Download Volcanic drumbeat seismicity caused by stick-slip

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
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NATURE GEOSCIENCE DOI: 10.1038/NGEO2146
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Ground
velocity (× 10−6 m s−1)
a
′ Hills Volcano, Montserrat
Soufriere
MBLY:BHY–-10 July 2003, 23:50:00 UTC
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Frequency (Hz)
15
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velocity (× 10−6 m s−1)
c
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HSR:SHZ–-03 December 2005, 06:00:00 UTC
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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
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NATURE GEOSCIENCE DOI: 10.1038/NGEO2146
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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
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4
M1
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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
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S1
Byerlee
frictional
strength
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c
10
M2
S2
0.1 m s−1
−1
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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
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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
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NATURE GEOSCIENCE DOI: 10.1038/NGEO2146
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Experiment 1
1.0
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MSH shear stress
MSH shortening
SHV shear stress
SHV shortening
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Experiment 2
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Experiment 3
0
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Experiment 4
Stress (MPa)
10
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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,
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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
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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.
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