JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 97, NO. B7, PAGES 11,097-11,116, JULY 10, !992
HorizontalLithosphereCompression
and Subduction:
ConstraintsProvidedby PhysicalModeling
ALEXANDER I. SHEMENDA
Instituteof Geophysics,
National Central University,Chung-Li,Taiwan,Republicof China
Physicalmodelingof the subduction
is performedwith a two-layeredmantlemodel(elastico-plastic
lithosphere
andlow-viscosity
asthenosphere)
andis governed
by the criteriaof similarity.Compression
of the lithosphere
in the
area of a passivecontinentalmarginhasbeenshownto producea bucklinginstabilityin the oceanicplate with
wavelengths
of 200 km onthe average.Later,a localizationof deformation
occursin saggingat somedistancefrom
the marginwherea stronglydislocatedlinear ridge is formeddue to the thrusting.The plate then experiences
a
failure alongthe inclinedzone,andsubduction
starts.The innertrenchslopewhichformsthereforehasa scraped
structure and include a block of crushed and dislocated oceanic crust and sediments in the lower section. If there is
an old inclinedfault strikingacrossthe compression
of an oceaniclithosphere,
it is on that fault that a subduction
zone is initiated.The innertrenchslopehasthen a differentstructureand forms,due to normalfaulting in the
frontalpartof the overriding
plate.Theformationof a subduction
zonerequiresa compression
that is smallerthan
that in the precedingcaseby a factorof 2 or 3. The subducting
plate experiences
an elastico-plastic
bendingand
(underspecificconditions)thrustingalong the zone, dippingfrom under the overridingplate oceanwardand
crossing
the entirelithosphere.
The bestagreement
betweengeneralized
relief in subduction
zonein the modeland
natureisachieved
whena shearyieldlimitxs= 1.3 x 108Pa,modulus
of elasticity
E abouta fewtimes10ll Pa,and
a thickness
H = 60 km, areadoptedfor thereal lithosphere.
INTRODUCTION
Recently, there is a tendencytoward a more active use of
physical(experimentalor scale)modelingin geodynamics.
This
is largely due to the mathematicaldifficultieswhich numerical
modelingencountersin constructingever more complex and
adequatemodels of geologic features, including subduction
zones.Onecanfrequentlyderivewieldy analyticaland numerical
solutionsonly by oversimplifications
in the statementof the
problem.Unfortunately,these simplificationlargely determine
the final result.Furthermore,it is frequentlynot evenclearhow
one shouldformulatethe problemmathematically,for example,
in caseswhere it involveslarge transientdeformationsin the
lithospherein subductionzones accompaniedby lithospheric
failure. Physical modeling can in principle obviate these
difficulties. However, everything depends on making
experimentaltechniquesthat would satisfy the necessaryrequirements,similaritycriteria, in the first place. That task was
tackled in different ways. Accordingly,different degreesof
similarity between the original and the<model have been
achieved.For example, Turner [1973] simulated subduction
qualitatively.Glycerin was used to model the upper mantle,
whilethedrivingmechanism
of subddction
consisted
in ascending gas bubbles.Jacoby [1976] and Jacoby and Schmeling
[1981] simulatedthe uppermantlewith moltenparaffin.Its surface coolsand crystallizesinto an upper layer, a lithosphere.
"Subduction" occured due to thermal convection in the melt and
lithosphere's
ownweight.Kincaidand Olson[1987] modeledthe
lithosphere
and the underlyingmantleusingsugarsyrupof variousconcentrations.
They studiedthe interactionbetweena slab
descending
underits ownweightanda transitionzoneat 670 km
depthin the mantle.The materialsusedin their paperallowed
modelparametersto be variedwithin sufficientlywide ranges,to
makequantitativeestimatespossible.
Copyright1992 by theAmericanGeophysical
Union.
Papernumber92JB00177.
0148-0227/92/92
JB-00177505.00
I have also done some joint work with colleaguesin the
physicalmodeling of subductionand accompanyingprocesses
[Shemenda,1979, 1981, 1984, 1985, 1989a,b,c; Grocholsl•yand
Shemerida,1985;Lobkovskyand Shemenda,1981; Lobkovs•kyet
al., 1980] usingspeciallyfabricatedhydrocarbon
compositional
systems
to modelthe lithosphere.Modelingwas performedwith
a two-layeredmantlemodelinvolvingelastico-plastic
lithosphere
and low-viscosity
asthenosphere.
A similaritycriteriahavebeen
satisfied in the modeling. The present paper is a further
extensionof this work. It containsa descriptionof the conditions
and results of mechanical subduction modeling in an
environmentof horizontalcompression.
GENERAL
MODELING
SCHEME
The followingfactorsshouldbe taken into consideration
when
determiningthe generalschemeof mechanicalmodelingof subduction.The mostimportantthing is the fundamentalfeatureof
uppermantle structure,namely,its two layers.The upper layer,
the lithosphere,consistsof stronger(or more viscous)material,
while the lower layer, the asthenosphere,has a strength
(viscosity)that is severalorderslower. Second,the lithospherein
the transitionregion from oceanto continentwhere subduction
zonesoften developis stronglyheterogeneous.
In suchregions
the lithosphereis thicker under the continentand thilmer under
the ocean.Last, lithosphericdeformationin subductionzones
occurs mainly under horizontal compressire stresses, as
illustrated,in particular,by seismological
evidence.
The next questionthat presentsitself concernsthe choiceof
rheologicmodelsfor the lithosphereand the underlyingmantle.
Numerousdata, includingevidencesfor plate rigidity and experimental deformation experiments [Goetze and Evans, 1979;
Kirby, 1980, 1983] allow the assumptionof an elastico-plastic
lithosphereas a first approximation[Lobkovskyand Sorokhtin,
1976; Lobkovskyand Shemenda, 1981]. It is clear that the
quantitativeparametersof tlfis lithospheremodel,the yield limit
-8 and the modulusof elasticityE, mustbe differentfrom those
derivedfrom experimentson rock deformationthat do not take
11,097
11,098
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
into accountscaleandtime factors.Theseparameters
musthave
someeffectivevalueswhichcanbe foundindirectlyfromvarious
MODEL
MATERIALS
Substitutionof the parametervalues typical of the prototype
geologic
andgeophysical
phenomena
associated
withlithospheric (nature)into (1) leadsto conclusionthat the yield limit of the
deformation
(in particular,gravityanomalies).
The choiceof a rheologicmodel for the asthenosphere
is
modellithosphere
•s for the valuesof p• andH that are realistic
underlaboratoryconditionsmustbe very small, of the orderof
governed
by the fact that its effectivestrength
or viscosity
is
10 Pa. A material having this strengthflows under its own
severalorderslessthanthat for the lithosphere.For this reason,
weightandbreakswhenheld in the hand.This is oneof the main
onecanusea fluid of verylow (evenzero)viscosity
to modelthe
difficultiesin the way of modelinglarge-scaletectonicprocesses;
asthenosphere
(the part played by the asthenosphere
is
it doesnotpermitoneto makespecimens
of modellithosphere
of
essentially
to makePascal'slaw hold beneaththe lithosphere,
requiredshapesandto performmechanicaloperations
with them
i.e., to maintainhydrostatic
equilibrium
underthelithosphere).
beforeand after the experiments.The difficulty can be obviated
The last questionto be resolvedis the driving force of
by using specialmodel materials.The lithosphereis modeled
subduction
is to be prescribed.
The mainsources
of platemotion
here by using a specially developedsystem of composite
are considered
to be slippingof the lithospherefrom mantle
materialsconsistingof alloys of solid hydrocarbons
(paraffins,
highsin mid-oceanic
ridges,actiononthe lithosphere
of mantle 7.1%, and ceresins,8.8%), mineral oils (61.1%), finely ground
(asthenosphere)
currents
whichproducesmalltractions
stresses powders (23%), with a small addition of surface-active
at the lithosphere
baseactingalongthe currents,
and gravita- substances
[Shemenda,1981, 1984, 1989c]. In structure,this
tionalsinkingof the lithospheric
slab into the mantlein the systemis thixotropicdispersionsof solid hydrocarbons
and
subduction zones.
powdersin oil. It possesses
elastico-viscoplastic
propertiesthat
The first two mechanismscan readily be replacedby local
are stronglydependenton the temperature;seeFigure 2. This
application
of lateralcompression
totheslabusinga rigidpiston. model material, as well as real rocks, exhibits different
Thisloadshouldbe appliedfar enoughfromthesubduction
zone
deformation
propertiesin differentrangesof temperatureT and
(or its placeof origin)for the boundary
effectsrelatedto the
strainrate g, from linear viscousto nonlinearviscousto plastic
loadingmethodto be negligible.
and brittle-dilatantproperties.To modelthe lithosphere
within
The third drivingmechanism
of subduction
(the slab being
the framework of the problem formulated above, these
pulledintothe mantleunderits ownweight)is modeledelseparameters
were chosenin sucha way that the yield limit •s
where[Shemenda,
1985, 1986].
satisfies
similarity
criteria(1) while beingweakly dependenton
Thus subductionis modeledin this work on a simplescheme
g
to
model
a
plastic
solid. The •(g) curvesin Figure 2d were
h•volving
an elastico-plastic
modellithosphere
overlaying
a very
derived
in
the
range
of
g usedin the modelexperiments.
They
lowviscosity
fluid,subjected
to horizontal
compression
bymeans
demonstrate
reallya minordependence
of Zson g in the plastic
of a piston(Figure 1).
flow regime.Also, •s almostdoesnot dependon the confining
SIMILARITY
CRITERIA
Modelingof subduction
within the frameworkof the above
scheme should satisfy the following similarity criteria
[Shemenda,
1983]:
xs/(p•gH)=const;
E/(p•gH)=const;
p•/pa=const;
Vt/H=const
(1)
pressure.
One morerequirement
which has beentaken into accountin
fabricatingthe modelmaterialswas that they shouldbe sufficientlyhard and solid at room temperature,while the above
propertiesshould exist at a slightly increasedworking
temperature
of the modelexperiments.
The plotsin Figure2d
wherezs,E, H, and p• are the shearyield limit, the modulusof characterizethe model material at the working temperature
elasticity,thickness
anddensityof the lithosphere,
respectively; 39.50C,where it has a very low yield limit. However,the
strongsolidat roomtemperature,
sothat
pais the asthenosphere
density;V is the slabvelocity;t is the materialis a sufficiently
one
can
perform
the
necessary
mechanical
operations
on it
time;andg is theacceleration-due
to gravity.Neglected
hereare
Poisson's
ratio in the lithospherewhich is unimportantin our withoutcausingbreakeage.
The mostconvenientand suitablematerial for modelingthe ascaseand the pressureof oceanwater on the plate surface.It
thenosphere
within the frameworkof the simpleschemedeshouldbe noted that the last conditionin (1) has a purely
scribed
above
provesto be pure water.Its densityis p•m= 103
kinematicmeaningand servesto convertmodeltime into geokg/m
3.
The
model
lithospherehas the same densitypin (it
logictime. The conditionimposesno restrictionon the process
rate in the model.
depends
ontheconcentration
of powder).
Fig.1. Scheme
ofthemodelexperiments
andtheexperimental
installation:
1,bath;2, "lithosphere";
3, electric
heaters;
4, piston;
5,
"asthenosphere".
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
11,099
EXPERIMENTAL INSTALLATION AND MODELING TECHNIQUE
'•"['$
.....
To performan experiment,water imitatingthe asthenosphere
is
pouredinto bath 1 (Figures 1 and 3) of dimensions40 x 8 x 20
cm. A model lithosphereplate is placed above. The plate
specimenis in direct contactwith the bath walls, but special
measuresare takento reducethe frictionbetweenthe plate and
the bathwalls to nearlyzero. Plane electricheaters3 are usedto
makethe entire systemthermostaticat the workingtemperature
380-420C(39.50 for most experimentsdescribedbelow). The
process
lastsabout2 hoursandis monitoredusingthermocouples
which canbe insertedinto the plate itself. Piston4 is then used
to producecompression
of the slab.The experimentalinstallation
ensuresa constantlevel of the "free"mantle (water) top during
the experiment. Plate deformation is studied through the
transparentbath walls and by using a special technique for
visualizingthe deformation.The techniqueis as follows. The
specimenis frozenbeforethe experimentand then cut longitudinally at the middle into two parts.The sectionof a part is then
treatedwith a specialstampto impressa grid matrix with lines
0.1 nun wide at intervalsof 2 nun which is filled up with a paint
suspensionafterward. The two halves are then re-attached
together.The resultingspecimenis placedinto the installation
and deformedafter heating.The experiment(compression)is
stoppedat the requiredstage.The modelis then allowedto cool.
The solidifiedspecimenis removedfrom the installationand cut
againalongthe previoussection.The grid is then measuredto
derivethe finite deformationand to identify faults. Circles 3-5
nun in diameterare also stampedinto the slab along with the
grid. Their deformationcan readily be used to derive the
directionsof the principalstrainand stressaxes.
The normal horizontalnonhydrostatic
(deviatoric)stresses•h
actingin the "lithosphere"at variousstagesof the experiment
were also determined.These stressescannot,unfortunately,be
measureddirectly,becausethey are very small. For this reason
the followingprocedurewas used:a seriesof experimentswas
conducted
underthe sameconditions.Prior to the experiments,
• ø-"
(Pa)
Fig. 2. Curvesshowingpropertiesof the model lithosphere(sheartesting).
•8 •'9 •o •
•:• 4•
(a) Summaryrelationships
x (s) for k = const(x ,s, andk are shearstress,
strain,andstrainrate,respectively)
and/; (•) for x = xs(xsis the shearyield
limit);(b) summary
relationship/;(x
); (c) - xs(T) relationship
for k = 2 x 10-2
s-I (r isthetemperature)
for themodelmaterialusedin thiswork;(d) - x (•)
curvescharacterizing
thematerialat T = 39.5øC(mostof theexperiments
in
T(ø0)
TI(Po)
this
paper
have
been
carried
out
at
this
temperature).
15
•
•: 2.58- 10-4c-'•
-----.• =q.6 ß'10
-qc-•
• =õ.sgßt0-qc-'•
10
o
I
02
I
11,100
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
the way acrossthe plate at an anglearound500 to the horizontal
at the plate edges,near the piston and the oppositebath wall
(Figure 4b). Simultaneouslyor somewhatlater, the specimen
losesbucklingstabilityand smoothsaggings
and elevationbegin
to form. Vertical displacements
in the plate in this and other
experimentscan be inferredfrom a horizontalblack line drawn
on the bathwall at the level of the plate top. The plate surfaceis
parallel to the line before deformation.Further compression
producesa "vertical"subductionnear one of the model edges
(usuallynear the piston,Figures4c-4./).It occursby successive
"breakingout" of model blocks along inclined shear (thrust)
faulting zonesand "trickling down" of these blocksalong the
piston.
Experiment2. The result of compressionof specimen
previouslyweakened at some place by thinning is shown in
Figure5. Deformationis, at the outset,localizedin the weakened
zone.At first, the thinnedregionis somewhatcontracted
laterally
with small cross-reverse
fracturesforming in its upper part,
similar to experiment1. This region then rises (Figure 5b).
the modellithospherewas thinnedat a certainlocationfrom Reversefaultingat the edgesof the rise becomesparticularly
below (a cut whosewidth was of the order of the specimen intensiveandcanproducea thickeningof materialthere.In cross
section two shear zones which cross the slab from surface to
thicknessH was made in the slab base all the way acrossit
perpendicular
to the directionof loading).The thinningwas bottomand dip towardthe centerof the weakenedpart gradually
madeeverlargerfrom experiment
to experiment,
until failure form at the margin of the weakenedzone. Completefailure
occurredat the weakened location. Knowing the greatest eventuallyoccursalongone of thesezones.Furthercompression
thicknessh of the thinnedlocationwhere failure occurs,allowed produces
subduction
of onefragmentof the brokenslabunderthe
the determinationof Oh:C•h= C•sx h/H, where os is the yield
other(Figures5d-5f). The specimenis rupturedat an angleclose
limit at normal load (in that case a plane deformationtakes to 450 (in crosssection),but the inclinationof the contactzone
betweenthe slabs relative to the horizon gradually decreases
place,andtherelationos• 2xsis valid[Kachanov,1969]).
during subduction.This occursbecausethe subductingslab
MODELING THE FORMATION AND DEVELOPMENT
worksout the materialof the overridingblock in a nonuniform
OF A SUBDUCTION
ZONE
manner.
The slab which is pushedinto the "mantle"is bent near the
resultingfault (subduction
zone)andformsa trench(Figures5d5J).An extendedrise of very smallamplitudeformsto the right
of it (this is the outerrise to be more clearly seenin the other
experiments).
same set of conditions to exclude accidental results. Below we
Deformationof the overriding(islandarc) plateis accompanied
describe
someof themosttypicalexperiments.
Unlessmentioned
by its frontalpartssubsiding
intothe "trench"andby the forma-
Severalhundredexperiments
havebeencarriedout underdifferingconditions
(composition
of themodellithosphere,
working
temperature,
strainrate) to modellithosphere
compression
and
subduction.
Experiments
wererepeatedseveraltimesunderthe
otherwisetheseexperiments
were carriedwith the following tion of an arclike rise somewhat to the left, which can be
modelparameters:
Xs
TM
• 15Pa;ETM
• 2 x 103Pa;Hm= 2.3 x 10-2 identified as the frontal arc.
m; p•m• p• = 103 kg/m3.Conversion
of the parameters
into
Experiment
3. Horizontalcompression
is appliedto a lithonatureusingsimilaritycriteria(1) yieldsthe following:Xs
ø = 1.3 x
spheremodelof thetransitionzonebetweenoceanandcontinent
10sPa;E = 1.7 x 10TMPa; H = 6 x 104m; pl• • p• = 3.3 x 103 (Figure 6). The model consistsof two parts of different
kg/m3 (superscripts
"o" and "m" denoteoriginal and model
parameters,respectively).These values are in fairly good
agreement
with the availableestimates
for the lithosphere
and
asthenosphere
parameters.This can serve as a formal
substantiation
of the adoptedmodelparameters.
As a matterof
fact, theseparametervalueswere determinedin the courseof
modelingitself.This will becomecleartowardthe end of this
paperwherewe discuss
the experimental
resultsobtained.The
velocityof horizontallithosphere
motionin the modelwas Vm=
2 x 10-5m/s on the average.Takinga meanvalueVo= 5 cm/yr
for the rate of subductionin nature,we can usethe last condition
in (1) to derivethat 1 min in the modelcorresponds
to about6 x
104yearsin nature.
Experiment
I. The modelof a uniformoceanicplate is subjectedto horizontalcompression
(Figure4). At the initial stageof
thisexperiment,
the modellithosphere
is moreor lessuniformly
plasticallycompressed
alongits entirelength.The resultis the
development
of numerous
shallowreversefaultscrosswise
to the
compression
onits initiallysmoothsurface.Thruststhenformall
thicknesses.
The thickerpart modelsthe continentallithosphere;
the thinner one models the oceanicplate. At first, uniform
compression
of thethinlithosphere
resultsin thedevelopment
of
surfacereverse faults as in experiment1 (Figure 4). The
"oceanic"
lithospherethen lossesstabilityand buckles(Figure
6b). A rise appearsat the zoneof thickness
contrast(i.e. at the
"continental
margin").Fartheroceanward
(to the left) a sagging
occurs
(Figures6b and6c). Continued
compression
increases
the
amplitudeof bucklingand reducesthe associated
wavelength.
All deformationthen concentratesin the sagging.Here, as a
resultof violentplasticcompression,
the specimenthickens(a
beadforms)with accompanying
thrustsformationandthickening
of materialin the top of the slab(Figure6c-6f). This produces
a
fracturedridge overlyinga more massive"lithospheric"
root
(Figures6f and 7b). Localizationof the deformation
gradually
createsnearlyorthogonal
shear(thrust)zoneswhich crossthe
slabfromtopto bottom(Figures6fand 7b). Furthercompression
produces
complete
failureof the "lithosphere"
alongoneof these
zonesand initiatessubduction
(Figures6d, 6e, 6g, and 7c).
Fig. 4. Resultof experiment1. Horizontalcompression
of the oceaniclithospheremodel.(a)-(f) Stagesof the modelprocess
(for explanations
seemain
text).
4i;:-:-'--"
............................................................................................................................................................
....::,•,
.."•$' *e?•:•,
--,--•--•.•*•.s***
-•'
..........
:
..-*:
.
***:...................................................
,
:.•;•:--.;.
*
:%-'
:':
?..-'
.................
•::...
-:?
Fig. 5. Resultof experiment
2. Compression
of a platecontaininga thinned
zone.
11,102
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
........
..:.•
:...........:•.•:.::..•:.,,•..•;:•.•.•:::.::;::•:-..-.-.•::
::.:::•
. ½-:....:-.:?.:
-...
............
::•.<•::•--•:•-•: .':•:.•
.......
•,•........................
.....
Fig. 6. Resultof experiment
3. Compression
of the modelof a transitionzone
from oceanto continent(the continuouslithospheremodel consistsof two
partsof differentthicknesses).
(a)-(e) Stagesof experimental
process
(general
view throughthe wall of the experimental
installation);(J) and(g) crosssectionsof the frozenmodelscorresponding
to (J) the stagesof deformation
localizationand(g) platefailureandsubduction
initiation(seeexplanations
in
the text).
Localizationof deformationin the "oceanic"plate dependson
It is interestingto note that the patternof modeldeformation
the parametersof the "lithosphere",particularly,on the yield obtainedin experiment3 (Figure 6) practicallypersists,if the
"continental"
and "oceanic"
partsof the specimenare separated
limit usof the plate and its brittleness(i.e., on the magnitudeof
The onlydifferenceis thatthereis
plasticdeformationAe prior to failure; see Figure 2a). For in- with a verticalcutbeforehand.
stance,increasedAe leads to strongerplastic crushingof the someverticaloffsetbetweenthe blocksalongthe cut in the latter
case,owingto the factthata thick slabundercompression
expespecimenin the zone of localizeddeformationand henceto a
broaderridge and "lithospheric"
root. Completefailure then oc- riencesa smalleruplift thana thin one.If, on the otherhand,an
the slabs,subduction
canoccuralongthat
curs after great deformations.Roughly the same consequences inclinedcut separates
haveshownthatthereis a criticalvaluefor
follow from decreasing'•s. Also, along with decreased'•s, one cut.The experiments
notesa smallerbendingamplitudew of the oceanicslab (i.e., the angle of inclination close to 900 which if exceeded,
deformationis localizedwith failure occurringat smallerw). On subduction is initiated at the cut.
The aboveprocedurefor determininghorizontalstressesin the
the other hand, increasingthe yield limit modifiesthe failure
mechanism.The localizationof deformationagainoccursin the modellithosphereshowsthat experiment3 (Figure 6) involves
deviatoricstresses
errwhichare closeto
saggingbut concentrates
at the edgesrather than at the center. horizontalcompressive
Shear (reversefaulting) zonesform there, precedingcomplete the yield limit orsat the stagewhena bucklinginstabilityarises
failure of the plate (Figure 7d). A subductionzone is then in the "oceanic"plate. With further deformation,localization
initiatedat one of these.Similar resultsfollow from decreasing accompanies
gradualfailure of the material, and err gradually
the thicknessof the "oceaniclithosphere"when '•s is held decreases,
approaching
a valueof about0.3cr•whichis necessary
constant.
to maintain the subduction.
Intermediatecases are also possible in which the bead
(localizationof deformation)
and shear(tlumst)faultsformat the
centerandon the flanksof the saggingareassimultaneously
at an
earlystage.Later,oneof themechanisms
beginsto dominate.
Experiment4. The "oceanic"plate is made longer and the
"continental"
one shorterin this experiment(Figure 8). Also,
theyare separated
with a verticalcut.The resultis similarto that
in experiment3. Experiment4 clearly indicatesa flexural
SHEMENDA:PHYSICALMODELINGOFSUBDUCTION
'•-
.•.-,.',.•:.-.-.•
11,103
bucklingof the "oceanic"plate. The localizationof deformation
developsas in experiment3 in the saggingregionclosestto the
continentalmargin.
Experiment$. This experimenttakesinto accountthe weightof
sedimentarymaterial which may accumulateat continental
margins. Such material exerts considerablepressureon the
underlying transitional and oceanic lithosphere. Model
"sedimentary"
wedge (dotted in Figure 9a) of a special lowstrength material having the following parameters when
converted
to nature:densityps
ø = 2.5 x 103kg/m3;heightof the
basehs
ø = 6 km; lengthlo = 150 km (Figure9) wasplacedon the
oceanic slab. This slab separated from the "continental
lithosphere"
by the verticalcut, bendsunderthe wedgeweight.
Similar to experiment4, compression
resultsin the "oceanic"
slab loosingits bucklingstability.However, in contrastto the
precedingexperimentsin which a rise forms directly at the
transitionzone from "oceanic"to "continental"lithosphere,a
depression
developedat this locationin experiment5, initially
enforcedby the sedimentload.In otherwords,the phaseof slab
flexurehas been displacedby •. Accordingly,the depressionin
whichdeformationis localizedand subsequent
failure of the slab
occurs,has shiftedtowardthe "ocean"(Figures9d and 9e). The
samepatternpersistsin principleif thereis no verticalcut at the
"continental
margin".The onlydifferenceis that in this caseboth
"oceanic"
and "continental"
platesare involvedin downwarping.
As a resultthe amplitudeof the bendingis reduced.
There is a critical value for the thicknessof the sedimentary
wedgeh8belowwhichthe phaseof slabflexureis not displaced.
Whenh8hasbeendiminishedby a factorof 1.5-2 comparedwith
experiment5, the displacementno longeroccurs.There is also
someamountof "sedimentary"
materialat the continentalmargin
in experiment4 (Figure 8) but it doesnot exert an appreciable
effecton slabdeformationundercompression.
It should be noted that the stress of the entire "oceanic" slab in
Fig. 7. Schemeof development
of the plate localizationdeformationzone
(fromexperimental
evidence,
experiments
3, 4, and5): (a)-(c) stagesof bead
("lithosphere"
thickening)development;
(d) anotherpossiblevariantof the
localization
deformation
andfailure in the lithosphere
(it is realizedfor diminishedthicknessH and increasedxs); the zone of violent plastic
compression
(bearingstrain)is shownin Figure7a by the stippledarea.
experiments3-5 is closeto critical, that is, it is closeto failure
alongits entire length.In someexperimentswith the conditions
mentionedabove,the "oceanic"plate experienced
failure in differentlocations,includingnear the bathwall and directlyin the
transitionzone underthe "sedimentary"
wedge(a fault formed
therethatwasdippingunderthe "continent").
However,the most
typicalresultswereas describedabove(experiments
3-5).
Fig.8. Resultof experiment
4; thisexperiment
differsfromtheprevious
bythelongerlengthof the "oceanic"
plate:in addition,thetwo
platesareseparated
by a verticalcut.
11,104
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
..........................................................
•:..:,. ......---:
.............
. ..................
.....--.•...•&,
.:•
....
.
-
:•-..•!
....
;:E.
.............................
. ?- ..::"
..
-
•:•
.:.X
..............
:.5:.%L::::•..
:•.%:;:::"%•L.
.........
•:;-----.-:-.-..
':............:.-?..::.
:•:•%;;7•::.:...:...::..
-.
:.............. . ...............................
-:-:w
............
,:e
...................
"" "•:•
...;:•;:.:.
-:,•s-:.•:
. ..
....
"....;}•;.:::
......-:;...:::•::::•.,--•,:.........?':.:-½.::•,:.:.**-*
• ............... ;.•;•&%':;:/'"':7;:..:.:...7:::::
•':- ............. ..........
........... :-:::...-.:
.,- . ..........
'/•'
....
";
..½:•.:...-.,•
, ..:.-
'
-........
.....:....
.......½
:-......:::.•.***::•::
.................
;•.............
:;•:':
...................
:"-.:•½½::•;•;•:---:•-•
............
.:--.::::.......
.:,..--,;c:;:;::,;
..
•:::::
.......
:
Fig.9. Result
of e•efiment5;•is e•efimentdiffe••om •e previous
by
'...................................................
•e
presence
ofa"sediment"
wedge
on
•e"oceanic"
plate
in•e"p•sive
continen•l
m•gin"
region
(•e wedge
isshorn
inFibre9abyalppied
"..............
;•:•:•:•:":
.......
•a).
Fig. 10. Resultof experiment
6. Compression
of a lithosphere
modelwhich
contains
a transverse
cutthoughtheentireplatedippingat an angleof 35ø:
xs
TM= 40 Pa, largerthan in the previousexperiments;
the placeof largest
bendingof thesubducting
plateis shownin Figures10band 10cby whitearrows(for otherexplanations
seethetext).
The next three experiments(experiments6-8) modeled subductionwith an assignedinclinedcrosscut
(fault) in the slab.The
cut was madeat a lower anglethan the faultsthat formedin the
precedingexperiments.This was doneto imitate later (well developed)subductionstagesfor which the contactzone between
the slabsis typically steeplydipping.Experiments6, 7, and 8
differby thevaluesof themodellithosphere
yieldlimit.
Experiment6. In this experimentthe slabhasa relativelyhigh
x•nvalueof 40 Pa. This leadsto large verticalslabdisplacements
in the subductionzone (Figure 10), producingan unrealistic
trenchdepthwhich amountsto severaltens of kilometerswhen
convertedto nature.The width of the trenchis alsotoo large.
Experiment7. The modellithospherehasa low Xs
TMvalueof 1.2
Pa. In this experimentthe range of vertical slab displacement
provedto be too small (Figure 11). Also, the resultingtrenchis
shallow,being the equivalentof only a few kilometersdeep.
Althoughthe depthvalueis realistic,the trenchis too narrowin
this experiment.Its width is about60 km when the scalefactor
has been taken into consideration,about half the width of real
trenches. In addition, the distance from the "trench" to the
"frontalarc"andthe width of the outerrise provedtoo small.
Increasingxs
TMcomparedto its valuein experiment7 improves
the parameters
characterizing
the overalltopography
of the subductionzone,makingthem closerto the actualsituation.For ex-
SHEMENDA:
PHYSICALMODELINGOFSUBDUCTION
11,105
Fig. 11. Resultof experiment7 (thisexperimentis characterized
by a lower
•n
s value:•ns= 1.2 Pa.
.............
.:...
........
.... ...
::.......
.
.........
...................
-..
. .........................
..:.....:....
...............................................................
.
......
...
Fig. 12. Resultof experiment
8 (x[ns
is the sameasin experiments
1-5' x• =
15 Pa).
ample,the outerrise and the trenchbecomewider. The width of
the frontalarc alsoincreases,
while its apexis displacedtoward
the "back-arc
basin" Thereis someincreasein trenchdepthand
possiblyin the heightof the outerrise (this is difficult to detect
owingto its verysmallamplitude).The bendingof the "oceanic"
slabbecomes
smoother
beforeit sinksinto the "mantle".The optimal value of xs
TMis about 15 Pa. It is this value which was used
in the experiment
8 (Figure12).
Experiments
6, 7, and8 measured
horizontalcompressive
deviatoricstresses
C•hactingin the "lithosphere"
duringsubduction.
Theyhavethe followingvalues:C•h= 0.2c• in experiment6; C•h•
(0.7-0.9)c• in experiment7; and C•h• (0.3-0.4)c• in experiment
8.
Experiment9. demonstratesthe effect of the thicknessof the
subducting
plate on the dimensionsof the trenchand the outer
rise. The thicknessof the "oceanic"plate is diminishedin this
experiment:
Hm= 1.5 x 10-2m. Thisrendersthe amplitudeof the
outerrise greater,suchthat its elevationcouldbe seenmore distinctly(Figure 13). At the sametime, outerrise becamenarrower
as did the trench.
Last,we notethe influenceof the inclinationof the platescontact surface on the topography of the subductionzone.
Experimentshave shownthat a lower angle makesthe trench
shallowerand the height of the outer rise smaller(Figure 14).
The rise alsogrowsin width. In addition,the frontalnonvolcanic
arc becomes broader and lower.
ANALYSIS
OF EXPERIMENTAL
RESULTS
The experimentshaveshownthat subduction
zonescanform as
a result of considerablehorizontalcompression
of the lithosphere.Different mechanismscan producea subductionzone,
dependingon the structureof the lithosphere.If the lithosphere
plateis moreor lessuniformalongthe directionof compression,
then its failure and the formation of a subduction zone occur due
11,106
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
Fig. 13.Resultof experiment
9 (thesubducting
platethickness
H isas1.5timessmaller
thenin theprevious
experiments).
stronglydislocated
ridge(Figures6land 7b) andtwo intersecting
shear(in crosssection)zones(Figure7b). Failurealongoneof
these results in the initiation of subduction. This mode of
initiation of a subduction zone causes a well defined
Fig. 14. Influenceof the dip angleof the interplatecontactzoneon the nonisostatic relief of a subduction zone. The thin horizontal line indicates the
level of the isostaticequilibriumof the lithosphere;
solidand dashedlines
correspond
to steeperandlowerdip angles,respectively.
heterogeneous
steplike structureto developon the innertrench
slopeformingafter failure in the lithosphere
(Figure7c). The
lower,steeperpart of the slopecomprises
a stronglydislocated
blockof upperlithospheric
rocksincludingoceanicsediments,
splinters
of crust,anduppermantle.The blockformsthe slope
breakdividingthe innerslopeinto two differentparts.In real
environments
a sedimentary
terracemust form in front of the
to the localizationof plastic deformationin somepart of the
slopebreak which exertsa dammingeffect for the sediments
lithosphere.That processtakes place when the compressire
comingfromthe islandarc as shownin Figure7c. Suchfeatures
stressin the plate reachesthe critical value, i.e., the yield limit
of structure
docanbe foundalongtheinnerslopesof someactual
for thelithosphere
c•s.Conversely,
if thereareweakezonesin the deep-sea
trenches(seeFigure15).
plate or inclined faults all the way acrossthe lithosphere The sequenceof vertical seafloormovementsin the frontal
(dipping at angles less than some critical value), then the areasof the innertrenchslopeinferredfrom the experiments
subductionwill initiate at the site of these features,becausein
should
alsobenoted,in particular,
at theareaof slopebreak'.
At
that caseinitiationof subduction
requiressmallercompressive first,whenthe slabloosesbucklingstability,this areasubsides
stresses. Below we consider variants.
(Figure7a). This is followedby uplift duringthe periodof
deformation
localization(Figure7b), and then by subsidence
Formationof a SubductionZone in a Homogeneous
OceanicLithospherein the TransitionZone
From
Continent
again when the trench forms and failure occurs in the slab
(Figure7c). The amplitudeof theseoscillationsin naturemust
to Ocean
amount to a few kilometers.
This scenariois the leasttrivial and perhapsthe mostgeneral
type of event.At first, increasingthe horizontalcompression
of
the lithosphereproducesreverse faulting in its upper layer
transverse
to the directionof compression.
Remembering
thatthe
upperlayerin the actuallithosphere
consists
of brittlematerialof
low strength,reversefaulting must be much more intensivein
nature.Further,the slab loosesbucklingstabilityand assumesa
wavelikeshapewith a wavelength3, that dependson the plate
parametersH, c•s, and E. As the compressionincreases,3,
decreases.
Prior to failure (localizationof deformation)in the
plate, 3,reachesaveragevaluesof around3H (i.e., about200 km
when convertedto nature)and is weakly dependenton the other
parametersof the "lithosphere".Afterward, the deformationis
localizedin oneof the depressions
(it maybe initiatedin several
depressions,
but continuesto develop in one only). The
lithosphere
therethickenswith the accompanying
formationof a
It follows from the experimentsthat a localization of
deformation
musthavebeenpreceded
by a bucklinginstability
in
thelithosphere.
Sucha phenomenon
perhapscanbe identifiedin
the northeastern Indian Ocean. It deserves a more careful
examination.
Intraplate deformationin the northeasternIndian Ocean. A
seismiczoneof intraplatedeformation
existsin this areawithin
the Indo-^ustralian
plate (seeFigure 16). The deformation
and
seismicity
are associated
with extensiveyoungNE thrusting
(Figure16) with which the observedseismicityis associated
[Levchenko,
1986].Fault densityvariesoverthe seafloor,but is
particularlygreat in the northernCentral Basin where.reverse
faultsoccurevery5-20 km [Levchenko,
1986].Faultingis seen
theresuperimposed
uponthebackground
of large-scale
basement
undulations
(folds)whichhavea wavelength•, of 100-300km
andamplitude1-1.5 km [Weisselet al., 1980]; seeFigure 17.
WEST
EAST
u
o
.•o
I
•
20
.
i
so km
J
Fig. 15.Interpreted
seismic
profilesacross
theIzu-Bonintrench[afterOgawaet al., 1989].
SRI
LANKA'""
NAZY
NIKITIN
RISE
li
ß
NINETY
RIDGE
o
EAST
//
/
i
I
I
700
BO
o
goø
t000
tt00
120
ø
t30o
tttOo
t500
Fig.16.Indo-Australian
plate:
1,subduction
zone;
2,collision
zones;
3 and4,plate
boundaries:
3,transform,
4, divergent
[Weiisel
et
al., 1980];5, epicenters
of earthquakes
withstrike-slip
fbcalmechanism;
6, thrustfaultmechanism;
7, directions
of themaximum
compressional
axis(fromin situmeasurements)
jSykes,
1970;SteinandOkal,1978];8, young(orrejuvenated)
faults;9, old
transform
faults[Levchenko,
1986];10,basement
highs
(pluses)
andlows(minuses)
[Weissel
etal., 1980](seeinset);
11,location
of
theprofile
shown
inFigure
17;12,position
ofthehypothetical
future
subduction
zone;13,Komorine
and85E ridges
[Levchenko,
1986].
Fig.17.Seismic
andfree-air
gravity
anomaly
profiles
across
theintraplate
deformation
zoneintheCentral
Indian
Basin
(theprofile
location
isshown
intheinsetoilFigure
16) [Weissel
etal., 1980].
11,108
SHEMENDA-'
PHYSICAL
MODELING
OFSUBDUCTION
The flexure in the surface of the basement and the faults which
Oceanis alsofairly consistent
with the bucklinginstabilitystage
in themodellithospherein experiments
4 and5, Figures8 and 9.
The flexure wavelength•, in the model (with the scale factor
takenintoaccount)andin natureare consistent
aswell, beingof
the order of a few hundredkilometers(200 km on average).
Also, •, is not constantalongthe oceanicplate in eithernature
compensation
due,forinstance,
to crustal
thickness
variation. (Figure17) or the model(Figures8 and 9) contraryto what one
The basementtopography
is isostatically
uncompensated,
which wouldexpectbasedon an elasticmodelof the lithosphere.
This
is likelydueto flexureof thewholethickness
of the lithospheric is a resultof thenonlinearplasticproperties
of theplate.
plate[Weissel
et al., 1980;Shernenda,
1989b].
The modelresultsare thus in essentialagreementwith actual
The cause of the intraplate deformationseems to be situation. However, a more careful analysis of intraplate
subhorizontal
northwest-southeast
trendingcompression
of the deformation
andthrustingin the IndianOceanraisesa numberof
In particular,thezoneof flexuredeformation
is mainly
lithosphere,
judgingby ampleseismological
[Sykes,1970;Stein questions.
bounded
by the regionadjoiningthe southern
edgeof Hindustan
and Okal, 1978; Wienset al., 1986] andgeomorphic
[Weisselet
al., 1980; Levchenko,1986] evidences(see Figure 16). This andSri Lanka(Figure16). This is notpredictedby the model.In
et al., 1990] haveestablished
compressionof the Indo-Australianplate seems to have addition,recentstudies[Levchenko
zoneis far fromhavinga simple
originatedas a result of the collisionbetweenHindustanand thatthe intraplatedeformation
of lineardepressions
andrisesstrikingnortheastaspreEurasia[Weisselet al., 1980]. The deformationitself has been structure
mostlyon the basisof gravitydata[Weisselet
considered
as a resultof flexuralbucklingin the Indo-^ustralian viouslysupposed,
Haxby, 1987], but rather is spotty.Thesequestions
platedueto thecompression
[Weissel
et al., 1980;Cloetinghand al., .•:•'"-3;
Wortel,1985]. The conditionsfor suchbucklingtc occ',:•r
have may in part be relatedto the fact that our simple"two-dimenbeenstudiedby mathematical
modeling[McAdooand Sandwell, sional"modelinghas not adequatelyrepresentedthe "three-dimensional"natureof the situationin the zone of intraplatede1985;Zuber, 1987].
The overallpatternof deformationin the northeastern
Indian formation,due to the complex geometryof the continental
cutit are largelyflattenedby the sedimentary
cover.At the same
time, the long-wavelengthbasementtopographyis clearly
reflectedin differentialfree-airgravityanomalies
whichreachAg
= 80 mGal there (Figure 17) [Weisselet al., 1980]. Suchhigh
values of z•g are difficult to explain by invoking isostatic
............
............
::::::::::::::::::::::::
•::-:•:::.•.•::.•
....
Fig. 18. Resultof experiment
10 (viewedfromabove);(a)-(d) stages
of themodelprocess;
darkandlightlinesonthe photographs
represent
reverse
faultstransversing
theentirelithosphere
thickness
anddippingnorthward
andsouthward,
respectively;
thedottedline
in Figure18aapproximately
outlines
theareaof mostintensive
plasticdeformation
at theinitialstageof theexperiment;
dashed
linein
Figure18dshowstheultimatepositionof thesubduction
zone.
SHEMENDA:PHYSICALMODELINGOFSUBDUCTION
margin.Below we presentthe result of an experimentwhich
takes'mtoaccountto a first approximation
the configuration
of
the continental
margin(i.e., the boundarybetweenthe thick and
thin slabs)in the northernIndianOceanandadjacentboundaries
of theIndo-^ustralian
plate.
Experimentl O.The northwesternIndo-Australianplate under
studyis a continuous
layer in the model(Figure 18). The plate
(layer) abutsa rigid stop(bath wall) in the northwest,while the
easternandwesternboundaries
of the plate,corresponding
to the
Sundatrenchand the Carlsbergand CentralIndian Ridgesare
free (the layerthicknessalongthemis zero,the liquid "mantle"
is at the surface).Compression
is producedby a pistonmoving
fromthe southeast
at a constant
rate(Figure18a).
Similar to the previousexperiments,the initial stage of
deformation
involvesa plasticcompression
of the "oceaniclithosphere"whichdid not, however,occuruniformlyoverthe entire
areabut with greaterintensityin the region(approximately
outlined by dotsin Figure 18a) that abuttedthe Indian block on the
south. Buckling stability in this region is lost on further
compression.
Two frontal folds which have a slightly curved
shapearoundthe "Hindustan"and decaytowardthe southwest,
northwestand south,are most prominent.Instabilitydevelops
approximately
in the sameway as in experiments3, 4, and 5
described
above(Figures6, 8, and 9). Small reversefault•,
on the plate surface,mostlyin depressions
(they cmmotbe seen
in thephotographs).
The deformation
thenare localizedin some
placesin the depressions,
causingthe formationof secondary
stronglydislocated"localized"rises (ridges)which complicate
the patternof initial "flexural"folding.Later, inclinedfaults
11,109
formtraversingthe entirelithosphere
thickness.
In contrastto the
preceding
experiments,
thesefaultsoccurat differentplacesand
can be inclined in oppositedirections.Figures 18a and 18b
showstwo suchfaultswhichhaveformedon the oppositesides
of the "flexural"rise and dip in oppositedirections(seeFigure
18 caption).This "irregular"locationof zones of deformation
localizationand faults is typical of three-dimensional
models.
Furthercompression
produces
thrust(underthrust)displacements
alongthe new faults,with the faultsthemselves
gettinglonger
(Figure18b).As they grow,slabinstability(flexure)occurson
both sidesof the fault zone (betweenit and the lateral plate
boundaries).
The foldswhicharisethereareperpendicular
to the
compressionaxis and are not conformablewith the trend of
"older"foldsin the centralzone.Upon the background
of fault
growthandfolddevelopment,
thrust-strike
slipfaultsariseonthe
easternsideof the "Hindustan"
at someinstantof time (Figure
18c). Faults also then occuron the sidesof the central zone in
conformance
with the trend of folds developingthere. These
faultsinteractwith thosepropagating
out of the centralzoneand
producethe ultimateshapeof a new convergent
plate boundary
the configuration
of whichis outlinedapproximately
by a dashed
line in Figure 18d. This boundarydid not form in one eventas a
singlezone of one-directionalsubductionbut resulted from a
sequence
of restincturings
in local subduction
zonesthat formed
at individualfaultsandhaddifferentpolarities.
Thisthree-dimensional
modelingfurtherconfirmsthe existence
of flexuralbucklingin the lithosphereof the Indian Oceanand
elucidates some of the finer details in the structure of the zone of
intraplatedeformation.
In particular,the experiments
corroborate
'i'
Fig. 18. (continued)
11,110
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
the intuitivelyunderstandable
causeof deformationconcentrating
in the northernCentral Basin as being due to the continental
Hindustanblockjutting out into the oceaniclithosphere.Also,
the model provides insight into the possiblecausesof the
complexirregular(spotty)structureof the deformationzone.It
may be relatedto risesof two types,thosedue to lithospheric
flexure
and due to the localization
of deformation.
Certain
stronglydislocatedbasementhighs that can be detectedin
seismicprofiles traversingthe onset of deformationcan be
interpreted
as "localization"
ridges.
Polarity of subductionzones; trapped back arc basins.
Experiments3-5 show(Figures6, 8, and 9) that failure in the
lithosphere
dueto horizontalcompression
canoccurnot directly
in the continentalmargin, even thoughthere are subvertical
faultsthroughthe entirelithosphere,
but at somedistancetoward
the ocean.This rathersurprising
resultis dueto bucklingin the
oceanicplate prior to failure. The wavelengthof the buckling
controlsthe distancefrom the continentalmarginto the location
of failure in the lithosphere.
...
ment3 (Figure6), exceptthatthe modellithosphere
hadfirst beenseparated
Experiments
haveshownthat completefailureof the "oceanic" with a longitudinalverticalcut intotwo halves:(a) sectionof the frozendeplatein zoneof deformation
localization
canoccuralongtwo in- formedmodel;(b) deformedmodelasviewedfromabove.
tersectingplanesdippingin oppositedirections(Figures6c and
7b). For example,the fault planein experiment3 (Figure6) dips separatedfrom the nascentisland arc and the continentby the
underthe "continent",
while in experiments
4 and 5 (Figures8 arising subductionzone can exist for a long time. The
and9) it dipsseaward.
It hasnotbeenreliablyestablished
which dimensionsof the basinare controlledby severalfactors.When
directionis the preferedone.A largeseriesof experiments
would the simplest "two-dimensional"case is consideredin which
be necessaryto come to a conclusionabout this. Both sedimentload at the continentalmarginis absent(experiments3
possibilities
seemequallylikelyasdemonstrated
by theresultsof and4, Figures6 and 8), the basinwidth d is half the wavelength
of lithosphereflexure at the stageof formationof the buckling
the followingexperiment.
Experiment
11. Compression
of a modellithosphere
consisting instability,i.e., is of the order of 100 km. The presenceof a
wedge in the continentalmarginmay significantly
of twopartshavingdifferentthicknesses.
The conditions
of this sedimentary
experiment
are the sameas thoseof experiment
3 (Figure6), increased (experiment5, Figure 9). Also, the configurationof
exceptthat the specimen
of modellithosphere
has first been thecontinentalmarginmayplayan importantpart in determining
separatedinto two halves by a longitudinalvertical cut. The
initial stagesof experiment11 are similar to the experiments
describedabove:the "oceanic"lithospherebendsas a whole and
thrust faulting developson the surface.After that a zone of
deformationlocalizationcommonto both halvesstartsto develop
where, as usual,conjugateinclinedthrustzones(faults) form.
However,completefailureof the "lithosphere"
in the two halves
occurredalongdifferentshear(thrust)zones,i.e., alongplanes
dippingin oppositedirections.As a result,subduction
beganto
developin oppositedirectionstoo, which graduallydisplaced
subduction
zoneson both sidesof verticalfault (cut); seeFigure
19.
Failureof the lithospherealongone or the otherdirectionshas
importantgeotectonic
consequences.
For example,if the surface
of the platefracturedipsunderthe ocean,as wasthe casein experiments
4 and5 (Figures8 and9), thenconsumption
in the resultingsubductionzone of the part of oceaniclithospherebetween the subductionzone and continentalmargin inevitably
leads to their collision and the result is that the subduction zone
is claimed.Consequently,
a new failure of oceanicplate occurs
directlyat the continentalmargin, and the subductionsettles
downto proceedtowardthe continent.In this process,structures
of the attachedsubduction
zonehappento belongto forearcareas
of thenew overridingplate.A similarepisodemayhaveoccurred
duringthe evolutionof the Andeanmarginof SouthAmerica,
this beingthe only convergent
plate boundarywheresubduction
goeson directlybeneaththe continent.
If, onthe otherhand,platefailurein the zoneof deformation
localizationoccursalongthe fault dippingunderthe continent(as
in experiment3, Figure 6), then a trapped marginal basin
the dimensionsof the trapped back arc basins. This was
graphicallyillustrated in experiment 10 (Figure 18). Local
subductionzones originate first near the protrusionsof the
continentallithosphereinto the ocean,and then propagateto
meet eachother alongthe shortestroutes.Resultingsubduction
zonedo not mimic the configurationof the continentalmargin.
Natural analogiesof trappedback arc basin are the Aleutian
Basin in the Bering Sea, the Sea of Okhotsk, excludingthe
Kurile troughand someothers.
Applicationof the modelto oceanictransformfaults. A small
compressive
or tensilecomponentis alwayspresentin oceanic
transformfaultsalongwith the main strikeslip one.The signand
magnitudeof that componentlargely determinethe relief and
deep structureof the transformfault [Ushakovet al., 1979;
Dubinin, 1987]. The modelin Figures7a and7b canformallybe
appliedto faultsinvolvingtransverse
compression.
Indeed,plates
of differentagesand hencedifferentthicknesses
are in contact
acrossa transformfault. If the transformfault is regardedas a
two-dimensional
feature,then strike-slipdisplacement
on it can
notproducelithospheric
deformation.
Deformation
maybe dueto
thenormaldisplacement
component,
in particular,compression.
Theproblemof lithospheric
deformation
in a transform
faultdue
to such a compressionis similar to that consideredabove
(Figures6, 8, and 9), if the fault itself is subvertical.
According
to experimental
resultsa ridge shouldformby the localizationof
lithosphericdeformation(including crustal deformation)at a
distance of about 100 km from the fault. Verification
of this
hypothesis
requiresa detailedanalysisof the relevanttransform
faults.This is not, however,a subjectof this work. We merely
mentionthat the "regionof influence"of sometransformfaults
SHEMENDA:
PHYSICAL
MODELING
OFSUBDUCTION
characterized
by transversecompression
does involve features
(ridges)that can be regardedas beingdue to localizationof a
lithosphericdeformation.The features in question are the
Gorindgeridgein the easternAzores-Gibraltarfault [Verzhbitsky
et al., 1989] and the seamounts
of the Hosshusystemsome100
km southwardof it. Anotherexampleis the northeastern
part of
the Owen transform fault in the Indian Ocean. There is also a
rise associated
with crustalthickeningon the northwestof it at a
distanceof about100 km [Whitmarsh,1979].
It is supposedthat northwardsubductionis already occurring
underthe GorindgeRidge [Le Pichonet al., 1970]. This supposition is also consistent with the model. Subduction can indeed
start arounda transformfault, providingthe amplitudeof the
transverse
compression
is largeenough.
To summarize,analogiesfor all stagesof failure occurringin
the oceaniclithosphereunder horizontalcompressioncan be
found in nature. The initial stage of the process,buckling
instabilitydevelopingin the lithosphere(Figure 7a), seemsto
take place in the northeasternIndian Ocean;the intermediate
stage,localizationof deformationwith crustalthickening(Figure
7b), applies to the Gorindge Ridge; with the final stage
illustratedby numerous
subduction
zones.
Initiationof a $ubductionZone on an Old Dipping Fault
There is another,simplermode of formationof a subduction
zonewhich can occurif an old dippingfault or weakenedzone
strikingacrossthe horizontalcompression
is present.In such
situations,subductionon the dipping fault will be initiated,
beforethe compressive
stressesthat are sufficientfor buckling
instabilityto developin the lithospherehave beenreached.The
innertrenchslopeproducedthereforewill havea structurethat is
muchdifferentfrom that in the precedingmodel.It is largely
controlledby a deformationat the frontaledgeof the overriding
slabwhich occurswhen the edge cavesdown on the surfaceof
the subductinglithosphereduring initial stagesof subduction.
This effectcanbe seenin experiments6-8 (Figures10-12) where
the originallyhorizontaloverridingslab subsidedabovea fixed
dippingfault at the beginningof the subductionprocess.The
subsidencetook place when the unsupportedportion of the
overridingwedgewasheavyenoughto overcomeits yield limit xs
(the xsof the wedgehasnot beenexceededin Figure 10 but has
been in Figures 11 and 12), i.e., when conditionsbecame
availablefor plasticdeformationin the wedge.The deformation
in questionwasa superposition
of flexureproducingextensionin
the upper layers of the wedge and compression
in the lower
layers,combinedwith shearing(normal faulting) (Figure 20).
Greaterdetail canbe discernedin experiment12 (Figure21).
11,111
Experiment12. A horizontallayer that possesses
dilatant-plastic propertiesis placedon a rigid baseconsistingof two parts
thatcouldbe displacedrelativeto oneanotherin a subvertical
direction(Figure21). Sucha displacement
makesone area of the
model lithospheresubsiderelative to the other. Althoughthe
displacement
in thelayeris subvertical,
faultsstrikingacross
that
directionformat the initial stageof the subsidence
(Figure21a).
Further developmentis dominatedby normal faulting, with
normalfaultsandgrabensformingon the surface.At first sight,a
puzzling situation emerges:in spite of the fact that the
lithosphere
as a wholeis underconsiderable
compression
in the
subduction
zone (includingthe trench),both trenchslopesare
tensionalfeatures(Figure 20) (extensionof the outer trench
slope arises due to bendingof the oceaniclithosphere,see
below).This structuredoesoccurin someregions,for instance,
in the Central American (see Figure 22), Tonga-Kermadec
trenches[Gnibidenkoet al., 1985] andsomeothers.
Returningto experiments
6-8 (Figures10-12), onenotesthat it
is onlythe mostfrontalpartsof the overridingwedgedescending
below the initial horizontal level during subductionwhich
experiencesubsidence.
Fartherup the slope,the wedgeis on the
contraryuplifted and forms an isostaticallyuncompensated
frontalarc.The uplift is alsoaccompanied
by plasticdeformation
thatproduces
reversefaultsas shownin Figure20.
The blocky structureof the overridingwedge which forms
duringthe initial subduction
stagescontinuesto developduring
subductiondue to variousfactors.For example,reversefaulting
can occur due to friction with the subductingslab on the
originallynormalfaultsthat haveforme'tin the forearcportions
of the wedge[Lobkovskyet al., 1980]. Still greaterchangescan
be associatedwith modified angle of dip for the contactzone
between the slabs. The change in dip may arise due to a
nonuniformrate of workingout (tectonicerosion[yonHueneand
Lallemand, 1990]) of material at the base of the overriding
wedge.If the dip becomessmaller(and, accordingly,
the forearc
regionsubsides,
while the mostfrontalportionof the overriding
wedgeis uplifted, Figure 14), then the directionof •novement
a
•..,11111,
iiiii,
ii
'7111//•'1111111111111111•
,•
Fig. 20. Schemes
of the overridingwedge(plate)deformation
(whensubduction is initiatedon a dippingfault) and of the quasi-steady
deformations
of
thesubducting
plate(seeexplanation
in thetext).
_., -tHrill,
iiii/,
Fig. 21. Resultof experiment12. Developmentof deformationin the clay
layer due to subsidence
of one part of the rigid baserelativeto another
(carriedoutby A.N. Bokun).
11,112
SHEMENDA:
PHYSICAL
MODELING
OFSUBDUCTION
NNE
_
,,¾',
,
..
' '
?..:?'
......
8 •m
¾ig.22. Schematic
sectionthrou• tl• Guatemalatrench[a•t•rAubouinet al., 1982].
alongthe faultsin the ovemdingslabshownin Figure20 will be
reversed.Sucheffectscan also occurwhen the pressureof the
subductingslab on the overriding one is changedowing to
changesin subduction
from the Chileanto the Mariana typesand
viseversa[Shemenda,
1985].
Stressesand strain in the subductingplate. While the bulk of
deformationbecomesextendedand vanishesaltogetherin the
limit. In contrast,increasingW as well as decreasingx8 makes
shear deformation
narrower
more intensive
and better defined
such that shear zone becomes
in outline
as is seen in the next
experiment.
Experiment13. Subduction
occursundera stiff stopdippingat
deformation and hence formation of the structure of the overridan angleof 450 which occupiesthe placeof the overridingslab.
ing wedgetakesplacewhenthe subduction
zoneis initiated,the
The subducting
plate experiences
a sharpflexurein front of the
subducting
plate experiences
largequasi-stationary
deformations stop.Its internaldeformation
canbe inferredfromFigure23. The
at all time. ll•ese were studiedby the techniquefor visualizing character of curvature in the transverse lines shows that shear
deformation
describedearlierbasedoncurvatureof the originally (reverse)faultingis dominant,developingaroundthe line AB in
rectangulargrid and of circlesdrawn on the model lithosphere. Figure 23. To see this, one shouldcomparethe experimental
Thetechnique
incorporates
the concepts
andfamiliarsolutions
of
pattern(Figure23) to the ideal scheme(Figure24) of pureshear
plasticitytheory. The subductingplate has been shown to
derivedby simple geometricalconstructions.
Althoughthe patternsareroughlysimilar,the experimentalresultis morecompliexperienceflexure in front of the subductionzone, leadingto
compression
of the materialat thebaseof the plateandextension cated. The causesof this are, first, that the shear zone is not
straightand, second,that practicallythe entire flexure zone inat the top (Figure20). Normal horizontalstresses
in the top and
volvescomparativelysmall deformation.Two otherzonescan be
bottomof the slab acrossthe trenchhave exceedthe yield limit
identifieduponthe background
of this deformation:
one lies in
in the area involvingthe outer(oceanic)trenchslopeand part of
the lowerpart of the intexion regionandthe other(ACD, Figure
the outer rise leading to plastic deformationthere. The
23) underthe stop(appropriateslidinglinesare shownin Figure
subductingslab has increasingcurvaturefrom the outer rise
with
towardsthe trenchduringlater stagesof subduction.
This leads 26). The lower zonedominatingthe slabbaseis associated
while the upperzone resultsfrom the
to increasingplastic deformationand developmentof plastic flexure and compression
fact that it is the upperlayersof the slabwhich are the first to
zonesinsidethe slab (dashedin Figure20). The growthof the
experience
the pressureexertedby the stop.Theyare, as it were,
deformation
is accompanied
by smalllinear normalfaultingon
the plate surfacein the outertrenchslopeparallelto the trench. pressed.intothe body of the rest of the specimen.In addition,
Becausethe averagestressin the plate duringsubductionis
frictionexertedby the stopactsas a brakeon the top of the slab
(the valueof frictionis relatedto angle¾).
compressive
in the crosssection(about0.3•s), the pictureis
asymmetrical
in that the lowerplasticzoneis thickerthanthe
upperone(Figure20).
The flexure of the subductingslab becomesmore complex
closer to the trench where the slab curvature is at a maximum. In
the zone of maximumbendingmarked as a stippledarea in
Figure 20, the thickeningupper and lower plastic zones are
merged and connectedby sliding lines which accommodate
shearing(reverse) faulting movements.When the region of
maximumbendinghas beenpassed,the thicknessof the plastic
zonesand the deformationin these decreasesharply,the slab
then sinkinginto the "mantle"without further deformation.It
shouldbe emphasized
that this situationis obtainedbecausethe
subducted
portionof the slabis in a hydrostatic
equilibriumwith
the surrounding"mantle"and doesnot experienceany dynamic
influencedue to it. If there is no equilibrium,the deformation
patternwouldapparentlychange.
To summarize,the comparatively
sharpchangein the direction
of movementof the subductingplate in the subductionzone
occurs,not only owing to extensionand contractionof plate
materials.
due to flexure but also due to shearing(thrusting)
motion. The significanceof the shear in terms of total slab
deformationdecreaseswith decreasingdip angle, •, of the
contact surface between slabs. The zone of shear (thrust)
Fig. 23. Resultof experiment13. Subduction
undera rigid stopdippingat an
angleof 450(thepartofthedeformed
andfrozenspecimen
in thesubduction
zoneis shownin the photograph;
the transverselinesin the plate had originally been vertical and perpendicularto the surface of the undeformed
specimen;
dashedlinesshowthe main slidinglines(seethe text for more explanations).
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
11,113
A•
B
Fig. 24. Platethickness
changingin the subduction
zoneandbendingof the
linesmarkedin the slabfor theidealcaseof pureshearalongthe straightline
AB.
Fig. 26. Slidinglinesin thesubducting
plate(seeexplanation
in thetext).
of the contactnonhydrostatic
pressureC•nwhich the subducting
plate exertson the overridingplate usingplasticitytheory.This
pressurehas proved to be C•n • -0.9x, [Shemenda,1979;
Lobkovskyand $hemenda,1981]. The full pressureP at each
pointof AC canbe derivedby addingthe term p•gzto C•n(z is the
verticalcoordinateof the point).
The mean pressurep•gz corresponds
to the full hydrostatic
equilibriumat depthz. The excessC•ndisturbsthe equilibrium,
producingsomenonisostaticuplift in the overlyinglayers(those
above the plate contact).The friction between the plates,
tendson the contraryto pull them downwards.The net vertical
pressure
C•vis: C•v= C•n+ x,tg•q.The frictionXnin experiment13
can be estimated from the value of ¾, the angle which
characterizes
the upperzone of uniformstressin Figure 23 as
= z,cos2¾[Hill, 1950]. Assumingthe pressureC•vto be fully
spenton producinga pistonuplift of the lithosphereareaslying
directlyabovethe line AC (Figures23 and 26), one can determine the uplift amplitude Ahn: /•n = -ffv/P•g = xs(0.9 Estimationof Departure From lsotasyin the $ubductionZone
cos2ytg•q)/p•g.
Substituting
the values• = 1.3 x 108Pa, •q = 420,
Analysisof the experimentalresults(Figure 23) allowedthe
¾= 220 (seeFigure23), we get/•hnv,1 km. Thus,theremustbe a
determination,at least in part, of the structureof the field of
free-air gravity anomalyfig abovethe nonisostatically
uplifted
slidinglines in the regionof a plasticdeformation(Figure 26)
layerof thicknessfihn:the anomalycanbe estimatedby usingthe
and the conclusionthat the plasticzoneACD abatingthe stop
formula for a plane parallel layer [Lobkovskyand Sorokhtin,
(overridingplate) is underuniformstress.This allowsderivation
1976]' Ag - 2•zfpl6h- 140 mGal, wheref- 6.67 x 10-7m/(kg x
s2)is the gravitationalconstant.
Positivegravityanomaliesof this
order are typical of actual subductionzones.If the interplate
W
E
frictionxnin the subduction
zonewere absent(¾= •/4), thenthe
0K• v ¾oVv
¾ 0KmgravityanomalywouldequalAg - 470 mGal.
When subductiondevelopsat a steeperangle, the shearzone
doesdegenerate
into a straightline in the experiments,
as shown
in Figure24. This is easilyseenin experiment1 in Figure4. The
existenceof sucha line (zone)andthe majorrole playedby shear
movements
in the oceanicplatein the subduction
zonehavebeen
hypothesized
byLobkovsky
andSorokhtin[1976].
Thus the width of the region of shear deformationin the
subducting
slab,its positionrelativeto the trench,andthe intensityof deformationin it dependon the specificsubduction
conditions.It canbe expectedthat whenthe shear(thrust)deformation in the regionof maximumflexureis largeenoughand concentrates
alonga comparatively
narrowzone(as in Figure23), it
should be detectable in the distribution of earthquake
hypocentres.
It is possiblethat the hypocentralswarmobserved
in the distributionsof earthquakesfor somesubductionzones
whichform the focalzone dippingoceanward(Figure25), have
just thisorigin.
400
•oo
•oe•9•
o //
"øe-
\
-
' •100
Elastico-plasticBendingof the LithospherePlate and Estimation
•eooof Its YieldLimit and Modulusof Elasticity
The excesspressurebetweenthe platesleadson the onehandto
a nonisostatic
uplift of frontalpartsof the overridinglithosphere
andonthe otherto bendingof the subducting
plateandformation
of a deep-sea
trench.On accountof the elasticpropertiesof the
/
lithosphere
andthepresence
of an effectivelyliquidbasebeneath
/
it, plate deformationdue to bending is transmittedover a
considerable
distanceseaward,creatingan extendedrise of small
amplitude known as the outer rise. This subduction-related
Iol, lo1
Iol0 !o11
ß
Io Ivvvl?
phenomenonis well known, suchthat there is little doubt that
the trenchandthe outerrise are causedby quasi-elasticbending
Fig. 25. Earthquakehypocenter
projections
on verticalplanestransversing
of the subducting
plate. Gunn [1947] was the first to suggesta
Japan (Honshu) subductionzone [$ychev and Tarakanov, 1976]: 1-5,
mathematicalmodel for this bending.Numerouslater studies
earthquake
foci projections;
1-4, magnitude
M from 7 to 3.5; 5, M is unknown;6, deepseatrenchaxis;7, crust.
were largelyconcerned
with refinementsof his modelin orderto
OKra
11,114
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
derive theoreticalsolutionsthat better corresponded
to actual
bathymetricprofiles across various subductionzones. Such
solutionswere used to evaluateparametersof the lithosphere.
This approach
encounters
severaldifficulties.Theyare relatedto
an indeterminacy
of the boundaryconditionsfor the bending
platein the subduction
zoneandthe nonstationarity
natureof this
bendingat the earlieststagesof subduction
(onlythesestagescan
usuallybe modeledmathematically).The relief at thesestages,
as shownby experimentalresults,is considerably
differentfrom
that at later subductionstages.As shown in Figure lob, the
maximumbendingof the subductingplate at the beginningof
subduction
occursin the upperpart of the outertrenchslope(see
the arrowin Figures10b and 10c), while practicallyno bending
is observedin the lowerpart.An equilibrium(steadystate)shape
of the bendingis establishedduring subduction,
with the part
having maximum curvaturebeing shifted trenchward(Figure
10e).The trenchbecomesshallowerandnarrowerin theprocess.
Certaindifficultiesalso arise when experimentalmodelingis
used. For example, a comparisonof experiments6 through8,
Figures10 to 12 yields a fairly reliable estimateof c•s,as the
plate shape in the subductionzone stronglydependson that
parameter.The best fit is obtainedin experiment8 (Figure 12)
for c•p• 2• m= 30 Pa, asmentionedearlier.AdoptingHo = 60 km
as lithospherethickness,we use (1) to get a value of c• = 2.6 x
108Pa. Similar valueshavebeen derivedby otherworkersfrom
gravitydata[Lobkovslcy
and Sorokhtin,1976; Ushakov,1968].
The effectivemodulusof elasticityE for the platehasalsobeen
varied. However, the changesin the deformationof the lithosphere were too small to be observed.Therefore numerical
modelingof the initial stageof subductionhas beenusedwithin
the framework
of formulation
which
is similar
to the initial
stagesof experiments6-8 (Figures 10-12) [Tishchenko,1985].
The value of c•7was fixed to be that which followed from the
experimentalmodeling. The results indeed show a weak dependenceof the shapeof the bendingplate on Eo. Any of the
valuesof E within range 10•0 to 10• Pa are suitable.Outsideof
that range,the amplitudeof the outer rise is either too small or
too large. The value which was used in the experiments
describedhere lies within the above range. The values of
lithosphereparametersadoptedat the startof this work c•ø = 2.6
x 108 Pa and Eo = 1.7 x 10•0 Pa thus follow from modeling
results.At the sametime they are consistent
with the resultsof
compression
produceda localizationof deformationthere in the
sagging(similarto in experiments3-5, Figures6, 8, and 9), the
plate experiencedfailure then and a new subductionzone
formed.
CONCLUSIONS
1. Compression
of lithospherein the areaof a passivecontinental marginproducesa bucklinginstabilityin the oceanicplate
havingwavelengthsof a few hundredkilometers.Later, a localizationof deformationoccursin a downwarpat somedistance
from the margin, with accompanyingthickening of the
lithosphere
and formationof a linear ridgedue to the thickening
and thrusting. The plate then experiencesfailure along the
dipping zone, and subductionstarts. The inner trench slope
which forms during failure of the lithospherehas a typical
scarpedstructure.Its lower part containsa dislocatedblock of
oceaniccrustand sedimentsformingthe slopebreak.In front of
this there is a "reservoir"
which
is filled
with
arc-derived
sedimentsto form a deep-seaterrace.Someactualtrencheshave
a similar structure.
Different variants of the above failure mechanism for a continu-
ous lithosphereare possibleif it containszones where the
lithospheric
thicknessor strengthis reduced.
2. Modelingof the situationexistingin the zone of intraplate
deformation
in the northeastern
Indian
Ocean corroborates
an
earlierhypothesis
of a bucklinginstabilityof the lithospheredevelopingin the area, and of the initiation of a new subduction
zone.
3. If there is an old dippingfault strikingacrossthe compressionof an oceaniclithosphere,it is on that fault that a subduction
zoneis initiated.The inner trenchslopehas a differentstructure
and formsdue to normal faulting which developsin the frontal
part of the overridingplate. The formationof a subductionzone
then requiresless compression
than in the precedingcaseby a
factor of 2 or 3.
4. In contrast to the overriding plate where deformation
developsmainly during the initiation stageof subduction,the
subducting
plate experiencescontinuallarge quasistationary
deformations. These are controlled in front of the subduction zone
It is interestingto notethat the width of the outerrise is 300 to
400 km on average.The plate bendingwavelength•, is then600
to 800 km. On the other hand, the bucklinginstabilityfor the
lithospherein the zone of intraplatedeformationin the Indian
Oceanhas a wavelengththat is smallerby a factorof three or
by an elastico-plastic
bendingof the oceaniclithospherethat increasescloserto the trench. The bendingbecomesso large directly in the subductionzone (under the overridingplate) that
shear(thrust)faultingcan develop(dependingon specificconditions) alongthe zone dippingunder the oceanand crossingthe
entirelithosphere.
An analysisof the stress-strainstate in the model subducting
plateyieldsthe pressureexertedby the subducting
lithosphereon
the overridingplate and permits an estimationof the free-air
positivegravityanomalydueto it. The anomalyamountsto a few
four. The difference
hundred milliGals.
other workers.
seems to be due to a different
horizontal
compression
of the lithospherefor both thesecases.With small
5. The best agreementbetweenthe generalizedrelief of the
subduction zone in the model and nature is achieved when the
or no compression,
•, reachesvalues of about 1000 km, while
followingeffectivevaluesare adoptedfor the real lithosphere:
whenthe compression
is closeto oh,the valueof •, diminishesto
shearyield limit z• = 1.3 x 108Pa; modulusof elasticityE about
a few hundredkilometers.Experimentshavebeencarriedout in
a few times 10• Pa, and thicknessH = 60 km.
which the subductionzone was "jammed"at some stage of
subduction(this was done by local cooling of "lithosphere"
material in the contact zone between the plates). Since
NOTATION
subduction
becameimpossible,the motionof piston4 (Figure 1)
lithosphereyield limit undernormalloading.
led to a greatercompression
of the model.This was accompanied
•s
lithosphereshearyield limit.
by a considerable
contractionin the lengthof the outerrise and a
horizontalnonhydrostatic
stressin the lithosphere.
growthof its amplitude.At the sametime the flexure (sagging) (•h
on the seaward side of the rise increased. Subsequent E
lithospheremodulusof elasticity.
SHEMENDA:
PHYSICAL
MODELINGOFSUBDUCTION
H
lithospherethickness.
thicknessof thinnedsegmentof theplate.
thicknessof the sedimentary
wedgeonthe passive
continentalmargin.
lengthof the sedimentary
wedge.
width of the marginalbasin.
nonisostatic
verticaldisplacement
of the surfaceof the
overridingplate.
lithospheredensity.
asthenosphere
density.
acceleration
dueto gravity.
gravitationalconstant.
h
hs
1
d
•n
Pl
shear stress.
deformation.
11,115
Jacoby,W.R., Paraffinmodelexperimentof platetectonics,Tectonophysics,
35, 103-113, 1976.
Jacoby,W.R., andH.Schmeling,Convectionexperiments
and drivingmechanism, Geol. Rundsch., 70, 207-230, 1981.
Kachanov,L.M., Principles of Plasticity Theory (in Russian),418pp.,
Nauka, Moscow, 1969.
Kincaid,C., and P.Olson,An experimentalstudyof subducting
slabmigration,d. Geophys.Res., 92, 13,831-13,840, 1987.
Kirby, S.H., Tectonicstressin the lithosphere:
constraints
providedby the
experimentaldeformationof rocks,d. Geophys.Res., 85, 6353-6363,
1980.
Kirby, S.H., Rheologyof the lithosphere,
Rev. Geophys.,21, 1458-1487,
1983.
Le Pichon,X., J.Bonnin, and G.Pautot, The Gibraltar end of the Azores-
Gibraltarplateboundary:An exampleof compressive
tectonics,
paperpresentedat UpperMantle CommitteeSymposium,
Flagstaff,Adz., July 1826, 1970.
Levchenko,
O.V., Geologicalstructure
of a zoneof intraplatedeformation
in
the CentralIndianBasin(in Russian),Ph.D. thesis,InstitutOkeanologii
strain rate.
frictionbetweenplatesin the subduction
zone.
Acad. Nauk SSSR, Moscow,' 1986.
nonhydrostatic
pressurebetweenplatesin subduction Levchenko,O.V., L.R.Merklin, and V.E.Milanovsky, On the structureof
•n
O'n
zone.
C•'V
verticalpressurein the interplatesurface.
T
temperature.
wavelengthof lithosphereflexure.
dip angleof the interplatesurfacein the subduction
zone.
anglecharacterizing
plasticdeformationin the subducting plate.
free air gravityanomaly.
plate velocity.
time.
deflectionof the lithospheresurfacefrom the isostatic
equilibriumlevel.
familiesof slidinglines.
Acknowledgments.
I thank A.N. Bokunfor use of unpublishedresult
of model experiment. I expressmy thanksto A.L. Grocholskyfor
generalassistance.I wishto thankL.I. Lobkovsky,O.G. Sorokhtin,and
S.A. Ushakovfor discussions
which were helpful in this work and E.A.
Tishchenkofor performanceof relevantnumericalexperiments. I also
thankreviewerP. Peltzerand editorfor helpfulcommentson manuscript
as well as J.M. Nesterand A. Smithfor the improvementof the English
version of the paper. This work was supportedby Moscow State
University, Research Center GEOSPHERE (Moscow), and National
ScienceCouncil, Republicof China.
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(ReceivedJune17, 1991;
revisedJanuary8, 1992;
acceptedJanuary16, 1992.)