Analysis of long-period events recorded at Mount Etna (Italy) in 1992, and their relationship to eruptive activity

Journal of Volcanology and Geothermal Research 114 (2002) 419^440 www.elsevier.com/locate/jvolgeores

Analysis of long-period events recorded at Mount Etna (Italy) in 1992, and their relationship to eruptive activity S. Falsaperla a;
, E. Privitera a , B. Chouet b , P. Dawson b a

Istituto Nazionale di Geo¢sica e Vulcanologia, Sezione di Catania, Piazza Roma 2, 95123 Catania, Italy b U.S.G.S, 345 Middle¢eld Road, MS 910, Menlo Park, CA 94025, USA Received 12 October 2000; received in revised form 26 July 2001; accepted 26 July 2001

Abstract Seismic activity recorded at Mount Etna during 1992 was characterized by long-period (LP) events and tremor with fluctuating amplitudes. These signals were associated with the evolution of the eruptive activity that began on December 14, 1991. Following the occurrence of numerous volcano-tectonic earthquakes at the onset of the eruption, LP events dominated the overall seismicity starting in January, 1992. The LP activity occurred primarily in swarms, which were temporally correlated with episodic collapses of the crater floor in the Northeast Crater. Source depths determined for selected LP events suggest a source region located slightly east of Northeast Crater and extending from the surface to a depth of 2000 m. Based on the characteristic signatures of the time series, four families of LP events are identified. Each family shares common spectral peaks independent of azimuth and distance to the source. These spectral features are used to develop a fluid-filled crack model of the source. We hypothesize that the locus of the LP events represents a segment of the magma feeding system connecting a depressurizing magma body with a dike extending in the SSE direction along the western wall of Valle del Bove, toward the site of the Mount Etna eruption. We surmise that magma withdrawal from the source volume beneath Northeast Crater may have caused repeated collapses of the crater floor. Some collapse events may have produced pressure transients in the subjacent dike which acted as seismic wave sources for LP events. 9 2002 Elsevier Science B.V. All rights reserved. Keywords: long-period event; crack; Etna; eruption; pit crater

1. Introduction Mount Etna is located along the eastern coast of Sicily (Fig. 1) in a complex geodynamic region dominated by convergence between Africa and Europe and the tensional processes of the Cala-

* Corresponding author. Tel.: +39-95-448084; Fax: +39-95-435801. E-mail address: [email protected] (S. Falsaperla).

brian Arc and Ionian boundary (e.g. Ghisetti, 1984; Malinverno and Ryan, 1986; Pollitz, 1991; Caccamo et al., 1996; Facenna et al., 1996; Cocina et al., 1997). The region is intersected by lithospheric fault systems with E^W, NE^SW, NW^SE and NNW^SSE orientations (Cristofolini et al., 1979; Ghisetti, 1979; Lanzafame and Bousquet, 1997; Monaco et al., 1997). The NNW^SSE oriented fault system crosses the eastern £ank of the volcano and plays an important role in the magmatic transport system beneath Etna (Frazzetta and Villari, 1981; Lo Giudice and Rasa',

0377-0273 / 02 / $ ^ see front matter 9 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 0 2 7 3 ( 0 1 ) 0 0 2 9 9 - 2

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Fig. 1. Permanent seismic network monitoring Mount Etna. Vertical component sensors are indicated by solid circles, three-component broadband sensors are marked by solid triangles. The two insets show the geographic location of Mount Etna and details of the active crater area, respectively. CC marks the location of the central crater.

1986; Ferrucci and Patane', 1993; Patane' et al., 1994; Bonaccorso et al., 1996). The persistent volcanic activity in the summit craters is characterized by phases of quiet degassing alternating with mild Strombolian activity, which occasionally evolves into fountaining and lava over£ows. Lateral eruptions may also occur

from fracture systems along the £anks of the volcano. Volcanic products range from tholeiitic to alkaline basalts, and analysis of recent erupted magmas reveals a composition spanning the Hawaiite and alkali basalt ¢elds (Armienti et al., 1989). The 1991^1993 eruption of Mount Etna pro-

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duced the largest lava e¡usion from this volcano in the past 300 yr. The eruption started on December 14, 1991, and terminated on March 31, 1993. During 473 days, 235U106 m3 of magma was erupted, forming a lava ¢eld extending over roughly 7.6 km2 (e.g. Barberi et al., 1993; Armienti et al., 1994; Calvari et al., 1994). The eruption developed along a fracture system originating near the SE subterminal crater and extending in the SSE direction along the western wall of the Valle del Bove, closely matching a previous fracture ¢eld formed in 1989. On December 14, 1991, brief episodes of lava fountaining occurred in the uppermost section of the fracture system, and two small lava £ows extended down the wall of Valle del Bove. Between December 14 and 15, 1991, eruptive activity resumed with a quiet e¡usion of magma accompanied by Strombolian explosions at the distal end (2200 m asl) of the fracture system. Strombolian activity faded during the following months and ceased by the middle of March, 1992. From March, 1992 through the end of March, 1993, eruptive activity was limited to a sustained lava £ow from the distal end of the fracture system. By early 1991, numerous swarms of volcanotectonic (VT) earthquakes started to occur in the western sector of the volcano at depths ranging from 30 to 3 km (Patane' et al., 1994). The out£ow of lava on December 14, 1991, was preceded at 01.47 GMT by a seismic swarm including more than 1000 VT earthquakes with magnitude ML v 1.0 (Ferrucci and Patane', 1993; Falsaperla et al., 1994). The source region of these earthquakes (Fig. 2) was located at high elevations beneath the southern £ank of the volcano, near the location where eruptive activity started (Ferrucci and Patane', 1993; Chouet et al., 1994a). VT activity virtually ceased on December 18, and only a few minor VT swarms occurred during the remainder of the eruption (Patane' et al., 1994; Falsaperla et al., 1994). VT swarms resumed in May, 1993, roughly 2 months after the termination of this eruption. Unlike VT activity, volcanic tremor was recorded during the entire episode of eruptive activity. Falsaperla et al. (1994) reported a sustained increase in the spectral amplitude of tremor at the

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Fig. 2. (a) Epicentral map, and (b) vertical E^W cross-section A^AP showing hypocentral locations of tectonic earthquakes (VT) and LP, events with error estimates for the latter. Open triangles and open circles indicate VT earthquakes in the 14 December, 1991 swarm and 15^18 December, 1991 sequence, respectively. Solid squares indicate LP events. Solid diamonds mark the location obtained from stacked traces for Families 1 and 3. The solid star marks the eruptive vent.

seismic station closest to the crater throughout 1991. The onset of the eruption was marked by a rapid increase in tremor amplitude over the course of about 1 h. Tremor amplitudes during this episode reached a maximum reduced displacement of 19 cm2 (Falsaperla et al., 1994). The tremor amplitudes remained at sustained levels until December 20, after which the tremor signal slowly faded. Only slight £uctuations in the background tremor amplitudes were observed after February, 1992. In contrast, long-period (LP) events became the dominant seismic activity recorded during the remainder of the eruption. LP seismicity is typical of regions where £uid dynamics plays a dominant role in the generation of elastic wave¢elds. The dominant role played by

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£uids produces a radiation spectrum characterized by distinct narrow-band peaks and distinguishes this seismicity from the B-type events described by Minakami (1974), whose broadband signatures

are characteristic of a source dominated by brittle failure of rock. LP events are a manifestation of pressurization inside magmatic and hydrothermal systems (Fehler and Chouet, 1982; Chouet et al., 1994b; Chouet, 1996; Gil Cruz and Chouet, 1997; Stix et al., 1997; Kumagai and Chouet, 2000). During the 1991^1993 Etna eruption, LP events usually occurred in swarms, although isolated LP events were observed beginning in January, 1992. The largest LP swarm occurred on September 6, 1992, and consisted of 60 LP events. During the periods February 26 through midMarch, 1992, on February 3, 1993, and March 28 through April 4, 1993, LP swarms were temporally correlated with visual observations of repeated collapses of the crater £oor in NE crater (Fig. 1), which led to the formation of a pit crater (Calvari et al., 1994; Coltelli et al., 1998). The three snapshots in Fig. 3 illustrate the evolution of the Northeast Crater morphology from 1991 to 1993. Although meteorological conditions and/or the presence of vapor inside the crater did not allow other simultaneous observations, the signature of LP events remained the same throughout 1992, suggesting that a similar process of incremental collapses operated throughout the entire period. The temporal correspondence between LP seismicity and crater £oor collapses represents a case history for Mount Etna, as this type of occurrence has not been reported for previous eruptions. In this paper, we focus on LP events recorded at Etna during the interval February^September, 1992. Our analyses are performed in the time, space, and frequency domains. The spectral peaks of the LP spectrum are used to model the LP source. Our seismic results are compared with gravimetric and ground deformation data to shed light on the dynamics of the magma feeder system during the 1991^1993 eruption.

Fig. 3. (a) Aerial view of Northeast Crater a few days after the beginning of the eruption (December 19, 1991, courtesy of Al¢o Amantia). Details of the inner part of the crater can be seen in the snapshots taken in July, 1992 (b) (courtesy of Paola Del Carlo) and June 6, 1993 (c) (courtesy of Sonia Calvari), showing vertical walls and £at £oor typical of pit craters. The photographs illustrate the deepening of the crater from 1991 to 1993.

2. Data We analyze LP seismicity recorded in the interval February^September, 1992, which covers one of the most active periods of seismic activity during the 1991^1993 eruption. The LP events were recorded by a permanent seismic network com-

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Fig. 4. Seismograms, spectrograms, and spectra of vertical ground velocity for stacked LP events in each of four LP families recorded at PDN. (a) Family 1, (b) Family 2, (c) Family 3, and (d) Family 4.

posed of nine stations (Fig. 1). The network is run by the Istituto Nazionale di Geo¢sica e Vulcanologia, in Catania, which has monitored the volcano continuously since 1989. The network includes seven analog stations equipped with vertical 1-Hz seismometers, and two digital stations (ESP and EGA in Fig. 1) featuring broadband (0.1^100 Hz) three-component sensors. A temporary digital station equipped with a threecomponent short-period sensor was also used at site TDF (Fig. 1). The seismic signals are transmitted either by cable or radio from the remote sites to Catania, where they are recorded on paper and processed by an automatic system that carries out real-time analyses and archives the digital data. Located 2.5 km from the summit craters, station PDN (Fig. 1) shows the earliest P-wave arrivals for all the LP events analyzed. As PDN is the sensor nearest to the source, we use this site as the reference station for our analyses. We selected a subset of LP events for our analyses based on their reduced displacement being above a minimum threshold amplitude. The reduced displacement for surface waves is given by Fehler (1983) as:

pffiffiffiffiffi pffiffiffiffiffiffi A 1 r RMSðuÞW 1 r ¼ pffiffiffiffiffiffiffiffi 2 2M

ð1Þ

where u is the measured displacement amplitude, A is the peak to peak amplitude of surface waves, 1 is the wavelength, r is the epicentral distance, and M is the instrument magni¢cation. LP events reaching a maximum reduced displacement of 104 cm2 were recorded in April and September, 1992, during the most energetic phases of seismic activity. Values of 110 cm2 were reported for LP seismicity recorded at Galeras (Colombia) during the emplacement and extrusion of a lava dome in 1991 (Gil Cruz and Chouet, 1997). We use 50 LP events with a minimum reduced displacement of 8 cm2 selected from the data recorded at PDN. 2.1. Temporal and spectral characteristics of the LP seismicity Chouet et al. (1994a) highlighted the di¡erences in waveforms and spectral content between closely located VT and LP events at Etna. VT events are characterized by clear P and S arrivals and broad-

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Fig. 5. Vertical component of ground velocity recorded at di¡erent stations for Family 1. (a) Station PDN, (b) station ESP, (c) station EGA, (d) station SCV, and (e) station CTS. The bottom trace shows the stack obtained at each station. Year, month, day, hour and minute at the onset of each event are indicated at the upper left of each trace.

band spectral contents with corner frequencies extending up to 10 Hz. LP events show emergent P phases, weak or non-existent S phases, and multiple narrowband spectral peaks with dominant frequencies below 5 Hz. The absence of a high-frequency phase at the beginning of each event distinguishes the LP events recorded at Mount Etna from those recorded at Redoubt (Chouet et al., 1994b) and Galeras (Gil Cruz and Chouet, 1997), where typical LP signatures are characterized by a high-frequency onset. This may be due to anelastic attenuation a¡ecting the signals observed at Etna, and/or source e¡ects.

Earthquake families are a recurrent feature of seismicity observed in volcanic areas (e.g. Okada et al., 1981; Malone, 1983; Stephens et al., 1994), and are attributed to similar source mechanisms operating in small volumes of rocks. Four families of LP events can be identi¢ed in the Etna data based on similarities between waveforms. These families represent 60% of the selected events. Fig. 4 shows a stack of LP events representative of each family at our reference station PDN. It is worth noting that a close similarity between signatures of events in each family is observed at each station of the network. For example, the

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Fig. 6. Vertical component of ground velocity recorded at station PDN for: (a) Family 2, (b) Family 3, and (c) Family 4. Note the di¡erent time scale in c. The bottom trace shows the stack for each family. Year, month, day, hour and minute at the onset of each event are indicated at the upper left of each trace.

waveforms for Family 1 recorded at various distances from the crater are depicted in Fig. 5. Three of the four families consist of events with individual duration of about 20 s, whereas Family 4 includes events with longer duration (about 40 s). The temporal distribution of LP events indicates that the four families are concurrent (see Figs. 5 and 6). No temporal evolution was observed in the signatures of LP events in individual families. Hypocenters for the best constrained LP events are located from ¢rst-arrival phase picks using a modi¢ed version of HYPOELLIPSE (Lahr, 1989), and a seven-layer velocity model derived from the velocity structure proposed by Hirn et

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al. (1991). An epicentral map and an E^W crosssection of LP and VT hypocenters for events recorded during the interval December, 1991^September, 1992 are shown in Fig. 2. The source region of LP events is located slightly east of Northeast Crater and extends from the surface to sea level. No VT event occurs within this region. The scattered distribution of LP hypocenters (Fig. 2) is the result of uncertainties in the P-phase picks. The observed similarity in waveforms within each family at each site suggests that the source volume may be signi¢cantly smaller than that determined by hypocentral locations. To improve the signal-to-noise ratio and reduce the location errors, we also compute the source locations for events of Families 1 and 3 using their stacked traces. We consider these two families, which show the strongest similarity in waveforms, to look for di¡erences in their relative location. The results of these analyses are depicted in Fig. 2 and can be compared with the locations obtained for individual events. Higher precision relative locations obtained using the cross-spectrum method of Fremont and Malone (1987) indicate that all LP events occurred within a restricted source volume a few hundred meters wide (S. Gambino, personal communication). Average spectra obtained at station PDN for each family are shown in Fig. 4. We used the spectral averaging method of Yuen (1978). The power spectra in Fig. 4 were obtained by stacking and averaging the spectra calculated for the vertical component of ground velocity for each event in a family. A 20-s-long window was used to calculate each spectrogram. LP events recorded at PDN exhibit a dominant peak at slightly di¡erent frequencies in each family. The dominant frequency is 3 Hz in Family 1, 3.3 Hz in Families 2 and 4, and 3.5 Hz in Family 3. Representative examples of power spectra obtained on the permanent network for events from Family 1 are depicted in Fig. 7. Narrow-band spectra are observed at all the stations for all the LP events analyzed. The energy is concentrated between 1 and 5 Hz, well below the usual frequency band of VT events recorded at the same stations. The frequencies of the spectral peaks recorded at two or more stations are listed in Table 1 for the four

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Fig. 7. Stacked spectra of vertical ground velocity obtained at ¢ve stations of the Etna network for the ¢rst family of LP events shown in Fig. 4a. Numbered arrows indicate peaks observed at two or more stations (see Table 1).

families of LP events. No spectral data are available at SCV for Family 4, and EGA for Families 3 and 4, as no records were obtained for these event families at these stations. Many common spectral peaks are observed at stations separated by distances of up to 20 km within our resolution of P 0.05 Hz. A comparison of the spectra in Fig. 7 highlights a range of excitation for spectral peaks observed at di¡erent stations, which is probably due to a combination of path and site e¡ects. Despite these di¡erences in spectral amplitudes, however, the evidence for common spectral peaks is compelling. As the wave¢elds recorded over such distant sites are obviously uncorrelated, some of the observed spectral features must be source related. In the following, we use polarization analyses to explore some of the other characteristics of the source of LP events.

2.2. Polarization analyses We use a method based on the algorithm of Flinn (1965), as developed by Jurkevics (1988), to determine the wave¢eld composition. Using three-component records, we calculate a covariance matrix whose eigenvalues and eigenvectors determine the amplitudes and directions of the particle motion polarization. In this procedure, the data are ¢ltered and polarization is estimated on overlapped, tapered windows. This method provides a powerful tool to characterize the composition of the wave¢eld when a suitable network geometry is available and/or dense seismic antennas are deployed. Our analysis is only partially representative of the overall seismic wave¢eld due to the limited number of three-component records available. Nevertheless, it sheds light on

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Table 1 Observed frequencies (Hz) of spectral peaks Peak

CTS

EGA

ESP

PDN

SCV

Family 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.98 ^ ^ 1.46 ^ 2.26 ^ 2.72 ^ 3.30 3.60 ^ 3.91

0.85 ^ 1.16 ^ 1.46 1.95 2.32 2.50 2.69 3.05 3.30 3.60 3.78 ^

0.85 ^ 1.10 ^ 1.46 2.01 2.26 2.44 2.62 ^ 3.30 ^ 3.78 ^

^ ^ 1.10 1.28 ^ 2.05 ^ ^ 2.69 2.99 3.30 3.54 3.78 ^

^ 1.02 ^ 1.34 ^ 2.01 ^ 2.44 2.62 3.05 3.25 3.54 ^ 3.91

Family 2 1 2 3 4 5 6 7 8 9 10 11 12 13

^ ^ 1.28 1.40 ^ ^ 2.62 2.81 ^ 3.30 3.60 ^ 3.91

0.85 1.16 ^ 1.46 1.95 2.50 2.69 ^ 3.05 3.30 3.60 3.78 ^

0.85 1.10 ^ ^ ^ 2.44 2.62 2.87 ^ 3.25 ^ 3.78 ^

^ 1.10 1.28 ^ 2.05 2.44 2.69 ^ 2.99 3.35 3.54 ^ 3.85

^ ^ 1.28 ^ 2.01 2.44 ^ 2.87 ^ 3.30 ^ ^ 3.91

Family 3 1 2 3 4 5 6 7 8

1.59 1.77 ^ ^ 2.87 ^ 3.30 ^

^ ^ ^ ^ ^ ^ ^ ^

1.53 1.83 2.26 2.69 2.93 3.11 3.35 3.85

^ 1.83 2.26 2.62 2.87 ^ 3.30 ^

^ ^ ^ 2.72 ^ 3.11 3.25 3.91

1.16 ^ ^ ^ 3.30 ^

^ ^ ^ ^ ^ ^

1.16 1.40 1.77 1.95 3.05 3.30 3.85

1.22 1.40 1.77 1.95 3.11 3.30 3.85

^ ^ ^ ^ ^ ^ ^

Family 4 1 2 3 4 5 6 7

some characteristics of the waves associated with the LP source. The subset of events analyzed consists of LP events representative of each family recorded at

station ESP (Fig. 8), with the exception of Family 2 for which no three-component record is available at this station. We also carried out analyses of LP events belonging to Families 2 and 3 re-

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Fig. 8. Example of polarization analysis performed at stations ESP (Family 1, Family 3, and Family 4) and EGA (Family 3). The seismogram at the top of the ¢gure depicts the vertical component. Zero degrees corresponds to the east^west direction in azimuth, and vertical direction for the incidence angle. The vertical band of shading marks the LP event onsets, which are dominated by P motion. The vertical dotted line identi¢es the largest component of motion in the LP record due to SH waves.

corded at stations TDF and EGA. Station TDF is located very close to the source region of LP seismicity and is also very near the cli¡ £anking Valle del Bove to the WNW (Fig. 1). Characteristics of the wave¢eld observed in the TDF records were thus attributed to a combination of near-¢eld and

topographic e¡ects. For this reason, no further attempt was made to interpret the polarization observed at TDF in terms of source properties. The polarization analyses at ESP and EGA highlight complex temporal patterns with high variability of the incident wavefront (Fig. 8).

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The general interpretation of these patterns suggests the presence of body waves arriving from a broad range of azimuths. Apart from body waves, particle motion analysis shows surface waves, some of which have retrograde elliptical motion characteristic of Rayleigh waves (Chouet et al., 1994a). We describe the main polarization characteristics shared at ESP and EGA by LP events in di¡erent families, focusing on the ¢rst arrivals and maximum of the normalized eigenvalue function. First arrivals (see vertical band of shading in Fig. 8) are dominated by waves with high rectilinearity and sharply varying azimuth. Incidence angles at the event onset are nearly vertical and vary slightly in LP events belonging to di¡erent families, probably re£ecting di¡erent source depths. The dominant eigenvalue is characterized by a high rectilinearity (see vertical dotted line in Fig. 8) and is polarized in the horizontal plane in a direction that is almost orthogonal to the ¢rst arrival direction. This feature suggests that these phases are dominated by SH waves. Overall, our polarization study reveals a wave¢eld characterized by a combination of body and surface waves, which show similarities in events belonging to different families. The main feature of the wave¢elds is the prevalent horizontal polarization. These results are in agreement with the ¢ndings of polarization analyses carried out on volcanic tremor and gas^piston events recorded at other volcanoes, such as Hawaii (Ferrazzini et al., 1991) and Stromboli (Chouet et al., 1997).

3. Crack model The similar signatures of the LP waveforms and common spectral peaks observed at all the stations suggest that a repeatedly activated resonator generated the LP events. Table 1 shows that the spectral peaks are not regularly spaced. Simple spherical models (Crosson and Bame, 1985), or organ pipe source models (e.g. Seidl et al., 1981; Chouet, 1985) cannot produce these types of harmonics. We assume that the observed spectral characteristics of LP events at Etna are produced

429

by a crack-like source, and compare the spectral peaks of the four LP families with the modes of resonance of the £uid-¢lled crack model of Chouet (1986, 1988, 1992). This model accounts for the interference of the lateral and longitudinal modes of resonance of the crack, which produces irregularly spaced peaks. In addition, a £uid-¢lled crack is an excellent generator of shear waves and thus can provide a natural explanation for the strong shear components observed in the signal. Chouet (1986) used a ¢nite di¡erence method to calculate the dynamic response of a rectangular £uid-¢lled crack. The impulse response of the crack depends on a dimensionless parameter called the crack sti¡ness de¢ned as: C¼

b L W d

ð2Þ

where b is the bulk modulus of the £uid, W is the rigidity of the solid, L is the crack length, and d is the crack aperture. The crack sti¡ness controls the speed of the crack wave, which is always slower than the acoustic speed of the £uid, leading to resonant periods that are longer than those expected from acoustic resonance. The dispersion characteristics of the crack wave can be described in terms of the dimensionless ratio e/a plotted as a function of dimensionless wavelength 1/L, in which e is the phase velocity of the crack wave, a is the acoustic speed of the £uid, and 1 is the wavelength. Dispersion curves are shown in Fig. 9 for several values of crack sti¡ness. A transverse crack sti¡ness may be de¢ned by replacing the crack length L by the crack width W in Eq. 2. In our analysis, we consider a crack containing a two-phase £uid composed of gas and liquid, and assume that the gas phase is dominated by water vapor. The robustness of our model is tested for di¡erent values of the ratio K/a, where K is the compressional wavespeed in the rock, which is assumed constant. 3.1. Application of the crack model The physical parameters of the solid (e.g. rigidity, density, P- and S-wave velocities) and £uid

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(e.g. bulk modulus, density, sound velocity) play a critical role in the estimation of the source dimension. We de¢ne these parameters by considering two plausible conditions representative of £uids mostly constituted by liquid (Model 1), or foam (Model 2). We also consider a third, more extreme condition in which the £uid is a pure gas (Model 3). The model parameters are ¢xed from thermodynamic conditions (Table 2). The values for Model 1 are based on thermodynamic condition number 3 in Table 2, and those for Model 2 represent average values of the parameters obtained in thermodynamic conditions 1, 2, and 4 in Table 2. Parameter values for Model 3 are based on literature data (see Appendix A). To determine whether the frequencies listed in Table 1 are compatible with the dispersion curves in Fig. 9, we calculate the dimensionless frequency XP = (e/a)/((K/a)(1/L)), in which e/a is obtained from the dispersion curves. We assume the oscillation mode associated with a speci¢c spectral peak, and use the wavelength 1 of that mode given by the model. The crack length, L, is then calculated from the observed spectral peak frequency, X, using the relation L = KXP/X. The match between our data and the dispersion curves is found by applying a trial and error procedure. We accept the ¢t when it is obtained on a su⁄cient number of spectral peaks in the sequence of Table 1, and is compatible with a single crack dimension within a tolerance of 10%. In our search for a match, we ¢rst ¢t the sequence of frequencies listed in Table 1 by assuming that these represent the longitudinal modes of vibration. The frequencies that do not ¢t are then treated as lateral modes using the same procedure. In that case, the parameter L is substituted with the parameter W in Fig. 9, and we calculate the

Fig. 9. Ratio e/a of the phase velocity of the crack wave to acoustic speed of the £uid, plotted as a function of dimensionless wavelength 1/L for various crack sti¡nesses ranging between 50 and 500. (Reproduced from Chouet, 1986, 1992; Chouet et al., 1994b.)

transverse crack sti¡ness Ct = (b/W)(W/d), which is directly derived from the ratio W/L. For each family, we apply a wide range of combinations of modes of resonance and spectral peaks for a variety of crack sti¡nesses. The procedure is repeated using di¡erent values of sound velocity (Table 2). We obtained one model (Model 2) which shows a reasonable ¢t for each family. Other models show a high number of frequencies that do not match the ¢xed crack dimensions. The results of the ¢ts are shown in Table 3. Longitudinal and lateral modes of resonance that match the observed spectral peaks of the four families are reported in Table 4. The few spectral peaks that do not match the models are interpreted as the results of departures from the rectangular crack geometry and/or simpli¢ed £uid dynamics

Table 2 Thermodynamic parameters Condition P H2 O Ag (MPa) (wt%)

bl bg bm cpg cvg cl m (g/cm3 ) (g/cm3 ) (g/cm3 ) (kJ/K kg) (kJ/K kg) (kJ/K kg)

am b b/W (km/s) (MPa)

1 2 3

10 10 25

1 2 1

0.47 2.57 0.76 2.57 0 2.56

0.02 0.02 ^

1.37 0.63 2.56

2.61 2.59 ^

2.15 2.13 ^

1.44 1.44 1.45

0.004 1.72 0.014 1.75 0 2

4

25

2

0.34 2.54

0.04

1.69

2.67

2.21

1.46

0.007 1.82

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25.6 0.0026 14.3 0.0014 1.7^ 1.7172 1.9U104 80.6 0.0081

K/am bm /bs 1.98 1.94 1.7

0.55 0.26 1.04

1.87

0.68

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in Chouet’s model. The overall results provide an argument in favor of the assumption that the frequencies listed in Table 1 are the e¡ects of source properties. 3.2. Excess pressure To complete our analysis, we consider the excess pressure vP acting at the LP source. The excess pressure may be estimated from the expression for surface waves given by (Aki, 1984): pffiffiffiffiffiffi 2ZRMSðuÞ 1 r RMSðvPÞ ¼ ð1=QR Þ1=2 ½V =ðN X b s bcÞ1=2

ð3Þ

where RMS(u) is the reduced displacement of surface waves, QR is the quality factor corresponding to the radiation loss, V is the volume of the crack, N is a factor characterizing the e¡ective depth of penetration of surface waves, X is the dominant frequency of LP events, bs is the density of the solid, b is the bulk modulus of the £uid, and c is the surface wave velocity. We estimate vP for the minimum and maximum values of the reduced displacements of Rayleigh waves. For the LP seismicity considered here, these reduced displacements range from 8 to 104 cm2 . The volume of the crack is di¡erent in each of the four families of LP events. The actual values of V we use for each model are reported in Table 3. We assume a homogeneous half space and ¢x N = 0.2 (Aki, 1984). Values of X are 3.0 Hz (Family 1), 3.3 Hz (Family 2), 3.5 Hz (Family 3), and 3.3 Hz (Family 4). These values correspond to the spectral peak having the largest amplitude at PDN. Based on the assumptions described in Appendix A, we ¢x bs = 2.47 g/cm3 , b = 1.8U104 , 25.6, 14.3, and 14 MPa, respectively, in the four simulations considered, and use c = 1.59 km/s. The quality factor QR is obtained from the re31 31 (Aki, 1984), where Q is lation Q31 R = Q 3Qi the apparent quality factor and Qi is the quality factor due to intrinsic losses at the source. The values of QR we consider for Models 1 and 2 are obtained from the results of Kumagai and Chouet (2000), and are representative of cracks

431

containing a pure liquid (Model 1), or foamy liquid (Model 2) for the physical conditions considered in our simulations. For all families we ¢x QR = 5 for a pure liquid (Model 1), and QR = 180 for a foamy liquid (Model 2) (Kumagai and Chouet, 1999, 2000) (Table 3). is negligibly small comFor a pure gas, Q31 i (Kumagai and Chouet, 2000) so pared to Q31 R that QVQR . Therefore, our estimate of QR for Model 3 is the result of a direct measurement of the quality factor for each family. The factor Q is given by (Aki and Richards, 1980): Q¼

X vX

ð4Þ

where X is the frequency of the dominant spectral peak, and vX is the bandwidth of the spectral peak measured at mid-spectral amplitude. From the largest spectral peak at PDN, we obtain Q = 17 for Family 1 and Family 2, Q = 13 for Family 3, and Q = 18 for Family 4 (Table 3). These values are used in Eq. 3 assuming QR wQ. The excess pressures estimated with Eq. 3 are listed in Table 3. Although there are remarkable di¡erences in the values of vP calculated for the three models, the range of variation in all families of LP events for a given model is quite small. The minimum and maximum excess pressures associated with the four families are 20 and 280 kPa for Model 1. In Model 2, vP spans the range 5^60 kPa, and in Model 3, vP is in the range 0.8^17 kPa.

4. Discussion and conclusions The locus of LP seismicity in 1992 is con¢ned to a small volume located southeast of the summit craters and ranging in depth from the surface to sea level (Fig. 2). No VT earthquake occurred in the same area immediately before and/or during the eruption. VT earthquakes were located in a wide area surrounding the region of LP hypocenters (Fig. 2). Chouet et al. (1994a) postulated that the lack of VT seismicity in this region may be due to the absence of strong barriers to magmatic intrusion along a pathway overlapping the NE

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Table 3 Longitudinal (Long) and lateral (Lat) modes of resonance Family 1 Model 1 C = 500 Ct = 466 b/W = 0.1 K/a = 1.7 QR = 5

Model 2 L = 388 m W = 370 m d = 7.8 cm V = 11 198 m3 vP = 21.9^284.4 kPa

Model 3

C = 500 Ct = 457 b/W = 0.1 K/a = 2.3 QR = 180

L = 396 m W = 362 m d = 7.9 cm V = 11 325 m3 vP = 4.9^64 kPa

X(Hz)

Long.

C = 200 Ct = 191 b/W = 0.1 K/a = 3.4 QR = 17

L = 386 m W = 365 m d = 19.3 cm V = 27 192 m3 vP = 1^12.7 kPa

W

X(Hz)

Long.

338

0.85 1.00 1.13 1.30 1.46 2.00 2.29 2.46 2.69 3.00 3.30 3.57 3.78 3.91

Vibration mode dimensions (m)

X(Hz)

Long.

0.85 1.00 1.13 1.30 1.46 2.00 2.29 2.46 2.69 3.00 3.30 3.57 3.78 3.91

L/2

Lat

L

W

424 W/2

2L/5

384 400

2W/5 L/3

380 358

W/3 2L/7

336 359

2W/7 L/4

354 376

W/4 2L/9

373 382

2W/9 L/5

394 417

0.85 1.00 1.13 1.30 1.46 2.00 2.29 2.46 2.69 3.00 3.30 3.57 3.78 3.91

Lat

L

W/2 2L/5

389 2W/5

L/3

368 412

W/3 2W/7 L/4 2L/9

395 356 369 415

W/4 L/5

343 407

2W/9 W/5 2L/11

338 350 385

2W/11

404

Lat

L

W/2 2L/5

W 353

403 2W/5

L/3 2L/7

340 386 353

L/4

390 W/4

2L/9

346 389

2W/9 L/5

393 378

W/5 2L/11

405

394

Family 2 Model 1 C = 500 Ct = 466 b/W = 0.1 K/a = 1.7 QR = 5

Model 2 L = 389 m W = 378 m d = 7.8 cm V = 11 469 m3 vP = 21.6^281 kPa

Model 3

C = 500 Ct = 480 b/W = 0.1 K/a = 2.3 QR = 180

L = 407 m W = 391 m d = 8.1 cm V = 12 890 m3 vP = 4.6^60 kPa

X(Hz)

Long.

C = 200 Ct = 183 b/W = 0.1 K/a = 3.4 QR = 17

L = 396 m W = 362 m d = 19.8 cm V = 28 384 m3 vP = 0.9^16.8 kPa

X(Hz)

Long.

Vibration mode dimensions (m)

X(Hz)

Long.

0.85 1.13 1.28 1.43 2.00 2.47 2.66 2.84 3.02 3.30 3.57 3.78 3.91

L/2

Lat

L

2L/5

406 2W/5

L/3 2L/7

388 358 359

2W/7 L/4

358 374

W/4 2L/9

373 382

2W/9 L/5

W

424

394 417

0.85 1.13 1.28 1.43 2.00 2.47 2.66 2.84 3.02 3.30 3.57 3.78 3.91

Lat

L

2W/5 L/3

W 368

418 W/3

L/4

403 422

W/4 2L/9

374 384

2W/9 L/5

393 404

W/5 2L/11

402 408

2W/11

404

0.85 1.13 1.28 1.43 2.00 2.47 2.66 2.84 3.02 3.30 3.57 3.78 3.91

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Lat

L

W/2 2L/5

W 353

354 2W/5

L/3

346 394

2W/7 L/4

379 389

W/4 2L/9

350 411

L/5

409 2W/9

2L/11

363 419

W/5

381

S. Falsaperla et al. / Journal Volcanology and Geothermal Research 114 (2002) 419^440

433

Table 3 (Continued). Family 3 Model 1 C = 500 Ct = 466 b/W = 0.1 K/a = 1.7 QR = 5

Model 2 L = 401 m W = 370 m d = 8.0 cm V = 11 869 m3 vP = 21.3^276.2 kPa

Model 3

C = 500 Ct = 489 b/W = 0.1 K/a = 2.3 QR = 180

L = 395 m W = 386 m d = 7.9 cm V = 12 045 m3 vP = 4.8^62.2 kPa

W

X(Hz)

Long.

356

1.56 1.80 2.26 2.66 2.93 3.11 3.30 3.88

2L/7

C = 200 Ct = 183 b/W = 0.1 K/a = 3.4 QR = 13

L = 412 m W = 378 m d = 20.6 cm V = 32 082 m3 vP = 0.8^10.2 kPa

X(Hz)

Long.

Vibration mode dimensions (m)

X(Hz) 1.56 1.80 2.26 2.66 2.93 3.11 3.30 3.88

Long.

Lat

L

2W/5 L/3 2L/7

397 391 2W/7

L/4

358 385

W/4 2L/9 L/5

396 413 420

Lat

L

W

424 2W/7

L/4 2L/9 L/5

396 374 384 417

2W/9 W/5 2L/11

359 402 375

1.56 1.80 2.26 2.66 2.93 3.11 3.30 3.88

Lat

L

W/3 2L/7 L/4

W 390

393 425 W/4

2L/9 L/5

350 399 434

2W/9 2L/11

393 408

Family 4 Model 1 C = 500 Ct = 460 b/W = 0.1 K/a = 1.7 QR = 5

Model 2 L = 402 m W = 396 m d = 8.0 cm V = 12 735 m3 vP = 20.5^266.7 kPa

Model 3

C = 500 Ct = 471 b/W = 0.1 K/a = 2.3 QR = 180

L = 393 m W = 370 m d = 7.9 cm V = 11 487 m3 vP = 4.9^63.5 kPa

X(Hz)

Long.

C = 200 Ct = 191 b/W = 0.1 K/a = 3.4 QR = 18

L = 400 m W = 381 m d = 20.0 cm V = 30 480 m3 vP = 0.9^12.3 kPa

X(Hz)

Long.

Vibration mode dimensions (m)

X(Hz) 1.19 1.40 1.77 1.95 3.08 3.30 3.85

Long.

Lat

L

2W/5 L/3

396 404

W/3 L/4 2L/9 L/5

W

395 366 413 423

1.19 1.40 1.77 1.95 3.08 3.30 3.85

Lat

L/3 2L/7 L/4 L/5

L 383 374 433 396

W/5 2L/11

branch of the fracture system which opened in 1989. Based on this assumption we suggest that anomalous thermal conditions may have strongly a¡ected the region in which LP events occurred. Thus, high temperatures due to magma intrusion may have e¡ectively prevented the brittle failure of rocks and attendant occurrence of VT earthquakes. The majority of LP events can be classi¢ed into four families on the basis of waveform similarity. Particle motion and polarization analyses provide evidence for the presence of both body and surface waves in the wave¢elds of LP events. The

W

370 378

1.19 1.40 1.77 1.95 3.08 3.30 3.85

Lat

L

2W/5 L/3 2L/7

372 403 399

2W/7 2L/9 L/5 2L/11

W

389 379 409 411

wave¢elds show dominant horizontal polarization. These features suggest that the source is an e⁄cient SH wave generator, and are indicative that the source geometry is incompatible with a simple spherical or vertical pipe-like object. Furthermore, spectral analyses reveal several dominant peaks that are common to records from widely separated stations for which the wave¢elds are obviously uncorrelated. The common spectral peaks are interpreted as evidence of a source effect, and are used to model the source. The source is modeled as a £uid-¢lled crack (Chouet, 1986, 1988, 1992), which is an e⁄cient SH-wave gener-

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Table 4 Application of the £uid-¢lled crack model Model

C

Ct

L

W

d

(m)

(m)

(cm)

Z

vP

K/am

bm /bs

b/W

Number of peaks matched

(kPa)

Family 1 1 2 3

500 500 200

466 457 191

388 P 25 396 P 18 386 P 18

370 P 21 362 P 26 365 P 26

7.8 P 0.5 7.9 P 0.4 19.3 P 0.9

5.35 7.29 24.42

21.9^284.4 4.9^64 1^12.7

1.7 2.3 3.4

1.04 0.50 0.05

0.1 0.1 0.1

13/14 14/14 12/14

Family 2 1 2 3

500 500 200

466 480 183

389 P 27 407 P 15 396 P 23

378 P 16 391 P 16 362 P 14

7.8 P 0.5 8.1 P 0.3 19.8 P 1.2

5.37 7.31 24.46

21.6^281 4.6^60 0.9^16.8

1.7 2.3 3.4

1.04 0.50 0.05

0.1 0.1 0.1

11/13 11/13 12/13

Family 3 1 2 3

500 500 200

466 489 183

401 P 15 395 P 24 412 P 17

370 P 23 386 P 23 378 P 24

8.0 P 0.3 7.9 P 0.5 20.6 P 0.9

5.38 7.33 24.53

21.3^276.2 4.8^62.2 0.8^10.2

1.7 2.3 3.4

1.04 0.50 0.05

0.1 0.1 0.1

8/8 8/8 8/8

Family 4 1 2 3

500 500 200

460 471 191

402 P 25 393 P 24 400 P 13

396 P 1 370a 381 P 12

8.0 P 0.5 7.9 P 0.4 20 P 0.6

5.38 7.34 24.56

20.5^266.7 4.9^63.5 0.9^12.3

1.7 2.3 3.4

1.04 0.50 0.05

0.1 0.1 0.1

6/7 6/7 7/7

a

Value computed for a single spectral frequency peak.

ator and can explain irregularly spaced peaks in terms of the interference between the lateral and longitudinal modes of resonance of the crack. We considered di¡erent values of the model parameters assuming physical conditions of the system that are representative of a pure liquid (Model 1), foam (Model 2), or pure gas (Model 3). We obtained a good match between our spectral data and the dispersion characteristics of a crack wave, from which we derived several crack models whose dimensions are listed in Table 4. The observed eruptive activity leads us to reject Model 3 as unrealistic. The remaining two models may be representative of actual conditions in the magmatic system, and di¡erences between these models may be ascribed to di¡erent source depths. Model 2 is the preferred solution because it is closer to the actual pressure conditions at the depth of the LP sources as inferred from analytical locations obtained from stacked traces. As the dimensions of the rectangular cracks obtained from our simulations are comparable, the di¡erences among Families 1, 2 and 3 may be explained as the result of slight variations in the position of the trigger of crack resonance. The results of high-precision, relative locations sup-

port this assumption, suggesting di¡erences in focal depths on the order of tens of meters (S. Gambino, personal communication) for LP events belonging to Families 1 and 3. LP events belonging to Family 4 have longer duration than those observed in the other three families. This increased duration of the signal may be explained by an increase in the impedance contrast between £uid and solid, associated with changes in the £uid properties. Speci¢cally, an increase in gas content would produce decreases in the bulk modulus and acoustic speed of the £uid. We surmise that slight changes in magma composition (for example, an increase in wt% H2 O) could be at the origin of the longer duration signals. The relationship between eruptive activity and LP seismicity is an intriguing aspect of the 1991^ 1993 eruption. Joint visual and seismological observations point to a temporal correlation between LP swarms and collapses of the crater £oor in Northeast Crater. This correlation is well documented for the interval from February 26 to midMarch, 1992, on February 3, 1993, and from March 28 through April 4, 1993. Although no simultaneous observations of the £oor of NE cra-

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435

Fig. 10. Three-dimensional map of b-value (for mean earthquake magnitude) in the shallow crust beneath Mount Etna (modi¢ed from Murru et al., 1999). The location of the £uid-¢lled crack (FFC) is shown in relation to the two ground deformation sources modeled by Bonaccorso (1996) (TC = tensile crack; EDB = ellipsoidal depressurizing body). The trace of the eruptive fracture (EF), b-value anomaly (1) (Murru et al., 1999), and positions of NE Crater (NEC), station PDN (PDN), and northern rim of Valle del Bove (VBR) are also indicated.

ter and LP events are available for the remainder of the LP sequence, the similarities in LP signatures throughout 1992 lead us to hypothesize that a similar process of incremental collapse was operating during the entire period. The repeated occurrence of such collapses produced a pit crater (Calvari et al., 1994; Coltelli et al., 1998). The relationship between seismic activity and pit crater formation has been reported for other volcanic areas (e.g. Garcia et al., 1998). However, this is the ¢rst time that a similar sequence has been observed on Mount Etna. This activity o¡ers a unique opportunity to study LP events in relation to changes in magma supply dynamics. Based on the temporal relationship between seismic and volcanic phenomena, we infer that the LP events represent pressure transients in the dike feeding the Mount Etna eruption. We suggest that mass evacuation during the sustained eruption resulted in a gradual decrease of pressure in the feeder dike beneath Northeast Crater, which led to incremental collapse of the crater £oor. This, in turn, triggered the excitation of the segment of

feeder dike located immediately beneath Northeast Crater. According to this hypothesis, the LP events originate in a shallow segment of the magma conduit beneath Northeast Crater. Fig. 10 shows the location of the crack and its spatial relationship with the magma feeder and other features inferred from geophysical data. Using electronic distance measurements, global positioning system (GPS), and tilt data, Bonaccorso et al. (1994) and Bonaccorso (1996) attribute the main part of the ground deformation ¢eld to two di¡erent sources that were active during the 1991^1993 eruption. The ¢rst source is a shallow tensile fracture whose spatial location is coincident with the eruptive fracture ¢eld. Micro-gravimetry and height change data (e.g. Rymer et al., 1993) provide further independent support for this interpretation. The second source is an ellipsoidal depressurizing body located slightly southwest from the summit craters at a depth of 3 km below sea level. Nunnari and Puglisi (1994) and Puglisi et al. (2000) con¢rm the presence of this depressurizing body based on independent

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analyses of GPS data. Other evidence for this latter source is provided in a study by Murru et al. (1999), who mapped b-values for local earthquakes recorded between 1990 and 1997. They identi¢ed a body with anomalously high b-values located southwest of the summit craters at depths of 4^5 km, which they interpreted as a magma chamber. Using synthetic aperture radar (SAR) data, Massonet et al. (1995) attributed the overall de£ation of Etna to a deep, depressurizing body located about 2 km east of the summit craters at depths of 12^14 km. The presence of this deeper source remains controversial (Puglisi et al., 2000). Lanari et al. (1998) reinterpreted the SAR data after removal of topographic e¡ects and obtained a source located 5.7 km below sea level. In a more recent study, Beauducel et al. (2000) concluded that the residual fringes observed on Mount Etna images after removal of the topographic effects may be a tropospheric artifact. The data analyzed in our study cover a time interval that only partially overlaps with the periods considered by other studies. The deformation ¢eld modeled by Bonaccorso (1996) may thus be re£ecting sources acting either concurrently, or at successive times, during the eruption. Based on the seismicity, we postulate a strict relationship between a magma body located about 2^3 km below sea level ^ the source for the main dike feeding the eruptive fracture system ^ and the volume within which LP events were generated. We suggest that LP activity was the result of magma transport in a source region beneath Northeast Crater. In our model, the LP source volume represents a part of the feeding system that links the deeper depressurizing magma body with the dike extending southeast along the western wall of Valle del Bove, toward the site where the surface breakout of lava was located.

Acknowledgements We are grateful to Massimo Pompilio and Giovanni Macedonio for their suggestions on thermodynamic simulations. We thank Milton GarcTes, Randy White, Javier Almendros and an anonymous reviewer for their reviews and sugges-

tions. This work was supported by Gruppo Nazionale per la Vulcanologia (Italy) and two Nato-CNR senior fellowships (n. 217.25 and n. 217.28).

Appendix A In our application of the £uid-¢lled crack model, the basic assumption is that LP events are generated by a pressure disturbance in a twophase £uid composed of liquid magma and gas. We also consider an extreme condition, in which we assume a £uid consisting of pure gas whose parameters are obtained from literature data. To constrain the physical conditions of the twophase £uid, we assume a temperature of 1100‡C based on ¢eld measurements of Etna lava (Calvari et al., 1994). The values of pressure P, which range from 10 to 25 MPa, are based on the hypocentral depths of LP events. To set up thermodynamic parameters (Ghiorso and Sack, 1995), we use the mean chemical composition of the lava erupted in 1991^1993 (Armienti et al., 1994) and a water content ranging from 1 to 2 wt% following Metrich and Clocchiatti (1989). We consider four thermodynamic conditions by taking into account the range of variation of water content and pressure (Table 2). Speci¢cally, conditions 1, 2, and 4 (Table 2) are representative of £uids mostly constituted by foam, whereas condition 3 is representative of a liquid. Although we ¢nd a relevant percentage of solid in two cases (conditions 1 and 2, Table 2), we neglect the presence of crystals. We assume that crystals would not produce marked changes in acoustic speed as long as we are dealing with a magma that behaves like a liquid. A bubbly liquid is characterized by a gas^volume fraction (ratio of the volume of gas to the total volume of the two-phase mixture) Ag = Vg / Vm 6 0.1 (Martinelli, 1991). Foams are in the range 0.1 9 Ag 9 0.9, and sprays are characterized by Ag s 0.9 (Martinelli, 1991). We estimate the values for gas density (bg ) and liquid density (bl ) compatible with physical conditions ranging from a single-phase liquid magma (condition 3, Table 2) to those of foams (conditions 1, 2, 4, Table 2).

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The density bm of the two-phase mixture is calculated as (Wylie and Streeter, 1983):

b m ¼ A g b g þ ð13A g Þ b l

ðA1Þ

The sound velocity of the liquid (al ) is ¢xed at 2.0 km/s based on measurements of basaltic melts (Murase and McBirney, 1973). The sound velocity of the foams (am ) is obtained from the expression (Hsieh and Plesset, 1961): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 b m f =ð1 þ f Þ ¼ þ ðA2Þ Q mP am al where j = Ag /Al , and Qm is the isentropic coe⁄cient of the mixture given by:

Qm ¼

mcpg þ cl mcvg þ cl

ðA3Þ

in which cpg and cvg are the speci¢c heats of the gas at constant pressure and constant volume, respectively, cl is the speci¢c heat of the liquid magma, and m is the mass ratio of gas to liquid. These parameters are listed in Table 2 along with the estimated sound velocities for the four thermodynamic conditions considered. In our model, b is related to the compressibility of the two-phase gas^liquid mixture representing the magma. As the compressibility of the gas bubbles is dominant (i.e. it is three orders of magnitude larger than that of the liquid), a reasonable approximation for b may be obtained by neglecting the contribution of the liquid. Therefore, assuming isothermal conditions and an ideal gas, b may be roughly expressed as (Van Wijngaarden, 1972; Lu et al., 1990): bW

P Ag

ðA4Þ

The values of b are listed in Table 2. For thermodynamic condition 3 (pure liquid), we use values of b in the range 1.7^1.9U104 MPa that are representative of experimentally determined values for basaltic melts (Rivers and Carmichael, 1987).

437

In our computations, the compressional wave velocity K = 3.4 km/s is based on results of a seismic tomography study by Hirn et al. (1991). Assuming the equivalence VrW between Lame¤ elastic moduli in the rock (Patane' et al., 1992), we use the corresponding shear wave velocity L = 2.0 km/s. Combined interpretations of gravity and deep dipole geoelectric data (Loddo et al., 1989) yield bs = 2.47 g/cm3 for volcanic rock at Mount Etna. The corresponding rigidity of the solid is W = bs L2 = 9.9U103 MPa. Using the above parameter values, we obtain the ratios b/W, K/am , and bm /bs for the four conditions listed in Table 2. The ratio b/W ranges from 0.0014 to 1.7172. As the dispersion curves are not too sensitive to the actual value of this ratio (Gil Cruz and Chouet, 1997), we assume a ¢xed value of b/W = 0.1, within the range of variation estimated. To simplify our analyses, we assume 1.5 and 2.0 km/s as minima and maxima for the sound velocity of the gas^liquid mixture. For a £uid consisting of pure gas, we use a sound velocity of 1.0 km/s (Gil Cruz and Chouet, 1997). Accordingly, we consider the three velocity ratios, K/am = 1.7, K/am = 2.3, and K/am = 3.4, and three density ratios, bm /bs = 1.04, bm /bs = 0.56 (mean value of the ratios obtained in conditions 1, 2, and 3), and bm /bs = 0.05 (density ratio for £uids mainly constituted by gas according to Gil Cruz and Chouet, 1997). The velocity and density ratios are then combined to re£ect conditions representative of £uids consisting of pure liquid (Model 1), foam (Model 2), and gas (Model 3), respectively (see Table 3). Finally, as the longer duration of seismograms in Family 4 is assumed to be related to changes in the properties of the £uid and solid that may affect the impedance contrast Z, we estimate Z according to Chouet (1992): sffiffiffiffiffiffiffiffiffiffiffiffi 3W b s ðA5Þ Z¼ bb f where bs and bf are the densities of the solid and £uid, respectively, W is the rigidity of the solid, and b is the bulk modulus of the £uid. The results are reported in Table 4.

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