JOURNAL OF PETROLOGY
VOLUME 55
NUMBER 3
PAGES 529^548
2014
doi:10.1093/petrology/egt075
Quantification of the Intrusive Magma Fluxes
during Magma Chamber Growth at Soufrie're
Hills Volcano (Montserrat, Lesser Antilles)
C. ANNEN1*, M. PAULATTO2, R. S. J. SPARKS1, T. A. MINSHULL3 AND
E. J. KIDDLEy
1
SCHOOL OF EARTH SCIENCES, UNIVERSITY OF BRISTOL, WILLS MEMORIAL BUILDING, QUEEN’S ROAD, BRISTOL BS8
1RJ, UK
2
DEPARTMENT OF EARTH SCIENCES, UNIVERSITY OF OXFORD, SOUTH PARKS ROAD, OXFORD OX1 3AN, UK
3
OCEAN AND EARTH SCIENCE, NATIONAL OCEANOGRAPHY CENTRE SOUTHAMPTON, UNIVERSITY OF
SOUTHAMPTON, EUROPEAN WAY, SOUTHAMPTON SO14 3ZH, UK
RECEIVED APRIL 25, 2013; ACCEPTED NOVEMBER 15, 2013
ADVANCE ACCESS PUBLICATION DECEMBER 20, 2013
Magma fluxes in the crust control the thermal viability and mechanical stability of magma chambers. We estimated the magma fluxes
required to generate the negative seismic velocity anomaly observed
below Soufrie' re Hills volcano, Montserrat. Growth of a magma
body by accretion of andesitic sills was simulated numerically and
the resulting temperatures and melt fractions were used to calculate
a synthetic anomaly of seismic wave velocity, which was filtered to
be comparable with the velocity anomaly obtained from a tomographic experiment. Petrology indicates that before it was reheated,
remobilized and erupted, the temperature of the magma residing in
the chamber was about 8508C. We ran simulations where convection
is assumed to be low and heat transfer is mostly by conduction and
simulations where convection is assumed to be vigorous enough to
rapidly cool the magma chamber to 8508C. In both cases, magma
chamber growth over the last 350 years results in tomography anomalies that are too strong, unless the magma was emplaced at an unlikely low melt fraction (50·5). Good fits between the modelled and
the observed velocity anomaly were obtained with sills 2^5 km in
radius emplaced over 6000^150 000 years, depending on the temperature and melt fraction of the emplaced magma. Because of a
trade-off between intrusion dimensions and emplacement durations,
the volumetric magma fluxes are restricted to 7 104 and
5 103 km3 a1. The velocity anomaly can be reproduced with a
chamber containing high melt-fraction magma or with a mush of
crystals and melt.The range of magma ages in the modelled magma
chamber is much wider than the crystal residence time of the erupted
*Corresponding author. Telephone: þ44117 954 54 26. Fax: þ 44 117 925
33 85. E-mail: [email protected]
y
Previously at School of Earth Sciences, University of Bristol, Wills
Memorial Building, Queen’s Road, Bristol BS81RJ, UK
andesite.This suggests that the eruption taps small pockets of recently
assembled magma and that the velocity anomaly is mostly due to a
non-eruptible mush.
magma chamber; magma flux; Montserrat; numerical
simulation; tomography
KEY WORDS:
I N T RO D U C T I O N
The construction and differentiation of the crust involves
the transfer of magma from the mantle to the lower crust
and from the lower crust to the upper crust and surface.
The flux of magma from depth to form and supply upper
crustal magma bodies (which in turn may feed volcanic
eruptions) is the main control on the thermal viability of
magma chambers (Annen, 2009) and on their mechanical
stability (Jellinek & DePaolo, 2003). It is now well accepted
that magma bodies grow incrementally by addition of discrete magma batches, which implies that intrusive magma
fluxes can vary greatly over time (e.g. de Saint Blanquat
et al., 2011). Magma fluxes can be inferred from a variety
of evidence. Average long-term fluxes (over tens of thousands to millions of years) are estimated by dividing intrusive volumes by the time span obtained with U-series
isotopes (Matzel et al., 2006; Leuthold et al., 2012), whereas
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VOLUME 55
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Soufrie're Hills is the youngest of the three volcanic edifices
of the island of Montserrat, which is part of the Lesser
Antilles volcanic island arc. Montserrat is mostly composed of andesites with minor amounts of basalts (Rea,
1974). The oldest rocks on Montserrat are dated at 2·6 Ma
(Harford et al., 2002), but volcanism might have started at
9 Ma when the northern part of the Lesser Antilles arc
migrated towards the west (Briden et al., 1979). The analysis
of submarine deposits indicates that Soufrie're Hills is at
least 250 000 years old (Smith et al., 2007; Le Friant et al.,
2008). Volcanic activity is characterized by periods of
103 to 104 years of relatively intense activity followed by
longer periods of dormancy (Le Friant et al., 2008). Active
periods are themselves interrupted by periods of quiescence of 103 years. The last high-activity period lasted
from 31ka to 17 ka (Harford et al., 2002). Activity resumed
6000 years ago (Trofimovs et al., 2013) and was marked by
the collapse of English’s Crater (Roobol & Smith, 1998).
The last eruption was about 350 years ago with Castle
Peak dome extruding within English’s Crater (Young
et al., 1998). Three volcano-seismic crises in 1897^1898,
1933^1937 and 1966^1967 (MacGregor, 1938; Powell, 1938;
Wadge & Isaacs, 1988) have been attributed to magma intrusions in the upper crust. The current eruption started
in July 1995 and was preceded by 3 years of increased seismicity (Aspinall et al., 1998; Wadge et al., 2013). Key dates
in Soufrie're Hills history are shown in Fig. 1.
The presence of amphibole in the crystal assemblage
erupted by the Soufrie're Hills magmas implies that the
depth of the top of the magma chamber is no less than
5^6 km (Barclay et al., 1998). Earthquake hypocentres are
located at depths shallower than 6 km (Aspinall et al.,
1998) and global positioning system (GPS) data fit a
point-source model (Mogi, 1958) with deformation source
at 6 km depth (Mattioli et al., 1998). Modelling of deformation in 2005^2007 indicates that the deformation is
related to a deeper magma chamber at 12^14 km depth
(Hautmann et al., 2010). Thus petrological and geodetic
data suggest that a 6 km deep magma chamber is connected to a deeper reservoir located at about 12 km depth
(Mattioli et al., 1998; Elsworth et al., 2008). According to
Elsworth et al. (2008), the current eruption responds to
flux from below into the deeper chamber and the magma
passes through the upper magma chamber without accumulating at this level.
Pyroxene (Murphy et al., 2000) and Fe^Ti oxides
(Devine et al., 1998) geothermometry, together with experimental studies (Barclay et al., 1998), indicate magma
temperatures of 840^8708C. Plagioclase^amphibole assemblages suggest temperature variations within the magma
body of up to 1008C. Complex mineral zoning, textures,
mineral chemistry variations and stable isotope data
imply disequilibrium related to magma mixing, convective
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Time BP (yrs)
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Montserrat oldest rocks
CONTEXT
MARCH 2014
Soufrière Hills oldest rocks
short-term fluxes (over years to decades) can be estimated
using ground deformation measurements (e.g. Sparks
et al., 2008; Pearse & Fialko, 2010; Parks et al., 2012).
Emplacement of granitoid intrusions is protracted and
may last from tens of thousands of years for relatively
small laccoliths (Leuthold et al., 2012) to millions of years
for batholiths (Coleman et al., 2004; Matzel et al., 2006).
Fluxes over hundreds or thousands of years are difficult to
determine because this time span is too small to be
resolved with radioactive isotopes and too long for most
deformation records. However, these fluxes control much
of the dynamics of shallow magma chambers and determine their ability to convect, differentiate and erupt
(Annen, 2009).
In this study we use seismic tomography results and numerical simulation of magma intrusion with additional
constraints from petrology and geophysics to quantify the
intrusive fluxes beneath Soufrie're Hills Volcano,
Montserrat, by testing out different hypotheses for the age
and dimensions of the current magma chamber.
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Fig. 1. Timeline showing the most relevant dates in Soufrie're Hills volcanic history (Harford et al., 2002; Trofimovs et al., 2013).
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ANNEN et al.
SOUFRIE'RE HILLS MAGMA FLUXES
processes and assimilation of older intrusions (Murphy
et al., 2000; Harford & Sparks, 2001; Couch et al., 2003;
Humphreys et al., 2009). These petrological data have
been interpreted as evidence of injection of basalt into a
shallow (5^6 km) magma chamber that reheated a cold
(830^8608C), highly crystalline (60^65 wt %) andesite
and initiated the current eruption (Barclay et al., 1998;
Devine et al., 1998, 2003; Murphy et al., 2000).
Mafic inclusions in the new andesites (since 1995) are
common and represent about 1% of the rock. The proportion of cryptic mixing of mafic magma into the andesite is
much higher, at several per cent or more (Humphreys
et al., 2009). However, according to Zellmer et al. (2003a)
these mafic magmas are not the parental magma of the andesite. The observation that U^Th isotopes are close to
secular equilibrium suggests protracted residence and differentiation of andesite magma at a deep level (lasting
4250 000 years), which contrasts with the very short
(5320 years) crystal residence time in the shallow magma
chamber, as inferred from Sr diffusion profiles in plagioclase (Zellmer et al., 2003b).
In these andesites, the crystal population is highly heterogeneous at the microscopic scale (Humphreys et al.,
2009), but the whole-rock is chemically homogeneous at
the macroscopic scale (Murphy et al., 2000; Couch et al.,
2001). This observation has been interpreted as evidence
for convective stirring and magma mixing. Oxygen and
H isotopes (Harford & Sparks, 2001; Zellmer et al., 2003a)
confirm that the erupted lavas contain a mixture of crystals with different histories and origins. In addition, the
andesites show evidence for reheating (Devine et al., 1998;
Murphy et al., 2000; Couch et al., 2001) and assimilation
of older intrusions (Harford & Sparks, 2001). All these
observations support a model in which magma pulses
of different origins were amalgamated and mixed
within the crust before erupting. Sparks & Young (2002)
suggested that cycles in seismic and geodetic signals
during the current eruption could be due to magma chamber overturns.
M AG M A C H A M B E R MO D E L S
In general, the geometry of magma chambers is not well
constrained. Many physical models rely on the assumption
that magma chambers are spherical or ellipsoidal.
However, models of magma chambers based on petrology
and geophysics range from sill-like or dyke-like chambers
to a plexus of interconnected sills and dykes, for mafic and
andesitic systems, and to large tabular magma chambers
for large dacitic and rhyolitic eruptions [for a summary,
see Zellmer & Annen (2008)]. There has been less attention
on how magma chambers nucleate and grow. A magma
chamber cannot start as a small sphere and grow by inflation, because for small volumes the pressure on the walls
of a spherical magma chamber is much higher than the
strength of crustal rocks and would result in dyke opening
and draining of the chamber (Jellinek & DePaolo, 2003).
Sheet intrusions are commonly observed in the field
(Menand, 2011, and references therein) and it is most
likely that a magma chamber starts as a sheet intrusion
(Gudmundsson, 2012), with the magma pressure resulting
in magma propagation at the tips. Recent studies of
medium to large intrusions, several hundreds of metres to
several kilometres thick, indicate that they formed by
stacking of smaller sheet intrusions (Searle, 1999; Searle &
Godin, 2003; de Saint-Blanquat et al., 2006; Pasquare' &
Tibaldi, 2007; Michel et al., 2008; Galland, 2012). Field observations, analogue experiments and stress analysis all
support a model in which magma is transported from
depth through dykes, which change their orientation to
form sills, either because they encounter a rheological barrier, or because of a change in the stress state of the crust
(Vigneresse et al., 1999; Kavanagh et al., 2006; Menand,
2008, 2011; Gudmundsson, 2011; Maccaferri et al., 2011;
Miller et al., 2011). The addition of these sheets builds up
an igneous body that can result in a magma chamber if
the sheet addition rate is large enough (Annen et al., 2008;
Annen, 2009).
Heat transfer models show that a magma chamber that
grows by accretion of sheet intrusions, if it becomes thick
enough, tends towards an ellipsoidal or even spherical
shape. Incremental growth results in large fluctuations of
temperatures and can explain the widespread evidence of
magma reheating and remelting before eruptions at
Soufrie're Hills and elsewhere (Devine et al., 1998; Murphy
et al., 2000; Bachmann et al., 2002; Druitt et al., 2012).
Alternatively, such reheating is commonly interpreted as
due to mafic injection into the magma chamber (Devine
et al., 1998; Murphy et al., 2000; Bachmann et al., 2002).
Incremental growth can also explain the contrast between
small-scale heterogeneities and large-scale homogeneity if
heterogeneous magma pulses are eventually homogenized
by convection before erupting (Davaille & Jaupart, 1993;
Jellinek & Kerr, 1999; Couch et al., 2001).
Paulatto et al. (2012) modelled the growth of the shallow
Soufrie're Hills magma chamber as resulting from the vertical stacking of sills and identified a model for which the
calculated seismic velocity anomaly corresponding to the
modelled temperatures and melt fractions, smoothed by
an appropriate filter, matched well the velocity anomaly
determined from seismic tomography. Importantly, they
showed that, although the inversion of tomographic data
suggested low melt fractions (7^10%), direct modelling
indicated that the low-velocity anomaly could also be due
to higher melt fractions (430%), representative of mobile,
eruptible magma. Here we comprehensively explore the
parameter space for the model and also include constraints
from petrology, to put limits on magma chamber dimensions and on magma fluxes.
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TOMOG R A P H Y
The seismic P-wave velocity structure beneath Montserrat
was constrained with first-arrival travel-time inversion of
active-source seismic data collected in December 2007,
during the SEA-CALIPSO experiment (Voight et al., 2010;
Paulatto et al., 2012). The inversion is based on the regularized least-squares approach developed by Hobro et al.
(2003), and has been explained in detail by Paulatto et al.
(2012). The starting model was a one-dimensional model
(1D) derived from a preliminary two-dimensional (2D) inversion of a subset of the data (Paulatto et al., 2010). The
model extends over an area of 45 km 50 km and to a
depth of 12 km, but is well constrained only to 7·5 km
depth.
The tomography revealed the presence of a low-seismicvelocity volume (LVV) extending vertically from 4 km to
at least 7·5 km depth and horizontally over an area of
6 km 8 km (Fig. 2). The LVV is slightly elongated in the
east^west direction. The largest negative velocity anomaly
beneath Soufrie're Hills is 0·7 km s1 (Fig. 2). The LVV
is attributed to the presence of partial melt and elevated
temperatures corresponding to the magma chamber feeding the current eruption. Partial melt is required because
the anomaly can be explained by temperature alone only
if temperatures were much higher than the known eruption temperature range of Soufrie're Hills andesite
(Paulatto et al., 2012).
TH ERMA L MODELS
The temperatures resulting from the amalgamation of
horizontal magma sheets (sills) are calculated with an explicit finite-difference code that solves the heat equation
rc
@T
@f
þ rL ¼ kr2 T
@t
@t
ð1Þ
where r is density, c is specific heat, T is temperature, L is
latent heat of crystallization or fusion, and f is melt fraction. k is thermal conductivity:
k ¼ Krc
ð2Þ
where K, the thermal diffusivity, is temperature dependent
and taken from Whittington et al. (2009). The values of the
physical parameters used in the simulation are reported in
Table 1.
The geometry of the modelled sills and magma chamber
is cylindrical and simulations are run on a vertical 2D
slice of a 3D system. A regular square grid and cylindrical
coordinates are used (Fig. 3). The boundary conditions are
a fixed temperature at the Earth’s surface (208C) and no
heat flux at the right and left boundaries. The condition
of no heat flux on the left boundary results from the symmetry of the system. A no heat flux condition on the right
boundary is valid as long as the numerical domain is
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large enough so that the temperature anomaly induced by
the sills does not reach the right boundary on the timescale
of the simulation. The bottom boundary condition is
based on the results of geodetic models for Soufrie're Hills
that indicate the presence of a second reservoir deeper
than 10 km (Mattioli et al., 1998; Elsworth et al., 2008;
Hautmann et al., 2010). We calculated the heat flux resulting from a 6 km radius spherical body at magmatic temperature, with a top at 12·5 km depth and a centre aligned
with the symmetry axis of the numerical domain (Fig. 3).
Beyond the horizontal extent of this deep body (6 km), the
heat flux is set to zero. This boundary condition underestimates the heat flux in the outer region, but our results are
weakly dependent on this assumption.
The emplacement of sills is simulated by setting the temperature of the cells corresponding to the location of the
sill to a magmatic temperature. Space is made for the successive sill by shifting the cells downwards below the sills.
According to Murphy et al. (2000) the melt fraction f at
8508C is 0·35. We assumed a solidus at 7008C (f ¼ 0) and
a liquidus at 9508C (f ¼ 1). The exact evolution of melt
fraction with temperature between these three points is
not well constrained and, for the sake of simplicity, we
assumed a linear relationship (Table 1). We considered that
the magma was not necessarily thermally at equilibrium
at the time of emplacement and might be undercooled.
The liquidus phases are missing in the crystalline assemblage of Soufrie're Hills products, which suggests that the
andesitic liquid came from a deeper level, where it can be
liquid at lower temperature, and crystallized by decompression (Blundy & Cashman, 2001; Annen et al., 2006).
The emplacement temperature is unlikely to be above
9008C considering the absence of clinopyroxene and the
abundance of amphibole in the crystalline assemblage. We
therefore tested the model with an emplacement temperature of 8508C and melt fractions of 0·5 and 1, and with an
emplacement temperature of 9008C and melt fractions of
0·675 and 1. Latent heat (3·5 105 J kg1; Hale et al., 2007)
is released by crystallization and absorbed by melting.
Emplacement of undercooled magma (all the cases,
except emplacement at T ¼ 9008C and f ¼ 0·675) results in
rapid crystallization, which approximates the process of
decompression crystallization (Blundy & Cashman, 2001),
and in the release of latent heat, which causes a transient
increase in temperature.
We ran two sets of simulations, which correspond to two
end-members in terms of heat transfer between the
magma chamber and the wall-rock. In the first set, we
assume that magma convection is weak enough to be neglected and heat transfer is by conduction only. In the
second set, we assume that convection is so vigorous that
the magma loses heat very rapidly until its melt fraction
is less than 0·35, and convection comes to a halt. To simulate this process, all the cells with melt fraction in excess
532
SOUFRIE'RE HILLS MAGMA FLUXES
ANNEN et al.
(a)
16˚50'
SH
CH
B’
16˚45'
SHV
C
C’
B
16˚40'
−62˚15'
(b)
20
−62˚10'
(c)
Section BB’ (km)
22
24
26
20
Section CC’ (km)
22
24
26
28
−2
0.5 0
−1.5
−2−1
−2.5
−3
0.5
5
−0.
2
0
0.5
Depth (km)
0
−0.5
SHV
−1−2
−1.5
0
0
4
.5
−0
.5
−0
6
8
−2
−1
0
vp difference (km/s)
1
Fig. 2. (a) Elevation map of Montserrat showing the locations of seismic stations used in the seismic tomography and the sections shown in (b)
and (c). (b, c) Seismic velocity anomaly beneath Soufrie're Hills calculated with respect to the average seismic velocity of the island; (b)
north^south section; (c) east^west section. SHV, Soufrie're Hills Volcano; SH, Silver Hills; CH, Centre Hills. See also Paulatto et al., 2012.
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JOURNAL OF PETROLOGY
VOLUME 55
of 0·35 are instantaneously and systematically set to a temperature of 8508C and a melt fraction of 0·35 and the
excess heat is transferred to the roof cells (Huppert &
Sparks, 1988). Below a melt fraction of 0·35, heat transfer
is by conduction only. We checked carefully that the law of
heat conservation was respected during this process.
The initial geothermal gradient for the simulations presented here is 508C km1. We ran a few tests with a lower
geothermal gradient of 308C km1 but the results we
Table 1: Values of parameters used in the simulations
Density r (kg m3)
2500
Specific heat c (J K1 kg1) 1000
Latent heat L (J kg1)
2 1
Diffusivity K* (mm s )
3·5 105
567·3/(T þ 273·15) – 0·062
T55738C
0·7320–0·00013(T þ 273·15) T45738C
Geotherm (8C km1)
50
Melt fraction f
0
T57008C
0·0023T – 1·63
7008C5T58508C
0·0065T – 5·175
8508C5T59508C
1
T49508C
T is temperature in 8C.
*Whittington et al. (2009).
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obtained were not significantly different. Temperatures
and melt contents are tracked during model evolution and
the final temperature and melt content distributions are
used to estimate expected seismic velocity anomalies. To estimate the effect of temperature we use a theoretical expression for the dependence of P-wave velocity on
temperature (Karato, 1993). The effect of melt content is
estimated with the self-consistent approach for the calculation of elastic properties of composite materials
(Berryman, 1980). These calculations are highly sensitive
to the microscopic geometry of the melt pockets (Tai Te,
1966). We used two melt models that represent end-members of the range of possible melt models, thus providing
an estimate of the sensitivity of our calculations. In the
‘tube’ model the melt resides in microscopic elongated
pockets at the edges of crystal grains, modelled as elongated spheroids. As the melt fraction increases the aspect
ratio of the pockets decreases eventually approaching the
shape of a sphere. In the ‘crack’ melt model, melt is
assumed to reside in microscopic crack-shaped pockets
modelled as low aspect ratio spheroids. The latter model
results in higher sensitivity to melt content and hence
stronger seismic velocity anomalies. The tube model is
more realistic for the magma storage region in
Montserrat, where pore shape is probably controlled by
crystal grain geometry (Kiddle, 2012).
T = 20 oC
q=0
q=0
sill
q = qm
q=0
Fig. 3. Model setup. The numerical domain, grid and sill are not to scale. q is heat flux; qm is the heat flux from a deep spherical magma chamber located outside the numerical domain. The geometry of the system is cylindrical in the horizontal plane normal to the figure.
Temperatures are computed at the grid nodes over a half domain with explicit finite differences.
534
ANNEN et al.
SOUFRIE'RE HILLS MAGMA FLUXES
Seismic velocities are also affected by fluid-related velocity dispersion mechanisms, such as the flow of melt between interconnected pockets (squirt flow). If seismic
frequencies are sufficiently low (low-frequency approximation) squirt flow equalizes pressure imbalances and
dissipates energy, resulting in reduced seismic velocities
compared with the case where squirt flow cannot happen
(high-frequency approximation) (Budiansky & O’Connell,
1976). The difference between the two cases is significant
only for the crack model. We adopt the low-frequency approximation, which leads to lower estimates of melt
volume and is more likely for Montserrat upper crustal
rocks (Kiddle, 2012).
R E S U LT S
Tomography results suggest the presence of melt between
about 5^6 km depth and at least 7·5 km depth (Paulatto
et al., 2012). We ran a series of magma body growth simulations with the first sill emplaced at 5, 5·5 or 6 km depth
and with sill radius varying from 1 to 5 km. Sills are
emplaced by under-accretion down to 8, 8·5 or 9·0 km.
The exact position of the first and last sill does not affect
significantly the results, so here we show only the simulation with sills emplaced from 5·5 down to 8 km. Based on
the geological record (Fig. 1), we tested the hypotheses
that the LVV is related to magma injection that started:
(1) at 250 ka (the magma body is as old as Soufrie're
Hills); (2) at 30^40 ka (the magma body started to grow
at the beginning of the last cycle of high activity); (3) at
17ka (the magma reservoir started to (re)fill at the end of
the last cycle of high activity); (4) 6000 years ago, when activity resumed with the formation of English’s Crater; (5)
350 years ago, after the last eruption before the current activity. We also ran models over 100 and 150 kyr to refine
our estimates of fluxes and durations.
In comparison with simulations where heat transfer is by
conduction only, the volumes of molten materials that are
produced with simulations that integrate convection are
larger and their temperatures are lower (Fig. 4). This
effect is noticeable only if magma is injected at high temperatures and high melt fractions, and it is never strong
enough to affect our conclusions regarding the fit with the
tomography model.
Final temperatures and melt fractions in the magma
body depend on how fast it was assembled (Fig. 5), on the
total heat content of the injected magma [i.e. on its temperature (sensible heat) and melt fraction (latent heat)
(Fig. 6)], and on the intrusion radius (Fig. 7). The log of
magma intrusive fluxes is shown in Figs 8^10 as contour
lines. This average flux corresponds to the total volume of
magma injected during the simulation divided by the duration of the simulation. Figure 8 shows which combination
of parameter values (magma heat content, simulation duration, intrusion radius) result in magma temperatures at
the end of the simulation that are hotter, colder or in the
same range of temperature (830^8808C) compared with
Soufrie're Hills magmas as determined by experimental
petrology (Barclay et al., 1998; Devine et al., 1998; Murphy
et al., 2000). At temperatures below 8508C, melt fractions
are less than 0·5 and the magma is unlikely to behave as a
fluid and be eruptible. We note that our modelled magma
chambers can be hotter than 8508C only in conductive
models. For emplacement durations of more than 100 kyr
and flux of less 103 km a1, the model temperatures are
always colder than the petrology-inferred temperatures,
independently of the effect of convection. Emplacement
over 250 kyr does not produce any melt, because each
magma pulse completely solidifies before the injection of
the next one.
Figure 9 shows where, in the parameter space, the modelled velocity anomaly fits the field tomography (Fig. 2);
that is, where its intensity is between 0·5 and
0·9 km s1 and the diameter of the 0·5 km s1 isoline is
between 2 and 4 km. For protracted chamber growth duration and/or magma emplaced with low heat content, the
seismic velocity anomaly is too weak to fit observations,
whereas short durations and high heat content produce an
anomaly that is too strong (Figs 5 and 6). A fit is dependent
on the chamber radius (Fig. 7) and on growth duration
(Fig. 6) (i.e. on the average magma flux), with longer duration requiring larger chamber dimensions (Fig. 9). A
chamber radius of 1km always produces anomalies that
are too small (Figs 7 and 9). Fits were found for chamber
radii from 2 to 5 km and a large range of durations
from 6 to 150 kyr (Fig. 9), but all fits involve fluxes that
are in a relatively restricted range between 7 104 and
5 103 km3 a1.
DISCUSSION
The current eruptive flux of Soufrie're Hills volcano is
about 7·5 102 km3 a1 (Sparks et al., 1998; Elsworth
et al., 2008; Wadge et al., 2013), but the average eruptive
flux over its lifetime is estimated as (1·5^
1·7) 104 km3 a1 (Harford et al., 2002; Le Friant et al.,
2004). Our estimated intrusive flux (Fig. 9) of 7 104 to
5 103 km3 a1 lies between these two values.
The model of incremental igneous body growth that is
now widely accepted implies that several magma fluxes
characterize the growth of igneous bodies (de Saint
Blanquat et al., 2011): a ‘long-term’ average flux, which corresponds to the total volume of an igneous body divided
by the total emplacement time, a ‘quasi-instantaneous’
flux, which corresponds to the emplacement of the smallest
unit, and one or a series of ‘intermediate fluxes’ corresponding to periods of high activity. In comparison with
plutonic fluxes based on radiogenic isotopes, the flux at
the origin of Soufrie're Hills LVV is higher than the fluxes
determined by Matzel et al. (2006) for Tenpeak intrusion
535
Depth (km)
536
0
400
800
26
Temperature (oC)
200
400
800
SHV
400
800
200
SHV
24
Y distance (km)
22
1200
28 20
20
30
26
Melt fraction (vol)%
10
10
30
SHV
10
30
SHV
24
Y distance (km)
22
40 −2
28 20
0
26
28 20
−0.5
−1
−1.5
SHV
24
1 −2
−1
0
vp difference (km/s)
−0.5
−1
SHV
26
Y distance (km)
22
(b) Strong convection
vp difference (km/s)
−1
−0.5
−2
SHV
−0.5
−1
−3.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−3
−0.5
SHV
−3.5
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
−1
−1.5
SHV
−0.5
−1
−1.5
SHV
24
Y distance (km)
22
1
28
NUMBER 3
8
6
4
2
0
−2
8
6
4
2
0
−2
20
(a) Weak convection
VOLUME 55
Fig. 4. Simulation results. (a) Heat transfer is by conduction only. (b) Strong magma convection results in rapid heat transfer to the roof. Emplacement duration is 6000 years. The intrusion
radius is 2 km. Magma is injected at 9008C with a melt fraction of unity. First column, temperature; second column, melt fractions; third column, unsmoothed seismic velocity anomalies assuming tube-shaped melt pockets; fourth column, smoothed seismic velocity anomalies assuming tube-shaped melt pockets; fifth column, unsmoothed seismic velocity anomalies assuming crackshaped melt pockets; sixth column, smoothed seismic velocity anomalies assuming crack-shaped melt pockets.
Depth (km)
JOURNAL OF PETROLOGY
MARCH 2014
Depth (km)
537
400
26
Temperature (o C)
800
600
800
6
8
200
400
0
SHV
400
800
200
SHV
24
Y distance (km)
22
4
2
0
−2
8
6
4
2
0
−2
20
1200
28 20
10
20
10
30
30
26
Melt fraction (vol)%
20
SHV
10
30
SHV
24
Y distance (km)
22
40 −2
28 20
24
0
28 20
−0.5
−1
SHV
24
1 −2
−1
0
vp difference (km/s)
−0.5
SHV
26
Y distance (km)
22
(b) Duration = 6000 yrs
26
vp difference (km/s)
−2
−0.5
SHV
−0.5
−2
SHV
−1
22
Y distance (km)
(a) Duration = 350 yrs
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
−
−3
SHV
−3
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
−1
SHV
−0.5
−1
−1.5
SHV
24
Y distance (km)
22
1
28
Fig. 5. Simulation results for duration of magma emplacement of (a) 350, (b) 6000, (c) 17 000, and (d) 30 000 years. The intrusion radius is 2 km. The temperature and melt fraction of the injected magma are 8508C and 0·5, respectively. Heat transfer is by conduction only. The columns are as in Fig. 4.
(continued)
Depth (km)
ANNEN et al.
SOUFRIE'RE HILLS MAGMA FLUXES
Depth (km)
538
0
400
800
26
Temperature ( oC)
400
600
200
SHV
400
600
800
200
SHV
24
Y distance (km)
22
1200
28 20
20
10
30
26
Melt fraction (vol)%
10
10
SHV
20
SHV
24
Y distance (km)
22
40 −2
28 20
−1
28 20
−0.5
SHV
24
26
Y distance (km)
22
0
1 −2
0
vp difference (km/s)
−1
SHV
(d) Duration = 30,000 yrs
26
vp difference (km/s)
−0.5
−1
SHV
−0.5
−1
−1.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−2.5
−0.5
SHV
−3
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
SHV
−1
−0.5
SHV
24
Y distance (km)
22
1
28
NUMBER 3
8
6
4
2
0
−2
8
6
4
2
0
−2
20
(c) Duration = 17,000 yrs
VOLUME 55
Fig. 5. Continued.
Depth (km)
JOURNAL OF PETROLOGY
MARCH 2014
Depth (km)
539
8
6
4
2
0
−2
8
6
4
2
0
−2
0
20
400
800
200
200
26
Temperature (oC)
400
600
800
SHV
400
600
SHV
24
Y distance (km)
22
1200
28 20
10
20
10
30
30
26
Melt fraction (vol)%
20
SHV
10
SHV
24
Y distance (km)
22
40 −2
28 20
−1
−0.5
−1.5
SHV
−0.5
−1
SHV
24
28 20
SHV
24
0
1 −2
−1
0
vp difference (km/s)
−0.5
SHV
26
Y distance (km)
22
(b) T = 900 C, f = 0.675
26
vp difference (km/s)
22
Y distance (km)
(a) T = 850 C, f = 0.5
1 −2
28 20
−1
0
26
vp difference (km/s)
−3
−0.5
SHV
−2.5
0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
SHV
−0.5
SHV
24
Y distance (km)
22
1
28
Fig. 6. Simulation results for different heat content of the magma that is repeatedly injected: (a) Temperature (T) is 8508C, melt fraction (f) is 0·5. (b) T is 9008C, f is 0·675. (c) T is 8508C, f is
unity. (d) T is 9008C, f is unity. The emplacement duration is 30 kyr and the intrusions radius is 2 km. Heat transfer is by conduction only. The columns are as in Fig. 4.
(continued)
Depth (km)
ANNEN et al.
SOUFRIE'RE HILLS MAGMA FLUXES
Depth (km)
540
0
400
800
26
Temperature (oC)
400
600
800
200
SHV
400
600
800
200
SHV
24
Y distance (km)
22
1200
28 20
20
20
10
30
30
26
Melt fraction (vol)%
10
10
30
SHV
20
SHV
24
Y distance (km)
22
40 −2
28 20
−1
0
28 20
−0.5
SHV
1 −2
24
−1
0
vp difference (km/s)
−0.5
SHV
26
Y distance (km)
22
(d) T = 900 C, f = 1
26
vp difference (km/s)
−2.5
−0.5
SHV
−2.5
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−3.5
−0.5
SHV
−3
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
−1
SHV
−1
−0.5
SHV
24
Y distance (km)
22
1
28
NUMBER 3
8
6
4
2
0
−2
8
6
4
2
0
−2
20
(c) T = 850 C, f = 1
VOLUME 55
Fig. 6. Continued.
Depth (km)
JOURNAL OF PETROLOGY
MARCH 2014
Depth (km)
541
8
6
4
2
0
−2
8
6
4
2
0
−2
0
20
400
800
26
Temperature (oC)
600
400
200
SHV
600
400
200
SHV
24
Y distance (km)
22
1200
28 20
20
30
26
Melt fraction (vol) %
10
SHV
SHV
24
Y distance (km)
22
40 −2
28 20
24
0
26
28 20
SHV
1 −2
24
−1
0
vp difference (km/s)
−0.5
SHV
26
Y distance (km)
22
(b) Radius = 3 km
vp difference (km/s)
−0.5
SHV
SHV
−1
22
Y distance (km)
(a) Radius = 2 km
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
−2.5
SHV
−1.5
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
−1
0
26
vp difference (km/s)
−0.5
SHV
SHV
24
Y distance (km)
22
1
28
Fig. 7. Simulation results for different intrusion radii of 2 km (a), 3 km (b), and 4 km (c). Emplacement duration is 100 kyr. Temperature and melt fraction of the injected magma are 9008C and
unity, respectively. Heat transfer is by conduction only. The columns are as in Fig. 4.
(continued)
Depth (km)
ANNEN et al.
SOUFRIE'RE HILLS MAGMA FLUXES
542
8
6
4
2
0
−2
0
20
26
400
800
o
Temperature ( C)
600
400
200
SHV
24
Y distance (km)
22
1200
28 20
26
10
20
30
Melt fraction (vol %)
10
SHV
24
Y distance (km)
22
40 −2
28 20
26
−1
0
vp difference (km/s)
−0.5
−1
SHV
24
Y distance (km)
22
1 −2
28 20
26
−1
0
vp difference (km/s)
−0.5
SHV
24
Y distance (km)
22
1 −2
28 20
26
−1
0
vp difference (km/s)
−3
−0.5
−1
SHV
24
Y distance (km)
22
1 −2
28 20
26
−1
0
vp difference (km/s)
−0.5
−1
SHV
24
Y distance (km)
22
1
28
VOLUME 55
NUMBER 3
Fig. 7. Continued.
Depth (km)
(c) Radius = 4 km
JOURNAL OF PETROLOGY
MARCH 2014
ANNEN et al.
SOUFRIE'RE HILLS MAGMA FLUXES
Radius (m)
(a) T = 850 C, f = 0.5
5.5
0
5
4.5
4
3.5
0
3
2.5
2
1.5
1 1
0.5 2
10
(b) T = 900 C, f = 0.675
−1
5.5
0cold
−1
5
hot
fit
4.5
4
3.5
0
−1
3
2.5
2
1.5
−2
1 −1
0.5 2
3
10
10
−3
−2
−3
−1
−2
−3
−4
−3
−2
−4
−5
10
3
10
4
10
5
Radius (m)
(c) T = 850 C, f = 1
5.5
0
5
4.5
4
3.5
0
3
2.5
2
1.5
1 −1
0.5 2
10
5.5
0
5
4.5
4
3.5
0
3
2.5
2
1.5
1 −1
0.5 2
10
−3
−2
−3
−2
−3
−4
−2
−3
−4
−5
3
10
−3
−2
−3
−4
−3
−4
−5
10
4
10
5
(d) T = 900 C, f = 1
−1
−1
−3
−2
4
10
Duration (yrs)
5
10
−1
−3
−2
−3
−1
−2
−3
−4
−2
−3
−4
−5
3
10
4
10
Duration (yrs)
5
10
Fig. 8. Comparison between simulations and petrological data plotted in radius^duration space for different magma emplacement temperatures T and melt fractions f. Grey squares indicate magma chamber temperatures at the end of the simulation similar to those determined by
petrology (830^8808C). Open circles indicate lower temperatures and open diamonds indicate higher temperatures. Contour lines are log of
fluxes in km3 a1.
(1·5 104 km3 a1) and Mount Stuart Batholith
(2·2 104 to 5·8 104 km a1) but it is comparable with
the 8 104 km3 a1 intrusive flux of the Torres del Paine
granite (Leuthold et al., 2012). However, it is about one
order of magnitude lower than the fluxes estimated on the
basis of ground surface deformation at Uturuncu (Sparks
et al., 2008) and at Santorini (Parks et al., 2012) and on the
basis of petrological study of the Santorini Minoan eruption products, which indicate that magma was injected in
the shallow reservoir shortly before the eruption with a
flux 45 102 km3 a1. These comparisons suggest that
the flux that built the Soufrie're Hills shallow reservoir is
intermediate between the long-term average fluxes that
form batholiths and the short-term fluxes that replenish
volcanic reservoirs.
From the perspective of plutonic^volcanic relationships,
the shape of intrusions exerts a strong control on heat
loss, so that with an equivalent flux, intrusive bodies with
the highest aspect ratio might not accumulate melt,
whereas bodies with lower aspect ratio would evolve into
eruptible magma chambers. For a magma body that
grows by addition of sills, temperature and melt fractions
are controlled by the sill addition rate. For example, if an
average addition rate of 3 cm a1 is needed to accumulate
eruptible magma (Hanson & Glazner, 1995; Yoshinobu
et al., 1998; Annen et al., 2008), the minimum flux required
to form a magma chamber is about 103 km3 a1 if the
magma body diameter is 4^8 km as is predicted for
Soufrie're Hills, whereas for larger systems, which can feed
a caldera-forming eruption and with a 20^40 km diameter,
543
JOURNAL OF PETROLOGY
VOLUME 55
(a) T = 850 C, f = 0.5
5.5
Radius (m)
5.5
5
4.5
4
3.5
0
3
2.5
2
1.5
1 −1
0.5 2
10
−3
−2
4.5
−3
4
3.5
−2
−1
0
3
−3
2.5
2
−4
1.5
1 −1
−2
−3
3
4
−4
−5
0.5
2
10
10
5
10
10
(c) T = 850 C, f = 1
5.5
0
5
−1
Radius (m)
−3
3.5
−2
−1
−3
2.5
2
1.5
1 −1
0.5
−2
−3
−4
−4
−5
2
10
3
10
weak −1
too small
too strong
Fit tomo
5.5
0
5
4.5
4
3.5
0
3
2.5
2
1.5
1 −1
0.5 2
10
−3
−2
4
0
0too
−3
−2
−3
−2
−1
−3
−4
−3
−2
−4
−5
3
4
10
5
10
10
(d) T = 900 C, f = 1
4.5
3
MARCH 2014
(b) T = 900 C, f = 0.675
−1
0
5
NUMBER 3
4
10
Duration (yrs)
5
10
−1
−3
−2
−3
−2
−1
−3
−2
−3
−4
−4
−5
3
10
4
10
Duration (yrs)
5
10
Fig. 9. Comparison between simulations and field-recorded tomography plotted in radius^duration space for different magma emplacement
temperaturesTand melt fractions f. Grey squares indicate synthetic velocity anomalies similar to field velocity anomalies. Upward-pointing triangles indicate synthetic velocity anomalies that are too weak. Downward-pointing triangles indicate synthetic velocity anomalies that are too
strong and diamonds indicate synthetic velocity anomalies that are too small. Contour lines are log of fluxes in km3 a1.
this minimum flux is 101^102 km3 a1 (Annen, 2009). In
other words, the flux needed to maintain a typical andesitic arc volcano magma chamber is at least one order of
magnitude lower than the flux required to assemble the
magma for a supereruption.
The residence times of crystals in the Soufrie're Hills
eruptive products are very short (5320 years; Zellmer
et al., 2003b). According to our calculations, the LVV
cannot be due to the growth of a magma chamber over
the last 350 years, unless emplacement temperatures and
melt fractions were very close to the pre-eruptive ones
that we are trying to match, because on such a short timescale the magma does not have time to cool and crystallize.
This would imply emplacement with a high crystal fraction of about 0·65^0·7. Magma viscosity strongly depends
on its crystal content and increases dramatically beyond a
critical crystal fraction, which usually falls between 0·4
and 0·6 (Marsh, 1981; Lejeune & Richet, 1995; Caricchi
et al., 2007), although, depending on the grain shape and
aspect ratio, the critical crystal fraction might be lower
(Mueller et al., 2010; Cimarelli et al., 2011; Schmeling et al.,
2012). Experiments show that crystal size bimodality can
increase critical crystal fraction to 0·66 (Castruccio et al.,
2010), but it is unlikely that a magma with a crystal fraction of 0·65^0·7 can be transported through a dyke.
Emplacement with crystal fraction of 0·5 or less is much
more plausible. In this case, matches can be found only if
the chamber grew over 6000 years or more. However, for
those simulations, the magmas in the chamber cover a
much wider age range than the 320 years suggested by
the plagioclase study of Zellmer et al. (2003b). Residence
times and tomography can be reconciled if most of the
544
SOUFRIE'RE HILLS MAGMA FLUXES
5
No fit
fit
−3
−2
0
5.5
−1
ANNEN et al.
4.5
−3
4
−1
3
−2
3.5
0
Radius (m)
deformation that the crust is unlikely to be able to accommodate. We expect early injections to be accommodated
by brittle deformation but as the system heats up and the
crust become more ductile, new magma volume might be
accommodated viscously, which might have consequences
on the behaviour of the ground surface deformation signal
(Pearse & Fialko, 2010).
−3
2.5
2
−4
−2
1
−3
1.5
CONC LUSIONS
−4
0.5
102
103
104
Duration (yrs)
105
Fig. 10. Comparison between simulation results and tomography,
integrating the rheological state of the magma. The grey squares
show the simulations that fit the field-recorded tomography and
where the simulated magma body melt fractions are less than 0·5;
that is, most of the magma is not eruptible. The open circles are for
simulations that either do not fit the field-recorded tomography or
where the magma is at a melt fraction of 0·5 or more. Contour lines
are log of fluxes in km3 a1.
low-velocity volume is a non-eruptible mush of crystals and
melt and the current eruption taps smaller bodies of
magma that have been assembled at shallow level during
the last few centuries. If we take into account this additional constraint (i.e. that the LVV is related to a reservoir
that is largely crystalline with a relatively small amounts
of melt), we find magma emplacement durations between
30 and 150 kyr and fluxes between 7 104 and
2·4 103 km3 a1 (Fig. 10).
Our results combined with data from geophysics, petrology and geochemistry support the following model.
Magma differentiates and resides over timescales of more
that 350 kyr (Zellmer et al., 2003a) as partial melt in a
lower crustal hot zone (Sparks & Young, 2002; Annen
et al., 2006; Hodge et al., 2012; Svensen et al., 2012). This
melt is episodically released to an intermediate magma
reservoir at a depth of 10^12 km, which in turn feeds a
shallow reservoir at 5^6 km depth, where most of the
magma partially crystallizes and forms a non-eruptible
mush. Occasionally, eruptions tap the magma that has
been recently injected and is still mobile. The long time
scale of deep melt storage, segregation and episodic ascent
might be related to the physics of melt separation in a
slowly accumulating region of basalt underplating
(Solano et al., 2012).
Our simulations do not include emplacement mechanics,
which is beyond the scope of this study. As discussed
above, magma chamber growth over less than 6000 years
requires emplacement at a very low melt fraction and
high viscosity. Another difficulty with emplacement over
short durations is that the fluxes and sill addition rates are
very high (9 102 km3 a1 and 7 m a1, respectively for
emplacement over 350 years) and would result in
The temperatures and melt fractions in a growing magma
body strongly depend on the heat content of the injected
magma and on the duration of the magma body growth.
We found that the low-velocity volume imaged by seismic
tomography that underlies Soufrie're Hills volcano can be
reproduced with intrusive magma fluxes in the range of
7 104 to 5 103 km3 a1 over durations that range
from 6 to 150 kyr depending on the intrusion radius (2^
5 km). Crystal residence times that are much shorter than
the age of our modelled magma reservoir might indicate
that the eruption taps small pockets of recently assembled
magma and that the low-velocity volume detected below
Soufrie're Hills is a non-eruptible crystalline mush. This
additional constraint limits the intrusive fluxes to a maximum of 2·4 103 km3 a1.
AC K N O W L E D G E M E N T S
We gratefully thank Bruce Marsh for his positive and
encouraging comments, and an anonymous reviewer for
helping us to clarify our argument.
FU N DI NG
This work was supported by a European Research Council
Advanced Grant (project VOLDIES). The tomography
experiment on which this work is based was supported by
the National Science Foundation, the National
Environment Research Council, the British Geological
Survey (BGS), Discovery Channel TV and the British
Foreign and Commonwealth Office.
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