Jun 10, 1996 - contribution to deformation, such as the Mauna Loa-. Kilauea system [Borgia, 1994] or the Cappadocia Volcanic complex [Pasquar⢠et al., 1993] ...
JOURNALOF GEOPHYSICALRESEARCH,VOL. 101,NO. B6, PAGES13,805-13,817, JUNE 10, 1996
Scaled experiments of volcanic spreading Olivier Merle D6partement desSciences dela Terre,Universit6 BlaisePascal, Clermont-Ferrand, France
Andrea Borgia lnstituto Nazionale di Geofisica, Rome, Italy
Abstract. Experiments wereconducted to studythe spreading of volcanicconstructs. Volcanoesare simulatedby a sandcone,andthe volcanicsubstratum is simulatedby a sandlayer(brittlesubstratum) overlyinga siliconelayer(ductilesubstratum). Similarity conditionsbetweennaturalvolcanoesand experimental prototypesled to the definition of dimensionless H numbers.Experiments determineH valueswhichpredictwhether or not spreading takesplace.Of particular importance aretheratiobetweenthe thicknessof the brittle substratum and the heightof the volcano(H2) and the brittle/ductileratioof the substratum (H3). H 2 indicatesthatthe volcanomustbe large
enoughto "break"thesubstratum beforespreading occurs, whereas H3 controls the styleof deformation. Duringspreading, thesedimensionless numbers change withtime, reaching valuesthattendtowardthoseobserved for stableconfigurations. Experimental valuesarecompared withthosefromwell-constrained naturalexamples. It is foundthat an essential requirement for volcanicspreading is thepresence of a low-viscosity layer within the substratum. Flow of the weak layerawayfrom the excessload is responsible
for thespreading. Theoverlying edificedisplays radialintersecting grabens, dueto concentric stretching, dissected summitareas;concentric zonesof thrustsandfolds form in the substratum aroundthe edifice,anddiapirsof the ductilesubstratum rise within
the fault zones.
Mars [Borgiaet al., 1990].Someof theseauthorsshow thatthin-skinned shortening, dueto foldingandthrusting,
Introduction
The processof volcanic spreadingis now being around the base of these volcanoesis compensatedby recognized as one of the mostrelevantin controllingthe sagging of theedificesandsummitextension. A weakbasal slow-ratelong-termstructuralandmagmaticevolutionof layerdecouples the deformation of the volcanoandof its volcanic edifices [cf. Delaney, 1992; Kerr, 1994; Borgia, 1994]. A volcanoof sufficientsize inducesstressesthat
immediate
de l/ries et al., 1993], PohsVolcano in CostaRica [Borgia et al., 1990], variousvolcanoesof Sumatraand Java [van Bernelien, 1956], Etna Volcano in Italy [Borgia et al., 1992], Marsili Seamountin the ThyrrenianBasin [Argnani
volcanoes.
et al., 1993],theCappadocia VolcanicComplexin Turkey [Pasquar•et al., 1993],the MaunaLoa-KilaueaVolcanic system[Borgia 1990, 1994; Borgia and Treyes,1992; Clagueand Denlinger,1994], and the OlympusMons on
contribution to deformation, such as the Mauna Loa-
substratum from that of the crust.
Borgia[1994] usednumericalanalyses to showthattwo maydeformits substratum; in turn,thisdeformation feeds elements of volcanoesare of particular importancein back stresseswhich deform the edifice; both stressesand drivingthe process: (1) the weightof the edificeontothe deformationinfluencethe evolutionof magmaby varying substratumand (2) the long-term deformationof the the boundaryconditionsof magmaticsystems. intrusive complexes. In this work, we use threeIn orderof increasing size,volcanicspreading is inferred dimensional(3-D) scaleexperiments to studythe influence to be activeat Concepcion Volcanoin Nicaragua[van Wyk of the first of these elements on the structural evolution of
Ourexperiments donotmodeltheeffectof theintrusive complexes; theycannotbe usedasexactscaleanalogs of volcanoeswherethe intrusivecomplexesgive the dominant
Kilaueasystem[Borgia,1994]or theCappadocia Volcanic complex[Pasquar•etal., 1993].Experiments tomodelthis contribution arepresented by Merle et al. [1993] andMerle and Vendeville[1995]. In addition,our experimentsdo not model the effect of subsidence due to crustal flexure under
Copyright 1996bytheAmerican Geophysical Union.
the load of volcanic edifices. This effect is especially
Papernumber95JB03736.
important for largefastgrowingvolcanoes suchashotspot volcanoes[McGovernandSolomon,1993;Borgia, 1994].
0148-0227/96/95JB-03736509.00
13,805
13,806
MERLE AND BORGIA:EXPERIMENTSOF VOLCANIC SPREADING
Dt-
(21 l
Figure 1. Schematic representation of thevolcanic spreading process asshown fromexperiments. (a) Cross section of theinitialstage. (b)Cross section afterdeformation showing theflowof theweaklayer (in black),thefoldingandfaultingthevolcano,andthehorstandgrabenstructures withinthevolcano. (c)Topviewafterdeformation showing therelationship between structures (grabens andtriangular horsts anda concentric ridge)andthestrainpattern associated withthespreading process (radialdisplacement, concentric stretching in thevolcano, andradialshortening in thesubstratum surrounding thevolcano). In theseexperiments,we considerthe volcanic edifice as being cooled, and we do not take into account any contributionof magmaforcesto the destabilisation process. Even though these approximationsmay appear to be an oversimplification of reality, we show that complex structuresdevelopwithin and aroundthe volcanoand that these structures
can be identified
both in the field and in
remote sensingimages.
Scaling The
scale model
of the volcano
is intended
to be
geometrically,kinematically and dynamically similar to
naturalvolcanoes. We usethestandard similarityconditions asexplained, for instance, byHubbert[1937]andRamberg [1981]. The model volcano(Figure 1) consistsof a cone constructedby pouringdry sandonto a substratum.Since we want to investigatethe effect of the load of the volcano only, the cone has no viscous or ductile core. The
substratum is a brittle upperlayer, dry sand,and a weak lower layer, viscoussilicone. Principalgeometricvariables(Figure1 andTable 1) are the height (H) and radius (R) of the sand cone, and the
depthto (D) andthethickness of (T) theweaklowerlayer. Of course,D is alsothethickness of the sandlayerin the substratum. Materialpropertyvariablesare the densitiesof
MERLE AND BORGIA: EXPERIMENTSOF VOLCANIC SPREADING
13,807
Table l. Average Geometricand MechanicalVariablesin Real and AnalogueVolcanoes Variable
Definition
Value
Dimensions
Field
Experiment:
H R D T
thickness of volcanic cone radius of volcanic cone thickness of brittle substratum thickness of weak substratum
1.2-3.0x103 5-20x103 0-10 '• 102-103
5x10-2•>2.3x10 -2 8.5x10-2•> 12.5x10 -2 5x10-3•>5x10 -3 5xl 0-3-•2.5x10 -•
m m m m
p•, p, t g (I)
densityof volcanic cone densityof substratum timespanfor deformation viscosity of weaksubstratum angleof internalfriction
2.5-2.8x103 2.0-2.5x103 10•2 10•7 30ø
1.4x103 1.4x103
kg m 3 kg m-3
3.5x104 2X104
s Pa s
g
gravity acceleration
9.8
30 ø
9.8
m s-2
The experimentalvalues are measuredat the start and end of the experimentsof figures 2c-2d.
One other dimensionless number must be related to the the sandvolcano(Pv)and of the substratum (Ps),the angle of internal friction of the brittle material ((I)), and the difference in density between the volcano and its viscosity(g) of the weaklayer (Table 1). The only forceis substratum: gravity (g). The time span in which most of the (4) deformationtakesplace is t. densiO; of substratum p• Thereforeaccordingto theBuckingham-11 theorem,there are 10 variablesminus3 dimensions equalto 7 independent Gravity is balanced in the sand by forces that resist dimensionlessnumbers(Table 2) that need to maintain the failure, in the siliconeby inertial and viscousforces.Thus, samevaluebetweenthe field andthe experimentalsystems the other three dimensionless numbers should be ratios of to guaranteesimilarity. theseforces.Observingthat a reasonablescalingparameter Of these,three numbersare obviouslythe geometric for the velocity of the processcould be the ratio between ratios of the system: the thicknessof the weak layer and the time spanin which
1-[4 = densiO; ofvolcano =P•.•_.
Hi=radius height of volcano =H of volcano R '
(1)
most of the deformation occurs (T/t), these numbers are
11.s =gravitational force =p•gHt (5) viscousforce 1-i2 =thickness ofbrittle layer =D, height of volcano H
1_i3 =thickness ofbrittle layer =D. thicknessof weak layer T
(2) I-I6=
failure resistanceforce viscousforce
=
2tanrI)p,g(H+D)t 31Lt
=tan(I)(•l-Is( 1+112) +1) (6)
(3)
Table 2. Average11Dimensionless Numbersin the Field andExperiments Dimensionless
Definition
Value
Variable
111 1-I2 1-I3 1-I4 11s 1I6
117
height/radiusof volcano brittle substratum/height of volcano brittle/weaksubstratum volcano/substratum density gravitational/viscous forces frictional/viscousforces
inertial/viscous forces
• tan(I) ,
Field
Experiment
0.15-0.2 0-1.5 0-15 1-1.4 790 82-327
0.58-->0.18
10©
10-12
0.1-->0.22 1-->2 1
1200 160
13,808
MERLEANDBORGIA:EXPERIMENTS OFVOLCANICSPREADING
inertial force_ P•T2 viscousforce
(7)
gt
achievevaluesof II 7 smallerthan 10-16 , because the experiments will lastfor toolonga timespan(t>106 S).
Still, to a very goodapproximation, the inertialforcesare which is the Reynolds number. In (5)-(7) the gravity, negligiblewith respectto the viscousforces.Thus this Accordingly, inertial, and viscousforcesper unit area scalerespectively numbermay receiveno furtherconsideration. to maintain similarity only the first five numbers need to as haveexperimentalvaluescloseto thoseof real volcanoes
gravitational force= p,gH,
inertial force =P'(T/t)2 - psT T t2
(8)
(Table 2).
(9)
Materials
of the Experiments
We usedry sandas an analogfor brittlerocks.The sand is a cohesionless granularmaterialthat fails accordingto viscous force - g(T/t) =g_.p__. (10) theNavier-Coulombcriterionof brittlefailure. The angleof T t frictioncI)is about30ø. It is considered a goodanalogfor The failure resistanceforce per unit area (failure stress, brittle rocks and has been used as such in many previous z) is estimatedvia the Coulomb-Navierfailure criterion experiments[e.g., Faugbreand Brun, 1984; I/endevilleet with no cohesion[Hubbert and Rubey, 1959]' a/., 1987; Merle and Vendeville,1995). We use siliconeto model the weak layer in the substratum.Silicone is a
a:= tanrD({J•{53),
(11)
Newtonian fluid with a viscosity of about104 Pa s. It is commonlyused to model the low-viscositystrata of
'where (• and {53are the maximumand minimumprincipal sedimentarysections[Cobbold,1993]. stressesgiven by The ratio betweenthe heightof our modelsand of real
(•,= p•g(H+O)
(12)
volcanoes (H*) is about1.6x10-s(1 cmrepresents 600 m),
whereasthe ratio betweenthe densitiesin experimentsand and since(•3 is equal to the stressdue to volcanicloading nature(p*) is about0.56. Sincegravityis the samebothin plus the stressdue to viscousdeformation, experiments and reality (g*=l), then,to a first orderof
•
it
=5-p'g(+D)-7'
(•3)
approximation, the stressratiomay be calculatedfrom
c•*=p*g*H•10 -•s.
(14)
The geometricratiosusedin our experiments(Tables 1 and 2) have values that model real volcanoesthat are 1-3 Thismeansthatourexperimental models areabout10s km high and 5-20 km in radius(11•=0.15-0.2).They overlie times weaker than real volcanoes. a substratumwith a weak layer at depthsrangingfrom 0 to 1500m (112--0-1.5) and 100 to 1000 m in thickness Experimental Procedure (Fi3=0.1-15).
During the experiments,the rate of spreadingdecreases In nature,114is on averagelargerthan 1. Thus,in some exponentially with time and most of the deformationis experiments, cast-iron powder is added to the sand to achieved in about 10 hours.The progressiveevolutionof increasethe densityof the volcanoprototypewith respect model deformation is recorded by overhead time-lapse to that of the substratum. As will be described in the following section,this ratio influencesthe complexityand the rate of deformationof the system,but it doesnot affect significantlythe type of deformation. The ratios of gravity to viscous forces, 115, and of fi'ictional to viscousforces, FI6, cannot be neglected,and they must maintain values in the experimentas close as possibleto the real ones.However, from the definition of H 6 given in (7) we observe that this number can be expressedas a function of FIs , 112,and cI). Thus this conditionis implicitly satisfiedoncethe otherquantitiesare equal.
Finally,the very smallvalueof 117( 10'2ø,Table2) indicatesthat in nature, inertial forces are negligible with respectto viscousforces.In our experiments,FI7 is about
10-12(Table2) andcannotreachtheextremelylow natural values. In fact, even using materials of very unusual
photographyof the model top surface.After the end of each experiment, models are serially sectionedand photographed.
Four differenttypesof experiments are described:the first is a sand cone with a substratum that has no weak
ductilelayer (only the brittle layer is present),the second is a cone with a substratumcomposedof a brittle layer overlyinga weakductilelayer,the thirdis like the second but is buttressedalong two edgesof the experimentalbox, andthefourthhasonly theductilelayer(no brittlelayeris present).
Experimental
Results
Substratum With a Brittle Layer Only The first experimenthasno siliconelayer at the baseof
properties, for instance, of highviscosity (}.t>106pa s) and the substratum(experiment0, seeTable 3), equivalentto ) of high low density(p,•oo layerin thesubstratum (T103years) foranedificetogrow.Ontheotherhand,for muchlargerviscosities (10•9Pa s) thetimeof deformation
then from (5), we obtain
(>106years) becomes longer thanthelifespan ofvolcanoes t=
Ils g
pgH
where1-Is is obtainedfrom the experiments.
(15)
[Shaw, 1987], and erosionwill smooththe topographic relief well beforespreading becomes significant. In conclusion, the interaction of dimensionless numbers
controllingthe spreading processis complex.A "ruleof Thus a first-order calculation indicates that in actual thumb,"however,is thatthe spreading rateis highfor a volcanoes the timescale for deformation is directly small1-I2 andH.•anda large114andII s.
13,816
MERLE AND BORGIA: EXPERIMENTSOF VOLCANIC SPREADING
correspond to volcanic constructs showing stable configuration.Once the collapseof the edifice starts,these two dimensionless numbers increase, and the deformation
c
l,sagging of the to the formation of a number of intersectingradial leaf undeformed cone;(b) H3=1-2,formation of a shieldedifice grabensand wedge horststhat is inverselyproportionalto with a concentricridge;and (c) 113
