Earth and Planetary Science Letters 359–360 (2012) 93–105
Contents lists available at SciVerse ScienceDirect
Earth and Planetary Science Letters
journal homepage: www.elsevier.com/locate/epsl
Fracture mode analysis and related surface deformation during dyke
intrusion: Results from 2D experimental modelling
M.M. Abdelmalak a,n, R. Mourgues a, O. Galland b, D. Bureau a
a
b
LUNAM Université, Université du Maine, CNRS UMR 6112, LPGN, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
Physics of Geological Processes (PGP), University of Oslo, Norway
a r t i c l e i n f o
abstract
Article history:
Received 17 May 2012
Received in revised form
24 September 2012
Accepted 6 October 2012
Editor: Y. Ricard
Available online 8 November 2012
Surface deformation analysis in volcanic edifices in response to shallow magma intrusion is crucial for
assessing volcanic hazards. In this paper, we discuss the effect of dyke propagation mode on surface
deformation through 2D laboratory models. Our experimental setup consists of a Hele-Shaw cell, in
which a model magma is injected into a cohesive model crust. Using an optical image correlation
technique (Particle Imaging Velocimetry), we measured the surface deformation, the displacements
and the strain field induced by magma emplacement within the country rock. We identify two types of
intrusion morphologies (Types A and B), which exhibit two evolutional stages. During the first stage,
both types resulted in a vertical dyke at depth; its propagation was controlled by both shear
deformation and tensile opening. The model surface lifted up to form a smooth symmetrical dome,
resulting in tensile cracks. During the second stage, Types A and B experiments differ when the dyke
reaches a critical depth. In Type A, the intrusion gradually rotates, forming an inclined sheet dipping
between 451 and 651. This rotation results in asymmetrical surface uplift and shear failure upon the tip
of the dyke. In Type B, the dyke tip interacts with tensile cracks formed during the first stage. This
fracture controls the subsequent propagation of the dyke toward the surface. In both types of
experiments, intrusions result in surface uplift, which can be accommodated by reverse faults. Our
study suggests that dykes propagate as viscous indenters, rather than linear elastic fracturing.
& 2012 Elsevier B.V. All rights reserved.
Keywords:
dyke
experimental models
surface deformation
strain analysis
viscous indenter
Linear Elastic Fracture Mechanics
1. Introduction
Surface deformation due to magma intrusions in volcanic
systems can be detected by geodetic survey (Cayol and Cornet,
1998; Froger et al., 2001, 2007; Pedersen and Sigmundsson, 2006;
Masterlark, 2007). Surface movements reflect the dynamics of
volcanic plumbing systems, such as the shape of magma intrusions, the magma pressure, and the emplacement mechanisms.
Recent experimental models even show that the time evolution of
surface deformation can be used to predict the location of a
preparing volcanic eruption (Galland, 2012). A proper understanding of the processes that govern surface deformation is
therefore crucial for unravelling magma transport dynamics
at depth.
A classical approach for analyzing surface deformation is through
forward or inverse modelling of surface deformation, using either
analytical or numerical models. Analytical models consider simple
shapes, such as an opening tensile crack (Bonafede and Danesi,
n
Corresponding author. Present address: Department of Geology, University
of Oslo, P.O Box 1047 Blindern, N-0316 Oslo, Norway.
E-mail address: abdelmalak_mansour@yahoo.fr (M.M. Abdelmalak).
0012-821X/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.epsl.2012.10.008
1997) or a pressurized cavity (Mogi, 1958; Pollard and Holzhausen,
1979; Fialko et al., 2001; Gudmundsson, 2006) in elastic half-space.
Numerical models can take into consideration more complex
shapes. The models predict the shape and the opening of the
intrusion, as well as the pressure of the magma. Nevertheless, such
approach considers static systems only, where the mechanism of
propagation and emplacement of the intrusions are not considered.
Former studies, however, show that surface deformation
strongly depends on intrusion propagation and emplacement
mechanism. There are two competing models of emplacement,
which provide contrasting surface expressions.
A first model for dyke emplacement is Linear Elastic Fracture
Mechanics (LEFM). This approach considers that dykes are open
fractures, the country rock being elastic everywhere but in a small
‘‘process zone’’ at the tip of the fracture. In this model, the magma
overpressure pushes on the dyke walls, leading to large tensile
stresses at the dyke tip. The surface expression associated with
this model is (1) no uplift above the dyke tip, and (2) two uplift
zones on each side of the dyke tip. It has also been suggested that
the emplacement of dykes result in subsidence of the Earth
surface, triggering the formation of grabens and normal faults
(Pollard et al., 1983; Mastin and Pollard, 1988; Rubin and Pollard,
1988). Such surface deformation patterns have been monitored in
94
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
viscosity of 16.6 Pa s and a density of 1400 kg m 3. The silica
powder is sufficiently fine grained (15 mm) to prevent the percolation of the Golden syrup. After manual compaction, the density
of the powder ranges between 1500 and 1700 kg m 3. The
powder fails according to a Coulomb criterion with cohesion
around 350 Pa and an angle of internal friction reaching 451
(Galland et al., 2006, 2009). Measurements were done in a
Hubbert-type shear box (Krantz, 1991; Schellart, 2000;
Mourgues and Cobbold, 2003). Due to its non-negligible cohesion,
the silica powder fails both in tension (open cracks) and shear
(faults).
volcanic rift zones; however, it is difficult to decipher whether
subsidence and normal faulting are triggered by the dyke or by
the regional tectonic extension. Moreover, many feeder dykes and
dykes arrested a few metres below the surface do not generate
faults or grabens (Gudmundsson, 2003). In addition, on volcanoes
with limited or no tectonic extension, dyke emplacement is
usually associated with surface uplift (Fukushima et al., 2005).
A second model considers that dykes propagate as viscous
indenters (Donnadieu and Merle, 1998), producing shear failure
at dyke tips. In such a model, the magma pushes the dyke tip
ahead, indenting the country rock along small-scale shear zones.
This model is in agreement with structural observations (Duffield
et al., 1986; Gudmundsson et al., 2008) and geophysical measurements (Roman et al., 2004). The occurrence of shear failure at
dyke tips has been observed in 2D laboratory experiments
(Kervyn et al., 2009), and may explain the splitting of dykes into
cone sheets close to the surface (Mathieu et al., 2008). The surface
deformation associated with this model, however, has not been
addressed.
In order to study the effect of dyke propagation mechanism on
surface deformation, we designed new 2-dimensional quantitative experiments of dyke emplacement. Our setup allows the
monitoring of both (1) the displacements and strain field in the
host rock at the vicinity of the dyke, and (2) the associated surface
deformation.
2.2. Scaling
The scaling procedure associated with magma intrusion in the
brittle crust is challenging because (1) the experiments aim to
simulate the coupling between fluid and solid mechanics, and
(2) the ranges of geological settings and viscosities of magma are
very broad. The principle is to define selected dimensionless
numbers, which characterize the geometry, the kinematics and
the dynamics of the simulated processes. The experiments are
representative of their natural prototypes if the values of these
dimensionless numbers in the experiments and in nature are
equal. The following scaling procedure is based on the standard
similarity conditions, as developed by Hubbert (1937) and
Ramberg (1981). This procedure was detailed and applied to
magmatic processes by Merle and Borgia (1996), Galland et al.
(2009, 2006), Mathieu et al. (2008) and Gressier et al. (2010).
The principal geometric input variable is the thickness of the
overburden (L), which is the same as the final intrusion length. The
output geometrical parameter is the intrusion thickness (e). Material properties are the densities of the magma (rm) and the country
rock (rr), the angle of internal friction (F) and the cohesion (C) of
the country rock, and the viscosity of the magma (Z). The experiments were performed in the natural field of gravity (g). The
moving piston imposed the injection flow rate (Q). The magma
flow velocity can be calculated from the thickness of the intrusion,
which is a result and not a parameter known a priori. However,
this parameter needs to be taken into account for the dimensional
analysis in order to consider the viscous stresses inside the
intrusions.
Nine variables characterize the physical system, three of them
having independent dimensions. According to the Buckingham-P
theorem (e.g., Middleton and Wilcock, 1994; Barenblatt, 2003)
and following Galland et al. (2009), we defined six dimensionless
numbers listed in Table 1. We chose the scale ratio between our
experiments and nature to be between 10 4 and 10 3, so that
1 cm in the experiments represents 10–100 m.
The first dimensionless parameter defines the geometric ratio
of the dyke. In nature, two aspects ratios are required to describe
entirely the 3-dimensional geometry of a dyke. In our 2D
2. Experimental setup and scaling
2.1. Model materials
Among the various methods used to study dyke propagation,
analogue modelling based on fluid injection into gelatin has been
used for many years (Hubbert and Willis, 1957; Pollard, 1973;
Rubin and Pollard, 1988; Takada, 1994; Kavanagh et al., 2006;
Menand, 2008). This material has the advantage to be transparent, it fails in tension, and its elastic properties are becoming
better known (Di Giuseppe et al., 2009). Nevertheless, it is too
cohesive to represent weak brittle rocks, and it is not scaled to
simulate plastic shear deformation. To overcome this difficulty,
Galland et al. (2006, 2009) and Mathieu et al. (2008) used
cohesive granular materials (silica powder, ignimbrite, and diatomite powder). These materials fail both in tension and in shear
at low differential stresses, so their behaviour is closer to that of
natural rocks.
Among the analogue materials described in the literature, such
as silica powder (Galland et al., 2003, 2006, 2009), diatomite
powder (Gressier et al., 2010), flour (Mastin and Pollard, 1988),
vegetable oil (Galland et al., 2006; 2009), and Golden syrup
(Mathieu et al., 2008), we chose to use Golden syrup as a magma
analogue and a fine-grained silica powder as a brittle crust
analogue. At room temperature (22 1C), Golden syrup has a
Table 1
Symbols, units, and values of the mechanical variables in nature and experiments.
L
C
f
rm
rr
Z
s
g
e
U
Definition of parameters
Field
Experiment
Dimension
Thickness (length scale)
Cohesion of brittle material
Angle of internal friction
Density of magma
Density of country rock
Viscosity of magma
Gravitational stress
Acceleration due to gravity
Intrusion thickness
Velocity of intrusion propagation
200–2000
105–107
30–40
2500–2700
2500–2900
104–106
4.9 106–107
9.81
1–10
1
0.2
350
40
1400
1500–1700
16,6 at 22 1C
3.1 103
9.81
2–5 10–3
0.5 10 3
m
Pa
Dimensionless
kg m 3
kg m 3
Pa s
Pa
m s2
m
m s1
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
experiments, where propagation was restricted in the third
dimension, only one aspect ratio has a physical significance:
P1 ¼ e=L:
ð1Þ
4
In nature, typical range for P1 for dykes is between 10
and
10 2 (Rubin, 1995; Geshi et al., 2010; Kavanagh and Sparks,
2011; Daniels et al., 2012). In the experiments, the length of the
dykes being 20 cm, and their thickness ranging from 1 to 5 mm,
P1 ranges from 5 10 3 to 2.5 10 2. These values overlap with
values of P1 in nature, though they correspond to the
lower bound.
For the brittle behaviour of the country rock, we use two
numbers:
P2 ¼ rr gL=C,
ð2Þ
P3 ¼ F:
ð3Þ
The angle of internal friction of the silica flour was measured
at 391 (Galland et al., 2006, 2009). It is thus in the range for
natural rocks (between 251 and 451; Schellart, 2000). The value of
P2 in our experiments is 9 (Table 2). The cohesions of natural
rocks span from 105 to 108 Pa (Schultz, 1995, 1996; Schellart,
2000; Voight, 2000; Thomas et al., 2004; Schiffman et al., 2006). If
we consider a scale ratio of 10 4, P2 in nature ranges between
5 10 1 and 5 102. The value of P2 in our experiments thus
falls right in the middle of this range, so that the silica flour is a
good representative of natural rocks in general. If we consider a
scale ratio of 10 3, P2 in nature becomes between 5 10 2 and
50; P2 in the experiments is thus close to the upper bound, and in
this case, the silica flour is representative of strong rocks, such as
unfractured basalts.
In order to scale the fluid properties and its injection rate, two
numbers need to be defined:
P4 ¼ ZLU=e2 C,
ð4Þ
P5 ¼ rm eU=Z:
ð5Þ
P4 is the ratio of viscous pressure drop along the intrusion to
the cohesion of the country rock. P5 is the Reynolds number,
which is the ratio between inertial and viscous forces. In nature,
according to field observations and theoretical studies, dyke
propagation velocities range from 10 2 m s 1 for viscous rhyolitic or granitic magmas (Clements and Mawer, 1992; Petford
et al., 1993), to about 0.1–1 m s 1 for less viscous basaltic magma
(Spence and Turcotte, 1990; Roman et al., 2004; White et al.,
2011). Magma viscosity depends on chemical composition, water
content, temperature, and volume fraction of crystals. It can
therefore vary widely from 10 Pa s for basaltic melts to 1018 Pa s
for partially crystallized granitic magma (Spera, 1980; Petford
et al., 1993; Merle and Vendeville, 1995). In this study, we will
consider the viscosity of common magmas, such as dry basalt,
andesite, and trachyte, which viscosity range is between
1000 Pa s and 106 Pa s. Dyke thickness typically range from 1 to
10 m. Thus, considering a scale ratio of 10 4, P4 ranges between
2 10 5 and 2 104. Considering a scale ratio of 10 3, P4 spans
between 2 10 6 and 2 103. In our models, Golden syrup
95
(viscosity¼16.6 Pa s) is injected at a velocity of 0.5 mm s 1 in
2 mm–5 mm wide dykes. Thus, P4 in our experiments range
between 0.2 and 1.2, which falls close to the middle of the range
of P4 for natural systems.
For both nature and experiments, the Reynolds number (P5) is
much lower than the critical value of 2000. This implies that
magma flows in both cases are laminar.
The last number is the ratio of hydrostatic forces to lithostatic
forces:
P6 ¼ 1rm =rr
ð6Þ
In our experiments, P6 ranges between 0.06 and 0.17, meaning that the Golden syrup is slightly positively buoyant. In nature,
the magma is neutrally, positively or negatively buoyant with P6
ranging between 0.06 and 0.13. Thus, our experiments are only
representative of buoyant magmas within dykes.
To summarize, there is a good match between the P numbers
calculated for natural systems and for our experiments. All the
dimensionless numbers can be satisfied by taking different length
scales, viscosity and timescales. Our experiments are physically
equivalent to shallow geological systems (o2 km). For example,
assuming a length scale ratio between 10 2 and 10 3, we
modelled intrusions with thicknesses ranging between 2 and
20 m, brittle rocks with cohesion between 0.5 MPa and 5 MPa
and magma viscosities between 104 and 106 Pa s. The results of
the experiments could also be upscaled to deeper systems involving thicker intrusions of more viscous magmas, in a stronger
brittle crust.
2.3. Experimental setup
We conducted experiments in two dimensions in order to
observe deformation during the dyke growth. Our apparatus
consisted of a Hele-Shaw cell, 50 cm long and 35 cm high and
2.5 cm thick. To reduce the silo effect (Mourgues and Cobbold,
2003), which may perturb the vertical stress, the walls were made
of glass with low friction and we limited the height of the models
to 20 cm (Fig. 1).
The silica powder was poured manually in the box. We were
careful to keep a homogeneous distribution of the powder. The
powder was manually compacted in order to control its density at
1500–1700 kg m 3. The Golden syrup was then injected at the
base of the powder with a moving piston through the injector
(Fig. 1). We calibrated the piston motion to keep a constant
injection velocity.
The injection of the Golden syrup resulted in the intrusion of a
thin dyke perpendicular to the wall of the cell. The propagating
dyke and the deformation of the host were observable through
the transparent glass wall, and photographed. We used a Particle
Imaging Velocimetry (PIV) technique to calculate displacement
and deformation fields in the host by optical images correlations
(White et al., 2003; Adam et al., 2005). This method operates on
the image texture and it is possible only if the material is not
homogeneous in colour. To avoid this, we added black powder of
silicon carbide in the silica powder, providing a grained texture.
Table 2
Average dimensionless ratios P for nature and experiments.
P1
P2
P3
P4
P5
P6
Dimensionless ratios
Mathematical expression
Field
Experiment
Field ratios for suitable values
Thickness/length
Gravitational stress/cohesion
Angle of internal friction
Viscous stress/cohesion
Re ¼ Inertial/viscous forces
Magma/country rock densities
e/L
rrgL/C
5 10 3–10 2
5 10 2–50
30–40
2 10–6–103
2.6 10 4–26
0.06–0.13
10 2
9
40
0.19–1.2
10 4
0.125
10 2
9
40
0.13
0.33–0.033
0.12
f
ZLU/e2C
rmeU/Z
1 rm/rr
96
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
2.5
Glass
cm
50 cm
Uplift and surface
fracturation
Glass
Silica
powder
~20 cm
35 cm
5 cm
Intrusion
Recording of velocity
15 cm
Injector
Injection
tube
Piston
Came
ra
Golden syrup reservoir
Fig. 1. Drawing of the experimental setup, consisting of Hele-Shaw cell (50 cm long and 35 cm high and 2.5 cm thick). The Golden syrup was injected at the base of the
model through a linear injector. To reduce the silo effect, walls were made of glass with low friction and the model height was limited to 20 cm. The propagating dyke and
the deformation of the host were observed and recorded through the transparent glass wall.
The amount of black powder being very small compared to that of
the silica powder, we assume that such addition does not modify
the mechanical properties of the silica powder. The displacement
field around the intrusion was computed by cross-correlation
from the translation and distortion of the particle pattern in
successive images with a given time interval of Dt ¼3 s. We used
five pixel wide correlation windows. As demonstrated by White
et al. (2001), PIV cross-correlation allows the calculation of
displacements with sub-pixel accuracy ( o0.1–0.2 pixel). In our
case, the side of each pixel is 140 mm, so that displacements down
to 30 mm can be monitored.
3. Results
3.1. Intrusion morphologies
We performed more than 20 experiments at room temperature (22 1C, constant fluid viscosity: 16.6 Pa s) with various
powder densities (ranging between 1500 and 1700 kg m 3) and
injection rates (0.5 10 3 and 1 10 3 m s 1). We did not
observe any significant influence of these parameters in the tested
ranges but we systematically obtained two kinds of morphologies
independent of the input parameters. We choose to repeat
several times the same experiment (six identical experiments
are shown in Fig. 2; height of powder: 20 cm, injection velocity:
0.5 10 3 m s 1) and we analyzed them by PIV. We present only
this series of experiments to discuss the formation of two distinct
intrusion morphologies (type A and type B, Fig. 2). Considering all
our intrusions, morphologies A and B appeared with the same
frequency. In all experiments, we distinguish two stages for the
emplacement of the intrusions.
3.2. Type A experiments
Stage 1 initiated with a vertical dyke, which grew from the
injector to a depth ranging between 7 and 9 cm below the surface
(Fig. 2a1–a3). During this stage, symmetrical gentle surface uplift
occurred over a large area directly above the apex of the dyke
(Fig. 3a). As a result, small open cracks formed at the model
surface; as the dyke propagated upward, the open cracks propagated downward (Figs. 2a and 4a–c). Generally, two cracks
formed symmetrically on each side of the vertical projection of
the dyke apex onto the model surface.
Stage 2 started when the dyke reached a depth of 7–9 cm
below the surface. It deviated gradually from vertical and became
inclined, with a dip ranging between 451 and 651 (Fig. 4c and d).
The surface uplift gradually localized over a small area directly
above the apex of the dyke, and the uplift accelerated significantly
(Fig. 3). Surface uplift remained broadly symmetrical. Closer to
the surface (stage 2b), the dyke flattened out even more, reaching
301 dip (Fig. 4e). Surface uplift kept accelerating, and became
strongly asymmetrical, the maximum uplift being directly above
the apex of the inclined sheet (Fig. 3). This last uplift generated
several open cracks upon the inclined dyke.
3.3. Type B experiments
Stage 1 of Type B experiments was very similar to that of Type
A experiments, with the propagation of a vertical dyke (Fig. 5a
and b), gentle surface uplift spread over a large area (Fig. 3b), and
open cracks affecting the surface.
Stage 2 in these experiments, in contrast, shows striking
differences with that of the Type A experiments. When the initial
vertical dyke reached 5–6 cm below the surface (Fig. 2b), it
sharply bent to horizontal, and subsequently bent to subvertical by following the traces of open cracks formed during
stage 1. When this sharp transition occurred, the surface uplift
accelerated, even more than in Type A experiments (Fig. 3). The
uplift became suddenly restricted to a very narrow area, bounded
by sub-vertical walls. Photographs of Fig. 5 show that this uplift is
associated with the upward movement of the block of flour
delimited by the two main open cracks formed during stage 1,
i.e. a popup structure.
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
5 cm
Surface
fracturation
and uplift
Dyke
segmentation
5 cm
Dyke
segmentation
Percolation
Surface
fracturation
and uplift
5 cm
Percolation
sheet
intrusion
Injector
Injector
Surface
fracturation
and uplift
5 cm
Surface
fracturation
and uplift
Injector
Injector
Surface
fracturation
and uplift
97
Surface
fracturation
and uplift
5 cm
5 cm
Percolation
sheet
intrusion
Injector
Injector
Fig. 2. Photographs of typical results of the two type intrusions: (A (a1, a2, a3)) and (B (b1, b2, b3)). In this whole series of experiments, the parameters were constant:
density ( 1500–1700 kg m 3) of silica powder; density (1400 kg m 3) and viscosity (16.6 Pa s) of Golden syrup; velocity of model magma (0.5 10 3 m s 1); overburden
thickness ( 20 cm) above the top of injector.
In a number of experiments, we observed the formation of
several small sheet intrusions radiating from the injector
(Fig. 2). Some of them grew a few centimetres vertically before
stopping, while others went down and stopped very quickly.
The formation of these small intrusions propagating in various
directions is certainly due to stress perturbations in the vicinity of
the injector.
In some experiments, the intrusions did not appear continuous
(Fig. 2a1 and b2). This phenomenon is probably due to segmentation of the dykes across the thickness of the cell. Locally, we also
observed parasitic flow of Golden syrup between the powder and
the glass wall (Fig. 2). This boundary effect mostly occurred in the
vicinity of the injector, i.e. far from the dyke tip at the transition
from stage 1 to stage 2. Therefore, we infer that it does not
influence the propagation of the dyke during the transition
between the two stages of emplacement.
3.4. Strain analysis
In order to quantify the strain field in the host material of the
intrusions, we applied PIV on two selected experiments, in which
the intrusions were continuous and where no percolation
occurred along the walls. Figs. 4 and 5 represent maps of the
incremental (Dt ¼3 s) horizontal and vertical displacements, and
shear strain in the entire models. Fig. 6 shows the detailed strains
calculated in the vicinity of the tip of the dyke.
3.5. Type A experiments
During Stage 1, the propagation of the vertical dyke produced
horizontal displacements on each side of the dyke, indicating
opening and enlargement of the intrusion (Fig. 4a1–c1).
These displacements were more prominent near the tip of the
dyke, and disappeared at its base (Fig. 4c1). Small amplitude
upward movements affected a broad symmetrical conical
area, with diffuse boundaries, of the overburden of the dyke
(Fig. 4a2). This cone became narrower, and the amplitude of the
displacements became larger, as the dyke propagated upward
(Fig. 4b2 and c2). The image analysis displayed very limited
shear strain in the model, except local V-shaped deformation
pattern in the vicinity of the dyke tip (Fig. 6a2). Strain analysis
showed that these small-scale deformation bands accommodate
both dilation and reverse shear. This local deformation
pattern, however, was not systematically recorded through time
(Fig. 6b2 and b3).
At the beginning of stage 2, the bending of the dyke produced
asymmetric horizontal displacement pattern (Fig. 4d1). The conical area affected by upward displacements kept narrowing and
became also asymmetrical: its right boundary where the dyke
propagated was diffuse, whereas its left boundary exhibited an
important displacement gradient (Fig. 4d2), which corresponded
to localized shear strain (Fig. 4d3). At the last stage of the
experiments, the right boundary of the uplifted conical area
became diffuse, whereas the right boundary became sharp, with
98
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
Surface uplift record
Surface uplift record
2
2
Strage 1 related uplift
1
Strage 1 related uplift
Surface topography
Strage 2a related uplift
Strage 2 related uplift
Strage 2b related uplift
1 cm
1 cm
1
0
0
Surface uplift
Surface uplift
5 cm
Surface
fracturation
Stage 2b
5 cm
Surface
fracturation
Stage 2a
Stage 1
Stage 1
Level of dyke
apex
Type A intrusion
Stage 2
Type B intrusion
Level of dyke
apex
Maximum surface uplift (cm)
1.2
Stage 1
1.0
Stage 2
Type A intrusion
0.8
Type B intrusion
0.6
0.4
0.2
0.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Level of dyke apex (cm)
14.0
16.0
18.0
20.0
Fig. 3. Topographic data plotted during the propagation of the dyke. (a) Data for Type A intrusion. Upper graph shows temporal topographic profiles drawn from
photographs. During the first stage of the dyke growth, the uplifted zone is symmetrical and smooth. In a second stage, the symmetry is slightly distorted and the uplift
moves to the right due to the dyke rotation near the surface. (b) Data for type B intrusion. The uplift remains symmetrical during the first and the second stages. The uplift
rate increases and is strongly influenced by two cracks, which accommodate significant reverse slip and generate a pop-up structure. (c) Plot representing the maximum
surface uplift with respect to the depth of the dyke apex. In the first stage the uplift rate is low and equal for both type of intrusions. The transition to the second stage is
characterized by an uplift acceleration. This acceleration is more important for Type B experiment than for Type A.
shear strain localization (Fig. 4e2 and e3). The final dyke trajectory followed this zone of strain localization.
3.6. Type B experiments
Stage 1 in Type B experiments was very similar to that of Type
A experiments. An initial vertical dyke produced horizontal
displacements on each side of the dyke, indicating opening and
enlargement of the intrusion (Fig. 5a1 and b1). During upward
propagation of the dyke, horizontal displacements mostly
occurred close to the upper tip of the dyke and became negligible
at its base (Fig. 5b1 and c1). Small amplitude upward movements
affected a broad symmetrical conical area of the overburden of
the dyke, with diffuse boundaries (Fig. 5a2 and b2). This uplifted
area became narrower as the dyke propagated upward. In this
initial stage, similarly to Type A experiments, shear strain in the
model is limited, except for a local V-shaped deformation pattern
in the vicinity of the dyke tip (Fig. 6a2 and a3). When the dyke
reached 7 cm below the surface, important shear deformation
occurred between the tip of the dyke and the model surface, while
the dyke remained vertical (Fig. 5c3). This is evidenced by the
sharp boundaries in the vertical displacement field (Fig. 5c2)
indicating that the upward displacement of the overburden was
accommodated by two conjugate reverse shear zones. These shear
bands are the downward continuation of the open fractures that
affected the model surface.
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
Fig. 4. Different stages of vertical dyke propagation for a type A intrusion (a–e). Pictures are analyzed by P.I.V. technique. Horizontal displacements (a1–e1), vertical displacements (a2–e2) and shear deformations (a3–e3) are
calculated between two successive pictures. The correlation window is five pixels wide.
99
100
Stage 1
Horizontal displacement
Vertical displacement
Shear strain
x 10 m
x 10 m
x 10 m
x 10 m
x 10 m
x 10 m
x 10 m
x 10 m
x 10 m
x 10 m
Fig. 5. Different stages of vertical dyke propagation for a type B intrusion (a–e). Pictures are analyzed by P.I.V. technique. Horizontal displacements (a1–e1), vertical displacements (a2–e2) and shear deformations (a3–e3) are
calculated between two successive pictures. The correlation window is five pixels wide.
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
Stage 2
Type B intrusion
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
101
Fig. 6. Different modes of vertical propagation of the dyke at the beginning of experiments. Left: original photographs. Centre: maps of horizontal strain. Right: maps of
shear strain. In (a1–a3) we can observe two small zones of dilation and reverse shearing, exhibiting a V–shape at the tip of the dyke. In (b1–b3) no deformation was
recorded at the top of the dyke.
Horizontal displacement
Shear strain
x 10 m
5 cm
Surface uplift
5 cm
crack
opening
a3
Dyke
Dyke
x 10 m
5 cm
3 cm
Surface uplift
5 cm
Dyke
Shear band
formation
b3
Dyke
3 cm
Fig. 7. Dyke propagation near the surface for the type A intrusion. (a) Beginning of stage 2. (b) End of stage 2. Left: maps of horizontal displacements. Centre: maps of shear
strain. Right: schematic diagram. The (a1–a3) pictures indicate rotation of stresses, which modifies the direction of propagation following a mode 1 (pure tension) opening.
The (b1–b3) pictures show the formation of a shear band that was infiltrated by the Golden syrup in the final stage.
Stage 2 started when the dyke tip intersected one of the shear
zones formed at the end of stage 1 (compare Fig. 5d with c3). The
upward movements of the overburden became strictly restricted
to a small domain bounded by the two reverse shear zones
formed at the end of stage 1, isolating a ‘‘popup’’ structure
(Fig. 5d2 and d3). The size of this popup structure remained
constant during stage 2. After a sharp bending, the dyke tip
followed the trajectory of one of the reverse shear bands. In the
shallowest centimetre of the model, additional reverse faults,
dipping at 301, formed on each side of the popup (Fig. 5e2 and e3).
4. Discussion
4.1. Validity of experimental procedure
By confining the models between two glass plates, the processes
simulated in the experiments are considered to be 2D, in plane strain
configuration, such as most mathematical and numerical models of
dyke emplacement (Pollard, 1973; Pollard and Holzhausen, 1979;
Bonafede and Danesi, 1997; Gudmundsson and Loetveit, 2005). In
such configuration, the dykes are expected to be continuous and
perpendicular to the walls of the cell. Nevertheless, although the
dykes were roughly perpendicular to the walls in our experiments,
we observed that they were not always continuous (Fig. 2). We infer
that some dyke segmentation occurred locally in the third dimension. This 3-dimensional effect can produce local additional strain
patterns, such as strain localization between two dyke segments
(Fig. 7b2).
Our results are very comparable to those obtained in 3D
experiments. Notably, the transition from a vertical dyke to an
inclined sheet has also been simulated in the 3D experiments of
Mathieu et al. (2008), Galland et al. (2009) and Galland (2012).
In addition, the depths of the dyke-to-inclined sheet transition in
our experiments (between 5 and 9 cm below the surface) were
similar to those obtained in these previously published
102
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
experiments (between 2 and 7 cm). This similarity suggests that
the boundary effects in our experiments played a minor role on
the studied processes, but we cannot totally exclude them.
In some experiments, we also observed parasitic flow of
Golden syrup between the powder and the glass wall, forming
large grey patches in the photographs (Fig. 2). The grey patches
can substantially perturb the image analysis to quantify the strain
field. Such boundary effect mostly occurred away from the dyke
tip. We thus infer that (1) it does not influence the propagation of
the dykes and (2) it does not change our strain analysis in the
vicinity and above the dyke tip.
4.2. Strain analysis and dyke propagation mode
The strain analysis is fundamental to constrain the deformation mechanisms at the dyke tips, and therefore to understand
their mode of propagation. The detailed strain analyses during
some time steps highlight the formation of V-shaped reverse
shear bands rooted at the dyke tips (Fig. 6a3). These shear bands
accommodate both dilation and uplift of the overriding material.
The dilation is compatible with the opening of the dyke, and the
uplift is compatible with the observed surface uplift. Our results,
however, do not show any evidence of normal faulting or
subsidence of the model surface. This result is compatible with
the model of viscous indenter proposed by Donnadieu and Merle
(1998) and Mathieu et al. (2008), but less with the classical theory
of LEFM, which predicts a more complex uplift pattern (Pollard
et al., 1983; Mastin and Pollard, 1988; Rubin and Pollard, 1988).
Our experiments show that tensile fractures form at the model
surface during the upward propagation of the dykes (Figs. 2, 4 and 5),
as observed on many active volcanoes. The experiments also show
that the model surface was uplifting at the same time, bending
the model surface like a smooth antiform (Fig. 3). Such surface
bending generates tensile stresses at the top of the antiform (Price
and Cosgrove, 1990). We thus infer that these tensile fractures
formed due to outer-arc stretching at the top of the antiform, but
not as a result of surface subsidence and normal faulting.
We noticed that the dykes in our experiments did not
propagate straight and that the dyke tips were irregular (Figs. 2,
4 and 5). Such complex shapes have been recognized in the field
(Pollard and Johnson, 1973; Francis, 1982; Delcamp et al., 2008)
as well as in experimental models (Mathieu et al., 2008; Kervyn
et al., 2009). Mathieu et al. (2008) suggest that this morphology is
also compatible with the viscous indenter theory: the small shear
zones produced by the propagation of the magma in its host rock
control the oblique propagation of the dyke tip.
These V-shaped shear bands, however, were not systematically
observed. Fig. 6b1–b3 shows an example where no stretching or
shear deformation is measured at the dyke tip. One can notice
that the morphology of this dyke is straighter than that of the
dyke of Fig. 6a. In this case, the dyke may grow by hydrofracturing
the country rock without plastic shear deformation. Mathieu et al.
(2008) also suggested that both hydraulic and shear-related
intrusions propagation could operate in the same time. Nevertheless, it is possible that shear deformation occurred, but being
so small that it cannot be detected by PIV analysis.
4.3. Shallow dyke propagation
The transition between stage 1 (vertical growth) and stage 2
(inclined propagation) occurred 9–5 cm depth below the surface
(Fig. 2). This two-stage evolution has been observed in the
experiments of Mathieu et al. (2008), Galland et al. (2009) and
Galland (2012). If stage 1 in both Type A and Type B experiments
is identical, stage 2 for each experiments type substantially differ.
The following paragraphs discuss these differences.
Type A intrusion is characterized by the progressive rotation of
the vertical dyke at a critical depth ranging between 7 and 9 cm
(Figs. 2a1–a3, 4). In Figs. 4 and 7a1 and a2, the displacements
indicate a zone of opening in front of the dyke tip and in the same
direction as that of the dyke, the displacement vectors being
perpendicular to the dykes (Fig. 7a3). Fig. 7a2 shows that no
major shear zone formed at the vicinity of the dyke when the
transition between stage 1 and stage 2 occurred. Therefore, the
rotation of the dyke to inclined sheet was not controlled by
structures like faults. Mathieu et al. (2008) proposed that the
inclined sheets that form cup-shaped intrusions developed at a
critical depth, above which shear failure at the tip of the dyke
becomes reverse. Nevertheless, Fig. 6 shows that local V-shaped
reverse shear deformation was recorded well before the formation of an inclined sheet, and thus cannot explain the rotation of
the dyke tip.
We propose instead that the formation of the inclined sheet
resulted from stress rotation. Stress rotation occurring around
shallow magma intrusions is a well-known phenomenon, which
is involved in the formation of, e.g. cone-sheets around punctual,
spherical (Anderson, 1936; Mogi, 1958; Gudmundsson, 2006)
and elongated overpressured magma reservoirs (Koide and
Bhattacharji, 1975), and cracks (Pollard, 1973; Bonafede and
Danesi, 1997; Gudmundsson and Loetveit, 2005). Such stress
rotation due to the near free surface also explains the formation
of (1) en-échelon dykes segments (Pollard et al., 1982) and (2)
saucer-shaped sills (Malthe-Sørenssen et al., 2004; Goulty and
Schofield, 2008; Polteau et al., 2008; Galland et al., 2009; Galerne
et al., 2011). Stress rotation occurs at shallow levels, as it becomes
easier for the dyke to lift up its overburden rather than pushing its
host laterally.
Once the inclined sheet initiated, we observed that the
mechanical system gradually developed significant asymmetry.
The surface uplift moved towards the direction of the inclined
sheet (Fig. 3a). Surface uplift subsequently became asymmetrical,
with the steepest slope being on the external edge of the uplifted
area, upon the tip of the propagating inclined sheet. During the
final stage of type A experiments, the differential uplift associated
with the steepest slope of the uplifted area was such that it
triggered the formation of a reverse shear band, which was
subsequently infiltrated by the Golden syrup (Fig. 7b1–b3).
At this stage, the mode of propagation is not hydraulic fracturing
any more, but shearing and then infiltration. The sheets appear
more regular and we noticed an acceleration of the magma
ascent. The development of such asymmetry during type A
experiments is compatible with the growth of a mechanical
instability. This hypothesis is in good agreement with the stability
analysis developed by Bunger (2005), which explained the asymmetrical development of near-surface fractures.
In our experiments, stress rotation may be favoured by the
boundary conditions. Indeed, our models are subjected to gravity
but not to tectonic stresses, such that the initial stress field is
close to isotropic. The only additional loading is the fluid pressure
in the vertical dyke. It is equivalent to a ‘line load’ which
commonly produces a radial stress distribution (Johnson, 1985).
Deviation from the vertical may be probably triggered by small
heterogeneities in the properties of the material. In nature,
additional extensional tectonic stresses or stresses due to surrounding inflating magma chamber may provide stronger anisotropic stress field which may prevent stress rotation and favour
the formation of purely vertical dykes (Geshi et al., 2010, 2012).
Intrusions of type B experiments showed a drastically different
evolution during stage 2 (Fig. 8). In contrast with Type A
experiments, we observed that stage 2 in Type B experiments
started when the dyke tip intersected with the trace of a shear
zone (Fig. 8a2), which formed at the end of stage 1. Note that this
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
103
Fig.8. Dyke propagation near the surface for the type B intrusion. (a) Beginning of stage 2. (b) End of stage 2. Left: maps of horizontal displacements. Centre: maps of shear
strain. Right: schematic diagram. The (a1–a3) pictures indicate shear deformation appears between the tip of the dyke and vertical tension fractures, which propagate
downward from the surface. The (b1–b3) pictures show one of these two cracks was intruded by the Golden syrup, which then reaches the surface. By propagating into the
vertical crack, the magma generates horizontal stresses, which close the second crack.
shear zone was the prolongation at depth of a surface open
fracture, which propagated downward while the dyke was
intruding (Fig. 8a3). Such downward open fracture opening is
similar to that described by Tentler (2005) in the rift of Iceland.
Subsequently, the dyke followed the trace of the shear zone, then
the open crack, until eruption (Fig. 8b3). This result shows that
plastic deformation, and especially faults, in the host rock can
substantially control the propagation of dykes. This is in good
agreement with the observations of Tentler (2005) and Valentine
and Krogh (2006), which show that dykes can follow normal
faults.
Our results suggest that significant plastic deformation can be
generated by the emplacement of sheet intrusions. This effect has
usually not been taken into account in former numerical and
analytical models of near-surface dyke intrusion, in which elasticity only is considered (Pollard and Johnson, 1973; Pollard and
Holzhausen, 1979; Fialko, 2001; Fialko et al., 2001; Gudmundsson,
2002; Malthe-Sørenssen et al., 2004; Goulty and Schofield, 2008).
Seismic data across sill complexes, however, show that the seismic
reflectors upon the tips of the sills are offset, suggesting that plastic
deformation plays a significant role in the vicinity of magma
intrusions (Hansen and Cartwright, 2006; Kavanagh and Sparks,
2011). Plastic deformation was also invoked to explain the formation of cone-sheets (Phillips, 1974) and the initiation of cup-shaped
structures at shallow depth in the experiments of Mathieu et al.
(2008).
Type B experiments show that the main shear zones that form
as a result of the intrusion of a dyke accommodate reverse shear
(Figs. 5 and 8). We also observed that as soon as the dyke tip
intersected one of the shear zones, the uplift became restricted to
the block separated by the two open fractures, and suddenly
accelerated (Fig. 5). This confirms that the model magma pushed
its overburden upward, and did not produce normal faults
and subsidence. Subsequently, the model magma intruded along
one side of the block, pushed it laterally and triggered the
closing of the conjugate open crack on the opposite side of the
block (Fig. 8b3). Our observations are in good agreement with the
field data of Gudmundsson et al. (2008), who described large
reverse slip on faults near vertical feeder dykes in rift-zone
grabens. Numerical models predicted such slips and also the
closure of crack and pre-existing faults (Gudmundsson and
Loetveit, 2005).
4.4. Surface deformation
Our 2D apparatus allowed us to compare the evolution of the
model surface deformation and the associated intruding dyke
(Fig. 3). In both Type A and Type B experiments, the two-stage
evolution of the maximum uplift was perfectly correlated with
the two-stage evolution of the underlying intrusions. In addition,
the evolutions of the maximum uplift during stage 2 of Type A
and Type B experiments were different. This difference reflected
the distinct mechanisms of magma emplacement. This shows that
the intrusion mechanism plays a major role on surface deformation. In volcanic systems, however, only the shape of the intrusions and the magma pressure are considered for inverting
surface deformation data (Amelung et al., 2000; Fialko and
Simons, 2001; Fukushima et al., 2005, 2010; Battaglia et al.,
2006; Pedersen and Sigmundsson, 2006; Wright et al., 2006;
Chang et al., 2007; Grandin et al., 2010a, 2010b; Woo and Kilburn,
2010). Therefore, considering the mechanics of magma intrusion
is necessary to interpret surface deformation in active volcanoes.
Our experiments also showed that the surface deformation in
Type A experiments evolved from symmetrical to asymmetrical
(Fig. 3a). This asymmetry directly reflected the asymmetrical
development of the underlying intrusion. Notably, the steepest
slope of the model surface is located right above the tip of the
intrusion, i.e. the shallowest part. Analyzing the asymmetry of the
surface deformation is thus crucial for detecting the shallow parts
of the intrusions. Such an analysis can thus be used as a tool for
predicting where the magma rises to the surface, and so where it
is likely to erupt. Thus the result supports that of Galland (2012),
which 3D models show that asymmetric development of the
ground deformation pattern corresponded with the asymmetric
geometry of the underlying intrusion. It could also be used to
characterize better the surface deformations induced by a magma
interacting with heterogeneities, mechanical discontinuities
(faults) and mechanical layering.
5. Conclusions
In this paper, we present results of laboratory experiments
that simulate shallow dyke emplacement. The experimental setup
allows us to monitor through time (1) the morphology of the
104
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
dyke, (2) the deformation field around the dyke, and (3) the
surface deformation associated with the dyke. The main conclusions of our study are summarized by the following points:
1. Some surface deformation data are compatible with Linear
Elastic Fracture Mechanics theory of dyke propagation (tensile
fractures at the surface). But most of our strain results in the
host rock suggest that dykes propagate as viscous indenters.
If this is the case, plastic deformation at the vicinity of dyke
tips plays a major role in dyke propagation.
2. Intruding dykes trigger surface uplift. The uplifted area narrows when the dyke propagates towards the surface. Consequently, open fractures dissect the model surface due to outerarc stretching. At depth, uplift is accommodated either by
diffuse deformation or localized small amplitude reverse
shear zones.
3. Dyke emplacement occurred in two stages: (1) at depth, dyke
propagates upward vertically; and (2) from 9–5 cm depth
below the surface, dyke is deflected from its vertical trajectory.
4. This second stage shows two different behaviours (Types A
and B) of the dykes. Type A corresponds to gradual rotation of
the dyke tip. Such rotation results from stress rotation due to
the near-free surface and the absence of tectonic stress. Type B
results from the interaction between the dyke tip and a reverse
fault formed during Stage 1 of the experiment. Here, the dyke
propagation is controlled by the fault trajectory. Note that
both Types A and B occur in experiments with identical initial
and boundary conditions.
5. The evolution of surface deformation is perfectly correlated
with the dynamics of dyke intrusion at depth. The two stages
of dyke propagation resulted in different uplift rates, and the
distinct types of intrusions produced contrasting uplift patterns. This shows that the mechanism of dyke propagation
plays a major role on surface deformation. Effects of mechanical layering on the path of hydrofractures and on surface
deformation will be tested in future experiments.
6. Our results are very comparable to those obtained in 3D
experiments. This similarity suggests that the sidewall effects
in our experiments played a minor role on the studied
processes. Nevertheless, future 2D and 3D experiments conducted strictly in the same conditions will be necessary to
quantify precisely this effect.
Acknowledgements
We thank Julien Collet and Geoffrey Lacour for their help in the
experimental modelling. The experiments were done in the
laboratory of Le Mans (University of Maine, France). We also wish
to thank Janine Kavanagh and Agust Gudmundsson for their
useful comments and constructive criticism that improved the
paper.
References
Adam, J., Urai, J.L., Wieneke, B., Oncken, O., Pfeiffer, K., Kukowski, N., Lohrmann, J.,
Hoth, S., van der Zee, W., Schmatz, J., 2005. Shear localisation and strain
distribution during tectonic faulting—new insights from granular-flow experiments and high-resolution optical image correlation techniques. J. Struct. Geol.
27, 283–301.
Amelung, F., Jonsson, S., Zebker, H., Segall, P., 2000. Widespread uplift and
‘‘trapdoor’’ faulting on Galapagos volcanoes observed with radar interferometry. Nature 407, 993–996.
Anderson, E.M., 1936. The dynamics of formation of cone sheets, ring dykes and
cauldron subsidences. Proc. R. Soc. Edinburgh 56, 128–157.
Barenblatt, G.I., 2003. Scaling. Cambridge University Press, Cambridge.
Battaglia, M., Troise, C., Obrizzo, F., Pingue, F., De Natale, G., 2006. Evidence for
fluid migration as the source of deformation at Campi Flegrei caldera (Italy).
Geophys. Res. Lett. 33, L01307.
Bonafede, M., Danesi, S., 1997. Near-field modifications of stress induced by dyke
injection at shallow depth. Geophys. J. Int. 130, 435–448.
Bunger, A., 2005. Near-Surface Hydraulic Fracture. University of Minnesota, p. 152.
Cayol, V., Cornet, F.H., 1998. Three-dimensional modeling of the 1983–1984
eruption at Piton de la Fournaise volcano, Reunion Island. J. Geophys. Res.
103, 18025–18037.
Chang, W.L., Smith, R.B., Wicks, C., Farrell, J.M., Puskas, C.M., 2007. Accelerated
uplift and magmatic intrusion of the Yellowstone caldera, 2004 to 2006.
Science 318, 952–956.
Clements, J.D., Mawer, C.K., 1992. Granitic magma transport by fracture propagation. Tectonophysics 204, 339–360.
Daniels, K.A., Kavanagh, J.L., Menand, T., Stephen, J.S.R., 2012. The shapes of dikes:
Evidence for the influence of cooling and inelastic deformation. Geol. Soc. Am.
Bull. 124, 1102–1112.
Delcamp, A., van Wyk de Vries, B., James, M.R., 2008. The influence of edifice slope
and substrata on volcano spreading. J. Volcanol. Geotherm. Res. 177, 925–943.
Di Giuseppe, E., Funiciello, F., Corbi, F., Ranalli, G., Mojoli, G., 2009. Gelatins as rock
analogs: a systematic study of their rheological and physical properties.
Tectonophysics 473, 391–403.
Donnadieu, F., Merle, O., 1998. Experiments on the indentation process during
cryptodome intrusions: new insights into Mount St. Helens deformation.
Geology 26, 79–82.
Duffield, W.A., Bacon, C.R., Delaney, P.T., 1986. Deformation of poorly consolidated
sediment during shallow emplacement of a basalt sill, Coso Range, California.
Bull. Volcanol. 48, 97–107.
Fialko, Y., 2001. On origin of near-axis volcanism and faulting at fast spreading
mid-ocean ridges. Earth Planet. Sci. Lett. 190, 31–39.
Fialko, Y., Khazan, Y., Simon, M., 2001. Deformation due to a pressurized horizontal
circular crack in an elastic half space, with applications to volcano geodesy.
Geophys. J. Int. 146, 181–190.
Fialko, Y., Simons, M., 2001. Evidence for on-going inflation of the Socorro magma
body, New Mexico, from interferometric synthetic aperture radar imaging.
Geophys. Res. Lett. 28, 3549–3552.
Francis, E.H., 1982. Magma and sediment—1. Emplacement mechanism of late
Carboniferous tholeiite sills in northern Britain. J. Geol. Soc., London 139, 1–20.
Froger, J.L., Merle, O., Briole, P., 2001. Active spreading and regional extension at
Mount Etna imaged by SAR interferometry. Earth Planet. Sci. Lett. 187,
245–258.
Froger, J.L., Remy, D., Bonvalot, S., Legrand, D., 2007. Two scales of inflation at
Lastarria–Cordon del Azufre volcanic complex, central Andes, revealed from
ASAR-ENVISAT interferometric data. Earth Planet. Sci. Lett. 255, 148–163.
Fukushima, Y., Cayol, V., Durand, P., 2005. Finding realistic dike models from
interferometric synthetic aperture radar data: the February 2000 eruption at
Piton de la Fournaise. J. Geophys. Res. 110, B03206.
Fukushima, Y., Cayol, V., Durand, P., Massonnet, D., 2010. Evolution of magma
conduits during the 1998–2000 eruptions of Piton de la Fournaise volcano,
Réunion Island. J. Geophys. Res. 115, B10204.
Galerne, C.Y., Galland, O., Neumann, E.-R., Planke, S., 2011. 3D relationships
between sills and their feeders: evidence from the Golden Valley Sill Complex
(Karoo Basin) and experimental modelling. J. Volcanol. Geotherm. Res. 202,
189–199.
Galland, O., de Bremond d’Ars, J., Cobbold, P.R., Hallot, E., 2003. Physical models of
magmatic intrusion during thrusting. Terra Nova 15, 405–409.
Galland, O., Cobbold, P.R., Hallot, E., de Bremond d’Ars, J., 2006. Use of vegetable oil
and silica powder for scale modelling of magmatic intrusion in a deforming
brittle crust. Earth Planet. Sci. Lett. 243, 786–804.
Galland, O., Planke, S., Malthe-Sørenssen, A., Neumann, E.-R., 2009. Experimental
modelling of shallow magma emplacement: application to saucer-shaped
intrusions. Earth Planet. Sci. Lett. 277, 373–383.
Galland, O., 2012. Experimental modelling of ground deformation associated with
shallow magma intrusions. Earth Planet. Sci. Lett. 317–318, 145–156.
Geshi, N., Kusumoto, S., Gudmundsson, A., 2010. Geometric difference between
non-feeder and feeder dikes. Geology 38, 195–198.
Geshi, N., Kusumoto, S., Gudmundsson, A., 2012. Effects of mechanical layering of
host rocks on dike growth and arrest. J. Volcanol. Geotherm. Res. 223–224,
74–82.
Goulty, N.R., Schofield, N., 2008. Implications of simple flexure theory for the
formation of saucer-shaped sills. J. Struct. Geol. 30, 812–817.
Grandin, R., Socquet, A., Doin, M.P., Jacques, E., de Chabalier, J.B., King, G.C.P.,
2010a. Transient rift opening in response to multiple dike injections in the
Manda Hararo rift (Afar, Ethiopia) imaged by time-dependent elastic inversion
of interferometric synthetic aperture radar data. J. Geophys. Res. 115, B09403.
Grandin, R., Socquet, A., Jacques, E., Mazzoni, N., de Chabalier, J.B., King, G.C.P.,
2010b. Sequence of rifting in Afar, Manda-Hararo rift, Ethiopia, 2005–2009:
time-space evolution and interactions between dikes from interferometric
synthetic aperture radar and static stress change modeling. J. Geophys. Res.,
B10413.
Gressier, J.-B., Mourgues, R., Bodet, L., Matthieu, J.-Y., Galland, O., Cobbold, P.R.,
2010. Control of pore fluid pressure on depth of emplacement of magmatic
sills: an experimental approach. Tectonophysics 489, 1–13.
Gudmundsson, A., 2002. Emplacement and arrest of sheets and dykes in central
volcanoes. J. Volcanol. Geotherm. Res. 116, 279–298.
Gudmundsson, A., 2003. Surface stresses associated with arrested dykes in rift
zones. Bull. Volcanol. 65, 606–619.
Gudmundsson, A., Loetveit, I.F., 2005. Dyke emplacement in a layered and faulted
rift zone. J. Volcanol. Geotherm. Res. 144, 311–327.
M.M. Abdelmalak et al. / Earth and Planetary Science Letters 359–360 (2012) 93–105
Gudmundsson, A., 2006. How local stresses control magma-chamber ruptures,
dyke injections, and eruptions in composite volcanoes. Earth-Sci. Rev. 79,
1–31.
Gudmundsson, A., Friese, N., Galindo, I., Philipp, S.L., 2008. Dike-induced reverse
faulting in a graben. Geology 36, 123–126.
Hansen, D.M., Cartwright, J.A., 2006. Saucer-shaped sill with lobate morphology
revealed by 3D seismic data: implications for resolving a shallow-level sill
emplacement mechanism. J. Geol. Soc., London 163, 509–523.
Hubbert, M.K., 1937. Theory of scale models as applied to the study of geologic
structures. Geol. Soc. Am. Bull. 48, 1459–1519.
Hubbert, M.K., Willis, D.G., 1957. Mechanics of hydraulic fracturing. In: Hubbert,
M.K. (Ed.), Structural Geology. Hafner Publishing Company, New York,
pp. 175–190.
Johnson, K.L., 1985. Contact Mechanics. Cambridge University Press.
Kavanagh, J.L., Menand, T., Sparks, R.S.J., 2006. An experimental investigation of sill
formation and propagation in layered elastic media. Earth Planet. Sci. Lett. 245,
799–813.
Kavanagh, J.L., Sparks, R.S.J., 2011. Insights of dyke emplacement mechanics from
detailed 3D dyke thickness datasets. J. Geol. Soc. 168, 965–978.
Kervyn, M., Ernst, G.G.J., van Wyk de Vries, B., Mathieu, L., Jacobs, P., 2009. Volcano
load control on dyke propagation and vent distribution: insights from
analogue modeling. J. Geophys. Res. 114 (B03401), 03426.
Koide, H., Bhattacharji, S., 1975. Formation of fractures around magmatic intrusions and their role in ore localization. Econ. Geol. 70, 781–799.
Krantz, R.W., 1991. Measurements of friction coefficients and cohesion for faulting
and fault reactivation in laboratory models using sand and sand mixtures.
Tectonophysics 188, 203–207.
Malthe-Sørenssen, A., Planke, S., Svensen, H., Jamtveit, B., 2004. Formation
of saucer-shaped sills. In: Breitkreuz, C., Petford, N. (Eds.), Physical Geology
of High-Level Magmatic Systems. Geological Society, London, Special Publications, pp. 215–227.
Masterlark, T., 2007. Magma intrusion and deformation predictions: sensitivities
to the Mogi assumptions. J. Geophys. Res. 112, B06419.
Mastin, L.G., Pollard, D.D., 1988. Surface deformation and shallow dike intrusion
processes at Inyo Craters, Long Valley, California. J. Geophys. Res.,
13221–13235.
Mathieu, L., van Wyk de Vries, B., Holohan, E.P., Troll, V.R., 2008. Dykes, cups,
saucers and sills: analogue experiments on magma intrusion into brittle rocks.
Earth Planet. Sci. Lett. 271, 1–13.
Menand, T., 2008. The mechanics and dynamics of sills in layered elastic rocks and
their implications for the growth of laccoliths and other igneous complexes.
Earth Planet. Sci. Lett. 267, 93–99.
Merle, O., Vendeville, B., 1995. Experimental modelling of thin-skinned shortening
around magmatic intrusions. Bull. Volcanol. 57, 33–43.
Merle, O., Borgia, A., 1996. Scaled experiments on volcanic spreading. J. Geophys.
Res. 101, 13805–13817.
Middleton, G.V., Wilcock, P.R., 1994. Mechanics in the Earth and Environmental
Sciences. Cambridge University Press.
Mogi, K., 1958. Relations between eruptions of various volcanoes and the
deformations of the ground surfaces around them. Bull. Earthquake Res. Inst.
Tokyo 36, 99–134.
Mourgues, R., Cobbold, P.R., 2003. Some tectonic consequences of fluid overpressures and seepage forces as demonstrated by sandbox modelling. Tectonophysics 376, 75–97.
Pedersen, R., Sigmundsson, F., 2006. Temporal development of the 1999 intrusive
episode in the Eyjafjallajökull volcano, Iceland, derived from InSAR images.
Bull. Volcanol. 68, 377–393.
Petford, N., Kerr, R.C., Lister, J.R., 1993. Dike transport of granitoid magmas.
Geology 21, 845–848.
Phillips, W.J., 1974. The dynamic emplacement of cone sheets. Tectonophysics 24,
69–84.
Pollard, D.D., 1973. Derivation and evolution of a mechanical model for sheet
intrusions. Tectonophysics 19, 233–269.
Pollard, D.D., Johnson, A.M., 1973. Mechanics of growth of some laccolithic
intrusions in the Henry mountains, Utah, II: bending and failure of overburden
layers and sill formation. Tectonophysics 18, 311–354.
105
Pollard, D.D., Holzhausen, G., 1979. On the mechanical interaction between a fluidfilled fracture and the earth’s surface. Tectonophysics 53, 27–57.
Pollard, D.D., Segall, P., Delaney, P.T., 1982. Formation and interpretation of
dilatant echelon cracks. Geol. Soc. Am. Bull. 93, 1291–1303.
Pollard, D.D., Delaney, P.T., Duffield, W.A., Endo, E.T., Okamura, A.T., 1983. Surface
deformation in volcanic rift zones. Tectonophysics 94, 541–584.
Polteau, S.P., Mazzini, A., Galland, O., Planke, S., Malthe-Sørenssen, A., 2008.
Saucer-shaped intrusions: occurrences, emplacement and implications. Earth
Planet. Sci. Lett. 266, 195–204.
Price, N.J., Cosgrove, J.W., 1990. Analysis of Geological Structures. Cambridge
University Press.
Ramberg, H., 1981. Gravity, Deformation and the Earth’s Crust. Academic Press,
New York.
Roman, D.C., Power, J.A., Moran, S.C., Cashman, K.V., Doukas, M.P., Neal, C.A.,
Gerlach, T.M., 2004. Evidence for dike emplacement beneath Iliamna Volcano,
Alaska in 1996. J. Volcanol. Geotherm. Res. 130, 265–284.
Rubin, A.M., Pollard, D.D., 1988. Dike-induced faulting in rift zones of Iceland and
Afar. Geology 16, 413–417.
Rubin, A.M., 1995. Getting granite dikes out of the source region. J. Geophys. Res.
100, 5911–5929.
Schellart, W.P., 2000. Shear test results for cohesion and friction coefficients for
different granular materials: scaling implications for their usage in analogue
modelling. Tectonophysics 324, 1–16.
Schiffman, P., Watters, R.J., Thompson, N., Walton, A.W., 2006. Hyaloclastites and
the slope stability of Hawaiian volcanoes: Insights from the Hawaiian
Scientific Drilling Project’s 3-km drill core. J. Volcanol. Geotherm. Res 151,
217–228.
Schultz, R.A., 1995. Limits on strength and deformation properties of jointed
basaltic rock masses. Rock Mech. Rock Eng. 28, 1–15.
Schultz, R.A., 1996. Relative scale and the strength and deformability of rock
masses. J. Struct. Geol. 18, 1139–1149.
Spence, D.A., Turcotte, D.L., 1990. Buoyancy-driven magma fracture: a mechanism
for ascent though the lithosphere and the emplacement of diamonds.
J. Geophys. Res. 95, 5133–5139.
Spera, F.J., 1980. Aspects of magma transport. In: Hargraves, R.B. (Ed.), Physics of
Magmatic Processes. Princeton University Press, Princeton, NJ, pp. 265–323.
Takada, A., 1994. Development of a subvolcanic structure by the interaction of
liquid-filled cracks. J. Volcanol. Geotherm. Res. 61, 207–224.
Tentler, T., 2005. Propagation of brittle failure triggered by magma in Iceland.
Tectonophysics 406, 17–38.
Thomas, M.E., Petford, N., Bromhead, E.N., 2004. Volcanic rock-mass properties
from Snowdonia and Tenerife: implication for volcano edifice strength. J. Geol.
Soc., London 161, 1–8.
Valentine, G.A., Krogh, K.E.C., 2006. Emplacement of shallow dikes and sills
beneath a small basaltic volcanic center—the role of pre-existing structure
(Paiute Ridge, southern Nevada, USA). Earth Planet. Sci. Lett. 246, 217–230.
Voight, B., 2000. Structural stability of andesite volcanoes and lava domes. Philos.
Trans. R. Soc. A: Math., Phys. Eng. Sci. 358, 1663–1703.
White, D.J., Take, W.A., Bolton, M.D., 2001. Measuring soil deformation in
geotechnical models using digital images and PIV analysis. In: Proceedings
of the 10th International Conference on Computer Methods and Advances in
Geomechanics, Tucson, Arizona.
White, D.J., Take, W.A., Bolton, M.D., 2003. Soil deformation measurement using
particle image velocimetry (PIV) and photogrammetry. Géotechnique 53,
619–631.
White, R.S., Drew, J., Martens, H.R., Key, J., Soosalu, H., Jakobsdóttir, S.S., 2011.
Dynamics of dyke intrusion in the mid-crust of Iceland. Earth Planet. Sci. Lett.
304, 300–312.
Woo, J.Y.L., Kilburn, C.R.J., 2010. Intrusion and deformation at Campi Flegrei,
southern Italy: sills, dikes, and regional extension. J. Geophys. Res 115,
B12210.
Wright, T.J., Ebinger, C., Biggs, J., Ayele, A., Yirgu, G., Keir, D., Stork, A., 2006.
Magma-maintained rift segmentation at continental rupture in the 2005 Afar
dyking episode. Nature 442, 291–294.