JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 97, NO. B13, PAGES 19,729-19,737, DECEMBER
10, 1992
SolidificationandMorphologyof SubmarineLavas'
A Dependenceon ExtrusionRate
Ross W. GRIFFrms
ResearchSchoolof Earth Sciences,
AustralianNational University,Canberra
JONATHAN H. Fn, rK
GeologyDepartment,ArizonaStateUniversity,Tempe
Theresultsof recentlaboratoryexperiments
withwax extrudedbeneathrelativelycoldwatermaybe extrapolated
to predictthesurfacemorphology
of submarine
lavasasa functionof the extrusion
rateandmelt viscosity.The
experiments
withsolidifying
waxindicated
thatthesurface
morphology
wascontrolled
byasingleparameter,
theratio
of thetimetakenfor thesurfaceto solidify,anda timescalefor lateralflow. For submarine
basaltsa solutionof the
coolingproblem(whichisdominated
byconduction
in thelavabutconvective
heattransferin thewater)andestimates
of lava viscosities
placethisparameterwithintheempiricallydetermined
"pillowing"regimeovera widerangeof
extrusionrates.This resultis consistent
with the observation
thatpillow basaltsare the mostcommonproductsof
submarine
eruptions.
Smoothersurfaces
corresponding
to thevarioustypesof submarine
sheetflowsarepredicted
for sufficientlyrapidextrusions
of basalticmagma.Stillhighereruptionratesin regionsof low topographic
relief may
producesubmarine
lavalakes.Minimumemplacement
timescanbecalculated
for submarine
volcanicconstructs
of
a singlelava flow type.
INTRODUCTION
Submarine basalt flows are the most common volcanic rocks on
solidifyingcruston the advanceof lava flowsanddomes,submitted
to Journalof Fluid Mechanics,1992].Thusthesurfacecoolingand
development
of thesolidcrustis a criticalprocess
in determiningthe
surfacemorphologyof lavasand,in somecases,may leadto crustal
earth.However, becausethe eruptionof submarinelavashasnever
beendirectlyobserved,ourabilityto inferemplacement
conditions control of the flow's advance.
from their morphologyis quitelimited.Despiterecentconcerted
In a seriesof laboratoryexperiments
withpolyethyleneglycolwax
effortsto catchdeep-seaeruptionsin action[e.g.,Chadwicket al., extruded onto the base of a tank filled with cold water, Fink and
1991;Haytnoneta/., 1991],the likelihoodof beingableto make Griffiths [ 1990, 1992] showedthat formationof solidcrustled to a
accurate
measurements
withpresentlyavailabletechnology
issmall. numberof typesof surfacemorphologyanalogousto thoseseenon
This situationcontrastswith that for subaerialflows, whosemorlava flows (Figure 1). Theseincludedleveesaroundflow margins,
phologyhasbeenrelatedquantitatively
to bothlavarheologyand surfacefolds similar in appearanceto thosefoundon ropy basalts,
effusionratein severalstudies[e.g.,Hulme,1974;FinkandFletcher, striatedsurfacesseparatinglargesmoothplatesalongrifting zones,
1978; Borgia et al., 1983; Baloga and Pieri, 1986; Rowlandand
andsmallbulbousstructures
similartopillow basalts(Figure2). Fink
Walker, 1990]. One way to overcomethis limitationto our underand Griffiths also found that the type of surfacemorphologydomistandingis to usetheoreticaland laboratorymodelsto relatelava
nantin eachexperimentdependedin a systematicmanneron therate
morphology
to effusionrate andrheology.Thisis theapproach
of
of extrusionandtherateof formationof crust:themostrapidcooling
thispaper.
and solidificationled to "pillow" morphology,whereas"rifting,"
When lava is extrudedontothe Earth's surfaceor the seafloor,it
"folding,"and"levees"occurredfor progressively
slowersolidificaspreadslaterallyunderthe influenceof gravity.It alsobeginsto
tion ratesor more rapid extrusionrates.At the lowest coolingrates,
solidify as a result of radiative or convectiveheat loss from its
no crustat all formed within the durationof an experiment.
surface.
By observation
weknowthatathinlayeratthesurface
ofthe
A theoreticalpredictionof the kind of surfacemorphologyto be
lava can become a solid crust within minutes in the case of subaerial
expectedunderprescribedlaboratoryor field conditions
is currently
eruptionsor within a few secondswhenthelava is underwater.The
beyondour capabilities;it wouldrequirecompletesolutionsfor the
timefor formationof thefirstsolidis determined
by theeruption coupledtemperatureand flow fields taking into accounttemperatemperatureand rate of heat loss from the surface,and thesesame
ture-dependentrheology,solidification,and the mechanicsof the
parameters
determinethesubsequent
rateof thickeningof thesolid
crust.Various attemptshave been made to predict aspectsof the
crust.The propertiesof the crust,in turn,controlits deformationin
overallspreading
of lavaflows[Walker,1973;Malin, 1980;Huppert
response
to stresses
appliedby the motionof the underlyingmelt
eta/., 1982; Blake, 1990], some consideringonly the thermal
[e.g.,Fink and Fletcher,1978].Undersomeconditions
(namely
problemin whichcoolingandsolidificationthroughoutmuchof the
rapidsolidification,
smallextrusion
rates,or highmeltviscosities)
depth of the lava column is assumedto bring the flow to a halt
thecrustcanalsoexercisesomedegreeof controloverthespeedof
[Pinkerton,1987; Crisp and Baloga, 1990]. However, thesepapers
advanceof the flow front [R. W. Griffiths andJ. H. Fink, Effectsof
have not addressedthe dynamicaleffectsof the cruston the overall
flow nor the relationshipbetweendeformationof the crustand the
Copyright1992by the AmericanGeophysical
Union.
underlyingflow.
In conjunctionwith theirlaboratoryexperiments,
F inkandGriffiths
Papernumber92JB01594.
0148-0227/92/92JB-01594505.00
[1990] employedan alternativeapproach.On the basisof a dimen19,729
19,730
GRIFFrrHS
ANDFINK:SUBMARINE
LAVAMORPHOLOGY
flow would have in the absenceof solid crust.In the experimentsthe
flowof wax withoutcrustwouldhavebeengoverned
by a balance
betweengravity and viscousstresses.
Equivalently,• is the lateral
distancefrom the vent,measuredin flow depths,at which solidcrust
is predictedto appear.Evaluationof this parameterfor each wax
experimentusing a theoreticalpredictionfor the surfacecooling,
alongwith the observationsof morphology,enabledempiricalvaluesof ß to be found at the variousmorphologicaltransitions:when
•>50, the wax flow reached the walls of the box without crust
appearing;
at25<•<50, solidformedneartheflowfromandcreated
levees which had to be broken or overridden before the flow could
advance;at 10<•<25 therewere cross-stream-oriented
folds similar
Fig.la. Transverse
folding
onflowfroma pointsource
(widthoftankis 30
• .....
:-
.;
........ . .... . ......... >½;•.•
........
...:..•...: ..............
.,..,,•j•-;;:;
.....;. ....::•:•. •..;,. •.
tothoseonropypahoehoeflows;at3<•<10 thewaxcrustdeveloped
platesandrift-like fractures,withmoltenwaxexposedalongtherifts
ultimately freezing and addingto the rigid surfaceplatesthat were
movingapart;and at W<3, crustdevelopedrapidlyat the vent and
spreadingproceededthroughlargenumbersof bulbousoutgrowths,
or "pillows."
The transitionsbetweendominantmorphologicaltypesoccurred
atapproximately
thesamevaluesof •Pforbothradialspreading
from
a smallhole[Fink andGriffiths,1990]andtwo-directional
spreading
from a narrow slit [Fink and Gri•ths, 1992] (with spreadingrate
appropriately
scaledfor eachcase).In mostrespects
themorphology
was also independentof the roughnessand slope of the base,
althoughfor a longnarrowslit(a line source)the"pillow"regimewas
observedonlywith a roughbase.With a smoothbase,"pillows"were
replacedin linear (two-directional)spreadingby an extensionof the
"rifting" regime, presumablybecausethe crust did not grip the
smoothbasenearthe flow front andthe two largeplatescouldslide
away on eachsideof the line sourcewithoutdecelerating.A gently
slopingbase(uptosixdegrees)gaveapreferreddirectionof flow, but
the dominanttype of surfacemorphologywasotherwiselittle affected.Thusthelaboratoryexperimentsshoweda reasonablyrobust
sequenceof transitionsbetweensurfacemorphologies,
transitions
whicharedescribedby valuesof a singleparameterrelatingcooling
rateto spreadingrate.The dependence
of morphologyon theparameter •P alone(at least for a givenmaterial)showsthat the surface
morphology,and thekind of behavioroccurringnearthe flow front,
Fig. lb. "•ng"
or Cate-lib spr½•ingon an ½x•ion •om a •n½source can be described in terms of the sourceconditions, extrusion rate, and
wh•e •sifion is in•c•
by •ows (t•k is 20 cmfromtopto
surfaceheat flux, with some influenceof basaltopography.
The laboratory observationsof surfacemorphologyprovide a
....................
?:;•
•:-•?•
;;•:•,•
...... ::...::,..
.•.•
..........
:.•:•...:
..•
............
..........
½:.L:•..-...•.:.•.•:;:•:%.
..............
s•:..:.s
...........
•?•::•:::,•½;::•.
-:•:;::½:½•--•:,.•:.•.
.;•,•.
.....';.•-•---•------------•--•...•..,•:..,"
-.-........•..:
.......
,.:...
.... --------------••
.......•..........•.,:•:
.....•--<•
Fig.lc.Sideviewofspr½•i•gfroma•½ soure•rough"½low"formation
½-cm-•ck flow movedtoward•e camera).
Fig. 1. •oto•aphs of t•½½mo•hologic
½n½
glycolwax uMcr coldwater,from•½
[•90,
•9•].
potentially powerful tool for interpretationof the eraplacement
conditionsfor lava flows. The experimentshave been carriedout
with convectivecoolingof wax beneathcold water, and the results
shouldbe of direct relevanceto submarinelava eruptions.In this
paperwe evaluatetheparameter•Pandmaketentativepredictions
of
flowmorphologyfor submarinebasalticlavas.Thesepredictions
are
functionsof the volumeflux, eruptiontemperature,andlava viscos-
ityatthe
vent.
However,
ifweconsider
only
mid-ocean
ridge
basalts,
therangeof venttemperatures
andviscosities
is likelyto bequite
limited,andtheextrusionrateis left asthemaindeterminant
of flow
morphology.
Thisopensthepossibility
thatobserved
morphology
maybeusedtoplaceconstraints
onvariations
of extrusion
ratealong
a ridge.
sionalanalysisandanassumption
of dynamicsimilarity,theyargued
SPREADING OF VISCOUS LAVA
thatthesurfacemorphology
depends
primarilyontherateof formation of crust relative
to the rate of lateral flow. The behavior can be
characterizedfor eachexperimentby a singledimensionless
parameter, •, which they definedas the ratio of the time takenfor the
surfaceof the wax to solidify and a time scale for horizontal
advection,the latterbeinga measurementof thetime requiredfor an
elementof extrudedwax to travel a distanceequal to the depththe
The depthandlateralvelocityof lava neara vent,with or withore
cooling,are determinedby the sourcevolumeflux Q, sourcegeometry, lava theology,gravitationalforce,andbasetopography.Cooling as a result of heat loss from the surfaceor baseof the lava
influencesthespreadingby alteringtherheologyof partsof theflow.
If thereis noverticaladvectivetransportof heatwithinthelava (i.e.,
GRIFF1THS
ANDFINK:SUBI•IARINE
LAVAMOm'HOLOO¾
Fig.2a. ALVIN viewof basaltpillowswith spreading
cracks(iqdividualpillowsapproximately
1m across)fromtheEastPacificRise.
Photocourtesyof RobertEmbley,NOAA.
Fig.2b. Archaean
pillowsfromsouthern
Ontarioshowing
darkglassyrinds.Pennearbottomof largestpillowfor scale.Photocourtesy
of StephenJ. Reynolds,ArizonaStateUniversity.
19,731
19,732
GmmT•S ANDFINK:SUBMARINE
L^v^ MORPnOLOG¾
no thermal convectionor shear-generated
turbulence),coolingis
confined to thin conductive boundary layers: a thin solid crust
develops.In this paperwe consideronly laminar(or near-laminar)
flows: thosehaving viscositiessmall enoughand velocitieslarge
enoughfor a Reynoldsnumberto be greaterthan about100 are
generallyunstableor turbulent, and conductionis not the sole
mechanismfor heat transportto their surfaces.Becausesolidification commencesmuchmore slowly at the basethanat the exposed
surfaceof a lava,we alsoneglectanyeffectsof basalcoolingonthe
overallflow or on developmentof the surfacecrustanditsmorphology. Thermalconvectionin the lava cannotcommence
withinthe
extremelyshorttimesrequiredfor a solid surfaceskinto form in
SURFACECOOLING AND SOLIDIFICATION
SurfaceFluxes
An analysisof the coolingof lava, assumingthat verticalheat
transferwithin the lava is by conductionandthatthe surfaceflux is
determinedby turbulentnaturalconvectionin the environment,is
summarizedby Fink and Griffiths[1990]. Convectivetransportis
expected
tobethedominantmechanism
forheatlossfromsubmarine
eruptions.However,thereis alsoa smallradiativetransfer,andfor
completeness
we includeestimates
of thisflux.Thusthesurfaceflux
F is givenby thesumof theconvective
flux Fcandtheradiativeflux
Ft.
The
magma
motion
is
assumed
to
be laminar (at leastnear its
contact with water.
surface),andwe showlaterthatthereis noneedto considerthermal
Assumingthatthe isothermalmelt beneaththesurfaceboundary
convectionwithin the magma.
layercanbe satisfactorilydescribedby a uniformviscosity,therate
of formationof surfacecrustcanbe comparedto therateof spreading
that would prevail in the absenceof cooling. For a flow with
Consideranelementof lavaextrudedat a timet=0 andtemperature
T1undera deeplayer of seawaterat temperature
Ta. At extremely
small
times
after
any
given
element
of
melt
comes
into contactwith
Newtonianrheologyand a very smallReynoldsnumberextruded
the
seawater,
a
conductive
thermal
boundary
layer
buildsup in the
ontoa horizontalplane,scalesfor thedepthH andvelocityU of the
water
adjacent
to
the
lava
surface
until
it
becomes
unstableandis
flow [Fink and Griffiths,1990] are,for radialspreading
froma point
sweptaway by convection.Using a boundarylayer analysis(and
source,
assumingsingle-phaseflow) it is straightforward
to showthat this
H- (pvQ/gAp)
TM,
U- (gApQ/pv)
•/2
(la)
and, for a line (slit) source,
H- (pvq/gAp)•r3,
surface
heatflux. However,
attimesmuchgreater
than10-2s,only
U- (gApq2/pv)
it3.
(lb)
The motionis drivenby the gravitationalaccelerationg actingon the
densitydifferenceAp=p-pa, wherep is the densityof thelava and
Pa is density of the environment.Flow is retardedby stresses
associatedwith the kinematic viscosityv (v--q/p, where •1 is the
dynamicviscosity).In (la), Q is the volumeflux from the vent,
whereasin (1b), q is thevolumeflux perunitlengthof thelinesource.
Constantsof proportionalityarenot shownherebutwill be of order
one; their precise values are not needed,as the dimensionless
parameterwhichwe will formusingtheabovescales
mustin anycase
be evaluatedempiricallyat the variousmorphological
transitions,
usinglaboratoryanalogexperimentsor field data.
The time for advectionof lava througha distanceequalto one
depthscale,ta=H/U, is foundfrom (1). Theratioof solidificationand
advectivetime scales•=ts/ta (whichcanbe thoughtof astheinverse
of a "solidification Peclet number," instead of the usual "heat flow
• = (gAp/pv)3/4Q1/4ts
a temporallysmoothed
flux isrequired.Increased
surfaceslopeand
roughness
shouldreduceboththeboundarylayertimescaleandthe
magnitudeof the fluctuations
in heatflux.
The convectiveflux Fcestablished
for convectionatlargeRayleigh
numbersin water,with smalltemperaturedifferencesandnoboiling,
is given by
Fc= J(Tc-Ta)4/3,
J = paCaT
(gOtalCa2/Va)
1/3,
(3)
whereTc(t) is thelava temperatureat thecontactsurface,Ota,ra, Va,
Pa, and Caare the thermal expansioncoefficient,diffusivity,kinematic viscosity,density,and specificheat(at constantpressure)of
the convectingfluid, and), is a constantwhosevalueis closeto 0.1
[Turner,1973;HuppertandSparks,1988].Themolecularproperties
of water are almostconstantin all existingtestsof (3). However,at
hightemperatures,
seawaterexhibitsa strongdependence
of thermal
expansioncoefficienton temperature[Bischoffand Rosenbauer,
1985]:for the seawaterat mid-oceanridges(3.2% to 3.5% salinity
and100-300bar),otvariesfrom1.5xl0--4attheambient
temperature
(0ø-10øC)
[Sverdrup,
1945]to 1.0x10
-2at350ø-420
ø(depending
on
Peclet number") then becomes
Radialspreading
boundary
layertimescale
isof order10-2s(taking
seawater
propertiesin Table 1). This is alsothe timescalefor the boundarylayer to
reform. Boundarylayer intermittence
resultsin fluctuationsof the
(2a) pressure).At conditionsclose to the critical point of seawater
(approximately
400øC,300 bar)theexpansion
coefficientbecomes
even larger. It is therefore important to make allowance for a
nonlineardensity-temperature
relation.
In orderto estimateW for a givenflow it is necessary
to evaluate
Convectiveheattransferfrom submarinelavasiscontrolledby the
the time tsrequiredfor the surfaceof thelavato coolfrom thevent dynamicsof a thin unstableboundarylayerin thewater(aswell as
temperatureto thesolidificationtemperature.
Thetimetsisusedhere conductionthrougha thin boundarylayer in the lava). As far aswe
astheprimaryindicatorof thedevelopment
of crustduringtheearly are aware, the effects of stronglynonlineardensity-temperature
stagesof solidificationof flow from thosepositionswherenewmelt relationson this form of convectionhave not beenparameterized.
is exposedto theenvironment.At muchgreatertimeswhenthe lava However,we arguethattheconvectiveheatflux dependson thenet
surfaceis farther from the vent and its temperaturehasapproached buoyancyin the boundarylayer and thereforeon an "effective"
the ambienttemperature,the crustthicknessbecomesinsensitiveto
averagevalue for Ota,which might be definedsuchthat Ota(Tc-Ta)=
thesurfacesolidificationtimeandisinsteadcontrolledlargelyby the &llo•Ot(T)(T-Ta)dz,
where
z=0atthecontact
surface
and15
isthe
thicknessof thethermalboundarylayer.However,we proceedunder thicknessof the unstableboundarylayer. The bestjustifiable aptheassumption
thatcrustmorphology,suchaspillowsandtransverse proximation for the effective Otais simply Ota=Ot(T*),where
folds,is determinedby the early stagesof developmentof thecrust T*=(Tc+Ta)/2. For the early stagesof coolingconsideredin this
and that the structureof any part of the flow is setlong beforethat paperwe will seethatT* variesfrom 350øCto 550øC,a rangeover
portionof the surfacehastime to coolto the ambienttemperature. whichtheminimum
expansion
coefficient
is Ota=3X10
-3,andthe
Linesource
• = (gAp/pv)2/3ql/3ts
.
(2b)
GRIF2rlTHS
ANDFINK:SUBMARINE
L^v^ MOReHOt.
Oa¾
19,733
TABLE 1. Values of Parametersfor Seawaterand BasalticLavasUsedin the Computationof
CoolingandTime Scalesfor LateralFlow of theLava
Parameter
Description
Value
Reference
Seawaterat Depths1000-4000m
Xla,Pas
Va,m2s'l,
Ca,Jkg'lK'1
r•a,m2s'1
Pt,kgm-3
dynamic
viscosity
kinematic
viscosity
specific
heat
thermal
diffusivity
density
lx10-3
lx10-6
4.0x103
lx10-7
1.00xl03
otat ambientT, K-1
ova
at -400øC,K-1
thermalexpansion
1.5x10
-4
-10-2
Ta, K
temperature
280
[Fofonoff,1962]
[Weastet al., 1989]
[Fofonoff,1962]
[Sverdrup,1945]
[BischoffandRosenbauer,1985]
[Diet•ch et al., 1980]
xl,Pas
102-104
[Hall, 1987]
v, m2s-1
0.04-4
Balsaltic
[Dietrich et al., 1980]
Lava
c,Jkg-1K-1
1.2x103
• m2 s-1
5x10-7
p,kgm-3
2.6x103
Ti, K
Ts, K
•
-1423
1003
0.9
emissivity
[Turcotteand Schubert,1982]
[WilliamsandMcBirney,1979]
[Hall, 1987]
(estimatefromMacdonald[1972])
[Ryanand Sammis,1981]
value assumed
The solidificationterrq•eratureTs is assumedto be the glasstransition.
maximumisof order10-1,for whicha morerepresentative
valueis
tta=0.01[BischoffandRosenbauer,1985].
An estimateof the radiative flux Fr which will be sufficientfor our
purposesis
Fr = ec•(Tc
4- Ta4),
(4)
where c• is the Boltzmann constantand •; is the emissivityof the
surface.Stefan'slaw (4) may tendto overestimatetheradiativeflux,
where somefraction of the radiationat long infraredwavelengths
will be absorbedwithin the thin conductivethermalboundarylayer
in the water and thereforeleft to be carried away as a part of the
convectiveflux Fc. However, most of the radiationpenetratesbe-
The problemof findingthetemperaturein thelavacanbereduced,
usingstandard
techniques,
tosolutionof anintegralequation[Carslaw
and Jaeger, 1959, p. 76]. The equationcanbe transformed
into
.._
-1_•.•l0tF(3*)
e-Z2/4•c(t-3')
d3*'
(5a)
T(z,t)
-T1
pc0c•)l/2
t•-3*
wherez is thedistancefrom thecontactsurface,and3.is a dummy
variable.In our casethe time-dependentsurfaceflux is
F(t) = eo[Tc(t)n- Ta4] + J[Tc(t)- Ta]n/3,
(5b)
wherep, c, and•carethedensity,specificheat,andthermaldiffusivity
ofthelava(values
areshown
inTable1),andTc=T(z=0).
Thedepth
yondtheboundary
layer(athickness
of-3xl0 -2mm)andaddstothe ofisothermscanbe tracedasfunctionsof time. The contacttemperatotal flux.
ture is found by solvingwith z=0.
Griffithsand Fink [1992] presentexplicitvaluesfor the surface
The computeddepthsof severalisothermsare shownin Figure•
fluxescalculatedfrom (3) and(4) andcomparethemwith thefluxes for thecaseof a basaltextrudedat 1423 K (1150øC)into seawaterat
from lava surfacesin subaerialenvironments.
Theyrangeup to 5000 280 K (7øC),assuming
0ta--0.01.The isothermat 1373K(1100øC)is
kW m -2.
chosenasanestimateof thesolidustemperaturefor basalts;1003+15
K (730øC)is thebestavailablevaluefor theglasstransition
temperaThe ContactTemperature
ture[RyanandSaramis,1981];and1200Kis simplyanintermediate
temperature.When 1 s haselapsed,the solidusandglasstransition
The idealizedcoolingproblemto be solvedis thatin whichmelt
temperaturehave propagated2 mm and0.5 mm, respectively,into
of uniform temperatureTl is suddenlybroughtinto contactwith
the lava. After this time the depth of theseisothermscontinuesto
overlyingwaterat temperature
Ta.Conductionin thelavaismatched
increase
as t1/2.In Figure4 we plot the evolutionof thecontact
to the total surfaceflux, which in turn dependson the surface
temperaturefor the above extrusion. The influence of radiative
temperatureandambientconditions.No allowancefor latentheatis
transportissmall,contributingonlyapproximately
5 K tothesurfacd
requiredover the small time scalesof interest,since the rapid
coolingor decreasingby 4% the time takenfor Tc to reachthe glass
quenchingby waterleadsto vitrificationof thelava surfacewith no
transition. The resultsare not radically differentif 0tais variedby a
crystallization
(seebelow).A solutionfor the contacttemperature factor of 5.
Tc(t),assuming
onlyconvective
transferfromthesurface,wasgiven
in dimensionless
form by Fink and Griffiths[ 1990].Here we calcuSolidificationTimes
late explicitly both the contacttemperatureandthicknessof solidified crustunderconditionsappropriatefor submarineextrusionsof
Our model is basedon the hypothesisthat flow morphologyis
basalt.Given this limited range of conditions,the resultsare more largelydependenton therelativeratesof lateralspreadingandcrust
accessiblewhen expressedin dimensionalform.
formation.We have presentedevidence[Fink and Griffiths, 1990,
19,734
GRwFrms^NI)FzNs::
SUBM^RtS•.
L^v^ Mo•P•IOI•OG¾
solidustemperature
andbeforeit reachestheglasstransition.
Work
onthecrystallization
kineticsofigneousrocksandlunarbasalts[e.g.,
Uhlmannet al., 1979;Dowry,1980;Kirkpatrick,1981]indicatesthat
homogeneous
nucleationandgrowthof crystalsto significantvol-
umefractions
requires
minimum
timesof order103-104
safterthe
melt is cooledfrom its liquidus.Heterogeneous
nucleationdue to
preexistingcrystalsmay decreasethe time to reachlargecrystal
fractionsbutnotby morethananorderof magnitude.
Thussolidificationnear the quenchedsurfaceinvolvesonly the formationof
10.3
glass,a prediction
thatis confirmed
bytheglassysurfaces
foundon
freshsubmarine
basalts[e.g.,BallardandMoore,1977;Chadwicket
al., 1991]. Carryingthe calculations
of isothermdepthsto greater
timesthanshownin Figure3, we findthatlargevolumefractions
of
crystalsareunlikelytoformbeforethelavasolidifiestoa glass,until
the solidificationfront hasmigratedto depthsof 50-100 mm (or at
0-4
aroundI hourafterthatpartof thesurfacewasexposedtothewater).
This prediction,too, is consistent
with the thickness
(50-60 mm
[MooreandLockwood,1978]) of observedglasslayersontheouter
10-5
0.01
0.001
0.1
surfaceof pillow basalts.
1
We conclude that the best estimate of the solidification time, rs,
Time (s)
appropriate
for usein extrapolating
laboratory
observations
of surto submarine
extrusions
of basaltis thetimetaken
Fig. 3. Numericalsolutions
for the depthof threeisotherms
beneatha facemorphology
horizontalsurfaceof lavainitiallyatuniformtemperature
(T1=1423K) after for thelavasurfacetocoolto theglasstransition
temperature.
Foran
it isbroughtintocontactwithseawater
atTa=280K. Valuesusedforphysical extrusion
temperature
of 1423K, rs-0.07s.Thiscalculated
solidifiquantifies
aregivenin Table1. A slopeof 1/2is shownfor comparison.
cationtime alsoappearsto be consistent
with observations
of the
1992] thatan importantmeasureof therateof crustdevelopment
is
thetime takenfor the contactsurfaceto beginto solidify.This time
visible radiation from submarinelavas. The red glow from an
elementof lavapersists
for approximately
1-3s afterit isexposed
to
thewaterat theneckof a newpillow outgrowth[TepleyandMoore,
canbe usedto evaluatethedimensionless
parameter•, butwedonot
1974]. From independent
measurements
the last visiblered glow
imply thatflow morphologyis in someway established
at thetime
fromlavacorresponds
to a temperature
of around900 K [Williams
solidfirstbeginsto formin theearlystages
of anextrusion.
Timesat
andMcBirney,1979].Althoughwepredictthesurface
tocooltothis
whichthe submarinelava surfacepassesthroughits solidusandits
temperature
within0.2s,thevisibleradiation
isexpected
topenetrate
glasstransition
temperature
havebothbeendetermined,
andcorrefrom the hot interior througha coolerglassycrustfor sometime.
sponding
solutions
fordifferenteruption
temperatures
areplottedin Hence, the two observationsand the presentcooling model are
Figure5. Thetimerequiredfor coolingto theglasstransition
varies
consistent
if theglassis upto 1 mmthickbeforeit becomes
opaque.
from 0.14 s at T1=1600K to 0.04 s at Tl=1300 K. Over thisrangethe
surface
always
coolsbelowthelavasolidus
inlessthan10-2s.
PREDICTED SUBMARINE MORPHOLOGY
The calculatedcoolingtimesaremuchtoosmallfor anycrystallization to occurin the thin surfacelayer after it coolsbelow the
Having an estimatefor the surfacesolidification
time, ts, the
parameter
ß canbeevaluatedusingequations
(2a) and(2b).Comparisonof these values of ß with thosefor the laboratorywax
1400
'•
••
1 0ø -
solidus
ß
ß
ß
ß
,
....
,
....
1300
10'1
1200
transitio•
glass
1100
glass
1000
10'2
N\
solidus.
900
i i ii•1111
, ßiIllIll I .......I ß• •kl
ii
800
10'4
0.001
0.01
0.1
1
Time (s)
Fig. 4. Solutionsfor thetemperature
of thecontactsurfacebetweenlavaand
seawaterfor the caseT1=1423K, Ta=280 K, and0ta=0.01with bothradiative
and convectivetransport(solid curve),0ta=0.01and only convectiveflux
(dottedcurve), and 0ta=0.002with bothradiationand convectionfrom the
lava surface(dashedcurve).
10-3
10-4
1300
.
.
, t,
,
,
I
1500
i
ß
ß
1600
Eruptiontemperature(K)
Fig.5. Thetimeelapsed
forthesubmarine
lavasurface
tocooltothesolidus
andglasstransitiontemperature,
asfunctions
of theextrusion
temperature.
GRIFFITHS
ANDFINK:SUBMARINE
LAVAMORPHOLOGY
19,735
experiments
may thenhelpusto understand
thesurfacemorphology totalflux from thevent,sincebranchingof theflow will effectively
of the submarine lavas.
reducethelocalflow rate.Filmsandvideosof submarine
portionsof
In Figure 6 we have plotted the calculatedvalues of ß for Hawaiianbasaltflows thateruptedsubaerially[Tepleyand Moore,
submarinebasaltsas a functionof the melt viscosity,q, and the 1974;Moore, 1975;Sansome,
1990]showthatpillowformationand
extrusionrate,Q andq, for bothradialspreadingfrom a pointsource growthis associated
withlocalflowratesof between
0.1 to2.0m3s-1.
(Figure6a) andspreadingin twodirectionsfromaline source(Figure
Theseestimatesfor viscosityand flow rate imply that W<3 is
6b), respectively.Estimatesof the viscositiesof basaltsfall in the probablefor mostsubmarineeruptions(Figure6). That is, extraporange102to 104Pas (103-105poises)
[Macdonald,
1972;Hall, lation of the empirical morphologicalregimes for the wax analog
1987].Flowratesforindividualeruptions
atmid-ocean
ridgesarenot placessubmarinelava eruptionslargelyin the"pillow"regime.This
wellknown
butmaywellbeupto103m3s-1m-1(102km3d-1kin-l). result is consistentwith the observationthat pillow basaltsare
By way of comparison,theextrusionof basalticandesitemagmain commonat bothoceanridgesandintraplatevolcanoes[e.g.,Moore,
the 1991 eruptionof Hekla Volcanoin Iceland(a volcanicsystem 1975]. If the wax resultscan be carded over in sucha directmanner,
attributedto a mantle hotspotat the mid-oceanridge) rangedfrom wealsopredict
thateruptions
withlavaviscosities
lessthan103Pas
2000m3 s-1duringinitialfissure-fed
activityto 1-12m3s-1during andflowramsgreater
than10m3s-1mayformintobroadplate-like
the following 2 months when lava issuedfrom a single crater
sheetflows (the "rifting" regime)which wouldbe eithersmoothor
coveredwithmillimeter-scale,
flow-parallelstriations.
At evenhigher
(another
hotspot
volcano)
pouredoutupto 780m3 s-1of tholeiitic flow ratesor lower viscosities,transverse
foldsmay develop.Any
basalt[LipmanandBanks,1987].Magmaflow ratesrelevantto the reductionof flow rate due to branchingof theselow-temperature
formationof surfacemorphologymayoftenbemuchsmallerthanthe basalticflows will accentuatethetendencyto formpillows. Submarine lava lakes,describedin detailfrom sitesalongtheGalapagosRift
[Gudmundsson
et al., 1992]. The 1984 eruptionof Mauna Loa
1 02
ß
"
ß "'
....
I
"
" ......
I
........
[
........
I
........
I
'
[Ballard et al., 1979] and East Pacific Rise [Lonsdale, 1977a;
Ballard et al., 1981], and extensive flood basaltson the Hawaiian
' '''
arch[Holcombet al., 1988] may representflowsthat advancewith
relatively little crustformation.These would be analogousto the
"levee" or "no crust" regimesidentified in our experimentsand
levees or no crust
folding
1 01
wouklrequireextremelyhigheffusionrates(greater
than2000m3s-1
m-1or3000m3s-1forlavawithaviscosity
of 102Pasextruding
from
rifting
W
11=10
2Pas
1 0ø
pillows
10-1
()••••
1 '•"104 • /
10-2
10'3
.
I
I IIIIII
I
, . II1.11
I
I ..,,.,1
,
. , ,..,,1
10'1
I
. , ,11,.1
'
'
,
i . ..
101
Q (m3/s)
102
........
i
........
i
ß
.
......
i
........
i
',
....
i
.
•
i
ß ß
levees or no crust
folding
1 01
rifting
10ø
rl=102Pas •
riftingor pillows
10'1
104
10'2 -" .'•' ...... •
10 3
/
/
........
b
• ........
10-1
'
........
q (m2/s)
• ........
101
.
. , 111
1o3
a linear or point sourcevent,respectively).
If magmaissuesfromalongsubmarine
fissure,theflow rate,q,per
unit lengthof the fissureis smallerthanthetotal volumeflux, Q, and
Figure 6b indicatesa shift to smallerW values,placingsubmarine
basaltsstill farther into the "pillow" regime than indicatedby the
point sourcemodel. On the other hand, the experimentswith line
sourcesrevealedno "pillow" regime when a smoothbasewas used.
Thusif the surfacesof previoussubmarineflows aresmoothenough
sothatnew lobescan slideacrossthem,thenelongateventsat ridges
may initiallyproducesheetflowsat theexpenseof pillows.As was
concludedfor point sources,sufficientlyrapidsubmarine
eruptions
from longfissurescouldproduceflowswhosesurfacesaresmooth,
apart from centimeter-scaletransversefolds and millimeter-scale
striations.The folds may be confinedto a region near the flow
marginsif extrusionfrom the ventwasrapidbutof shortduration.
Subaerialdike-fedfissureeruptionsnormaflyare thermallyunstable,constrictingto one or a few point-sourceventswithin a few
hours[Delaney and Pollard, 1981]. This tendencywould be enhancedfor eruptionsinto cold seawater.Thus the experimentsin
whichwax extrudesfrom a fissureareprobablyonlyrelevantto the
early stagesof most submarineeruptions.
The resultsshownin Figure 6 can help explain distributionsof
flow typesdescribed
fromavarietyof submarine
environments
[e.g.,
Lonsdale, 1977a, b; van Andel and Ballard, 1979; Ballard et al.,
1979, 1981;BonattiandHarrison,1988].Forexample,Bonattiand
Harrison [1988] measuredthe areascoveredby sheetflows and
pillowsonmapsfrommanydifferentmid-oceanridgesegments
and
founda positivecorrelationbetweenthe proportionof sheetflow
coverageand the spreadingrate of the ridge.They suggested
that
sheetflow formationis favoredin lavasthathavehighereruption
temperaturesand extrusionrates and lower crystallinitiesand viscosities.Althoughit seemslikely thatsomeoftheseconditions
might
be associatedwith fast spreadingridges,Bonatti and Harrison
Fig. 6. Values of the dimensionless
solidificationtime W for submarine
basaltseruptedat T]=1423K asafunctionof extrusion
rateandmeltviscosity
for (a) radialspreading
fromapointsourceand(b) spreading
in twodirections
from a line source.Morphologicregimesindicatedby thelaboratoryexperi- [1988] could not determine which would most influence flow mormentsof Fink and Griffiths [1990, 1992] are shown.
phology. In contrast,the dimensionlessvariable, W, allows us to
19,736
Gram'ms ANDFINK:SUBMARINE
LAVAMO•I•OI. OG¾
calculatethe relative importanceof thesefour factors.For example,
if we assumethateruptiontemperatureandcrystallinitycontrollava
viscosity(v), as describedby variousexperimentalstudies[e.g.,
Shaw, 1969; Pinkerton and Stevenson,1992], then from Fink and
Griffiths[1990, equations(3) and (12)] we find thatthe distanceat
which surfacesolidificationfirst occurs(and hencethe flow mor-
phology)
variesas(Q3/v)I/8.Thusvolumeflowrateshould
havea
Acknowledgments.
We thankDerek CorriganandTony Beasleyfor constmctionof equipmentand assistance
with the experiments
and Robert
EmbleyandWilliamChadwickforhelpfuldiscussions
aboutsubmarine
flow
morphology.
Thepaperwasimprovedsignificantly
byreviewsfromWilliam
Chadwickand an anonymous
referee.Researchwassupported
by NASA
grantNAGW 529 from the PlanetaryGeologyandGeophysics
Program,
NationalScienceFoundation
grantEAR 9018216,anda visitingfellowship
from the AustralianNationalUniversity.
strongerinfluenceonmorphologythancrystallinityorlavaviscosity.
REFERENCES
Some of the most detailedmaps of submarinelava flows yet
compiledarefrom the summitregionof Axial Volcanoon theJuan Ballard,R.D., andJ.G.Moore,Photographic
Atlasof theMid-AtlanticRidge
Riff Valley, 114p., Springer-Verlag,
New York, 1977.
de FucaRidge[Embleyet al., 1990]. Thesemapsdistinguish
pillows
from lobate,ropy, andjumbled sheetflows. Althoughthereare no Ballard,R.D., R.T. Holcomb,and Tj.H. van Andel, The GalapagosRift at
86øW, 3, Sheetflows, collapsepits, andlava lakesof the rift valley,J.
observationsof the latterthreetypesduringformation,their appearGeophys.Res.,84, 5407-5422, 1979.
ancesuggests
thattheymaycorrespond
tothemorphologic
sequence Ballard,R.D., J. Francheteau,T. Juteau,C. Rangan,andW. Normark,East
seenin our experiments(with jumbled sheetflows equivalentto
PacificRiseat 21øN:The volcanic,tectonic,andhydrothermal
processes
leveedflows).Thus,if we assume
a lavaviscosity
of 102Pas,Figure
6a lets us infer that the flow typesrequirethe following extrusion
rates:
pillows
< 1 m3s-1
lobate sheet flows
<
1 m 3 s-1
<
100m3s-1
3000m3 s-1
( ropysheetflows
< 3000m3s-1
( jumbledsheetflows
100 m 3 s-1
of the centralaxis, Earth Planet. Sci. Lett., 55, 1-10, 1981.
Baloga, S.M., and D. Pieri, Time-dependent
profilesof lava flows. J.
Geophys.Res.,91, 9543-9552, 1986.
Bischoff, J.L., and R.J. Rosenbauer,An empirical equationof statefor
hydrothermal
seawater(3.2 percentNacl), AM J. Sci., 285, 725-763,
1985.
Blake, S., Viscoplasticmodelsof lava domes,in Lava Flowsand Domes:
Emplacement
Mechanismsand Hazard Implications,IAVCEI Proc.
Volcanol.,vol. 2, editedby J.H. Fink, pp. 88-128,SpringerVerlag,New
Theseestimatesconstitutethefirstattemptstoestablish
thephysical
York, 1990.
conditionsneededtoform specifictypesof submarine
lavamorphol- Bonatti, E., and C.G.A. Harrison,Eruptionstylesof basaltin oceanic
spreadingridgesandseamounts:
Effectof magmatemperature
andviscosogy. However, they are basedon a directextrapolationfrom wax
ity,
J.
Geophys.
Res.,
93,
2967-2980,
1988.
experiments,and their validity for lava, with its vastly different
mechanicalpropertiesand generallymore complexemplacement Borgia,A., S.R. Linneman,D. Spencer,L.D. Morales,and J.A. Brenes,
Dynamics
of lavaflow fronts,ArenalVolcano,CostaRica,J. Volcanol.
histories, must be further tested in future studiesthat include careful
Geotherm•Res., 19, 303-329, 1983.
examinationof lava flow structurefrom a variety of submarine Carslaw,H.S.,andJ.C.Jaeger,
Conduction
ofHeatinSolids,
2ndEd.,510pp.,
OxfordUniversityPress,New York, 1959.
settings.
Finally, for submarinevolcanicconstructs
madeof a singlelava Chadwick,W.W., R.W. Embley, and C.G. Fox, Evidencefor volcanic
eruptionon the southern
Juande FucaRidgebetween1981and 1987,
flow type, like pillow mounds,our modelingallowsus to calculate
Nature, 350, 416-418, 1991.
minimumemplacementtimes.For example,Figure6a indicatesthat Crisp,J.A., and S.M. Baloga,A modelfor lava flows with two thermal
J. Geophys.
Res.,95, 1255-1270,1990.
a subcircular
pillowmoundwitha volumeof 106m3andaviscosity components,
Delaney,P.T., and D.D. Pollard,Deformationof hostrocksandflow of
magmaduringgrowthof minettedikesandbreccia-bearing
intrusions
near
days (it could take longer if effusion were not continuous).These
ShipRock,New Mexico.U.S.Geol.Surv.Prof.Pap. 1202,61 pp., 1981.
typesof estimatesare neededto developstrategiesfor observing Dietrich,G., K. Kalle, W. Krauss,andG. Siedler,GeneralOceanography,
submarineeruptionswhoselocationsaredetectedby thepresence
of
625 pp., JohnWiley, New York, 1980.
hydrothermalmegaplumes[Embleyetal., 1991] or othersignsof Dowty, E., Crystalgrowthandnucleationtheoryandthe numericalsimulation of igneouscrystallization,
in PhysicsofMagmaticProcesses,
edited
activity.
of 102Pa s couldnothaveformedin lessthan106s, or roughly12
by R.B. Hargraves,pp. 419-485, PrincetonUniversityPress,Princeton,
N.J., 1980.
CONCLUSIONS
A sequence
of morphologictransitionsobservedon thesurfaceof
a wax analogto lava flows can be comparedto the structureof
submarinelavas by using a simple viscousgravity-drivenflow
scaling,alongwith estimatesfor coolingof the lava surfacedueto
turbulent
natural convection
in the seawater. The main task involved
is a calculationof the time requiredfor the lava surfaceto solidify
after it comesinto contactwith seawater.A directapplicationof the
laboratoryresultsfor morphologictransitionsto submarineconditionspredictsthatbasaltsaremostlikely to form intopillows,while
lobate, ropy, and jumbled sheet flows and lava lakes form from
progressively higher flow rates and/or lower viscosities
(crystallinities).Extrusionfrom a fissurealsofavorsdevelopment
of
pillows unlessthe substrateis smoothenoughto allow the new lava
to slideoverit, in whichcasethevarioustypesof sheetflow will be
favored.In mostcasessuchfissureeruptionswill evolveto oneor a
few isolatedsubcircular
ventsquiterapidly.Themorphologic
similarities betweenlaboratorywax flows and submarinelavasare an
encouragingindication that these types of simulationsmay help
answerimportantquestionsaboutthe emplacementof lavason the
sea floor.
Embley,R.W., K.M. Murphy,andC.G. Fox,High-resolution
studiesof the
summitof Axial Volcano,J. Geophys.Res.,95, 12,785-12,812,1990.
Embley,R.W.,W.W. Chadwick,M.R. Perfit,andE.T. Baker,Geologyofthe
northernCleft segment,JuandeFucaRidge:Recentlavaflows,sea-floor
spreading,
andtheformation
ofmegaplumes,
Geology,
19,771-775,1991.
Fink, J.H., andR.C. Fletcher,Ropypahoehoe:
Surfacefoldingof a viscous
fluid, J. Volcanol.Geotherm.Res.,4, 151-170, 1978.
Fink,J.H., andR.W. Griffiths,Radialspreading
of viscous-gravity
currents
withsolidifyingcrust,J. FluidMech.,221,485-509,1990.
Fink, J.H., andR.W. Griffiths,A laboratoryanalogstudyof themorphology
of lavaflowsextrudedfrompointandlinesources,
J. Volcanol.Geotherm.
Res.,in press,1992.
Fofonoff,N.P., Physicalproperties
of seawater,in TheSea,vol. 1,Physical
Oceanography,
editedby N.B. Hill, JohnWiley, New York, 1962.
Grdfiths, R.W., and J.H. Fink, The morphologyof lava flows in planetary
environments:
Predictions
from analogexperiments,
J. Geophys.
Res.,in
press,1992.
Gudmundsson, A., N. Oskarsson, K. Gronvold, K. Saemundsson,O.
Sigurdsson,
R. Stefansson,
S.R.Gislason,P. Einarsson,
B. Brandsdottir,
G. Larsen,H. Johannesson,
and T. Thordarson,The 1991 eruptionof
Hekla, Iceland, Bull. Volcanol., 54, 238-246, 1992.
Hall, A., IgneousPetrology,573 pp., LongmanScientificandTechnical,
Harlow, England,1987.
Haymon,R.M., andthe ADVENTURE Team,Activeeruptionseenon East
PacificRise, Eos, Trans.A GU, 72 (46), 505-507, 1991.
Holcomb,R.T., J.G.Moore,P.W. Lipman,andR.H. Belderson,
Voluminous
GRIFFITHS
ANDFINK: SUBMARINE
LAVAMORPHOLOOY
submarinelava flows from Hawaiian volcanoes,Geology,16, 400-404,
1988.
Hulme,G., The interpretation
of lava flow morphology,
Geophys.
J. R.
Astron. Soc., 39, 361-383, 1974
19,737
Sansome,F., Pele meetsthe sea, 27 minute video, LavaVideo Productions,
Honolulu, Hawaii, 1990.
Shaw,H.R., Rheologyofbasaltin themeltingrange,J. Petrol.,10, 510-535,
1969.
Huppert,H.E., andR.S.J.Sparks,Meltingtheroof of a chambercontaining Sverdrup,H.U., Oceanographyfor Meteorologists,246 pp., Allen and
Unwin, London, 1945.
a hotturbulentlyconvecting
fluid,J. FluidMech.,188, 107-131,1988.
Huppert,H.E., J.B. Shepherd,H. Sigurdsson,
and R.S.J.Sparks,On lava Tepley,L., andJ.G. Moore,Fire UndertheSea:The Originof Pillow Lava,
domegrowth,with applicationto the 1979lavaextrusionof theSoufriere
16mm soundmotionpicture,MoonlightProductions,
MountainView,
of St Vincent, J. Volcanol.Geotherm.Res., 14, 199-222, 1982.
Calif., 1974.
Kirkpatrick,R.J.,Kineticsof crystallization
of igneousrock,Rev.Mineral., Turcotte,D.L., andG. Schubert,Geodynamics,
450 pp.,JohnWiley, New
8, 321-398, 1981.
Lipman, P.W., and N.G. Banks,Aa flow dynamics,Mauna Loa 1984, in
Volcanismin Hawaii, editedby R.W. Decker,T.L. Wright, and P.H.
Stauffer,pp. 1527-1567,U.S.Geol.Surv.Prof.Pap. 1350, 1987.
Lonsdale,P.,Structuralgeomorphology
of afast-spreading
risecrest,theEast
PacificRisenear3ø25'S,Mar. Geophys.
Res.3, 251-293,1977a.
Lonsdale,
P.,Abyssalpahoehoe
withlavacoilsattheGalapagos
rift, Geology,
5, 147-152, 1977b.
Macdonald,G.A., Volcanoes,
510pp.,Prentice-Hall,EnglewoodCliffs,N.J.,
1972.
Malin, M.C., Lengthsof Hawaiianlava flows, Geology,8, 306-308, 1980.
Moore,J.G.,Mechanismof formationof pillowlava,Am.Sci.,63, 269-277,
1975.
Moore,J.G.,andJ.P.Lockwood,Spreading
cracksonpillowlava,J. Geol.,
York, 1982.
Turner,J.S., BuoyancyEffectsin Fluids, 368 pp., CambridgeUniversity
Press,New York, 1973.
Uhlmann,D.R., P.I.K. Onorato,and G.W. Scherer,A simplifiedmodelfor
glassformation,Proc. Lunar Planet. Sci Conf., lOth, 375-381, 1979.
vanAndel,Tj.H., andR.D. Ballard,TheGalapagos
Rift at 86øW,2, Volcanism,structure,
andevolutionoftherift valley,J. Geophys.
Res.,84, 53905406, 1979.
Walker,G.P.L., Lengthsoflava flows,Philos.Trans.R. Soc.London,Ser.A,
274, 107-118, 1973.
Weast,R.C., D.R. Lide, M.J. Astle,andW.H. Beyer(Eds.),Handbookof
Chemistryand Physics,70th ed., CRC Press,BocaRaton,Fla., 1989.
Williams,H., andA.R. McBirney,Volcanology,
397pp.,Freeman,Cooper,
San Francisco,Calif., 1979.
86, 661-671, 1978.
Pinkerton,H., Factorsaffectingthe morphology
of lavaflows,Endeavour,
11, 73-79, 1987.
J.H. Fink, GeologyDepartment,
ArizonaStateUniversity,Tempe,AZ
85287-1404.
R.W. Griffiths, ResearchSchool of Earth Sciences,Australian National
Pinkerton,H., and R.J. Stevenson,
Methodsof determiningtherheological
propertiesof lavasfrom theirphysico-chemical
properties,
J. Volcanol. University,GPO Box 4, CanberraACT 2601, Australia.
Geotherm.Res.,in press,1992.
Rowland, S.K., and G.P.L. Walker, Pahoehoeand aa in Hawaii: Volumetric
flow rate controlsthe lava structure,Bull. Volcanol., 52, 615-628, 1990.
Ryan,M.P., andC.G. Sammis,Theglasstransition
inbasalt,J. Geophys.
Res.,
86, 9516-9539, 1981.
(ReceivedMarch 2, 1992;
revised June29, 1992;
acceptedJuly 8, 1992.)