In the last decade several studies have indicated that magma within volcanic conduits can undergo repeated failure and healing, thus, providing a realistic source mechanism for the peculiar sequences of low-frequency earthquakes that often announce eruptions. Although geological observations, laboratory experiments, and numerical modelling support such a hypothesis, the links between geophysical observations and the proposed models remain qualitative. This study focuses on providing constraints to the relationship between the occurrence of repeating earthquakes and magma fracture at andesite volcanoes. Empirical modelling of viscosity is incorporated into the fundamental physics of magma fracture in order to assess whether and where the conditions for brittle failure are met within volcanic conduits. A case study from the 1995-ongoing eruption of Soufrière Hills Volcano, Montserrat, is presented. The locations of earthquakes from a pre-eruptive low-frequency seismic swarm illuminate a relatively compact source volume at depths of 100–300 meters below sea level. Viscosity modelling confirms that the Soufrière Hills magma could rupture at those depths.
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 Activity at andesite volcanoes is often characterized by surface extrusion of viscous lava and continuous growth of summital domes, interspersed with violent, short-lived, explosions. The hazards from this type of eruptions are well known, due to sudden transitions between effusive and explosive regimes, and the propensity of lava domes to collapse spawning devastating pyroclastic density currents.
 Lava dome collapses and explosions are often anticipated by cyclic ground deformation [Voight et al., 1999] and elevated earthquake activity [Goto, 1999; Green and Neuberg, 2006; Moran et al., 2005; De Angelis, 2009]. Over the last two decades there has been a growing appreciation of how long-period and hybrid earthquakes (hereinafter collectively referred to as low-frequency) may reflect magma transport underneath volcanoes. Low-frequency (LF) seismograms are characterized by relatively long durations, lack of obvious secondary phases, and spectra distinctly peaked in the 0.5–10 Hz band [McNutt, 2005]. Remarkable swarms of several thousands LF earthquakes, often with almost identical waveforms, can occur days to minutes prior to large explosive eruptions and lava dome collapses, and are therefore frequently used for short term eruption forecasting. Despite their extensive use in eruption early warning, their source mechanisms remain unclear. Early studies have associated LF seismicity with the resonant oscillation of subsurface, fluid-filled, cracks and conduits [Chouet, 1986] triggered by localized source-time functions (e.g. gas released by the collapse of a magmatic foam or phreato-magmatic interactions). Modelling efforts have suggested that sequences of self-similar LF earthquakes may result from the stick-slip motion of solid plugs along the margin of volcanic conduits [Iverson et al., 2006], or within lava domes. Shallow degassing and fluid circulation may, additionally, be responsible for an increase in pore pressure, promoting friction-controlled slip on pre-existing fault surfaces within conduits or lava domes. Recent studies have proposed that mechanisms of non-explosive fragmentation may be associated with the viscous flow of silicic magma: the onset of LF swarms would reflect shear fracture of magma driven by strain-rate dependent stress accumulation at the margins of volcanic conduits [Goto, 1999; Gonnermann and Manga, 2003; Tuffen et al., 2003]. Volatile and fluid phases present in the source region, along with frequency-dependent attenuation effects, may account for the prominent LF coda of seismograms. To date, non-explosive fragmentation of magma has been suggested from observations on clastic textures at ancient dissected conduits [Tuffen et al., 2003], inferred by earthquakes patterns during andesite lava dome eruptions [Goto, 1999; Neuberg et al., 2006], and modelled for multiphase flows within volcanic conduits [Gonnermann and Manga, 2003]. These models suggest that highly viscous magma may fracture and heal repeatedly, providing a stable and rechargeable mechanism for the generation of LF earthquakes at silicic volcanoes.
 In this paper we present a case study from the eruption of Soufrière Hills Volcano (SHV). Empirical modelling of magma viscosity, based on measurements of matrix glass composition, is conducted in order to ascertain whether and where the conditions for magma failure are likely found in the volcanic conduit. A remarkable pre-dome collapse sequence of repeating LF earthquakes is analysed by waveform correlation methods; earthquake locations are presented and discussed within the framework of magma fracturing.
2. Magma Fracture
 Magmas are primarily silicate melts with viscoelastic rheology, which essentially behave like Newtonian fluids at low strain rates (i.e. the relationship between stress and strain rate is linear). As the rate of deformation increases, approaching the timescale of viscoelastic relaxation of the melt, a change, termed glass transition, may occur to non-Newtonian behaviour (i.e. the stress-strain rate relationship becomes non-linear). Silicate melts can thus transition from fluid to solid-like response [Ichihara and Rubin, 2010], and undergo brittle fracture depending on the state of stress, strain rate, and temperature conditions. Maxwell's theory of viscoelastic deformation provides a theoretical framework for the study of magma fracture in silicic magma. Webb and Dingwell  showed that unrelaxed deformation is observed during viscoelastic flow if the product between the strain rate, , and melt viscosity, ηs, falls in the range 107–1010 Pa. Shear stress is accumulated because of deformation during flow, and eventually released by means of fracturing when the shear strength of the melt, τs, is exceeded:
 Melt viscosity in equation (1) can be replaced with the apparent viscosity of crystal bearing magma [Caricchi et al., 2008; Holland et al., 2011]. The shear strength of natural andesite magma lies in the range 106–108 Pa. The velocity profile across the conduit is assumed parabolic, and the flow properties can be calculated according to Poiseuille's theory. The strain rate varies across the conduit, and it is maximum at its margins:
Q is the volumetric flow rate, and R is the conduit radius. From equations (1) and (2) one can infer that for given volumetric flow rate and conduit size, magma undergoes brittle fracture if viscosity exceeds a threshold defined by
 The condition of equation (3) is illustrated in Figure 1a for a magma with shear strength of 107 Pa [Voight et al., 1999; Tuffen et al., 2003] and a conduit radius of 15 m, consistent with values reported at SHV [Neuberg et al., 2006]. Also shown are the volumetric flow rates measured at SHV during June–August, 1997. The plot suggests that in order to achieve shear fracture at the observed rates of 7 − 9 m3/s, magma viscosity must exceed 4 − 3 · 109 Pa · s.
 In order to assess whether and where the conditions for brittle failure are met at SHV, we modelled the viscosity of magma empirically. First, we evaluated melt viscosity following Giordano et al. ; next, the results were incorporated into calculations of magma viscosity using the model of Costa et al. . The data employed in the calculations of melt viscosity (see Table S1, auxiliary material) are electron microprobe measurements of matrix glass compositions at SHV [Harford et al., 2003]. For modelling purposes we assumed that the magma is H2O saturated. Water is the dominant volatile phase (both within the melt and any co-existing vapor phase), and concentrations of CO2 and S are comparatively minor [Barclay et al., 1998; Rutherford and Devine, 2003]. Water solubility is modelled following Ghiorso and Sack . We calculated magma viscosity at the temperature of 850 °C [Murphy et al., 1998] and for a total crystal content (accounting for both phenocryst and microlites) of between 35–55 wt%. Murphy et al.  report that the petrology of SHV magma is consistent with crystal contents of up to 65–75 wt% although it should be noted that these numbers reflect crystallinity recorded in dome rocks, where decompression induced crystallisation is most effective. The results, illustrated in Figure 1b, are consistent with theoretical and experimental estimates previously published by Voight et al.  and Sparks . Figure 1b shows that magma at SHV is capable of rupturing in the upper 2000 m of the conduit (the reader should note that zero elevation in Figure 1b corresponds to a height of 900 m above sea level, the estimated elevation of the vent at SHV) depending on its crystallinity. At greater depths, either more crystalline magma or higher strain rates are required in order to offset the effect of larger amounts of dissolved volatiles, which lower viscosity. Upon magma ascent volatiles exsolve causing viscosity to rapidly increase, thus, brittle failure can be accommodated by lower strain rates. In general, higher values of magma crystallinity extend the range of depths where brittle failure may occur.
3. Earthquake Multiplets
 Almost all eruptions at andesite volcanoes are accompanied by LF seismic activity. Shallow LF earthquakes associated with volcanic activity can produce groups of nearly identical waveforms, usually termed families or multiplets. During 1996–1997, LF seismicity was commonplace at SHV, and invariably accompanied surface extrusion of lava and preceded dome collapses and explosions. In this study we review an episode of repetitive LF seismicity leading to a partial dome-collapse and explosive activity on June 25, 1997. This event is sadly remembered because the associated pyroclastic flow activity caused 19 casualties, and it is one of the most extensively studied in the history of the SHV eruption. Green and Neuberg  analysed the seismic data, and classified the repeating LF earthquakes into several families by means of single-station cross-correlation procedures; Neuberg et al.  extended previous results by calculating the locations of 55 highly correlated events within the swarm.
 In this study we performed accurate screening of the seismic data from multiple stations, during the period June 22–25, 1997, in order to extract individual earthquakes from the continuous seismograms, and to identify multiplets. The data were collected through the Montserrat Volcano Observatory (MVO) seismic network, at the time operated by the British Geological Survey. The network (Figure S1 of the auxiliary material) consisted of five broadband seismometers Guralp CMG-40T (30 seconds cutoff period) and three Integra LA100/F vertical instruments (1 second cutoff period). We employed an event-detection algorithm based on the short-term average/long-term average (STA/LTA) ratio [Withers et al., 1998] with STA and LTA windows of 0.8 and 7 seconds, respectively. A single-station earthquake trigger corresponded to a STA/LTA ratio of 2.5 or greater. An event was declared if triggers were found for at least 4 stations, within 4 seconds of each other. We, then, used a cross-correlation method that requires waveform similarity on multiple stations [Thelen et al., 2010] in order to identify possible earthquake multiplets. A 10-second window starting 2 seconds before the trigger time, encompassing each earthquake, was employed for the comparison; a cross-correlation coefficient of at least 0.75 on 3 stations was required for an event pair to be declared a multiplet. 21 multiplets containing more than 10 events were recognized; multiplets with less than 10 events were discarded. Figure 2 displays the 6 largest multiplets; also shown are earthquake occurrence rates throughout the swarm.
 Locating LF earthquakes with poor signal-to-noise ratios and emergent P-wave arrivals, such as those within multiplets, was challenging. Therefore, we leveraged waveform similarity and applied the following procedure to obtain reliable locations for individual LF events: i) all LF earthquakes within each multiplet were aligned according to maximum cross-correlation and stacked (i.e. summed together) in order to produce an average seismogram with improved SNR; ii) P-wave arrivals were measured from multiplet stacks; iii) the P-wave arrivals obtained from the stacks were used for every earthquake within the corresponding multiplet (all P-wave arrivals were visually inspected to ensure overall picking quality and several dubious picks were discarded); iv) steps i)-iii) were repeated for every station in the network; v) every earthquake with more than 4 valid picks was located using the procedures described by Rowe et al. , and only locations that satisfied additional quality criteria (RMS < 0.2 s, horizontal error < 1 km, vertical error < 2 km, gap < 135) were retained. This procedure resulted in a total of 257 located LF events, which corresponds to about 15% of the total number of repeating LF earthquakes identified by the cross-correlation analysis. The results, illustrated in Figure 3, show that located earthquakes cluster approximately underneath the summit of SHV, slightly streaking along the North–West/South–East direction, at depths of 0.1–0.3 km below sea level (b.s.l.). The locations obtained in this study could not be compared with the authoritative MVO earthquake catalog, which is incomplete, as MVO do not systematically locate LF earthquakes during large seismic swarms. Good agreement was, however, found with the locations presented by Neuberg et al. [2006, Figure 2] that cluster at about 0.5 ± 0.1 km b.s.l. The average vertical and horizontal location errors obtained in this study were 0.34 and 0.23 km, respectively. The average location RMS residual was 0.16 s, about one order of magnitude larger than the value of 0.013, or 1 sample at 75 Hz, published by Neuberg et al. , which they translated into a spatial uncertainty of ±40 m. It can be speculated that such discrepancy is due to differences in the uncertainty assigned to individual picks, the velocity model and station corrections employed.
4. Conclusive Remarks
 Volcanic LF earthquakes often precede eruptions by days to hours, and are therefore used in short-term eruption forecasting. Several recent studies have suggested that shear fracture of magma is a viable candidate to explain the occurrence of repeating LF seismicity at silicic volcanoes. Within the framework of these models magma failure represents a source mechanism, in many respects similar to ordinary faulting in rocks.
 In this study we have proposed the combined use of empirical modelling of magma viscosity and location of LF seismicity in order to assess whether they may provide clues on the feasibility of magma fracture. This approach was tested on a case study from the 1995-ongoing eruption of Soufrière Hills Volcano, Montserrat. For viscosity modelling we employed electron microprobe measurements of matrix glass compositions of samples collected at SHV during 1997. The results of modelling, when incorporated into the fundamental physics of magma fracturing, suggested that the characteristics of SHV magmas are, indeed, compatible with brittle failure. We, then, analysed an episode of repeating LF seismicity at SHV during June 1997. We extracted repeating waveforms from the continuous seismic record and located 257 earthquakes at depths of 100–300 m b.s.l. Viscosity modelling showed that the critical conditions to induce magma fracture at pertinent crystallinity and strain rates can be achieved at a level within the conduit consistent with the derived seismic depths. Earthquake clustering reflects the elevated waveform similarity, and it is consistent with a stable source mechanism such as magma fracture. The identified depth of LF earthquakes also coincides with a region where magma is fed into a quasi-cylindrical conduit from depth through a dyke as proposed by Hautmann et al. . The dyke-conduit transition would result in a bottle-neck effect likely to increase strain rates, thus, promoting magma fracture. The absence of seismicity further up in the conduit may be ascribed to large increase in crystallinity and rheological stiffening as magma ascends towards the surface. This may lead to even higher strain rates at shallower depths resulting in viscous dissipation and aseismic slip.
 Understanding magma faulting and its relationship to the generation of LF volcanic seismicity may well hold the key to eruption prediction. This paper demonstrates that a cross-disciplinary approach to the study of volcanoes is pivotal in order to decipher their inner workings. Further investigations of the multiphase nature of magma, and the relative importance of crystal phases and interstitial melt on controlling viscosity, is critical to unravel the dynamics of magma fracture. On the other hand seismic studies should be continued in order to develop methods for assessing LF earthquake source mechanisms more reliably. If robust links can be established between theoretical and conceptual models, laboratory experiments, petrological observations, and geophysical measurements, this could rapidly lead to realistic estimates of magma migration prior to the onset of volcanic eruptions, and thus, pay high dividends in the mitigation of related hazards.
 The seismic data used in this research were provided by the British Geological Survey (BGS). S. De Angelis thanks friends and colleagues of the BGS for their constant support during his tenure as seismologist at the Montserrat Volcano Observatory, insightful discussions, and for maintaining a valuable seismic database of the eruption. The authors are indebted to Glenn Thompson of the University of Alaska Fairbanks for thought-provoking discussions on the significance of the seismic and petrological data employed. The authors thank J. Gottsmann and V. Zobin for their insightful reviews that improved the manuscript.
 The Editor thanks Joachim Gottsmann and Vyacheslav M. Zobin for their assistance in evaluating this paper.