalized for each trace. For RDN, the shaded box corresponds to an interval during which the signals for both events are distorted due to clipping; gain-ranging occurs at the end of this interval, so the amplitudes of the RDN signals are reduced by a factor of 10 compared to the earlier part of the record. Note the high degree of coherence between the signals at each station. As illustrated by these examples, only dilatations are observed at RDN, NCT, and RDT when the onsets of the initial P-waves are clear. At RED, however, there is often ambiguity in ascertaining the polarity of the initial P-waves due to the relatively weak, emergent character of the signals. For the earlier of the two events the dilatational onset at RED is clear, but for the second event the weak onset is probably obscured by noise, so that the apparent onset about 0.03 s later is compressional. Note that relative delay for the apparent onset of the second event at RED is about half the dominant period of the signal; in each case where the apparent ®rst motion at RED is compressional the relative onset time has a similar delay.
Using conventional location methods that involve picking P- and S-wave onset times, 2 the bestconstrained LP event locations determined by Lahr et al. (1994) have relative offsets of up to 500 m, although when measurement errors are considered 2 The identi®cation of S-waves for LP events in this swarm is problematic due to the narrow band character of the signals and to the fact that only single-component, 1-Hz vertical sensors were present at the three closest recording stations. Nonetheless, the high degree of similarity among LP waveforms allows phases to be consistently picked for all of the events, so that any bias to event locations resulting from the mis-identi®cation of a secondary phase is expected to be systematic.
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the locations are indistinguishable from a point source. Cross spectral analysis (e.g. Poupinet et al., 1984) offers the potential for obtaining more precise relative locations than conventional methods, but the emergent onsets and relatively narrowband spectral character of the LP event signals are not ideally suited to this type of analysis (e.g. FreÂmont and Malone, 1987; Scherbaum and Wendler, 1986). Furthermore, the interpretation of apparent delays on the order of the digital sampling interval is ambiguous because such delays can be caused either by small spatial offsets between sources or by small differences in source±time functions (e.g. Scherbaum and Wendler, 1986), or by small changes in velocity along the source-to-receiver path (e.g. Poupinet et al. 1984), such as might be caused by the opening of cracks as pressure increases within the volcano prior to eruption. With these limitations in mind, we applied cross spectral analysis to the signals at NCT for four events in each of four time periods near 3, 7, 11, and 14 h UT on December 14 to search for variations in the P-to-S time interval with respect to a master event that occurred late on December 13. The results suggest that interval variations on the order of 0.02 s (about 2.5 times the digital sampling interval) may be present, but the intervals do not systematically increase or decrease through time. The spread in S±P intervals corresponds to a radial offset from NCT of about 130 m, which is within the bounds of the crack size (280±380 m long, 140± 190 wide) determined by Chouet et al. (1994). Thus, within the context of this model, the evolution the waveforms may be caused by a change in the position of the trigger on the crack wall, as discussed below. The intermittency patterns, temporal magnitude distribution, and gradual evolution in the waveforms described above are key observations used by Morrissey and Chouet (1997) in their investigation of various models for the triggering mechanism of LP events at Redoubt under choked-¯ow conditions. In their preferred model, the shock wave which develops in the ¯ow becomes coupled to and remains in contact with the crack walls. The shock front maintains a quasi-stable position along the walls that is controlled by pi/po, the ratio of crack inlet and outlet pressures (Fig. 15). Above a critical value (about 2.48 in Fig. 15) the position of the shock front is very sensitive
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Fig. 15. Position of a shock front along the crack wall (along the Xdirection) as a function of the ratio of inlet-to-outlet pressure (pi/po) in the crack under conditions of supersonic ¯ow (from Morrissey and Chouet, 1997).
to pi/po, so that small, short-term perturbations in pi/po above the critical value will cause large, rapid excursions of the shock front along the crack walls. The force on the walls associated with the excursion of the pressure step at the shock front triggers LP events (Morrissey and Chouet, 1997). This force, and hence the size of the LP events, are related to the size of the pressure drop at the shock front and the distance that the shock front moves along the wall. Thus, the spectral content of the trigger can vary with both the duration of the excursion and the rate at which the shock front propagates. Longterm variations in pi/po will cause the equilibrium position of the shock front to migrate slowly along the walls, thus effectively changing the trigger position without radiating seismic energy and providing a mechanism to account for the gradual evolution in the waveforms. 3.3. Origin of secondary events The spatial relationship between repetitive secondary events and the dominant LPs cannot be easily resolved due to the weak signals produced by individual events at stations more distant than RDN. An attempt was made to improve the signal-to-noise ratio for the secondary events at the more distant stations by stacking similar events in the time domain
using the times of peak correlation at RDN for reference (Fig. 2). While ®rst-order differences in the waveforms are apparent, the P-waves have emergent onsets with arrival time uncertainties on the order of 0.1 s. Perhaps most signi®cant is the relative P-wave arrival at RED, which appears to be about 0.02 s early for LP1 events with respect to the predominant source. This time difference corresponds to a minimum spatial offset of about 50 m between the origins of these two event types. Uncertainties in determining the relative P-wave onsets for LP2 events allow for, but do not necessitate, even greater spatial offsets, but probably not more than a few hundred meters. If the waveforms represent spatially distinct sources, then one interpretation for the increased incidence of LP2 events near 9 h UT is that it represents increased ¯ow of magmatic ¯uids through a new or pre-existing pathway. The shunting of the ¯ow of magmatic ¯uids away from the crack that is the origin of the predominant LP events was suggested by Chouet et al. (1994) as a mechanism for reducing the pressure differential across the crack and thus reducing the sizes of the largest events. More striking than the differences in the waveforms are overall similarities in the spectra of the three event types (Fig. 2b). At each station most of the energy in the signals is in the same frequency band (about 1± 2.5 Hz), and there are many common spectral peaks, although with different relative amplitudes. Chouet et al. (1994) present evidence that the dominant spectral peaks in the LP events are a source effect rather than path or site effects. This conclusion is buttressed by the hybrid event that occurred during the swarm (Fig. 10). Thus, the nearby spatial origins and spectral similarities of the three LP event types raise the possibility that they could be generated by the same source excited by different modes of the triggering mechanism. The laboratory experiments of Meier et al. (1978), who studied the supersonic ¯ow of air through a rectangular duct, show that the shock wave can impinge on the walls either symmetrically (both walls) or asymmetrically (only one wall), with each mode producing very different patterns of pressure oscillations along the walls of the duct. These different modes of interaction between the shock front and the crack walls in the triggering model proposed by Morrissey and Chouet (1997) may account for the three different LP waveform signatures.
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4. Conclusions Linear correlation proved to be a powerful tool for detecting and classifying events with similar waveforms in the LP swarm that preceded the December 14, 1989 eruption at Redoubt Volcano. Sequences with repetitive waveforms are commonly observed at volcanoes, so that adapting this technique to near realtime monitoring could aid in quickly associating events that are in close spatial proximity and have similar source mechanisms. The magnitude distribution of the dominant event type in the mid-December swarm at Redoubt is characterized by an unusual banded structure in which the average magnitude of each band varies slowly through time and peaks near the time that the rate of seismic energy release is highest. Bifurcations that appear in these bands are associated with quasi-periodic behavior in intermittency and magnitude that are reminiscent of the behavior in some non-linear systems near the onset of chaotic behavior. Temporal variations in the correlation coef®cients through time re¯ect a gradual evolution of the waveforms, with the most rapid changes occurring in a several-hour period that coincides with the peak in seismic energy release. The cause of the waveform evolution is uncertain, but based on relative P- and S-wave arrival times, any spatial migration of the source is limited to about 150 m or less. Through time, the positions of peaks in the spectra of the LP events remain stable while the relative amplitudes of these peaks change. Within the context of a model of choked ¯ow through a crack as the source of LPs, the changes in the waveforms could be caused by migration of the triggering mechanism along the walls of the crack. An additional constraint on the source mechanism of the predominant LPs comes from an analysis of the signals of some discrete, non-repetitive waveforms in the swarm, which can be shown to closely correspond to linear superpositions of the dominant waveform with offsets on the order of 0.25 s; such cases can be interpreted as indicating the minimum repeat time for the triggering mechanism. Besides a predominant event type, two previously unrecognized families of repetitive LP events were identi®ed in the Redoubt swarm. These secondary events are too small to be clearly observed at other than the closest station, so that their location with
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respect to the predominant events cannot be constrained using P- and S-wave arrival times. However, the spectra of the predominant and secondary events share common spectral peaks, which suggests that they may represent different excitation modes of the same source. A single hybrid event was also identi®ed which provides important evidence that the dominant frequencies in the spectra of the LP events is a source rather than a path or site effect. Acknowledgements Reviews by R. Aster, E. Del Pezzo, D. Hill, F. Klein are gratefully acknowledged. W. Ellsworth kindly provided the computer programs that were modi®ed to perform the cross-spectral analysis. References Aster, R.C., Scott, J., 1993. Comprehensive characterization of waveform similarity in microearthquake data sets. Bull. Seismol. Soc. Am. 83, 1307±1314. Chouet, B.A., 1992. A seismic model for the source of long-period events and harmonic tremor. In: Gasparini, P., Scarpa, R., Aki, K. (Eds.). Volcanic Seismology. IAVCEI Proceedings in Volcanology, Springer-Verlag, Berlin, pp. 133±156. Chouet, B.A., 1996. Long-period volcano seismology: its source and use in eruption forecasting. Nature 380, 309±316. Chouet, B.A., Page, R.A., Stephens, C.D., Lahr, J.C., Power, J.A., 1994. Precursory swarms of lone-period events at Redoubt Volcano (1989±1990), Alaska: their origin and use as a forecasting tool. J. Volcanol. Geotherm. Res. 62, 95±136. Eaton, J.P., O'Neill, M.E., Murdock, J.N., 1970. Aftershocks of the Park®eld±Cholame, California earthquake: a detailed study. Bull. Seismol. Soc. Am. 60, 1151±1197. Fehler, M., 1983. Observations of volcanic tremor at Mount St Helens Volcano. J. Geophys. Res. 88, 3476±3484. FreÂmont, M.J., Malone, S.D., 1987. High precision relative locations of earthquakes at Mount St. Helens, Washington. J. Geophys. Res. 92, 10,223±10,236. Hurst, A.W., 1992. Stochastic simulation of volcanic tremor from Ruapehu. J. Geophys. Res. 51, 185±198. Julian, B.R., 1994. Volcanic tremor: nonlinear excitation by ¯uid ¯ow. J. Geophys. Res 99, 11859±11877. Koyanagi, R.Y., Chouet, B., Aki, K. 1987. Origin of volcanic tremor in Hawaii, Part I. Data from the Hawaiian Volcano Observatory 1969±1985. In: Decker, R.W., Wright, T.L., Stauffer P.H. (Eds), Volcanism in Hawaii. U.S. Geol. Surv. Prof. Pap. 1350, 1221±1257. Lahr, J.C., Chouet, B.A., Stephens, C.D., Power, J.A., Page, R.A., 1994. Earthquake classi®cation, location, and error analysis in a volcanic environment: implications for the magmatic system of
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the 1989±1990 eruptions at Redoubt Volcano, Alaska. J. Volcanol. Geotherm. Res. 62, 137±152. Latter, J.H., 1979. Volcanological observations at Tongariro National Park, 2 Types and classi®cation of volcanic earthquakes, 1976±1978, New Zealand Dept. Sci. Ind. Res., Geophys. Div., Wellington, Rep. 150. Malone, S.D., 1983. Volcanic earthquakes: examples from Mount St. Helens. In: Kanamori, H., Boschi, E. (Eds.), Earthquakes: Observations, Theory, and Interpretation. Elsevier/NorthHolland, Amsterdam, pp. 436±455. Meier, G.E.A, G. Grabitz, W.M. Jungowski, K.J. Witczak, and J.S. Anderson, 1978. Oscillations of the supersonic ¯ow downstream of an abrupt increase in duct cross section, Mitteilungen aus dem Max-Planck Institut fuÈr StroÈmungsforschung und der Aerodynamischen Versuchsanstalt, GoÈttingen, 65. Moon, F.C., 1987. Chaotic Vibrations: an Introduction for Applied Scientists and Engineers. John Wiley and Sons, Inc, New York. Morrissey, M.M., Chouet, B.A, 1997. Numerical investigation of choked ¯ow dynamics and its application to the triggering mechanism of long-period events at Redoubt Volcano, Alaska. J. Geophys. Res. 102, 7965±7983. Nicholl, M.J., Wheatcraft, S.W., Tyler, S.W., 1994. Is Old Faithful a strange attractor? J. Geophys. Res. 99, 4495±4503. Poupinet, G., Ellsworth, W.L., Frechet, J., 1984. Monitoring velo-
city variations in the crust using earthquake doublets: an application to the Calaveras fault, California. J. Geophys. Res. 89, 5719±5731. Power, J.A., Lahr, J.C., Page, R.A., Chouet, B.A., Stephens, C.D., Harlow, D.H., Murray, T.L., Davies, J.N., 1994. Seismic evolution of the 1989± 1990 eruption sequence of Redoubt Volcano, Alaska. J. Volcanol. Geotherm. Res. 62, 69±94. Qamar, A., St. Lawarence, W., Moore, J.N., Kendrick, G., 1983. Seismic signals preceding the explosive eruption of Mount St. Helens, Washington, on 18 May, 1980. Bull. Seismol. Soc. Amer. 73, 1797±1813. Rogers, J.A., Maslak, S., Lahr, J.C., 1980. A seismic electronic system with automatic calibration and crystal reference. U.S. Geol. Surv. Open-File Report 80-324. Scherbaum, F., Wendler, J., 1986. Cross spectral analysis of Swabian Jura (SW Germany) three-component microearthquake recordings. J. Geophys. 60, 157±166. Seidl, D., Schick, R., Riuscetti, M., 1981. Volcanic tremors at Etna: a model for hydraulic origin. Bull. Volcanol. 44, 43±56. Stephens, C.D., Chouet, B.A., Page, R.A., Lahr, J.C., Power, J.A., 1994. Seismological aspect of the 1989±1990 eruptions at Redoubt Volcano, Alaska: the SSAM perspective. J. Volcanol. Geotherm. Res. 62, 153±182.
Evolution of the December 14, 1989 precursory long-period event swarm at Redoubt Volcano, Alaska C.D. Stephens*, B.A. Chouet US Geological Survey, 345 Middle®eld Road, M/S 977, Menlo Park, CA 94025, USA Received 30 July 1998; revised 18 January 2000; accepted 2 February 2000
Abstract The intermittency pattern and evolution in waveforms of long-period (LP) seismic events during the intense, 23-h swarm that preceded the December 14, 1989 eruption of Redoubt volcano are investigated. Utilizing cross correlation to exploit the high degree of similarity among waveforms, a substantially more complete event catalog is generated than was available from near realtime detection based on short-term/long-term amplitude ratios, which was saturated by the high rate of activity. The temporal magnitude distribution of the predominant LP events is found to have an unusual banded structure in which the average magnitude of each band slowly increases and then decreases through time. A bifurcation that appears in the uppermost band shortly after the peak in magnitudes is characterized by a quasi-periodicity in intermittency and magnitude that is reminiscent of one of the classic routes to chaotic behavior in some non-linear systems. The waveforms of the predominant events evolve slowly but unsteadily through time. These gradual changes appear to result from variations in the relative amplitudes of spectral peaks that remain stable in frequency, which suggests that they are due to differential excitation of a single, resonant source. Two other previously unrecognized, repetitive waveforms are also identi®ed, but the signals from these secondary events are not clearly recorded at distances beyond the closest station. Similarities among the spectra of the predominant and secondary events suggest that the signals from these events also could represent different modes of exciting the same source. Signi®cant changes in the rates and the sizes of the largest of these secondary events appear to coincide with the peak in the size distribution of the predominant LPs. At least some of the non-repetitive LP waveforms in the swarm appear to be the result of the superposition of signals from the rapid repetition of predominant LP source, thus placing a constraint on the repeat time of the triggering mechanism for this source. A lone hybrid event, which has a waveform character intermediate between the predominant LP events and high-frequency volcano-tectonic events, was also identi®ed in the swarm; the occurrence of this event provides important evidence that the low-frequency character of the LP events is a source rather than a path or site effect. q 2001 Elsevier Science B.V. All rights reserved. Keywords: volcano; long-period earthquakes; precursors; swarms; Redoubt
1. Introduction
* Corresponding author. Tel.: 11-650-329-4752; fax: 11-650329-5163. E-mail addresses: [email protected] (C.D. Stephens), [email protected] (B.A. Chouet).
The eruption of Redoubt volcano (Fig. 1) on December 14, 1989 was preceded by an intense swarm of long-period (LP) seismic events of about 23 h duration (Power et al., 1994). Most of these events have remarkably similar waveforms with dominant frequencies near 2 Hz (Fig. 2), and span at
0377-0273/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0377-027 3(00)00308-5
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Fig. 1. Seismograph stations on or near Redoubt Volcano that were operating during the December 14 swarm. Redoubt is an andesitic volcano situated near the eastern end of the Aleutian volcanic arc about 175 km southwest of Anchorage (inset; the northeast-trending Aleutian trench is located just off the southeast edge of the map area).
least two orders of magnitude ranging up to M1.6. Near the onset of the swarm the incidence rate of LPs was about once per minute, but as the swarm progressed their rate continually increased until at least 5 h prior to the eruption, at which time the seismic signals from individual events began to overlap and produce nearly continuous tremor. Throughout the interval of tremor the average spectral signature has dominant peaks matching those in the spectra of the earlier LP events (Stephens et al., 1994), which suggests that the source processes of LP events and tremor are genetically linked (e.g. Latter, 1979; Seidl, 1981; Fehler, 1983; Malone, 1983; Koyanagi et al. 1987; Hurst, 1992; Chouet, 1992). Chouet et al. (1994) modeled the seismic signals from the LP events in this swarm as the resonant vibrations of a single, magmatic ¯uid-®lled crack induced by unsteady ¯uid ¯ow. Their proposed triggering mechanism is the interaction between the crack walls and a shock wave that developed in the ¯uid as the ¯ow became supersonic downstream from a constriction in the crack. In this model, the ¯ux of
magmatic ¯uids through the crack is controlled by the pressure differential between a sealed, shallow hydrothermal system above the crack and an underlying magmatic reservoir (Fig. 3). Temporal variations in the size of the largest LP events and the average rate of seismic energy release, both of which peaked between 10 and 12 h before the eruption (Lahr et al., 1994), were interpreted by Chouet et al. (1994) as re¯ecting changes in the pressure differential between these two systems. Since the origin of the LP events likely originates in the dynamics of magmatic ¯uids, we were motivated to investigate whether some aspects of the swarm, in particular the intermittency of the LP events and the transition to tremor, re¯ect behaviors characteristic of non-linear systems. For example, one of the classic routes to chaotic behavior in non-linear systems driven by a time-varying forcing function is through a cascade of period-doubling sequences in intermittency (e.g. Moon, 1987). Evidence for chaotic behavior has been reported in the pattern of eruptions of the hydrothermal system at Old Faithful (Nicholl et
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al., 1994), and such behaviors are expected on the basis of theoretical models of ¯uid ¯ow in volcanic systems (e.g. Julian, 1994). In order to study the intermittent behavior of the LP swarm at Redoubt it was ®rst necessary to obtain a more complete record of events than was available from automatic, near real-time detection based on short-term/long-term amplitude ratios (e.g. Power et al., 1994) because this technique was desensitized by the high rate of activity. Taking advantage of the similarity among the waveforms, we employed cross correlation (e.g. Aster and Scott, 1993) to identify events in continuous recordings of the swarm. The event catalog we obtained is estimated to be nearly complete for events larger than about magnitude 0.5. While patterns such as period-doubling sequences in intermittency were not clearly evident, other important features were discovered that provide important constraints on the source mechanism of the LP events. 2. Event detection and classi®cation 2.1. Predominant events Event detection was based on locating peaks in the linear correlation function between a reference event and the time series of the swarm. Initially the record from station NCT was selected for processing because nearly all of the LP events recorded on-scale (the highest amplitudes of only a few of the largest events slightly exceeded the clipping level), and because the signal did not gain-range 1 throughout the swarm. Correlation parameters, selected on an empirical basis, include a correlation window length of 10 sÐ intermediate to the signal durations of the largest events (about 30 s) and the shortest time intervals between discrete smaller eventsÐand a minimum peak correlation coef®cient of 0.68 to declare a 1 Automatic gain-reduction by a factor of 10 occurs in the VCO of some seismic stations when the signal exceeds twice the clipping level (Rogers et al., 1980). Once triggered, gain-ranging persists for a minimum of 6 s and until the signal no longer exceeds clipping for at least 6 s. Although gain-ranging transitions are instantaneous with respect to the digitizing interval, signi®cant distortion of the signal in the form of spurious, high-frequency pulses is often observed in the interval between the time that the signal ®rst clips and the activation of gain-ranging, and is thought to be due to the discriminator losing lock.
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detection. In general, the correlation function in the neighborhood of similar events is oscillatory about a central peak, with side lobes at intervals roughly commensurate with the dominant period in the waveforms. To ensure that detection is based on relatively sharp peaks in the correlation function, the amplitudes of peaks adjacent to and of the same polarity as the central maximum were required to be less than 0.707 times the amplitude of the central peak. The relative sizes of the events were determined from the average absolute amplitude of the signal in the correlation window. This parameter was found to be more reliable and more consistent between stations than magnitudes determined from maximum peak-totrough amplitude and period measurements. Under the assumption that the waveforms scale linearly with event size, the magnitudes are then proportional to the log of the average signal amplitude, which are calibrated to local magnitude, M, using a set of located events for which magnitudes are determined from maximum-amplitude/period measurements (e.g. Eaton et al., 1970). After the ®rst pass of event detection, it was noted that the peak values of the correlation coef®cients gradually but continually decreased with increasing time separation from the reference event (Fig. 4a), even for events of comparable size and high signalto-noise ratios. This systematic variation suggested that the waveforms were gradually evolving. A similar result was observed using different reference events that occurred later in the swarm (Fig. 4b, c). To account for this evolution in the waveforms, the detection algorithm was designed to update the reference event whenever a new event with a correlation coef®cient at or above a designated threshold was detected (Fig. 4d). The revised reference event is formed by stacking two waveforms in the time domain: the ®rst is a normalized version of the current reference event scaled by a factor of 0.9, and the second is a normalized version of the newly detected event scaled by a factor of 0.1. A measure of the rate at which the waveforms evolve is obtained by correlating each new reference event with the initial reference event (Fig. 4e, f). The increased sensitivity of the detection algorithm is indicated by both the generally higher correlation coef®cients for all events and the greater number of events detected. The smallest events of this type detected at NCT
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Fig. 2. (a) Waveforms of a typical predominant LP (M 1.5) that occurred at 04:18, and stacked waveforms for LP1 and LP2 events recorded at the stations RDN, RED, NCT and RDT. The signals from LP1 and LP2 events cannot be discerned at stations more distant than RDN unless the signal-to-noise ratio is enhanced by stacking in the time domain. Accordingly, events with correlation coef®cients of 0.9 and larger at RDN were used to generate the stacked waveforms, and include 89 events of LP1 and 65 events of LP2. All of the waveforms for the 04:18 event and all of the RDN traces are aligned by the P-wave onsets, which can be clearly read. For each of the other stations, where the P-wave onsets are less certain, both stacked traces are aligned by the same offset as the 04:18 event relative to RDN. For the 04:18 event the signal at RDN is clipped during much of the ®rst 1 s following the P-wave arrival before gain-ranging begins, and clipping at RED produced a single spike about 4 s after the P-wave and several spikes in the last 1.5 s of the trace. (b) Normalized velocity spectra corresponding to the waveforms in (a).
were about M 0.2 (Fig. 5). However, the detection and completeness levels are not uniform through time due to changes in the signal-to-noise ratio which, in general, is a function of both amplitude and frequency. For example, as the activity rate increased the effective background noise level was also elevatedÐparticularly at frequencies near the dominant peak in the waveform spectraÐdue to the fact
that inter-event times approached the coda duration of individual events. Under the assumption that the general shape of the spectra of the background noise remains stable, an approximate measure of the temporal variation in background noise level was obtained by computing the median of the absolute values of the signal within 5-min intervals (Fig. 6). In general, events could be detected only if their size,
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Fig. 2. (continued)
expressed as the mean absolute amplitude of the signal in the correlation window, exceeded this threshold. Smaller events also typically have lower correlation coef®cients, but this appears to be due to a lower signal-to-noise ratio rather than a signi®cant difference in waveform shape (Fig. 7). This detection method clearly fails in cases where there is signi®cant interference between two or more events within the correlation window. Such instances are not easily recognized by other than a visual inspection of the seismograms, and thus their impact on the completeness of the catalog is dif®cult to quan-
tify. While the likelihood of such occurrences was greater later in the swarm when the rate of activity was highest, cases of overlapping events were identi®ed throughout the swarm (e.g. Fig. 8). We estimate that relatively few events of about M 0.5 and larger were undetected due to overlapping events, and that the ®nal catalog is nearly complete at this level prior to about 14 h UT (all absolute times in this paper are in UT). Fortuitously, at the closest station RDN many events with magnitudes at or below the detection threshold at NCT generally have much higher
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Fig. 3. Schematic model of (a) magmatic ¯uid ¯ow and (b) temporal pressure distribution prior to the December 14 eruption of Redoubt (from Chouet, 1996). The LP source is a crack connecting a perched magma chamber with volatiles at pressure Pm to a shallower hydrothermal reservoir at lower pressure Ph. This system is sealed by the dome emplaced at the end of the previous eruption in 1966. Prior to the initial eruption the pressure differential across the crack, which controls the rate of ¯uid ¯ux, varies through time due to differing rates of pressurization in the magma chamber and the hydrothermal system.
signal-to-noise ratios and are also relatively free of distortions from clipping and gain-ranging which affected larger events. Thus, many additional events ranging to as small as 20.5 and a few as large as about 0.9 were detected by applying waveform correlation to the record from this station (Fig. 5). That relatively few of these additional events have magnitudes above about 0.5 is consistent with the inferred completeness level for events detected at NCT. However, it is apparent from the temporal distribution of magnitudes that the detection threshold at RDN began to increase much earlier than at NCT, and by about 11 h UT the detection level is about the same at these two stations. 2.2. Secondary events At RDN, many events were identi®ed that correlate poorly (i.e. corr. coeff. , 0.69) with the predominant waveform type and are too small to be readily discerned at more distant stations. The waveforms of these events are also dominated by low frequencies near 2 Hz. By visual inspection, many of the secondary events were found to be characterized by one of two distinct repetitive waveforms (Fig. 2). Catalogs of these two event families, termed LP1 and LP2, were
generated using correlation detection with an evolving reference event. For LP1 events a correlation window length of only 4 s was used because in the seismograms it was observed that LP1 events occasionally, but not systematically, preceded larger predominanttype events by several or more seconds and could be readily distinguished on the basis of the distinct 5 Hz energy in the ®rst few seconds of the waveform. For LP2 events, a correlation window length of 7 s was used mainly because most of the energy was contained in this duration of signal. However, because the amplitudes in the ®rst 1 s of the LP2 signals typically have a low signal-to-noise ratio, it was necessary to stack the signals from 20 selected events to produce a reliable initial reference waveform for detecting these events. LP1 events were present throughout the swarm (Fig. 9). The sizes of the largest LP1 events remained at about the same level until about 9 h UT, at which point they began to increase slowly until the time of the eruption. LP1 events were detected frequently in the last few hours before the eruption when the predominant event type could no longer be detected. However, the relative enhancement in the detection of LP1 events during this interval is probably due to
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Fig. 4. Correlation coef®cients for the predominant LP waveform. (a±c) Coef®cients for 1095 events commonly detected using three different ®xed reference events. In each case, the time of the reference event is indicated by a `V' at the top of the plot. (d) Coef®cients for 1449 events detected using a reference event that was allowed to evolve (see text). For 65% of these events the correlation coef®cient is 0.9 or larger. Note that in general the correlation is much better throughout the swarm than for any case using a ®xed reference. (e) Coef®cient of the evolving reference event at NCT with respect to the starting reference event. The reference event was updated whenever the coef®cient of a newly detected event was 0.95 or larger (see text), which occurred for 664 events. (f) Coef®cient of the evolving reference event at RDN. The correlation threshold for updating the reference event was also 0.95, but only 82 events met this criteria, largely because signal distortions from clipping and gain-ranging contributed to generally lower correlation coef®cients. Note the similar trends in the plots for NCT and RDN.
the shorter correlation window emphasizing the characteristic higher-frequency onset of these waveforms. LP2 events, on the other hand, were nearly absent prior to about 9 h UT, but once active, both the rate and the size of the largest of these
events increased continually until the time of the eruption. Although the waveforms for some discrete longperiod events appear to be unique, in at least one case the waveform can be closely approximated by
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Fig. 5. Magnitude distribution through time for 1877 predominant-type LPs. Circles indicate 1448 events detected at NCT, of which 1201 were also detected at RDN, and crosses indicate 429 events detected only at RDN. Gray curve below is a normalized plot of seismic energy release, as measured by the sum of the squared signal amplitude in 10-min intervals. The interval labeled `Continuous Tremor' was characterized by inter-event times that were generally shorter than the coda durations of individual events, so that event detection was hindered by low signal-tonoise. The arrow at 11:44 indicates the approximate time interval shown in Fig. 11. There are two brief (15 and 10 m) intervals of missing or discontinuous data starting at 23:24 on December 13 and 04:48 on December 14. At the upper right, the cumulative (heavy solid curve) and interval (shaded bars) numbers of events are shown as a function of magnitude. Note the signi®cant departure from a linear distribution in the cumulative magnitude frequency distribution above the estimated magnitude completeness threshold of 0.5, and the large dip in the interval distribution centered near M 1.2.
Fig. 6. Relationship between event signal amplitude (circles), as measured by the absolute amplitude within the correlation window, and background noise (solid curves), which is approximated by the median of the absolute amplitude within 5-min intervals. Amplitude is measured in digital counts. For both NCT (a) and RDN (b) relatively few events were detected with signal amplitudes below the median signal amplitude, so the latter can be used to estimate the magnitude detection threshold. While the magnitude detection threshold at NCT increased only slightly throughout the swarm, the threshold increased by about 0.5 magnitude units at RDN, with the most rapid increase occurring between about 9 and 12 h. The apparent low density of events in the amplitude range of about 2.8±3 at RDN is an artifact caused by partial clipping of the signals; for larger events that triggered gain-ranging, the fraction of clipped signal during an event was much smaller.
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Fig. 7. Correlation coef®cient as a function of synthetically reconstructed signal-to-noise ratio. The signal at NCT from a relative large event (M 1.5) that occurred near 7 h was used as a reference. Noise from four different inter-event periods was in turn added to successively smaller versions of this signal, and in each case the summed signal was correlated against the original reference signal. Signal-to-noise is the ratio of the average absolute amplitude of the derived signal to the median of the absolute amplitude of the noise segment. The dashed line indicates the assumed detection threshold.
a linear superposition of two predominant waveforms offset in time by 0.27 s (Fig. 8). This observation is important because it provides a possible constraint on the maximum duration of the triggering mechanism. The inferred time offset between the events is comparable to the pressure pulse of 0.5 s duration used by Chouet et al. (1994) to model the dominant LP source. Similarly, some of the other apparently unique waveforms in the swarm may represent the superposition of seismic waves events that occurred close in time. The shortest interval suggested by these instances is on the order of 0.06 s. 2.3. Hybrid event The precursory swarm on December 14 was devoid of volcano-tectonic (VT) earthquakes (Stephens et al., 1994), even though such events were common after the ®rst eruption and include locations near the LP source (Power et al., 1994; Lahr et al., 1994). VTs are distinguished from LPs by a broader-band spectral signature enriched in higher frequencies, and are thought to be caused by brittle failure in rock. However, one event which is apparently a unique occurrence in the entire swarm on December 14 has a waveform which is very similar at low frequencies (below about 5 Hz) to that of the predominant LP type, but is distinguished by an unusually high-
Fig. 8. (Top) Seismograms showing one of the non-repetitive waveforms in the swarm (observed waveform) that correlated poorly with the predominant waveform (master) but closely corresponds to the linear superposition (synthetic) of time-shifted versions of the dominant waveform. (Bottom) Spectra of the three waveforms normalized in the 3±4 Hz interval. Note that peaks in all of the spectra occur at the same frequencies, but the peak near 2 Hz which dominates the master event is suppressed in the synthetic by destructive interference due to the offset between the summed traces.
frequency (near 10 Hz) onset and a clear compressive ®rst motion at RDN (Fig. 10). The similarity of these waveforms at low frequencies suggests that the two events had nearby origins (within about 150 m), although a precise relative location could not be determined because the higher-frequency event was recorded clearly only at RDN. The crack thickness (less than about 20 cm) for the LP source modeled by Chouet et al. (1994) is very small compared to the wavelength (about 500 m) of the seismic waves in the high-frequency onset of the hybrid event, so it is unlikely that attenuation effects in the source region can account for the observed difference in frequency content. Similar events with waveform characteristics intermediate to VTs and LPs, termed hybrids by Lahr et al. (1994), occurred frequently after the initial eruption and were located to within a few hundred meters
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of the predominant LP source of the December 14 swarm. These later hybrid events are thought to involve coupled volumetric and double-couple sources, and represent the interaction between brittle rock failure and resonance of a ¯uid-®lled crack. Thus, the observed differences in frequency content and ®rst motion at the beginning of the signal at RDN for the hybrid event on December 14 are interpreted as source rather than path effects.
3. Discussion 3.1. Magnitude distribution
Fig. 9. Magnitude distribution of LP1 (a) and LP2 (b) events. Note that the magnitudes of the largest events of either type are at or near the detection threshold for NCT (e.g. Fig. 6). Because of the relatively small sizes of these events and the shorter correlation windows (4 s for LP1 and 7 s for LP2) used to detect them, only those events with correlation coef®cients of 0.8 and larger are included. The apparent upper limit of about M 0.3 for LP2 events after 16 h is due in part to clipping of the signal.
Fig. 10. Seismogram and spectrum for the M 0.0 hybrid event at 08:01 (thin lines), and for an M 0.5 predominant-type LP that occurred about 21 s earlier (heavy lines). These two signals are remarkably similar except for the high-frequency onset of the hybrid event, which is re¯ected in a small peak at 10 Hz in the spectrum, and its clear compressive ®rst motion, which is opposite to that of the LP (unclear at this scale).
Based on a relatively small set of detected events, Lahr et al. (1994) noted an unusual bi-modal distribution in the frequency±magnitude relationship of the LP events. The frequency distribution of the more complete catalog of events presented here (Fig. 5, upper right) is consistent with this earlier observation and contrasts sharply with the typical linear Guternberg±Richter relationship found for VT earthquakes during the eruption sequence (Lahr et al., 1994). Viewed as a function of time and with a more complete record of events, the magnitude distribution reveals a striking multi-banded structure (Fig. 5). Similar, but less pronounced banding is apparent in the temporal distribution of magnitudes of LP events that preceded the May 18, 1980 eruption of Mount St Helens (e.g. Figs. 4 and 5 in Qamar et al., 1983). At Redoubt, the banding appears most distinct between about 6 and 10 h UT on December 14, when the largest LPs occur and the rate of seismic energy release is highest (we note that the principal features of this distribution persist even when events with correlation coef®cients less than 0.9 are excluded). Within at least the uppermost band the average magnitude initially increases, but at a gradually diminishing rate, until about 10 h before the eruption, and then decreases at an accelerating rate until at least a few hours before the eruption when discrete events can no longer be identi®ed. This unusual timefrequency distribution of events in the precursory LP swarm is consistent with the inference that the source process for these events is not controlled by brittle-elastic behavior. Shortly after the peak in magnitudes, at about 9 h
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Fig. 11. Example of intermittency of predominant LPs during a 5-m interval. The onset of each event is indicated by a `V' symbol with the magnitude above. Note the fairly regular pattern of alternating large and small magnitude and inter-event times.
UT, the uppermost band appears to bifurcate. Over the next 3 h the average magnitude in both branches decreases, but more rapidly within the lower branch so that it eventually appears to merge into the next lower band (Fig. 5). During this time period, the recurrence of LPs is characterized by intervals within which events from the upper and lower bands occur alternately in time, and the larger events repeat, to within a few seconds, about every minute (e.g. Fig. 11). These patterns, which persist up to several tens of minutes, are reminiscent of quasi-periodic behavior that precedes transitions to chaos in some non-linear systems (Moon, 1987). A second but less distinct bifurcation of the upper branch develops shortly after 12 h. 3.2. Evolution of the predominant LP source Progressive changes in the waveforms of the predominant LP events are evident at both NCT and RDN (Fig. 12). This evolution tends to occur gradually but at a variable rate, with the most rapid changes occurring between about 6 and 8 h UT at both stations, in approximately the same time interval that the largest LPs occur. Chouet et al. (1994) suggested that the size of the LPs is controlled by the pressure differential driving magmatic ¯uids through the crack. If source
properties otherwise remained stable through time, then the waveforms of comparable-sized events occurring before and after the peak in magnitudes would be expected to have generally similar shapes. Instead, the continuing divergence of the waveform shapes, relative to initial reference event, after the peak in magnitude (e.g. Fig. 4e) indicates that other properties of the source must also be continually changing through time. An important constraint on possible causes for the evolution in waveforms comes from the spectra of the LP events, in which the position of the peaks remain stable through time (Fig. 13). If these peaks correspond to resonant modes the source, then this observation implies that the geometry of the source and the bulk properties of any ¯uids within it must have remained relatively ®xed through time. Thus, temporal variations in the relative amplitudes of the peaks (for example, compare the peaks at 2.0 and 2.2 Hz in Fig. 13) can account for most of the temporal variations in the waveforms. Such amplitude variations could be produced either by altering the spectral content of the triggering mechanism or by relative spatial offsets between triggers acting on a single crack. We note that the generally high values of the correlation coef®cients among the predominant LP
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waveforms result mainly from similarities in the relatively high-amplitude, long-period components of the signals near 2 Hz, which contain most of the energy in the signals. At these longer periods, signi®cant changes in waveform shape tend to develop gradually during the swarm. At higher frequencies, however, and particularly within the emergent onsets of the waveforms, much greater variability is evident
Fig. 13. Normalized velocity spectra for the LP events of Fig. 12 recorded at NCT. Note the stability in the positions of peaks in the spectra through time as the relative amplitudes of these peaks change.
among events, even for those that occur nearby in time (Fig. 14). The greater variability observed at higher frequencies it attributed to differences in the space±time characteristics of the source triggering mechanism, whereas the long-period component of the signals is controlled by the resonant modes of the ¯uid-®lled crack that presumably change less rapidly through time. Fig. 12. Representative seismograms from successive hours of the swarm illustrating the evolution of the predominant LP waveforms at NCT (a) and RDN (b). The events all have magnitudes in the range 1.3±1.4 and have correlation coef®cients of 0.99 at NCT. Traces are normalized and aligned at 0 s by the detection times at NCT. Note the difference in time scale for the two stations. The signals at RDN begin clipping about 0.25 s after the P-wave onset, and gain-ranging occurs about 1 s into the record, as indicated by the square-wave pulses superimposed on the traces about 4 s into the record (3 s after gain-ranging begins); the RDN traces have not been corrected for gain-ranging so that the P-wave onsets can be more clearly observed.
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Fig. 14. Details of the P-wave onsets for two large LP events separated in time by about 90 s. For each station, the upper trace corresponds to an M 1.38 LP at 10:02:15 UT, and the lower trace to an M 1.45 LP at 10:03:45 UT. The traces are aligned in time by ®rst cross correlating the initial 1 s of the signals at NCT and then applying a constant offset in time to the traces for each of the other stations. Amplitudes are normalized for each trace. For RDN, the shaded box corresponds to an interval during which the signals for both events are distorted due to clipping; gain-ranging occurs at the end of this interval, so the amplitudes of the RDN signals are reduced by a factor of 10 compared to the earlier part of the record. Note the high degree of coherence between the signals at each station. As illustrated by these examples, only dilatations are observed at RDN, NCT, and RDT when the onsets of the initial P-waves are clear. At RED, however, there is often ambiguity in ascertaining the polarity of the initial P-waves due to the relatively weak, emergent character of the signals. For the earlier of the two events the dilatational onset at RED is clear, but for the second event the weak onset is probably obscured by noise, so that the apparent onset about 0.03 s later is compressional. Note that relative delay for the apparent onset of the second event at RED is about half the dominant period of the signal; in each case where the apparent ®rst motion at RED is compressional the relative onset time has a similar delay.
Using conventional location methods that involve picking P- and S-wave onset times, 2 the bestconstrained LP event locations determined by Lahr et al. (1994) have relative offsets of up to 500 m, although when measurement errors are considered 2 The identi®cation of S-waves for LP events in this swarm is problematic due to the narrow band character of the signals and to the fact that only single-component, 1-Hz vertical sensors were present at the three closest recording stations. Nonetheless, the high degree of similarity among LP waveforms allows phases to be consistently picked for all of the events, so that any bias to event locations resulting from the mis-identi®cation of a secondary phase is expected to be systematic.
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the locations are indistinguishable from a point source. Cross spectral analysis (e.g. Poupinet et al., 1984) offers the potential for obtaining more precise relative locations than conventional methods, but the emergent onsets and relatively narrowband spectral character of the LP event signals are not ideally suited to this type of analysis (e.g. FreÂmont and Malone, 1987; Scherbaum and Wendler, 1986). Furthermore, the interpretation of apparent delays on the order of the digital sampling interval is ambiguous because such delays can be caused either by small spatial offsets between sources or by small differences in source±time functions (e.g. Scherbaum and Wendler, 1986), or by small changes in velocity along the source-to-receiver path (e.g. Poupinet et al. 1984), such as might be caused by the opening of cracks as pressure increases within the volcano prior to eruption. With these limitations in mind, we applied cross spectral analysis to the signals at NCT for four events in each of four time periods near 3, 7, 11, and 14 h UT on December 14 to search for variations in the P-to-S time interval with respect to a master event that occurred late on December 13. The results suggest that interval variations on the order of 0.02 s (about 2.5 times the digital sampling interval) may be present, but the intervals do not systematically increase or decrease through time. The spread in S±P intervals corresponds to a radial offset from NCT of about 130 m, which is within the bounds of the crack size (280±380 m long, 140± 190 wide) determined by Chouet et al. (1994). Thus, within the context of this model, the evolution the waveforms may be caused by a change in the position of the trigger on the crack wall, as discussed below. The intermittency patterns, temporal magnitude distribution, and gradual evolution in the waveforms described above are key observations used by Morrissey and Chouet (1997) in their investigation of various models for the triggering mechanism of LP events at Redoubt under choked-¯ow conditions. In their preferred model, the shock wave which develops in the ¯ow becomes coupled to and remains in contact with the crack walls. The shock front maintains a quasi-stable position along the walls that is controlled by pi/po, the ratio of crack inlet and outlet pressures (Fig. 15). Above a critical value (about 2.48 in Fig. 15) the position of the shock front is very sensitive
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Fig. 15. Position of a shock front along the crack wall (along the Xdirection) as a function of the ratio of inlet-to-outlet pressure (pi/po) in the crack under conditions of supersonic ¯ow (from Morrissey and Chouet, 1997).
to pi/po, so that small, short-term perturbations in pi/po above the critical value will cause large, rapid excursions of the shock front along the crack walls. The force on the walls associated with the excursion of the pressure step at the shock front triggers LP events (Morrissey and Chouet, 1997). This force, and hence the size of the LP events, are related to the size of the pressure drop at the shock front and the distance that the shock front moves along the wall. Thus, the spectral content of the trigger can vary with both the duration of the excursion and the rate at which the shock front propagates. Longterm variations in pi/po will cause the equilibrium position of the shock front to migrate slowly along the walls, thus effectively changing the trigger position without radiating seismic energy and providing a mechanism to account for the gradual evolution in the waveforms. 3.3. Origin of secondary events The spatial relationship between repetitive secondary events and the dominant LPs cannot be easily resolved due to the weak signals produced by individual events at stations more distant than RDN. An attempt was made to improve the signal-to-noise ratio for the secondary events at the more distant stations by stacking similar events in the time domain
using the times of peak correlation at RDN for reference (Fig. 2). While ®rst-order differences in the waveforms are apparent, the P-waves have emergent onsets with arrival time uncertainties on the order of 0.1 s. Perhaps most signi®cant is the relative P-wave arrival at RED, which appears to be about 0.02 s early for LP1 events with respect to the predominant source. This time difference corresponds to a minimum spatial offset of about 50 m between the origins of these two event types. Uncertainties in determining the relative P-wave onsets for LP2 events allow for, but do not necessitate, even greater spatial offsets, but probably not more than a few hundred meters. If the waveforms represent spatially distinct sources, then one interpretation for the increased incidence of LP2 events near 9 h UT is that it represents increased ¯ow of magmatic ¯uids through a new or pre-existing pathway. The shunting of the ¯ow of magmatic ¯uids away from the crack that is the origin of the predominant LP events was suggested by Chouet et al. (1994) as a mechanism for reducing the pressure differential across the crack and thus reducing the sizes of the largest events. More striking than the differences in the waveforms are overall similarities in the spectra of the three event types (Fig. 2b). At each station most of the energy in the signals is in the same frequency band (about 1± 2.5 Hz), and there are many common spectral peaks, although with different relative amplitudes. Chouet et al. (1994) present evidence that the dominant spectral peaks in the LP events are a source effect rather than path or site effects. This conclusion is buttressed by the hybrid event that occurred during the swarm (Fig. 10). Thus, the nearby spatial origins and spectral similarities of the three LP event types raise the possibility that they could be generated by the same source excited by different modes of the triggering mechanism. The laboratory experiments of Meier et al. (1978), who studied the supersonic ¯ow of air through a rectangular duct, show that the shock wave can impinge on the walls either symmetrically (both walls) or asymmetrically (only one wall), with each mode producing very different patterns of pressure oscillations along the walls of the duct. These different modes of interaction between the shock front and the crack walls in the triggering model proposed by Morrissey and Chouet (1997) may account for the three different LP waveform signatures.
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4. Conclusions Linear correlation proved to be a powerful tool for detecting and classifying events with similar waveforms in the LP swarm that preceded the December 14, 1989 eruption at Redoubt Volcano. Sequences with repetitive waveforms are commonly observed at volcanoes, so that adapting this technique to near realtime monitoring could aid in quickly associating events that are in close spatial proximity and have similar source mechanisms. The magnitude distribution of the dominant event type in the mid-December swarm at Redoubt is characterized by an unusual banded structure in which the average magnitude of each band varies slowly through time and peaks near the time that the rate of seismic energy release is highest. Bifurcations that appear in these bands are associated with quasi-periodic behavior in intermittency and magnitude that are reminiscent of the behavior in some non-linear systems near the onset of chaotic behavior. Temporal variations in the correlation coef®cients through time re¯ect a gradual evolution of the waveforms, with the most rapid changes occurring in a several-hour period that coincides with the peak in seismic energy release. The cause of the waveform evolution is uncertain, but based on relative P- and S-wave arrival times, any spatial migration of the source is limited to about 150 m or less. Through time, the positions of peaks in the spectra of the LP events remain stable while the relative amplitudes of these peaks change. Within the context of a model of choked ¯ow through a crack as the source of LPs, the changes in the waveforms could be caused by migration of the triggering mechanism along the walls of the crack. An additional constraint on the source mechanism of the predominant LPs comes from an analysis of the signals of some discrete, non-repetitive waveforms in the swarm, which can be shown to closely correspond to linear superpositions of the dominant waveform with offsets on the order of 0.25 s; such cases can be interpreted as indicating the minimum repeat time for the triggering mechanism. Besides a predominant event type, two previously unrecognized families of repetitive LP events were identi®ed in the Redoubt swarm. These secondary events are too small to be clearly observed at other than the closest station, so that their location with
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respect to the predominant events cannot be constrained using P- and S-wave arrival times. However, the spectra of the predominant and secondary events share common spectral peaks, which suggests that they may represent different excitation modes of the same source. A single hybrid event was also identi®ed which provides important evidence that the dominant frequencies in the spectra of the LP events is a source rather than a path or site effect. Acknowledgements Reviews by R. Aster, E. Del Pezzo, D. Hill, F. Klein are gratefully acknowledged. W. Ellsworth kindly provided the computer programs that were modi®ed to perform the cross-spectral analysis. References Aster, R.C., Scott, J., 1993. Comprehensive characterization of waveform similarity in microearthquake data sets. Bull. Seismol. Soc. Am. 83, 1307±1314. Chouet, B.A., 1992. A seismic model for the source of long-period events and harmonic tremor. In: Gasparini, P., Scarpa, R., Aki, K. (Eds.). Volcanic Seismology. IAVCEI Proceedings in Volcanology, Springer-Verlag, Berlin, pp. 133±156. Chouet, B.A., 1996. Long-period volcano seismology: its source and use in eruption forecasting. Nature 380, 309±316. Chouet, B.A., Page, R.A., Stephens, C.D., Lahr, J.C., Power, J.A., 1994. Precursory swarms of lone-period events at Redoubt Volcano (1989±1990), Alaska: their origin and use as a forecasting tool. J. Volcanol. Geotherm. Res. 62, 95±136. Eaton, J.P., O'Neill, M.E., Murdock, J.N., 1970. Aftershocks of the Park®eld±Cholame, California earthquake: a detailed study. Bull. Seismol. Soc. Am. 60, 1151±1197. Fehler, M., 1983. Observations of volcanic tremor at Mount St Helens Volcano. J. Geophys. Res. 88, 3476±3484. FreÂmont, M.J., Malone, S.D., 1987. High precision relative locations of earthquakes at Mount St. Helens, Washington. J. Geophys. Res. 92, 10,223±10,236. Hurst, A.W., 1992. Stochastic simulation of volcanic tremor from Ruapehu. J. Geophys. Res. 51, 185±198. Julian, B.R., 1994. Volcanic tremor: nonlinear excitation by ¯uid ¯ow. J. Geophys. Res 99, 11859±11877. Koyanagi, R.Y., Chouet, B., Aki, K. 1987. Origin of volcanic tremor in Hawaii, Part I. Data from the Hawaiian Volcano Observatory 1969±1985. In: Decker, R.W., Wright, T.L., Stauffer P.H. (Eds), Volcanism in Hawaii. U.S. Geol. Surv. Prof. Pap. 1350, 1221±1257. Lahr, J.C., Chouet, B.A., Stephens, C.D., Power, J.A., Page, R.A., 1994. Earthquake classi®cation, location, and error analysis in a volcanic environment: implications for the magmatic system of
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