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LETTERS PUBLISHED ONLINE: 4 MAY 2014 | DOI: 10.1038/NGEO2146 Volcanic drumbeat seismicity caused by stick-slip motion and magmatic frictional melting J. E. Kendrick1,2*, Y. Lavallée1, T. Hirose3, G. Di Toro4,5, A. J. Hornby1, S. De Angelis1 and D. B. Dingwell2 During volcanic eruptions, domes of solidifying magma can form at the volcano summit. As magma ascends it often forms a plug bounded by discrete fault zones, a process accompanied by drumbeat seismicity. The repetitive nature of this seismicity has been attributed to stick-slip motion1 at fixed loci between the rising plug of magma and the conduit wall2,3 . However, the mechanisms for such periodic motion remain controversial4–7 . Here we simulate stick-slip motion in the laboratory using high-velocity rotary-shear experiments on magma-dome samples collected from Soufrière Hills Volcano, Montserrat, and Mount St Helens Volcano, USA. We frictionally slide the solid magma samples to generate slip analogous to movement between a magma plug and the conduit wall. We find that frictional melting is a common consequence of such slip. The melt acts as a viscous brake, so that the slip velocity wanes as melt forms. The melt then solidifies, followed by pressure build up, which allows fracture and slip to resume. Frictional melt therefore provides a feedback mechanism during the stick-slip process that can accentuate the cyclicity of such motion. We find that the viscosity of the frictional melt can help define the recurrence interval of stick-slip events. We conclude that magnitude, frequency and duration of drumbeat seismicity depend in part on the composition of the magma. Dome-building eruptions are frequently accompanied by ‘drumbeats’ (Fig. 1); swarms of small magnitude earthquakes with stable source locations that indicate a recurrent scenario3 , which have been alternatively modelled as resonance of a fluid-filled crack/chamber, or fracture and stick-slip at the conduit margin1–5,8 . The high-temperature fracture of magma has been shown to be seismogenic9,10 and the conditions which can yield failure are now relatively well understood11 . Shear zones preserved in exogenic dome rocks record evidence of cataclastic gouge zones12–14 and pseudotachylytes15 formed at the conduit margins, which may allow magma to ascend as a largely solid plug11 . When strain is localized in this way, the frictional forces begin to impinge on the buoyancy-driven system, controlling ascent and regulating the eruption15 . The mechanical contribution of such shear zones on eruptive behaviour remains largely unconstrained and, as yet, experimentally unexplored. Frictional properties of rocks are generally described in terms of rate-and-state friction laws16 ; fault strength and frictional properties show a complex dependence on both the magnitude and velocity of slip14,17–19 . The mechanical work-rate involved in slip generates heat, which can lead to flash heating and frictional melting17,18,20 . Previous studies indicate that melting ensues at slip rates >0.1 m s−1 (ref. 21) and may act as either a lubricant or a brake22 , yielding the potential for unstable slip which is a fundamental requirement for stick-slip motion16,20 . Stick-slip is a time-dependent phenomenon generally attributed to a fault system that, on slip, dissipates energy until the fault sticks, allowing stress build-up until the next slip event4,16,20 . In volcanic conduits, even near-steady-state ascent conditions are expected to undergo short-term fluctuations due to the balance of internal and external forces1,4 . This is a consequence of several factors, including magma pressure (and energy stored elastically by compressible magma), plug mass and interactions with conduit wall rock, which serve to variably dampen the natural oscillation timescale4 . Such a phenomenon may exploit the velocity-weakening nature of the slip zone, which may host gouge14 or frictional melt15 , creating a self-regulating stick-slip cycle1,4 ; yet, the propensity for frictional melting (under volcanic conditions) and the resultant rheology shown herein suggest that frictional melt may impose additional mechanical forces (enhanced by chemical and rheological changes) on the slip plane. High-velocity rotary-shear (HVR) experiments on andesite from Soufrière Hills Volcano (SHV) and dacite from Mount St Helens (MSH), conducted at upper-conduit stress conditions, provide records of shear stress (τ ) during slip. These experiments demonstrate the ease with which magma re-melts at the slip rates investigated; starting from room temperature, formation of a continuous layer of frictional melt can occur in just 25 cm slip or at only 0.1 m s−1 (Fig. 2 and Supplementary Table 1), a rate commonly achieved during magma ascent2,23 . The distance at which a continuous melt layer forms decreases with increasing normal stress or slip rate24 (Fig. 2). Ambient temperatures in conduits during dome emplacement range from 600 to 900 ◦ C, nevertheless, friction experiments performed on dolerite at 20 < T < 1, 000 ◦ C determined similar values for the friction coefficient (µ; ref. 25) to the peak values (M1) measured here (see Supplementary Table 1). The similarity of µ for a large range of temperatures and rock compositions supports the extrapolation of our mechanical data to volcanic conduits. Before melting, the shear stress of rock–rock friction is predicted to increase with normal stress (σn ) according to Byerlee’s law26 : τ = µσn where µ is 0.6–0.85. At the initiation of sliding, rock–rock friction and comminution produces gouge, and during slip the friction 1 Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool L69 3GP, UK, 2 Department of Earth and Environmental Sciences, Ludwig Maximilian University, Theresienstr. 41/III, 80333 Munich, Germany, 3 Kochi Institute for Core Sample Research, JAMSTEC, Kochi 783-8502, Japan, 4 Dipartimento di Geoscienze, Università degli Studi di Padova, Via Gradenigo 6, 35131 Padova, Italy, 5 Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy. *e-mail: [email protected] 438 NATURE GEOSCIENCE | VOL 7 | JUNE 2014 | www.nature.com/naturegeoscience © 2014 Macmillan Publishers Limited. All rights reserved. NATURE GEOSCIENCE DOI: 10.1038/NGEO2146 LETTERS Ground velocity (× 10−6 m s−1) a ′ Hills Volcano, Montserrat Soufriere MBLY:BHY–-10 July 2003, 23:50:00 UTC 1 0 −1 b 10 −80 −100 5 0 −120 −140 0 200 400 600 800 1,000 1,200 1,400 1,600 dB (rel 1 m s−1) Frequency (Hz) 15 1,800 Time (s) Ground velocity (× 10−6 m s−1) c Mt. St Helens, USA HSR:SHZ–-03 December 2005, 06:00:00 UTC 5 0 −5 d 10 −80 −100 5 0 −120 −140 0 200 400 600 800 1,000 1,200 1,400 1,600 dB (rel 1 m s−1) Frequency (Hz) 15 1,800 Time (s) Figure 1 | Drumbeat seismicity at Soufrière Hills (SHV) and Mount St Helens (MSH) volcanoes. a, A 30-min continuous seismic record (grey) from SHV station MBLY, showing a sequence of repeating earthquakes and the smoothed Hilbert transform envelope (black). Earthquakes occurred during active lava dome extrusion and preceded the largest dome collapse event in the history of SHV on 12 July 2003. b, Spectrogram of a showing a high degree of spectral coherence (similarity) between earthquakes. c, 30-min continuous seismic record (grey) at MSH station HSR on 3 December 2005 and the smoothed Hilbert transform envelope (black) during spine extrusion. d, Spectrogram of c. coefficient (proportional to shear stress) decreases from an early maximum to a steady state (M1–S1, Fig. 3a) in agreement with other friction studies on igneous rocks22 and gouge14 . This slip-weakening can result in a lower rock–rock, slip-zone shear stress (S1, Fig. 3a) than that predicted by Byerlee’s law (Fig. 3b). The rate-dependence of rock–rock friction tends towards velocity-weakening, but does not vary systematically across the velocity range measured here (Fig. 3b). As discrete melt patches form along the contact17,18 shear stress increases drastically and heating rates can exceed 2,000 ◦ C s−1 . A second, higher peak emerges as a continuous molten layer forms (M2, Fig. 3a and Supplementary Movie 1), resulting in the first manifestation of the viscous brake. This is followed by slipweakening and, as the melt zone thickens, melt expulsion and viscosity-controlled slip dominate to produce a second stage of steady-state sliding27 (S2, Fig. 3a). Shear-to-normal stress ratios reach 1.8 for the peak stress (M2) and 1.3 for the steady-state (S2) regime (Fig. 3c and Supplementary Table 1). Although it may be mechanistically misleading to describe the relationship of shear-to-normal stress in a melt-bearing slip-zone as a friction coefficient22 , an empirical correlation is nevertheless observed27 (Fig. 3c). Furthermore, melt is more notably velocity-weakening than rock–rock slip-zones owing to the shear-thinning potential of melt suspensions28 . Under the same deformation conditions, SHV samples exhibited faster melting than MSH (Fig. 2). We attribute this to their contrasting mineral assemblages (Supplementary Table 2 and Figs 2 and 3) and to the initial presence of interstitial glass in the SHV sample (surpassing its glass transition (Tg ) at ∼700 ◦ C). The steady-state surface temperature of the slip-zone does not vary systematically with velocity, but the temperatures tend to be higher in MSH dacite at the same conditions (Supplementary Fig. 4). The frictional melts have different compositions (Supplementary Table 3); the MSH dacite melt viscosity is one order of magnitude higher than the SHV andesite melt (despite the temperature difference), determined using the GRD viscosity model29 (Supplementary Fig. 4). As slip properties following melting are controlled by viscosity19 , the shear resistance is lower (at the same conditions) in the melt produced in SHV andesite (Fig. 3c). Having established the slip properties of the samples, a set of variable-rate controlled experiments were used to mimic rapid velocity fluctuations (stick-slip behaviour) in volcanic conduits. These experiments confirm the extremely strong velocityweakening behaviour when fault friction induces melting in volcanic rocks, in agreement with a shear-thinning rheological behaviour for these crystal-bearing melts28 . Experiment 1 demonstrates that once a steady-state shear stress is achieved in melt, a near-instantaneous increase in shear stress NATURE GEOSCIENCE | VOL 7 | JUNE 2014 | www.nature.com/naturegeoscience © 2014 Macmillan Publishers Limited. All rights reserved. 439 NATURE GEOSCIENCE DOI: 10.1038/NGEO2146 LETTERS a 0.1 m s−1 0.4 m s−1 1.0 m s−1 1.5 m s−1 Melt distance (m) 16 12 6 M2 5 S2 4 3 2 M1 1 0 8 0 5 10 4 M1 9 8 2 4 6 8 10 7 Shear stress (MPa) 0 Normal stress (MPa) Figure 2 | Melting efficiency according to axial stress and slip rate. The slip distance at which a continuous melt layer forms is dependent on normal stress and slip velocity (0.1, 0.4, 1.0 and 1.5 m s−1 ) for MSH dacite (green) and SHV andesite (blue). The melting point used is the mid-point of the maximum shear stress during the experiment (M2 in Fig. 3a), error bars represent the duration of said maximum and in some cases are smaller than the symbol used (Supplementary Table 1). The data set demonstrates that melting is favoured at higher normal stress and velocity, and in SHV andesite. 6 15 0.1 m s−1 0.4 m s−1 1.0 m s−1 1.5 m s−1 MSH SHV 20 5 4 3 2 1 0 S1 Byerlee frictional strength 5 4 3 2 1 0 0 2 4 6 8 10 Normal stress (MPa) c 10 M2 S2 0.1 m s−1 −1 0.4 m s 1.0 m s−1 1.5 m s−1 MSH SHV 9 8 Shear stress (MPa) ensues from rapidly decreasing the velocity, after which a new stable shear stress is apparently easily attained as long as melt production is sustained (Fig. 4). We note that the original steady shear stress is rapidly reinstated when velocity is returned to the higher rate. When velocity is decreased further, the shear stress increase overwhelms the structural relaxation of the high-viscosity melt produced by the MSH dacite (leading to sample failure), whereas the SHV andesite frictional melt maintains slip. Experiment 2 sees the MSH dacite melting significantly later than SHV andesite as slip rate is increased, then, as it is decreased, shear stress gradually increases until the melt viscosity becomes too high to achieve structural relaxation at the imposed slip rate— inducing failure across the glass transition. The viscous brake effect is observed earlier in the more silica-rich, higher-viscosity melt of the MSH dacite, which thus fails first (Fig. 4). In Experiment 3 the initial low-slip velocity results in melting for SHV andesite but does not achieve steady state; subsequently, the first high-velocity segment lowers the shear stress due to velocity-weakening. For MSH dacite, melting does not occur until the end of the first high-velocity segment, and the system remains unstable until the third cycle, when steady state is achieved. From then on, a petrological/rheological equilibrium is maintained as the slip rate varies cyclically. In Experiment 4 the base slip velocity is lowered to conditions at which frictional melting is precarious, and as such a number of high-velocity segments are required to establish a melt zone (Fig. 4). Furthermore, after melt forms, low-slip-velocity segments induce an abrupt increase in shear resistance in the MSH sample, which brings the slip-zone to a viscous halt. In the SHV sample, the lower viscosity of the frictional melt allows slip to persist, yet, with each velocity cycle, incremental melting increases the shear resistance to slip and enforces the viscous brake (see also Fig. 4; Supplementary Fig. 5). So what role must we attribute to frictional melt during strainlocalized conduit ascent? Consider the following scenario: magma ascends at depth in the volcanic conduit as a result of buoyancy forces, which provides a driving stress that helps to dictate the bulk ascent rate. This is hindered by a dense magma plug which blocks the upper conduit and allows pressure build-up in the compressible magma below, and the detailed manner (akin to a damped oscillator1 ) in which the magma ascends is then controlled 440 10 6 Distance (m) b 0 S1 1,400 1,200 1,000 800 600 400 200 0 Shortening (mm) SHV Temperature (°C) MSH Shear stress (MPa) 20 7 6 Byerlee frictional strength 5 4 3 2 1 0 0 2 4 6 8 10 Normal stress (MPa) Figure 3 | Slip-zone properties of magma. a, Example HVR run (5 MPa axial stress, 0.4 m s−1 slip rate) with shear stress (green), shortening (black) and temperature (grey) versus slip distance (see thermographic Supplementary Movie 1). Rock–rock maximum (M1) and steady state (S1) and melt maximum (M2) and steady state (M2) shear stress are highlighted. b, Rock–rock shear versus normal stress for M1 and S1. c, Melt shear versus normal stress for M2 and S2. In b and c triangles, squares, diamonds and circles represent velocities of 0.1, 0.4, 1.0 and 1.5 m s−1 respectively. Solid symbols represent M1 and M2 (open symbols, S1 and S2) for MSH (green) and SHV (blue) samples. The Byerlee frictional behaviour (µ = 0.6–0.85) is shown in grey. by the plug mass and the interaction of the plug and magma with surrounding rock4 . Seismic energy is released when new magma with a quasi-constant phase, state and temperature (and thus rheological properties) ascends and arrives at a location where the stress/strain conditions for failure are met. For a given ascent rate and plug mass, constant conditions provide a fixed spatial locus for repetitive ‘drumbeats’1 (Fig. 1) which occur in swarms of similar events3 . When the magma fails, slip ensues and rock–rock friction initially controls slip (M1, S1, Fig. 3a) as the magma below the plug decompresses (perhaps with a concertina-like effect in the magma column). We postulate that comminution and frictional work then NATURE GEOSCIENCE | VOL 7 | JUNE 2014 | www.nature.com/naturegeoscience © 2014 Macmillan Publishers Limited. All rights reserved. NATURE GEOSCIENCE DOI: 10.1038/NGEO2146 LETTERS Experiment 1 1.0 8 0.8 0.6 2 0.4 1 0 10 0.2 0 5 10 15 20 25 30 35 0.0 6 4 2 Shortening (mm) 3 1.2 Velocity (m s−1) Stress (MPa) 4 Velocity MSH shear stress MSH shortening SHV shear stress SHV shortening 0 Distance (m) Experiment 2 3 1.0 Stress (MPa) 0.4 1 0.2 0 0 5 10 15 20 25 30 35 40 45 0.0 8 4 Shortening (mm) 0.6 Velocity (m s−1) 0.8 2 12 0 Distance (m) 1.1 3 0.9 2 0.7 1 0.5 0 0 5 10 15 20 25 30 35 40 45 10 0.3 8 6 4 2 Shortening (mm) 4 Velocity (m s−1) Stress (MPa) Experiment 3 0 Distance (m) Experiment 4 Stress (MPa) 10 0.9 8 0.7 2 0.5 1 0 0.3 0 5 10 15 20 25 30 35 40 45 0.1 Velocity (m s−1) 1.1 6 4 2 Shortening (mm) 3 0 Distance (m) Figure 4 | Variable rate HVR experiments and viscous braking. A set of four velocity profiles used to mimic extrusion rate variations, specifically stick-slip behaviour in volcanic conduits. The imparted velocity, resultant shear stress and shortening are shown for MSH and SHV samples at an axial stress of 2 MPa: the shortening is visibly stepped as more melt is produced and ejected during higher velocity segments, and the shear-thinning melt rheology accounts for shear stress fluctuations, whereas the higher shear stress of the MSH dacite slip-zone relative to SHV is due to the higher viscosity of the melt, facilitating a more effective viscous brake. readily lead to the formation of a melt layer, which increases shear resistance to sliding (M2 and S2) as the viscous brake comes into effect. This brake acts as a feedback mechanism, whereby the shearthinning rheology of the melt intensifies the brake and halts slip (the ‘stick’ of stick-slip motion). This strong velocity-weakening effect, which exceeds that of gouge-hosting shear zones13,14 , could serve to increase the damping effect1,4 , with the potential to amplify both the magnitude and velocity of slip events relative to previous estimates. During this process, the bulk magma ascent rate remains constant, and so the local velocity decrease allows magma pressure to build below the plug4,6 , until eventually the conditions for failure are met and the magma seismogenically fractures (the ‘slip’), repeating the process. Over time, volcanoes undergo varying eruption rates which will change the frequency with which failure criteria are met and this scenario will arise. Changing ascent velocity, or perhaps extending or diminishing the magma plug4 , can manifest as swarms of earthquakes with different periodicity; for example, at SHV, ‘drumbeat’ frequency increased in successive swarms during the build-up to dome collapse30 . But in addition to supply rate, the material properties of the magma dictate the magnitude, frequency and duration of seismic events; for example, at Mount St Helens, NATURE GEOSCIENCE | VOL 7 | JUNE 2014 | www.nature.com/naturegeoscience © 2014 Macmillan Publishers Limited. All rights reserved. 441 NATURE GEOSCIENCE DOI: 10.1038/NGEO2146 LETTERS events were larger, longer and further apart than at Soufrière Hills (Fig. 1). This correlates with the slower melting (more slip in S1) and more effective viscous brake of the silica-rich dacitic magma. We conclude that frictional melting is a common feature of highviscosity magma ascent, especially during eruptions with ‘drumbeat’ seismic activity, where the viscous properties of the slip-zone have an important control on the dynamics of slip in the upper conduit. Methods High-velocity rotary-shear experiments. HVR experiments31 were conducted under atmospheric conditions. Two hollow cylindrical cores of 24.98 mm (inner diameter of 9.2–9.5 mm) were fixed into the apparatus and pre-grinding at 0.2 MPa and 200 r.p.m. commenced. For the experiments each sample was rotated at up to 1,500 r.p.m. (max. 1.5 m s−1 for the given sample geometry) at a set axial stress of up to 10 MPa (slip distance varies from the axis of rotation, hence an equivalent slip velocity is defined17 ). Axial force, shortening (the change in length of the cores as gouge or melt is ejected from the slip surface) and torque were measured at a sampling rate of 200 Hz, and shear stress calculated as a function of displacement. Experimental repeatability is shown in Supplementary Fig. 1, with any difference attributed to sample variability. For the results in Fig. 3, error is considered as the upper and lower values of shear stress observed in any given portion of the experiment (M1, S1, M2 and S2), and when measuring the melting distance (Fig. 2) the error was the difference (in m) from the start to end point of the M2 shear stress peak Supplementary Table 1. Experimental runs were recorded with a thermographic camera (H2640 NEC\Avio with a resolution of 90 × 90 µm2 per pixel) at a rate of 30 frames per second to monitor thermal production associated with friction; this depicts only the surface temperature of the sample, and no correction was added for the slip-zone, so the measurement represents a minimum temperature. Received 2 October 2013; accepted 27 March 2014; published online 4 May 2014 References 1. Iverson, R. M. et al. Dynamics of seismogenic volcanic extrusion at Mount St Helens in 2004–05. Nature 444, 439–443 (2006). 2. Costa, A., Wadge, G. & Melnik, O. 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A new rotary-shear high-velocity frictional testing machine: Its basic design and scope of research. Struct. Geol. 39, 65–78 (1994). Acknowledgements The authors wish to acknowledge the Starting Grants SLiM (306488) and USEMS (205175) as well as the Advanced Grant EVOKES (247076) of the European Research Council. Author contributions J.E.K. conceptualized, performed and analysed the experiments. Y.L., T.H. and A.J.H. performed the experiments and helped with the mechanical and thermal data analysis. G.D.T. analysed the mechanical data. S.D.A. produced the seismic analysis to constrain the experimental conditions. D.B.D. conceptualized and analysed the experiments as well as supervising the rheological modelling. All co-authors contributed to the manuscript. Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.E.K. Competing financial interests The authors declare no competing financial interests. NATURE GEOSCIENCE | VOL 7 | JUNE 2014 | www.nature.com/naturegeoscience © 2014 Macmillan Publishers Limited. All rights reserved.