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The influence of edifice slope and substrata on volcano spreading

Audray Delcamp a,b,,1, Benjamin van Wyk de Vries a,2, Mike R. James c,3

a Laboratoire Magmas et Volcans CNRS-UMR 6524, Observatoire du Physique du Globe de Clermont, Universit Blaise Pascal, Clermont-Ferrand, Franceb Department of Geology, Trinity College Dublin, Dublin 2, Irelandc Lancaster Environment Centre, Lancaster University, Lancaster, UK

a b s t r a c ta r t i c l e i n f o

Article history:

Received 20 August 2007

Accepted 17 July 2008Available online 31 July 2008

Keywords:

volcano spreading

edifice morphology

sector Grben

faulting

oceanic volcano

Gravitational volcano spreading is caused by flow of weak substrata due to volcanic loading, and is now a

process known to affect many edifices. The process produces extension in the upper edifice, evidenced by

grben andnormal faults, andcompression at thebase, seen in strikeslip faultsand thrusts. Where spreading

is identified, host volcanoes have a range of fault densities, variable rift and grben shapes, and different

degrees of structural asymmetry. Previous studies have suggested a link between edifice shape and structure

and the proportion of brittle to ductile material in the substrata or lower edifice. We study this link using

refined sand cone analogue models standing on a brittleductile/sandsilicone substrata. Two scenarios have

been investigated, thefirst mainly represents oceanic volcanoes with a ductile layer within the edifice (type I),

wherethereis anouterductile free surface. Thesecond represents most continentalvolcanoesthathaveductile

substrata (type II). We apply the model results to natural examples and develop quantitative relationships

between slope, brittleductile ratio fault density, spreading rate and structural style. Displacement fields

calculated from stereophotogrammetry show significant differences between different slope models. We find

that more faults are produced when the cone is initially steeper, or when the brittle substratum is thinner.

However, theeffectof thebrittle layer dominatesover that of slope. Thestrikeslip movementsare found to be

an essential feature in the spreading mechanism and the grben are in fact transtensional features. Strikeslip

and graben faults make a conjugate flower pattern. The structures produced are well-organised for type II

edifices, but they are poorly organised for type I models. Type I models represent good analogues for oceanic

volcanoesthatare commonlyaffectedby large slumpsbounded byan extensional zone andlackof well-formedsector grben. The well-observed connection between oceanic volcano rifts and large landslide-slumps is

confirmed to be a consequence of spreading.

2008 Elsevier B.V. All rights reserved.

1. Introduction

Volcano spreading is a becoming a well accepted theory and has been

studied both in the field (Van Bemmelen, 1949; Borgia and Van Wyk de

Vries, 2003) and in the laboratory using numerical and analogue

modelling (Borgia, 1994; Merle and Borgia, 1996; Van Wyk de Vries and

Matela,1998; Walter et al., 2006, Morgan, 2006). Spreading is linked to the

presence of ductile substrata (for example sediments), which deform

under the load of the overlying volcanic edifice (Van Bemmelen, 1949;

Borgia, 1994; Merle and Borgia, 1996). Spreading can be triggered in the

volcano itself especially in oceanic situations, if there are low strength

layers (LSL) that can be composed, for example, of hydrothermallyaltered

levels, weak sediments and mass slumping products (Oehler et al., 2005).

Summit grben and basal thrusts are typical spreading structures

(Merle and Borgia, 1996), butstrikeslip faults arealso closely associated

with spreading (Borgia and Van Wyk de Vries, 2003). The main features

are well displayed on small continental arc volcanoes, such as

Concepcin(Fig.1), and other Nicaraguan volcanoes such as Mombacho,

Nicaragua (Van Wyk de Vries and Borgia, 1996; Van Wyk de Vries and

Francis, 1997; Borgia and Van Wyk de Vries, 2003; Shea et al., 2008).

These volcanoes spread laterally on thick lacustrine and ignimbrite

layers, and have either intensive fracturing of a young edifice, as at

Concepcin, or well developed graben faults, as on Maderas, or faults

and large sector collapses associated with spreading, as at Mombacho.

The relationship between sector collapse and gravity spreading was

established by Van Wyk de Vries and Francis (1997), radial spreading

tends to stabilisethe edifice (Van Wykde Vries and Borgia,1996; Oehler

et al., 2005), while spreading on one side cangenerate collapse (Wooller

et al., 2004). Larger arc edifices also show spreading features, such as

Poas, Costa Rica(Borgia et al., 1990), where thehuge Alejuela fault forms

a compressionalfeature below theedifice,whilean axial grabencuts the

Journal of Volcanology and Geothermal Research 177 (2008) 925943

Corresponding author. Laboratoire Magmas et Volcans CNRS-UMR 6524, Observa-

toire du Physique du Globe de Clermont, Universit Blaise Pascal, Clermont-Ferrand,

France. Tel.: +34 4 73346763.

E-mail addresses: [email protected] (A. Delcamp),

[email protected] (B. van Wyk de Vries), [email protected]

(M.R. James).1 Tel.: +35 3 18961440.2 Tel.: +34 4 73346763.3 Tel.: +44 1524 593571.

0377-0273/$ see front matter 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.jvolgeores.2008.07.014

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mailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.jvolgeores.2008.07.014http://www.sciencedirect.com/science/journal/03770273http://www.sciencedirect.com/science/journal/03770273http://dx.doi.org/10.1016/j.jvolgeores.2008.07.014mailto:[email protected]:[email protected]:[email protected]


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hyaloclastic-sediment layers, hydrothermal levels and conceivably the

magmatic reservoir. These models can also represent any volcano

that has developed LSL within the edifice, such as terrestrial volca-

noes with significant sedimentary or pyroclastic aprons that become

incorporated in the edifice. Examples of volcanoes are La Reunion,

Guadeloupe and Hawaii (e.g. Oehler et al., 2005).

The second (type II) can represent volcanoes built on a continuous

sedimentary base, and is essentially similar to that used by Merle and

Borgia (1996). Either a sea-bound volcano or a terrestrial one may

have this scenario. A volcano in the sea could have a thick substratum

of sediment, such as the Canary Islands (Ye et al., 1999), and low

strength layers within the edifice, such as Piton de la Fournaise (Merle

and Lnat, 2003). A terrestrial volcano can also have both LSLs in it, so

type I and type II scenarios may occur in any situation. They representuseful end members for consideration.

The model set-ups are shown in Fig. 2. A rigid base is covered by

a ductile silicone putty layer to the required diameter and the model

is then constructed using silica sand (mean diameter: 200 m) mixedwith plaster. In type II models, volcano slope and the thickness of

ductile substratum have been varied. The ductile substratum mea-

sures 0.6/0.7 cm (120/140 m in nature) in E experiments, and from 1.3

to 1.5 cm (260 to 300 m in nature) in F experiments (Table 1). For both

experiments (E and F), the volcano slopes have been constructed at

about 10, 20and 30. Further experiments have been done to test the

influence of a brittle component in the substrata, by adding a layer of

sand-plaster mix on top of the silicone base (see Table 1).

Models can be assembled in 10 min and subsequently deform over

1 to 10 h (representing scaled periods of 6103

6104

years). Model

evolution is recorded with a 6 mega-pixel digital camera, located

vertically above the model and automatically imaging every 10 min.

Horizontal displacements were determined from the image

sequence by tracking black markers placed on the model surface.

Tracking was automated using a patch correlation technique imple-

mented in Matlab from which theimagexy coordinates are obtained

for each marker in every image. From these data two velocity values

have been calculated: instantaneous horizontal velocity (the mean

target velocity between two consecutive images) and total mean

velocity (the averagetarget velocity between thefirst andlast images).

These two values allow the complex deformation fields to be sum-

marised and easily compared between models.

In order to quantify vertical motions, some experiments were

monitored with two additional digital cameras (6 mega-pixel CanonEOS 300D's) that had been pre-calibrated for photogrammetric

work. The cameras were located obliquely above the model and

were synchronised to obtain image pairs every 15 min. Initial 3D

coordinates of the target points were calculated using standard close-

range laboratory photogrammetric techniques, such as described in

Donnadieu et al. (2003). Point positions were determined to precision

of b0.02 mm (tending to be closer to 0.01 mm in xy) using the

programme VMS (Visual Measuring Software [www.geomsoft.com]).

With the imaging geometry defined, target positions throughout the

image sequences were calculated using tracked target positions and

ray intersections (implemented in Matlab). The additional uncertain-

ties involved with the tracking and changing orientations of the

markers decreased the precision of their locations to 0.1 mm in z.

The use of points allows the deformation field on the models to be

Fig. 2. Experimental set up. On type-I oceanic volcano, a ductile layer (silicone) is included in the volcano whereas for type-II continental volcano, the ductile layerextends underand

outside the edifice.

927A. Delcamp et al. / Journal of Volcanology and Geothermal Research 177 (2008) 925943
http://www.geomsoft.com/http://www.geomsoft.com/


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obtained but does not give a detailed 3-D surface description of the

model.

2.2. Scaling

Scaling assures the necessary conditions for having the same

geometric, time and force ratios between models and natural cases.

We use a standard two-stage scaling procedure, in which the first

step is to scale models with respect to natural cases and laboratory

constraints (Table 2A). The second step is to cast dimensionless num-bers from the parameters that we are interested in, and assure that

these also have the same range in model and nature. The scaling and

materials are similar to those used by Merle and Borgia (1996), with

modifications by Cecchi (2003), and are based on basic principles of

Hubbert (1937) and Ramberg (1981).

Length scale (l) is fixed by laboratory space restrictions, and is

around 5105, where 5 cm in model equals 1 km in nature. Density of

thegranular mixtureis 1500kg m3, scaling as() 0.55 to rock density of

2600 kgm3 (Merle and Borgia,1996). Gravity is the samefor model and

nature and thus scales as g=1. Stress and cohesion are scaled through

the product of length, density and gravity, giving as 2.9105 Pa.

Viscosity of the analogue material varies from 104 to 105 Pa s (values

obtained from rotational viscometer measurements). Using a low

estimate of natural viscosity, such as given by Arnaud (2005) for Piton

de Neiges breccia (1016 Pa s) we can scale the viscosity as=1012, and

the highest viscosity silicone thus scales to 81016 Pa s.

We can check the consistency of the scaling with the velocity,

length and stress ratios through the dimensionless number:

1=vf1: 1

Velocity is measured independently to viscosity in models at

characteristically about 5 mm per hour, or 1.6106 m s1. Velocity

estimates for Etna, Concepcin and Hawaii vary from 1 cm to 10 cm

per year, or 1.5109 m s1 (Murray et al., 1977; Owen et al., 1995;

Borgia and Van Wyk de Vries, 2003). This gives a velocity ratio v of

103. This can be used in Eq. (1), and gives a product near to 1. Thus

the model scaling is closely balanced (Table 2).

2.3. Dimensionless numbers

We have 13 parameters in themodel, which areexpressed with the

3 dimensions: length, time and mass. Using the -Buckinghamtheorem, we establish 9 dimensionless numbers using the methodset out in Middleton and Wilcock (1994). The volcano height for type I

includes the thickness of ductile substratum, which constitutes the

entire edifice height (ductile layer is included in the volcano). For type

II models, the ductile layer is below the edifice and is thus included in

the substrata thickness but not in the edifice height.

Table 1

Experiment description (initial parameters). In bold: type I models, in italics: type II models

Angle h d b r v rs Other information Number of structures

(m) (m) (m) (m) (m)

A1 30 0.7 0.005 0 0.135 0.125 Dirty silicone 23

A2 30 0.07 0.011 0 0.135 0.125 Dirty silicone 21

A3 30 0.07 0.013 0 0.135 0.125 Dirty silicone 20

B1 20 0.055 0.005 0 0.145 0.125 Dirty silicone 28

B2 20 0.055 0.01 0 0.145 0.125 Dirty silicone 35

B3 20 0.055 0.015 0 0.145 0.125 Dirty silicone 28C1 10 0.035 0.005 0 0.145 0.125 Dirty silicone 8

C2 10 0.03 0.01 0 0.145 0.125 Dirty silicone 11

C3 10 0.04 0.015 0 0.145 0.125 Dirty silicone 23

D1 10 0.035 0.005 0 0.15 0.125 Dirty silicone 0

D2 10 0.035 0.01 0 0.17 0.125 Dirty silicone 12

D3 10 0.04 0.015 0 0.17 0.125 Dirty silicone 13

D4 10 0.039 0.002 0 0.145 0.125 Clean silicone 0

D6 10 0.03 0.002 0 0.105 0.125 Clean silicone 0

D7 30 0.07 0.003 0 0.145 0.125 Clean silicone 19

E1 30 0.06357 0.00643 0 0.14 0.39 Dirty silicone 49

E2 20 0.0538 0.0062 0 0.1375 0.33 Dirty silicone 30

E3 10 0.0276 0.0074 0 0.15 0.325 Dirty silicone 25

F1 30 0.056 0.014 0 0.15 0.3 Dirty silicone 37

F2 20 0.0412 0.0138 0 0.15 0.32 Dirty silicone 28

F3 10 0.025 0.015 0 0.145 0.325 Dirty silicone 22

M 20 0.016 0.024 0 0.15 0.31375 Dirty silicone 33

E1sp 30 0.0644 0.0056 0 0.135 0.24 Clean silicone 41



Brittle 0 30 0.0525 0.0075 0.015 0.13 16

Brittle 1 30 0.0625 0.0075 0.015 0.12 9

Brittle 2 20 0.078 0.007 0.02 0.125 2

Brittle 3 20 0.074 0.006 0.015 0.12 6

Brittle 4 20 0.08 0.01 0.015 0.15 1

Brittle 5 30 0.075 0.01 0.005 0.12 17

Brittle 6 30 0.078 0.012 0.02 0.11 0.5

Brittle 7 0.05 0.012 0.004 0.10 27

Brittle 8 0.055 0.01 0.004 0.10 19

Brittle 9 0.046 0.01 0.008 0.08 8

Brittle 10 0.022 0.013 0.008 0.09 7

Brittle 11 0.06 0.0125 0.012 0.1225 15

Brittle 12 0.065 0.012 0.012 0.115 12

Brittle 13 0.052 0.009 0.016 0.08 7

Brittle 14 0.062 0.0077 0.016 0.09 3

Brittle 15 30 0.062 0.01 0.01 0.105 6Brittle 16 20 0.075 0.01 0.01 0.15 0

928 A. Delcamp et al. / Journal of Volcanology and Geothermal Research 177 (2008) 925 943


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Thefirstfour-numbers are the geometrical description.1istheslope of the volcano, 2 is a measure of the propensity to deform, 3indicates the position of the ductile layer involved in spreading and

thus differentiates type I from Type II cases. 4 is the balance ofresistance to rate of spreading given through height of volcano and

thickness of deformable strata.

Note that 1 value is a proxy of the edifice slope angle (edifice

height/edifice radius). 1 is used as a measure of slope in the fol-lowing analysis. Each model had a slightly different slope, though

groups of models were constructed near to 10, 20 and 30. The va-

riations in the 1 values reflect the variation in slope angle for eachexperiment, and small errors in measuring the height of a cone. The

5 and 6 describe material properties and the last three numbersdescribe the balance between driving and resisting forces (Table 3).

The values for the models and nature are compared in Table 4.

Theratio of each is near 1, which arguesfor good scaling, except for

the last three numbers, which depart significantly. The inertial forces

(9), for example are not well scaled, as usual for such models.However, the system is far away from the turbulent regime and thus

thiswill not cause major dissimilarityas discussed by Merle and Borgia

(1996). The ratio of experimental to field 7 values is also small but,

because field viscosity values are poorly constrained and range overseveral orders of magnitude, this is relatively insignificant. The basic

scaling in Table 2 ensures that velocity scaling is reasonable,evenif the

forces involved are not perfectly balanced. The large uncertainties in

velocity, viscosityand resistance of natural rocks, however makedirect

velocity comparisons difficult. Deformation fields, however, should be

comparable, as they are largely controlled by the geometry of the

system, which is well scaled.

3. Results: structural surface observations

3.1. Type I volcano

The internal ductile layer models formed a range of structural

features including: graben-forming conjugate fault sets, sub-radial

individual normal faults, fault-bound slumps, and small collapses.

They generally developed one or several zones that spread out more

on fault-bound slumps (Fig. 3A and B). We also observed minor struc-

tures, such as small independent fractures, secondary small faults and

en-chelon fractures. The en-chelon fractures occurred mainly along

the conjugate faults that formed the sector grben showing that

the deformation is accommodated by strikeslip as well as dip-slip

movement.In some models, single sub-radial faults are created, rather than

pairs of graben faults, producing a half-graben. In many cases, these

sub-radial faults were cut by minor conjugate faults. These single

faults were roughly parallel to a nearby graben.

Regarding the grben, an important observation is that angles

between the conjugate faults that form them are smaller for 10 slope

than for 20 slope volcanoes. Cones steeper than 20 do not produce

easily measurable angles, but the whole edifice is intensively faulted

and fractured. In this steeper case, individual grben overlie each

other and measurements are not possible.

Although we observed a large range of structures with this I-type

set up, these experiments are not reproducible: the density, the

distribution, and the orientation of these structures vary too greatly

for us to quantify them.

3.2. Type II volcano

In contrast to the type I volcano, the structures produced in the II

type volcano are well defined and reproducible (Figs. 4 and 5).

3.2.1. Experiments without brittle substrata

For experiments using a cone placed directly onto the ductile

layer, a typical feature is the formation of a well-defined ring of sub-

radial conjugate grben on the outer edge of the volcano, with

significant strikeslip movement along the conjugate faults. The ring

of grben does not widen radially, but does migrate progressively

outwards with time (Figs. 4 and 5). A flattened, fractured, central

part of the edifice is a characteristic feature of all the models. This

Table 2

Scaling used in themodels based on theapproaches ofMerleand Borgia (1996), VanWyk de Vries andMerle(1996), Cecchi et al.(2003). A. Basic scaling parameters used to constrain

the model. B. Range of parameters in model and natural equivalents

A

Parameters Units Model Nature Ratio ()

Length (l) m 0.05 1000 5 105

Density () kg m3 1500 2700 0.55

Gravity (g) m s2 9.81 9.81 1

Stress () kg m1 s2 100 3.6 106 2.8105

Viscosity () kg m1 s1 10,000 1016 1012

Velocity (v) m s1 1.6106 1.5109 1067

Time (t) s 1 min 40 years 4.7 108

l / v None 313 231 1.3

B

Parameters Definitions Values Units

Models

(M)

Natural equivalent

(N)

h Volcano height 0.030.07 6001400 m

rv Volcano radius 0.1050.17 21003400 m

d Ductile substrata thickness 0.0020.015 40300 m

b Brittle substrata thickness 00.02 0400 m

rd Substratum radius 0.1250.39 25007800 m

Substratum viscosity 10,00080,000 101681016 Pa s

v Volcano density 15201550 20002700 kg m3

d Substratum density 9301450 20002700 kg m3

u Displacement velocity 1.6 106 1.5109 m s1

0 Cohesion 66340 104108 Pa

g Gravity acceleration 9.81 9.81 m s2

Angle of internal friction 3036 30

t Deformation time 10 h (36,000 s) 24,000 years time



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Table 3

Description of the numbers and their meanings

Formules Comments

1volcano heightvolcano radius

hrv

These are the geometrical description of studied system. 1 corresponds to the tangent of the v

2 volcano height

thickness of ductile layer h

d

2 is the balance between loading (h) and amount of deformable material (d).

3 volcano radius

ductile layer radius rv

rd

3 is a geometrical description of the position of the ductile layer, and if it is inside the volcano

4 thickness of brittle layer

thickness of ductile layer b

d

4 is a measure of the amount of material in the substrata that resists ( b) and allows (d) deform

5 volcano densityductile layer density

vd

This number describes physical properties of the materials. Densities of volcano and ductile substudied by Merle and Borgia (1996). They concluded that this ratio influences the deformation r

6 ta n=coefficient of internal friction Angle of internal friction corresponds to the repose angle of volcano. The tangent of this angle i

7 potential energy

viscous force g v h d d

vThis number represents the balance between potential energy accumulated by the volcano ( Van

layer.

8resistance force to the failure

viscous force

0 1 2tanffiffiffib

p gvh tan 1 b

h i h

v

This number describes the balance between the resistance force to the failure that affects brittle

responsible of ductile layer creep (substratum). This number is a combination of the resistance t

9 inertial force

viscous force d v d

This number corresponds to the Reynolds number. It represents balance between inertial and vi


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deformation creates small horsts that isolate vestiges of the original

topography (Fig. 4). These horsts and the grben are less well defined

for 30 models, where there is a high fault density and where grben

overlap (Fig. 5). At the cone base small folds developed at the silicone

surface.

3.2.2. Experiments with brittle substrata

When a brittle layer is added to the model set up, the deformation

remains similar for very low brittle layer thickness. The only

difference is that concentric folding and thrusting is emphasised at

the base of the cone and that fractures begin to appear at the base of

the cone. Basal folding and thrusting occurs only when the ductilelayer is thin (for 2N4) and when the brittle layer is thin as well

(4b0.5). Where folds are produced, the folded belt migrates slowlyoutwards and enlarges progressively. If models with thin brittle

substrata are left for a long time (several hours) the folds tend to loose

amplitude and disappear. For thicker brittle layers (4b0.5) the cone

grben relay to discrete strikeslip faults beyond the cone base. The

pattern formed is that of a set of radiating conjugate faults (Fig. 6).

In the cone, the structures change as the proportion of brittle

substrata increases: fewer grben form with increasing thickness until

about 4=1.5, when only a single major transverse graben is formedthat passesthrough the edifice centre. A fewsecondary minor conjugate

faults form from this central feature (as in Fig. 7). Over 4=2, nodeformation is observed.

Table 4

Comparison of number range between model and nature

Dimensionless

variables

Definition Values Ratio

(M:N)

Model

(M)

Nature

(N)

1 height: radius of volcano 0.200.52 0.280.41 1

2 v olcano height: substratum

thickness (b+d)

0.6623.33 215 1

3 v olcano radi us: substratumradius 0.36

1.36 0.84

0.43

1

4 brittle: ductile layer 02.85 01.33 1

5 v olcano den sity: s ubstratum

density

1.071.62 0.71.35 1

6 coef ficient of internal friction 0.570.72 0.57 1

7 p otent ia l energy: viscous f orc e 103104 0.13 102105

8 resistance failure fo rce:

viscous force

6273353 101105 1

9 inertial force: viscous force 3 10102109 10191021 1010

Fig. 3. Example of an oceanic type-I model. A: experiment B1 (see Table 1), 1=0.38, 2=11. Variation of ductile layer thickness (expressed with 2) has no influence on number of

grben, but the volcano slope does (expressed with 1). B: sector spreading and collapse around the substrata on the C3 model ( Table 1, 1=0.27, 2=2.66).



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Fig. 4. Example of a continental type-II model. E2 model (Table 1), slope of 20 (1=0.43, 2=8.67). A: model after 30 min, grben are composed of normal faults with strikeslip

component shown by en-chelon fractures. B: same experiment after 90 min.

Fig. 5. Example of a continental type-II model. F1 model (Table 1), slope of 30 (1=0.46, 2 = 4). A: model after 30 min. B: model after 90 min. Note the higher but less well-defined

structure density.



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For models with no brittle layer, the steeper cones (30) have a

greater structure density and conjugate grben widen inwards atopening angles from 41 to 69 with a mean of 56. Grben for 30

cones are not clearly formed due to a high fault density, but become

more clearly defined with increasing brittle layer thickness. The

grben formed in 10 and 20 models are well defined and are

separated from each other by undeformed wedges. For these

slopes, angles between conjugate faults are lower, varying between

10 and 45. The strikeslip nature of the deformation is seen clearly

in displacement maps, where individual wedges tend to have a uni-

que displacement vector (Fig. 6). These wedges, or sectors, are for-

med by a diamond-shaped segment enclosed by the area between

two conjugate grben and their associated strikeslip faults. Sec-

tors can also be formed by more than one graben pair, enclosing a

minor graben. The style of deformation is like that of sector spread-

ing, described by Van Wyk de Vries and Francis (1997) and Wooller

et al. (2004). Such sectors form most readily with thicker brittle

layers, where fewer grben form in the cone (Fig. 7). These sprea-ding sectors probably form preferentially in areas where slight

asymmetry of the sand cone or of the brittle layer occurs (Cecchi,

2003).

4. Results: time evolution of the surface structures

4.1. Type I volcanoes

In most models, the grben and sub-radial faults begin to form in

less than 15 min, which scales to b600 years in nature. The rest of the

deformation is expressed by the widening of these fractures and

faults. Most microstructures are also formed right at the start and/or

after a few minutes and are concentrated in a central chaotic or

polygonal fracture region.

Fig. 6. Two models showing the influence of volcano profile on deformation field and the distribution of related spreading structures. A: simple (idealised) cone model, and B:

graduallycurved (realistic)profile.Note in A howdeformationstopsat thebase of thecone andthatin B deformation is much more widespread andseparated into thefault-bounded

sectors. In this model, the brittle layeris formed by the gently decreasing lowerslope of the volcano. C: plotof the horizontaldisplacement against radial distance for differentsectors

in the model in B and the whole model for A (in grey). Inset shows the sectors differentiated in the graph. The simple cone model (A) has a uniform distribution of displacement,

which decays rapidly at the basal thrust. Note that in contrast, each sector of the gradually changing slope model (B) has a characteristic displacement magnitude that decays more

slowly and linearly with distance.



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Fig. 7. Example of preferential sector spreading after 110 min; spreading is limited at model edge and with a thick brittle layer ( 4=2). Strikeslip faults are developed from grben

that propagate beyond the edifice. Few grben have formed.

Fig. 8. A: differentevolution of grbenmorphology with time. B:distribution of theprincipal stresses atthe brittle/ductilecontact on a model with a thin brittle layer (onthe left) and

with a brittle layer (on the right).



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4.2. Type II volcanoes

Structures appeared rapidly, usually before 10 min (400 years) and

deformation slowed to unobservable, or became fixed on one set offaults after 1 h (2400 years in nature). The deformation after this

point consisted of slight widening and significant deepening of the

grben. Secondary graben also formed inside the original ones, as

shown by step structures along the graben walls ( Fig. 4). These step

structures were not clear or even absent on 30 slope models.

The outer termination of the grben, at the foot of the 10 and 20

slope cones, were seen to open up progressively and some of graben

terminations formed two additional small external grben with

parallel walls (Fig. 8A). During deformation in one single model, the

angles between sets of conjugate faults were seen to either stay

constant, increase or decrease (Fig. 8A).

5. Results: parameters affecting structural style

5.1. Type I volcanoes

The dimensionless numbers that describe model geometry (1,

2, 3 and 4) are compared with the number of structures. Thegrben, sub-radial faults and other faults are counted, but not micro-

fractures andcollapsefeatures that we consider as minor or secondary

structures.

1 corresponds to the tangent of the volcano slope and plays animportant role in the displacement velocity (not measured for the

type I, but visible to the naked eye as a qualitative measure). With an

initial slope of 10 (0.20b1b0.27), deformation was slow, the edifice

slid in one or more preferential directions (Fig. 3B), and few grben

were formed. The number of structures increased with1. The greater

the slope, the denser the faulting, until at around 30, when the fault

density was too high to measure (Fig. 9A). The number of structures

was not influenced by variations in either 2 or 3.With the initial qualitative visual inspection of type I models, we

observed little order in the distribution of structures, and an absenceof reproducibility. This is clearly confirmed in the dimensionless

number study as said previously, especially with 1 vs. number ofstructures (Fig. 9A). The present dimensionless number study high-

lights thus the unpredictable behaviour of the type I volcano models

previously noticed in our structural observations.

5.2. Type II volcanoes

For a volcano model standing on ductile substrata, a clear

correlation between number of graben and 1 (volcano slope)occurs (Fig. 9B). 2 has no clear effect on structure density, as seenbefore for type I models. The variations of3 here were not sufficientto observe a relationship.

A variation in the brittleductile ratio (4) of the substrata changedthe number of structures (Fig. 9D). The number of structures decreased

markedly with a small increase in the thickness of brittle material, and

spreadingstopped completelywhen4N2. This limit is slightly lower in

ourmodels than that found by Merle and Borgia (1996). We suggest this

difference is due to slightly different experimental conditions, such as

different silicone, different density ratios (density ratio of sand/silicone

is near 1, whereas in the previous study it was over 1), and that we use a

cohesive granular mixture that retards deformation. Note thatthe effect

of the slope is diminished by the addition of the brittle substratum and

the effect of this layer dominates the deformation (Fig. 9C).

Numbers 5, 6, 7 and 8 do not have any role in the graben

density. However, the viscosity is of course important for the displace-

ment velocity. Changing the viscosity however did not appreciably

change the type and density of structures produced.

Fig. 9. A: number of grben (except central microfractures) vs1 (volcanoheight/volcano radius) for oceanic volcanotype model. B: number of grbenvs 1 forcontinental volcano

type model. It is clear that number of grben increases with increasing slope. C: number of grben vs 1 for continental volcano type model with a brittle layer. The effect of this

substratum predominates over the effect of the slope. D: number of grben vs 4 (thickness of brittle layer/thickness of ductile layer) for continental volcano type model.



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6. Results: horizontal displacement velocity using 2D images (type

II models)

In most models, horizontal velocity was high at first, and then

decreased exponentially to a constant rate (Fig.10A). Models with low

brittle thickness left for many days continued to deform, while those

with a thicker brittle layer (1 cm) reduced to a stable condition after

about 48 h (natural time=105 years). For models E2 and E3 (20 and

10 slope respectively, no brittle layer), the black markers showed aconstant displacement between images. However, we observe a small

initial acceleration for the E2 model.

Horizontal velocities are smaller with lower initial volcano slope

(1) and increase with 2, because of an increase of ductile substratathickness (Fig. 10B and C). Thus, with equal slope, velocities increase

for a thicker ductile layer. As expected, the less viscous the substrata,

the more rapid the deformation.

For all the models with no brittle substrata (whatever slope and

ductile layer thickness), horizontal displacement is minimum at the

centreand the footof the edifice andgreatestbetweenthesetwo areas

(Fig. 11). For modelswith a brittle layer, the pattern is different andthe

displacement propagates much further beyond the edifice.

7. Results: 3-D distribution of the displacement (type II models)

Displacement was characterised further using 3D target coordinates

obtained by photogrammetry, the results of which are synthesised in

Fig.12. For a singlemodel,we obtain 3figures, thefirstcorresponds tototal

velocity magnitudevariation, thesecond is the horizontal component and

the third the vertical component. The X-axis represents time. The Y-axis

representsradial distance from thecentreof the model,so zero is thecone

top and the greatest number is the model edge. Associated colours give

displacement magnitude for each distance and time. Dark blue areas are

those with no data.

Fig.12A represents velocity (m/s) in space and time fora 30 model

with no brittle layer. Velocity magnitude generally decreases from

centre outwards, but we observe a peak at 6 cm, at the mid-flank of the

edifice. Areas with lower initial displacement magnitudes attain more

rapidly a constant velocity, or stop. Maximum horizontal and verticalvelocity is not in the same place. The horizontal velocity component

obtained by this method shows the same distribution as previously

obtained for vertical photography (2D, see results, Section 6), with a

maximum on the volcanoflank. In contrast, the vertical velocity reaches

a maximum at the centre and decreases outwards.

Fig.12B records the displacementfields for a 10 model with no brittle

layer. Velocity fields look like Fig. 12A, but here horizontal displacement

maximum is lower and is more concentrated at the centre, the defor-

mation continues longer and decreases less rapidly. As before, areas with

lower initial displacement are those that attain more rapidly a constant

velocity or stop.

8. Discussion

8.1. Type I models

8.1.1. Discussion on the model structures:

Type I models do not produce a reproducible and predictable

structural pattern. Our observations suggested to us that this is

probably related to variations in the thickness of the thin brittle

Fig.10. A: evolution of the velocity with time with models with different 2 values (2= h / d). Velocity corresponds to the displacement of a point between 2 images taken with an

interval time of 10 min. B and C: mean of displacement velocity (mm/min) vs 1 (B) and 2 (C). For all the models, velocities are calculated over 1 h, except for E1 model (calculated

over 50 min).



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boundary (The brittle part of thevolcano model hasa diameter greater

than the ductile layer and thus forms this thin brittle boundary). This

layer acts as a barrier and consequently slightly limits the ductile level

spreading (Fig. 2). This is confirmed by comparing with the type II

experiments with no brittle layer, a set up that is equivalent to a type I

with limited brittle boundary. In these models, the structures are

reproducible, which confirms the role of the thin brittle boundary in

creating variability.

While a quantifi

cation of the deformation for type I models isdifficult, it is possible to state that structure density increases with

slope. In addition, qualitative statements can be made about the type

of deformation. The most striking result is the appearance of

spreading sectors bounded by sub-radial faults associated with

localised lateral movements (Fig. 3B). The smallest irregularity in

model construction allows these features to be formed. The sectors

tend to inhibit the formation of well-formed grben. Instead, sub-

radial faults form in a sector that slumps outwards and an entire part

of the edifice slowly slides outwards, creating a collapse scar-like.

These slow moving slumps are not rapid landslide-debris avalanches,

but rather an equivalent to the slowly deforming slumps predicted

over Low Strength Layers (LSLs) as described by Oehler et al. (2005).

The slumps slowly deform over an equivalent of thousands of years.

Small avalanches of sand from the front of these are the equivalent of

landslide-debris avalanches in nature.

8.1.2. Natural examples

We expect the type I models to be a good analogue of oceanic

volcanoes and it is noticeable that few oceanic shield volcanoes, or

island arc edifices have well-formed graben structures like those

seen on on-land volcanoes. For example, no Hawaiian volcano has

sector graben, nor the Canary Island volcanoes, nor Martinique,

nor Stromboli. There are some exceptional cases, such as Manam

(Papua New Guinea) and Piton des Neiges, La Runion Island (Fig.13),

where the morphology appears to suggest graben formation andGuadeloupe.

Commonly such oceanic volcanoes have well developed slumps

behind and around which rift zones are located (Oehler et al., 2005;

Walter et al., 2006). Such an organisation (Fig. 13) is seen in the

models, with the slumps bounded by extensional fault zones. This is

the area where dyke injection would be localised (e.g. Walter and

Schmincke, 2002).

For such models and natural cases, the thin, uneven brittle

boundary at the outer edge of the edifice is analogous to the uneven

distribution of strong (lavas, consolidated hyaloclastites) and weak

layers (sediments, brecciated hyaloclastites, debris avalanche brec-

cias) inherently created at a growing oceanic volcano. The edges of

many oceanic volcanoesare cut by km-scale slumps andcollapse scars

that are evidence of the instability and variability in lithology of such

zones (Fig. 13).

Fig. 11. Horizontal deformation field (mean velocities) ofE1 (1=0.5, 2= 10.88), F1 (1=0.46, 2=5) and E3 (1=0.23, 2= 4.73). Vertical scale is different between E1, F1 models

andE3 model.The velocities areless in thelowerslopemodel (compare A andC) buta thicker ductile layer creates highervelocities (compareA and B).Notethe broader deformation

field for the lower slope model (C).



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8.2. Type II models

8.2.1. Effect of the volcano slope on the deformation

For type II models the initial (i.e. at the start of the experiments)

angle between conjugate grben faults increases with the volcano

slope. This may be generated by the angle of intersection bet-

ween the faults and the topography. A steeper slope will produce a

more oblique intersection lineation with a fault of constant dip.

For example, for a flat volcano the intersection would be the fault

strike, for a vertical cliff the intersection would be at 90 to the

strike. Predicted opening angles of grben for a variable slope and

for constant 60 graben fault dips were calculated, and these angles

are close to those measured. This confirms the hypothesis and sug-

gests that graben opening angle variations are only a geometrical

effect, and does not correspond to either fault dip, or fault strike

variations.

Fig.12. A: displacement velocities for a model with an initial slope of 30. On the top: evolution of the velocity during time. In the middle: evolution of the horizontal component ofvelocity during time. At the bottom: evolution of the vertical component of the velocity during time. The centre of the deformation corresponds to the centre of the volcano. B:

displacement velocities for a model with an initial slope of 10. On the top: evolution of the velocity during time. In the middle: evolution of the horizontal component of velocity

during time. At the bottom: evolution of the vertical component of the velocity during time. The centre of the deformation corresponds to the centre of the volcano. (For

interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)



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An additional observation is that as volcano slopes reduce duringthe deformation the grben widen, rather than narrow. This must be a

structural rather than slope effect. The increase of a graben opening

angle that occurs with increasing time in some models is probably

related to block rotation, where one sectoropening is compensated by

a graben closure elsewhere, or by pure lateral movement on the

adjacent fault. Thus, opening and closing of grben during the

deformation are a response to differential block movements. Such

block movements are well seen in some displacement fields (Fig. 6C).

When no brittle substrata are present, the structure density

increases with increasing volcano slope (Fig.9B). This is best explained

as an effect of higher stress concentrations. A steeper volcano has

higher potential energy and creates a more intense stress field.

With higher stresses more points in the edifice exceed the material

strength, thus more faults are produced.

Note that we did not find any relationship between 2 andstructures (volcano height/substratum thickness ratio). However, Van

Wyk de Vries and Matela (1998) showed that a difference occurs

when the ductile layer is significantly thicker. With increasing 2more sagging occurs and less radial spreading until about 2=1,where sagging replaces spreading. When the ductile substratum has a

thickness of 40 cm for example for a cone of 10 cm, volcano sagging is

observed and no grben are formed (Cecchi, 2003).

8.2.2. Effect of the brittle layer on the deformation

Adding a brittle component to the substrata decreases the number

of grben produced (Fig. 9D). Above a brittleductile ratio of2, no

grben are formed. The effect of volcano slope on graben is less

significant with a brittle layer present and this layer dominates the

structural relationships.

Fig.13. A:Imageof Manamisland, PapuaNew Guinea(fromNASAimage library),grben areclearlyobservedon theisland. B:DEM andstructuralsketch of LaRunion Island; grben

aredisplayed at thecentre of theisland while a sectorslump occursto theeast on Piton de la Fournaise. Thereare also some costal slumps.C: model C3(Fig.3 B), notethe similarity in

structural pattern between La Runion Island and the model.



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With brittle layer present there is the observed relay from edifice

conjugate graben to basal strikeslip faults. This relay can be

explained through the reorganisation of the stress field as the load

effect diminishes outwards (Fig. 8B). At the cone foot and on the

brittle/ductile boundary, 1 is radial and 3 vertical for a thin brittle

layer creating a thrusting regime. However, with a thicker brittle layer,

the vertical load under the brittle layer becomes 2 at this boundary

and thus a strikeslip fault regime is created. This result is similar to

that predicted by Cyr and Melosh (1993) for Venusian volcano stressfields.

8.2.3. Fold and thrust formation

Folds and thrusts were a common feature of the experiments of

Merle and Borgia (1996), but strikeslip faults were not mentioned.

Thelack of strikeslip faulting observed in the previous experiments is

due to the use of pure sand that does not preserve the fine structure

associated with the transverse movements. The prevalence of folds in

the previous experiments can be associated to the use of pure conical

sand piles. In such models, the sharp junction between the sand pile

and the substrata creates a stress locus and induces thrusting. In the

models here, the junction is subtler, as in real volcanoes (see Fig. 1),

and such stress loci do not exist (Fig. 6).

8.2.4. Displacement rates and time of deformation

Displacement fields show the summit flattening by vertical drop,

and the mid-flanks steepening up, as they have the most horizontal

movement. The steeper cones have a more localised displacement

field than flatter cones, where the horizontal displacement extends

further afield.

In some models there is an initial velocity increase (like for E2 and

E3 modelsin Fig.10A). This might correspond to thenecessary time for

an edifice to accumulate stress before failing (Borgia and Van Wyk de

Vries, 2003). In addition, it may be related to the time taken to form

fault structures that weaken the edifice. Subsequently displacement

can increase on these lubricating structures. Decrease of velocity, a

common characteristic for all the models, can be explained by the

decrease in load potential as the edifice flattens.

Borgia et al. (2005) using an analytical approach, suggested thatfolds at Vesuvius should migrate outwards from the base rapidly,

coming to a halt at the end of spreading after about 7200 years. Fold

areas around our volcano edifice models also migrate progressively

outwards. Migration rates in our models are much smaller than those

calculated. In our models that are comparable to the Vesuvius

situation, if no brittle resistant layer is included, spreading continues

with the progressive migration of folds up to ten times longer than

calculated by Borgia et al. (2005). This discrepancy may be partly a

scaling related feature (as the 7 to 9 are not closely scaled), orrelated to uncertainties in the natural values chosen. The difference

may also come from their use of the lubrication approximation of

the NavierStockes equation that does not take into account non-

Newtonian behaviour, the resistance of the edifice nor the brittle

substrata. For a Vesuvius-like situation, with significant brittle sub-stratum that appears to exist in the sections provided by Borgia et al.

(2005), our model suggests that the deformation will be slower and

propagate further afield. The discrepancy between theoretical and

analogue models requires further investigation.

8.2.5. Natural examples

We describe the spreading features a variety of volcanoes: Concep-

cin and Maderas (Nicaragua), La Soufrire (Guadeloupe), Merapi

(Indonesia), Mount Etna (Sicily) and Mount Haddington (Antarctic

peninsula).

8.2.5.1. Nicaraguan volcanoes. For some Nicaraguan volcanoes,

detailed mapping by Van Wyk de Vries and Borgia (1996) and Borgia

and Van Wyk de Vries (2003), showed that erosional features where

principally controlled by faulting and fracturing relating to spreading.

Maderas shows numerous large faults on the edifice that extend to the

volcano base (Fig. 14A). In contrast, Concepcin does not show such

clear edifice faults. This is due to the rapid resurfacing by recent

eruptions. However, triangular facets on Concepcin (Fig. 14A) can be

made out, and in some places clearlycan be seen to coincide with faults.

At the base of Concepcin, clearly expressed folds are cut by significant

gullies that host strikeslip faults.

For Maderas volcano (Van Wyk de Vries and Borgia, 1996) we

counted at least 9 grben and for Concepcin 6 grben. The volcanoes

sit on1 km of ductile sediments without a major brittle layer and are

about 30 in slope.

Fig. 14. Structural maps of Concepcin and Maderas (Nicaragua), La Soufrire volcano

(Guadeloupe) and the Merapi and Merbabu volcanoes (Indonesia). The maps

graphically show the grben density and distribution that can be used to determine

the range of probable substrata brittle/ductile thicknesses. The structural pattern seen

at Concepcin is very similar to that in the analogue models, and shows how drainage

can be influenced by the spreading features, especially the basal strikeslip faults.

Similar structural features are inferred for La Soufrire and the Indonesian examples. In

both cases some faults have been identified in the field (e.g. Van Bemmelen, 1949) as

well as by our DTM analysis.



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8.2.5.2. La Soufrire. For La Soufrire (Fig. 14B), morphological

analysis provides a structural framework that has then been partially

confirmed by field analysis. For La Soufrire our preliminary fieldwork

indicates that there is about 200 m of brittle strata under the edifice

composed of debris avalanche breccias and lahars, below, which asimilar thickness of saturated altered and hydrothermally active rocks

behave in a ductile manner. Our preliminary mapping shows several

small grben, high on the volcano flank, a major slump, and some

strikeslip faults low on the volcano flank.

8.2.5.3. Merapi. Drainage on the Indonesian examples shows very

distinct linear patterns that are strikingly similar to those expected

for sector grben and outer strikeslip conjugate faults (Fig. 14C).

Some linear valleys also coincide with the faults identified by Van

Bemmelen (1949). We believe, therefore, that the drainage pattern

is controlled by the spreading structures, as in Nicaragua. Thus,

the analysis of river valleys, as done here, is a useful way of finding

subtle but important spreading-related structural features. The

number of graben-like structures on each volcano example can be

counted. We count 3 graben-like structures and a sector spreading

area directed towards the SW. There are also many lineaments at

the base of the cones, that may be related to gullies occupying strike

slip faults. Merapi has a thick sedimentary basement with estima-

tes ranging from 8 km (De Genevraye and Samuel, 1972; Smyth, 2005)to 11 km (Untung and Sato, 1978). Van Bemmelen (1949) described

a sequence of Cretaceous to Tertiary marine limestones, marls and

volcaniclastic sediments that are 12 km thick. From this we note

that Merapi must have a substrata that is a thick mix between ductile

and brittle layers, favouring spreading, but that the rapid resurfacing,

has limited the number of grben that have clearly formed on the

edifice.

8.2.5.4. Mount Etna. InthecaseofEtna(Fig.1), there arejust three clear

grben. The volcano substrata is constituted by 200 m to 600 m of

ductile layers overtopped by around 300 m of brittle layer essentially

composed by lava flows (Andronico et al., 2001; Branca and Ferrara,

2001; Branca 2003). Etna is a very rapidly resurfaced volcano, so

fractures and faults may well be hidden under recent lava flows.

Fig. 15. A: DEM of Andean volcanoes (Sajama and Macizo de Pacuni, N. ChileBolivia), note the ring of grben-like valleys on each structure. B: DEM of Andean volcanoes near Putina,

Bolivia. Note the occurrence of sector spreading like features. C: model E2, ( Fig. 4). D: model brittle1, (Fig. 7, Table 1); note the morphological similarity between these models and

the natural examples shown in A and B.



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8.2.5.5. Mt Haddington. Mt Haddington (Fig. 1) lies directly on a thick

Cretaceous clay and mudstone sequence with few sandstone and

conglomerate bands. The edifice has an extremely low slope, due to

rapid eruption of basaltflows into a thin marineor glacial environment

(Smellie et al., 2006). The volcano has no clear graben, but is cut by

several fault-bound blocks that may accommodate limited spreading.

This flat volcano is an endmember, where no effective slope creates no

effective edifice deformation.

8.2.5.6. Andean volcanoes. Large areas of the Andean Altiplano in

Northern Chile, Bolivia and Peru are underlain by thick sedimentary

successions, on which volcanoes have grown. Many of these edifices

have a morphology that is very close to that seen in the models

(Fig.15). The central areas of such edifices are generally highly altered

and brecciated, as would be expected from the models. These edifices

have often been strongly glaciated, and there is a strong erosion

control on the morphology, however the original drainage pattern

may originate from spreading-related structures.

Using the known parameters (especially the brittle/ductile thick-

ness ratio) for different natural volcanoes and regarding the graben

number, we can investigate the link found previously in our models

between 4 and the graben number shown in Fig. 9D. The resultinganalysis shows that many more faults are counted in the models than

in the natural examples. The reason for this discrepancy is probably

that in nature, faults are covered (e.g. Borgia and Van Wyk de Vries,

2003; Norini and Lagmay, 2005), eroded or restricted to hard-to-

detect fracture zones, while in the model they are clear and easily

visible. This makes a full quantitative comparison difficult, however

the number of grben counted on shallow volcanoes, with little brittle

substrata clearly rise with the steepness of the cone. Thus Mt

Haddington has no real graben, Etna three, and Concepcin many.

The older Andean edifices have a greater number of possible grben,

nearing thenumbers counted in the models. This maybe because they

have had longer to deform, and because there has been limited

resurfacing and structures have been exploited by erosion.

Finally, volcanoes with appreciably thick brittle layers tend to have

fewer faults, more strikeslip faults and sector spreading. Thus, Con-

cepcin and Maderas have more faults than Merapi and La Soufrire, forexample, and these two volcanoes clearly slump one way, while the

deformation at Concepcin and Maderas is near-radial.

9. Conclusions

Our study of relationships between the initial morphology of a

volcano and the structures subsequently produced by volcano

spreading shows that volcano slope and thickness of substrata brittle

layer have a major control on the both structural style and displace-

ment fields. In all the models the central part of volcano is intensely

fracturedwith a polygonal fracture set. For volcanoes lyingon a ductile

layer that extends below the edifice (type II), such as most continental

volcanoes and oceanic volcanoes on thick ductile substratum, the

structures are well developed, and form a distinct pattern. If the lowstrength ductile layer is smaller than the edifice diameter (type I),

structures are chaotic and are associated with sector spreading, slumps

and collapses. These latter models are good analogues for oceanic

volcanoes built with many low strength layers, and show that rifts are

probablya consequence of spreading sectors, and that the relationship

between riftsand slumps is spreading-controlled. The recognition that

the structureof oceanic volcanoesmost closely resembles models with

integral low strength layers is a strong indication that such volcanoes

create their ownweakbasesas they grow, as suggestedby Oehleret al.

(2005). Thus, the pelagic sediment layer invoked as a dcollement by

Nakamura (1980) is just one component to be taken into account with

the weak basal edifice.

The volcano slope effect is only important for structure density

when there is no significant brittle layer. When present, the brittle

substratum controls the number and style of structures. With in-

creasing brittle substrata, graben numbers reduce and they begin to

propagate beyond the edifice, where they transform into strikeslip

faults. Small variations in brittle layer proportions favour a single

sector-spreading style, a result also found by Cecchi (2000). This takes

the form generally of two majorstrikeslip faultsjoined to a dominant

graben or rift that traverses the edifice like for example Mount Etna

(Fig.1). The established relationship between the graben number and

4 allows for the characterisation of the conditions that generate thestructural pattern at a volcano, as shown for example at Merapi,Merbabu and La Soufrire. For Maderas, where there is no significant

brittle layer the large number of faults is consistent with a lack of this

brittle layer.

Displacement fields vary with slope, being of greater magnitude

and centrally-concentrated with steeper slopes and of lower magni-

tude and more disperse with lower slopes. The maximum horizontal

component is on the mid-flanks, and the main vertical component on

the summit. The displacement field also changes as a brittle layer is

included. In this case, deformation is transmitted well beyond the

edifice to the model boundaries and with increasing brittle thickness

the radial profile of displacement flattens, as more displacement is

transferred outwards.

We note that strikeslip deformation is an integral feature of volcano

spreading and that the sector grben are essentially a conjugate system

of strikesliptranstensional faults rather than simple grben. This

study shows how the structure of a natural volcano to be analysed and

for relationships to be determined between the initial shape of the

edifice, the thickness of the ductile and brittle substrata and an estimate

of the deformation field is possible.

Acknowledgements

We thank Valentin R. Troll and Olivier Merle for instructive

comments, as well as the two reviewers: Adelina Geyer and Gianluca

Gropelli. This research has been partly funded by the French ANR

projects VOLCARISK (La Runion) and VOLCANRISK (Antilles). The

information on Mt Haddington in Fig. 1 is provided from fieldwork

carried out by van Wyk de Vries for the British Antarctic SurveyLCHAIS project led by John Smellie.

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