JOURNALOF GEOPHYSICAL RESEARCH, VOL.102,NO.B6,PAGES11,943-11,956, JUNE10,1997
Effect of anisotropy onoceanic uppermantletemperatures, structure,and dynamics Elizabeth HardingHearnandEugeneD. Humphreys Department ofGeological ScienCes, University ofOregon, Eugene
Mu Chai and J. Michael Brown Geophysics Program, University of Washington, Seattle
Abstract. Olivineandorthopyroxene crystals composing theoceanic upper mantle alignunder progressive simpleshearstrain.Because thethermal diffusivities (r) andviscosities oftheseminerals areanisotropic, mineral alignment affects vertical heatflowandupper mantle dynamics. The vertical thermal diffusivity ofuppermantle peridotite decreases withprogressive simple shear strain, leading tohigher temperatures intheshallow upper mantle thanpredicted byanisotropic half:space coolingmodel.This,in turn,causes highersurface heatflow,shallower oceanbasins, weaker asthenosphere, andslightlythinnerlithosphere. Viscosity associated withanorientedsimpleshear strain(r/sh),suchasthatcaused by platemotion,alsoevolves withprogressive strain, though r/shathighstrains hasnotbeencharacterized. Regardless of theevolution of r/.,.h with strain, theeffectsof thermaldiffusivityanisotropy onuppermantletemperatures, surface heat flow,lithosphere thickness, asthenosphere viscosity andshearstress attheplatebottomremain evident. Shearheatingelevates thegeotherm bymorethanr anisotropy except in theyoungest o,'ean andin cases withsignificant shearweakening ora slowlymovingplate(lessthan-3 cm/yr).
Themagnitude ofshear heating effects depends onhowr/sh increases ordecreases athighstrains. Formodels in which•shincreases asa functionof strain,shearheatingelevates temperatures beyond reasonable uppermantleestimates (i.e.,above1400øC), suggesting thatsuchstrain . induced viscosity increases arenotlikely. Wepresent a modelfor oceanuppermantlecoolingand deformation thatincludes uppermantlethermaldiffusivityanisotropy andshearheating.This modelpredicts heatflow,shearwavesplittimes,lithosphere thicknesses, andbasindepthswhich areconsistent with observations butsuggests thatbasaltractions onoceanplatesarelowerthan previously thought.
Introduction
weak (010)[100] slip systemsin the transportvectorplaneand their [010] axesverticallyoriented[cf. Zhang and Karato, 1995; Anisotropy in the oceanicuppermantlehasbeenrecognized Ribe, 1989a;Etchocoparand Vasseur,1987]. Other numerical by severalstudies,most of which are basedon seismicobservamodelssuggest thatolivinecrystalsalignwith theirweakslipsys-
tions.Early Pn findings[Hess,1964] suggested alignmentof olivine[100]axesin thedirection of platemotion.Morerecently, surface waveand shearwavesplittingstudies[e.g.,Nishimura andForsyth,1989;Farra and Vinnik,1994;Kuo and Forsyth, 1992]haveconfirmed thepresence of uppermantleanisotropy to depths of up to 200 km in old oceanmantle[Nishimura and
temsorientedat someanglewith respectto the shearplane[cf. Wenket al., 1991; ChasteI et al., 1993]. In either case,LPO
shouldbe well developed in andabovethe asthenosphere, where totalstrainsaregreatest(FigureI). Sinceolivineandorthopyroxeneare anisotropic with respectto thermaldiffusivity•c(Table1), their alignmentchangesthe upper mantle verticalthermaldiffu-
Forsyth, 1989].Latticepreferred orientation (LPO)of anisotropicsivity. The conductivecomponent of verticalthermaldiflhsivity olivineandpyroxenecrystalsin the uppermantleis directly (r•) in the uppermantledecreases by up to 25% relativeto the observed in peridotites from severalophiolitecomplexes [cf. isotropicvalueas the low-r olivine [010] crystallographic axes
Turner,1942; Ave'Lallemantand Carter, 1970; Christensen, becomevertically(or near-vertically)aligned[Chaiet al., 1996]. 1984;Nicolasand Christensen, 1987]as well asin deformation Orthopyroxene alignmenthas little effect becauseits vertically experiments [ZhangandKarato,1995]. alignedcrystallographic axis, [100], exhibitsthermaldiffusivity Experiments andnumerical modelssuggest thatLPOdevelops intermediateto its extremevalues (Table 1). This strain-induced
inresponse to progressive strainandbecomes increasingly well low-•c• mantle horizon will impede heat flow and raise the developed asstrainincreases [cf.ZhangandKarato,1995;Ribe, geothermin the upper mantle,therebyweakeningthe astheno1989a; Etchocopar andVasseur, 1987;Wenk etal., 1991].Exper- sphereand elevatingthe oceanbasins. Figure 1 schematically iments, ophiolite analyses, andsomenumerical models indicate illustrateshowolivinecrystalalignment,creatingan uppermantle thatathighsimple shearstrains, o!ivinecrystals alignwiththeir zonewith low •, affectsT andshearviscosityin the uppermantle.
Copyright 1997 bytheAmerican Geophysical Union. ?aper number 97JB00506. 0148-0227/97/97JB.00506509.00
The uppermantleshearviscositythatresistsplatemotion01.,.h) alsovarieswith progressive shearstrain,thoughthisvariationhas been characterizedonly at low strains. If crystalsalign at some angleto the macroscopic transportvectorat highstrains[Wenket 11,943
11,944
HEARNET AL.: OCEANICUPPERMANTLE ANISOTROPY
total
Kv
T
log1'1
mid-ocean ridge
.•.....%z'•.....•.
T=0C u=10cm/y_.r
_
,
200
I'-1
400
ß
•.,,
[
I T=1330C u=Ocm/¾r
6OO
Increasing plate age
........
-
Figure1. Conceptual diagram of ourmodelshowing representative œtotal, K',T, andlog(r/.,)profilesat a givendistancefrom the mid-oceanridge. We assumethat LPO developsunderprogressive simpleshearstrain in the
asthenosphere and is preserved in the bottomof the coolingandthickening lithosphere. The alignmentof anisotropic olivineandpyroxene crystals in areaswithhighetot•t reduces r in theverticaldirection, raisingtemperaturesandtherefore reducingr/.,.h.(r/anisotropy is notassumed.)Foreaseof illustration, strainellipsesrepresenting strains of upto 3 areshown;muchgreater strains areactuallyattained in oceanasthenosphere.
We developedseveralmodelsto estimatethe effectof thermal that shearviscosityincreases as the varietyof slip dislocation and mechanicalanisotropyon upper mantle viscosityprofiles. aL, 1991; Ribe and Yu, 1991; Chastelet aL, 1993], we assume
planesfavorablyalignedfor plate motionsheardeclines.On the otherhand,if the weak olivine and pyroxeneslip planesalign withthesimpleshearflowdirection[cf.ZhangandKarato,1995; Ribe, 1989a;Etchocoparand Vasseur,1987;Nicolasand Poirier, 1976],viscositymayapproach an asymptotic valuelowerthanthe initial (unstrained)shearviscosity. In this case,deformationis accommodated primarily by the weak slip system,which is alignedwiththetransport vector,anddeformation by othermechanismswill be activatedonly at low rates,andwill contribute relativelylittle to the bulk viscosity.We recognizethat theseideas do not accountfor imperfectalignmentof crystalsat highstrains (asnotedin ophiolites[cf. Christensen,1984;Nicolasand Chris-
Becauser anisotropyis better characterizedthan r/ anisotropy, we explorethe effectsof •' anisotropyon developingoceanlithosphereand evaluatehow the straindependence of shearviscosity
tensen,1987]whichcouldinterferewith weakening, or for the effectsof syntectonic recrystallization at highstrains[Nicolaset
We developtwo groupsof anisotropic uppermantlemodels, as well as an isotropicreferencemodelfor comparison.The reference modelrepresentsmantle viscosityand heat flow basedon currentlyacceptedrelations. We modif3tthe referencemodelto accountfor anisotropicthermal diffusivity and shear heating. Becausethe behaviorof peridotirer/.,. h at extremestrainsis not
al., 1973].
Table1. ThermalDiffusivity Value
x I 0-6 m 2/s Ol•ine
100 010 001
2.16 1.25 1.87
O•hopyroxene 100 010 00I
1.26 1.06 1.66
Weightedaverage for peridotite(70% olivine)
All values arefromChaietal. [1996].
1.63
71.,.h(s) (wheres refersto macroscopic simpleshearstrainof the peridotiteaggregate)could interferewith or intensifythese effects.We considercaseswith increasing anddecreasing r/.,.h(s), as well as caseswith strainindependent r/.,.h(S).We alsoexplore the effectof shearheating,whichis significant in casesfor which viscosityincreasesor remainsconstantwith increasingstrain.
Modeling
known,we runouranisotropic modelswithseveralhypothesized viscosityfunctions.
Deformation and Cooling
We simulate a seriesof one-dimensional oceanicuppermantle profilesbeneatha rigidplatemovingat 10 cm/yrwith respect toa
stationary interiormodeled at 600 km depth(Figure1). Wecalculatetemperature (T), pressure (P), andshearviscosityat nodes
spaced at 10km depthintervals.Givenviscosity profiles, wecalculatea seriesof relativestrainrate (•) profiles,andfromthese we calculate shearstrain(s) profiles.Strainrateis calculated with • =(dufdz+ dw/dx)/2,in whichx andz represent thehorizontalandverticaldistances, respectively, andu andw represent
HEARN ET AL.' OCEANIC UPPER MANTLE ANISOTROPY
Thermal Diffusivity m2/sxlO-6
the horizontal andvertical velocities, respectively. In ourcase of
simple shear, strain ratebecomes •=(du/dz)/2. Assuming that
0.9
viscosity varies much morerapidly withdepth thanwithhorizontaldistance, shear stress cronthehorizontal planeisatanypositionnearlyindependent of depthandthestress termdoesnot influence thestrain rate.Tocalculate •(z), wenotethatforsim-
0 km
.
0 km
•.,.h(Z)
1.2
1.3
1.4
1.5
1.6
1.7
1.8
100
100 MY
6(X) km
•dz = cr
1.1
MY
thedepth-integrated shear rateequals theplaterateuo: uo = 2
1
0
ple shear 2•(z)=cr/r!.,.h(Z) foraconstant stress o'chosen such that 6(X) km
11,945
200
(1)
Thisyields
150 MY
::r 300 6(X} km
3
• = 2S•7.,.h(Z) 1 forS=uo 1o!.,•fish(Z) dz (2)
400
The initial temperatureprofile represents the uppermantle
beneath a spreading center.Temperatures fromCordcryand Phipps Mo•xan[1993]areusedforthetop20kmof thespreadingcenter profile.At 20 km,thetemperature is 1330øC, and
50O
below20 km we add an adiabaticgradientof 0.3øC/km.We use
anexplicitfinitedifference scheme to calculate temperature profilesforolderlithosphere anduppermantleawayfromthespread-
6OO
ingcenter at 0.5 Myr increments. Temperatures arecomputed 2. TheJr(P,T) for uppermantleprofiles of several ages, assuming verticalthermaldiffusion anda DirichlettemperatureFigure derivedfrom Schatzand Simmons[1972], Zaug et al. [1992], and
(r) boundary condition of 0øCat thesurface.Valuesof parame- Chaiet at. [1996] (see text). The dashed line represents r = 10-'6m2/s, thevalueusedin mostof ourmodels.
tersusedin our models are shown on Table 2.
Calculations of deformationand coolingare straightforward,
buttheequations requirerv andr/.,.h, whicharefunctions of tem-
perature, pressure, andstrain.Thefollowing sections describe howwe modelthedependence of r,, andr/.,.h ontheseparameters. fusivity [Zaug et al., 1992], and scale the relation to yield Behaviorof r (P, T). Thermaldiffusivityof uppermantle 1.63x 10-6 m2/sat thelithosphere surface to matchtheexperi-
peridotites is a function of pressure andtemperature [cf.Schatz mental r value from Chai et aI. [1996] (the Schatzand Simmons andSimmons, 1972;Scharmelli,1982;Zaug et al., 1992]. Zaug [1972]relation gives a r ofabout1.5x 10-6 m2/satsurface T and etaI.[I 992]findthatforperidotites, theconductive component of P), we producethe r(P, T) profilesshownin Figure2. Because r ispressure dependent andincreases by 4%/GPa.Thepressureof uncertaintyregardingthe temperaturedependenceof Jr and dependence of theradiative component of Jrfor olivineis only other effects(suchas phasetransitions)that could causefurther slightly sensitive to pressure [Shankland, 1970].Thetemperatureuncertaintyin uppermantler(P, T) models,we concentrate on a dependence of Jrfor mantleperidotites is moredifficultto deter- simpler model in whichJrisfixedata valueof 104 m2/s,which
minethanthepressure dependence because boththeconductivehas been commonlyusedin mantlemodels[Turcotteand Schuandradiative components arehighlysensitive totemperature, and bert, I982]. This choiceis made to maintain as much simplicity a broadrangeof estimates of the radiativeandconductive r as possibleandto allow straightforward comparison of isotropic
components existsin the literature[cf. Schatzand Simmons, reference
model results with results from models modified to
1972;Scharmetti,1982].
accountfor anisotropy.Comparisonsimulationsrun using the If we assumea Jr(T) relationship derivedfrom the thermal Jr(P, T) modelshownin Figure2 are discussed in the modelsenconductivity relationof Schatzand Simmons [1972],assumea sitivitysection.In general,the exactchoiceof r for the reference 4%/GPaincrease in the latticeconduction partof thethermaldif- modeldoesnot significantlyinfluenceour findingson the effects of Jrand r/anisotropy.
Table2. ModelParameters andBoundaryConditions Parameter
Value
E*
540 kJ/mol
V* a
1.5x 10-5m3/mol 3.0x 10-5m3/øC
ce p
1.17 kJ/kg øC 3300 kg/m 3.
V6•x) To T6•x•
0 cm/yr 0øC 1530 øC
r uo
10-6m2/s 10cm/yr
Behavior of r/sh(P, T). We assumethat deforrp. ation occurs via dislocation creepat all depthsin the uppermantle.With E* and V* representingactivationenergy and activationvolume, respectively, and cr andR representing shearstresson the horizontalplaneandthe gasconstant, the effectiveviscositycanbe calculated with
a• expE*+PV*) ....RT rl•#.= or2.----
(3)
wherea is a scalingfactor[Karatoand Wu,1993]. After groupingthepreexponential expression intoa singletermCo,whichwe useto incorporate straindependence, theexpression for effective shearviscosity associated withshearalonghorizontal flowplanes (rL,.h) is
11,946
HEARN ET AL.: OCEANIC UPPERMANTLE ANISOTROPY
•l.•.•,(e) =CcexpE*+PV RT' *) '
section of thispaper,wediscuss another modelin whichonlythe
(4)
At the ridge,Ce is assumed to equalits isotropicvalue(C0), whichis chosento yield a minimumasthenosphere viscosityof
conductive componentof x-is modeledasanisotropic. Anisotropicr/. Because theevolutionof r/.,.h at extreme strains is notwell understood, we investigate two possibleeffectsof LP0
r/.,.h soasto bracket likelyshearviscosity behavior athigh 5 x 10TM Pa s. In theisotropic reference model,Cc is heldcon- on strains:weakeningand hardening.If we assumethat olivineand stant.
pyroxene aligncrystallographically suchthattheirweakslipsystemsareoriented closelyto theflowdirection, precluding signifiAnisotropicBehaviorof r andr/ cantactivation of secondary mechanisms, theresultisweakening. Forsimplicity, we assume aninitiallyisotropic uppermantlein This is consistent with pastmantlemodelsaccounting forr/ all of our models.Any previouslydevelopedLPO (regardless of anisotropy [cf. Christensen, 1987;Richterand Daty, 1978],in thedirectionof crystalalignment)will onlycauseLPO to develop whichshearviscosity wasassumed to declineascrystals aligned morerapidly[Ribe,1989a];hencethisassumption is conservative understrainor as streaksof distinctmineralogiccompositions withrespectto LPO development (andtherateof •'v decline). formed. To model weakening, we assume that the hard AnisotropicJr'. We modelthe effectof r anisotropyon verti- ((010)[001 ]) olivineslipsystem accommodates 8% of totalslipat cal thermaldiffusivity (r,,) by reducingverticalthermaldiffusiv- the onsetof simplesheardeformation[Wenket al., 1991;Ribe ity with increasingstrain. This decreaseis due to alignmentof and Yu,1991], andthatno slipis accommodated on thissystem at anisotropic olivine crystalswith strain. Sinceboth the radiative high e, and we scalethe shearviscosityevolutionbasedon the andconductivecomponents of •' in peridotiteare potentiallysig- relativeslip systemstrengthspresentedby Bai et al. [1991]. nificantat uppermantletemperatures andpressures, we mustcon- Using thesestrengthvaluesproducesa minimum r/.,. h valueat siderthe anisotropyof bothcomponents.Anisotropyof the con- extremestrainsof abouta third of rio. Additionalweakening ductive componentof x- for olivine and pyroxenehas been couldoccurif strongdeformation mechanisms otherthanslipalso observedin experiments[Chai et al., 1996] and is attributedto diminishin importanceat high strains,but the magnitudeof this anisotropy of the phononmeanfree pathdueto the orthorhombic effectis not quantified,andwe do notmodelit. latticestructureof both minerals(which doesnot changewith T Alternatively,we could postulatethat olivine crystalsalign aslongasbothphasesarestable). suchthattheirweak (010)[100] slip systemsattainan equilibrium Anisotropy of theradiativecomponent of r arisesmostlyfrom statewith an averageangleinclinedto the flow direction(or that the anisotropy of the photonmeanfree path(2). We assume that olivine crystalsalign on averagewith their weak slip systems in crystaldimensions in theuppermantleare of the orderof 0.5-4 the flow plane but with significantorientationscatter). In this mm,comparable to ,t [cf:Ave'Lallemantand Carter,1970;Nico- case, shear viscosity could stabilize at a value higher thanthe las and Poirier, 1976]; at 1300 K, 2 in olivine is 1 to 2 mm
[Schatzand S#nmons,1982]. For grainsof aboutthe dimension of the meanfree path,,g is limited by grainboundaryscattering, and the anisotropyof radiativeheat transportis controlledby crystalgeometry.Ellipsoidalstrain of crystalsresultingfrom simpleshearwithin the asthenosphere may cause•',.,,,•anisotropy becauseheat transfer in the vertical direction is preferentially hampered by scatteringat grainboundaries, makingverticalr,.,,a lower thanit would be for a randomlyorientedperidotiteaggregate.
The functionwe chooseto approximaterv(e) is
unstrainedviscosity. After 7=0.87 (e=0.44) Wenket at. [1991] find that peridotiteeffectivestrengthincreasesby a factorof 2 as the hard ((010)[001]) slip systemactivityincreasesfrom 8% to
20%, consistent with aboutan orderof magnituder/.,.h increase (assuminga power law rheologywith n=3.5). With increasing alignment,the weak slip systemsof olivine progressively rotate into orientationsthat preventtheir contributionto the shearstrains requiredfor plate transport. This causesr/.,.t,to increaseup to somethreshold,beyondwhich anotherdeformationmechanism (suchas diffusioncreepor grain boundarysliding)mustbe activated [Wenk et al., 1991]. In this case, we model shearviscosity
as increasingup to a thresholdvalue, after which it remainsconstant with respectto strain. This is reasonableas long as any where• represents themeanthermaldiffusivity, whichis obtained active nonslip mechanismsare not dependenton LPO, and the of olivineslip systemsare maintainedin a stateof by averagingthe thermaldiffusivitytensorovera 4x solidangle orientations for orthopyroxene andolivine,andtakinga weightedmeanof the dynamicequilibriumat high strains. two valuesassuminga mantle compositionof 70% olivine and The ratesof strengthening or weakeningof our •l.,.h(e) functhoughsomeguidelines exist.For 30% orthopyroxene.Basedon the experimentalfindingsof Chai tionsarenot well constrained, etal. [1996],• at 298øKand1 atmis 1.63x 10-6 m2/s(seeTable weakeningmodels,alignmentof the crystalswith the flowplane !). With alignment,•'•, approachesa minimum value of about occursat smalltotal strainsrelativeto strainstypicalof oceanic
r,,(e)= •(! -0.25e-2*)
(5)
Peridotitedeformation experiments [Zhangand 1.2x 10• m2/s,a reduction of 25% compared to• (under surface asthenosphere. P and T conditions).This value is a weightedaverageof the r Karato, 1995] showthat in simpleshear,LPO asymptotically valuesfor heatflow alongtheolivine [010] andthe orthopyroxene approachesalignmentwith flow at strainsof 1.5. Furthermore, seismicand petrofabricstudiesof uppermantleanisotropy near [ 100] axes. ridges[Hess,1964;Christensen, 1984]suggest qualiEquation(5) reduces•-• with a characteristic shearstrainof 1, mid-ocean rapidly. For strengthening shearvisconsistent with experimentalfindingsof rapidLPO development tativelythat LPO develops with simpleshearstrain[Zhangand Karato, 1995]. The r,, func- cosity models,the thresholdstrain beyondwhich straindepenceaseshasbeenestimated at about7= 1 (e=0.5) tion is basedon datafor conductivex- anisotropyonly,becauseno denceof r/.,.h dataareavailablefor radiativer anisotropy.Giventhe arguments [Wenketa!., 1991]. We modela varietyof ratesfor boththe viscositycasesby representing above,radiative•' anisotropyis comparablein senseto conduc- weakeningand strengthening tive r anisotropyandis likely moreextremein magnitude.Thus r/.,.h(e)with simple ramp functions,in which r/.,.•,increases or linearlyup to a threshold strainvalueof 1 to 10,and this r anisotropymodelshouldbe considered a conservative first decreases estimate of itstruedirectional behavior.In thesensitivity analysis then remains constant at a value between 0.3 and 100 times its
HEARN ET AL.: OCEANIC UPPER MANTLE ANISOTROPY
11,947
withintheasthenosphere increases withtime. The unstrained value(%). Thesefunctions aredesigned to approxi- mumviscosity andbroadening of the asthenosphere are dueto mate viscosity athighstrains andaresimplifications toperidotitestrengthening viscosity undersmallstrains.Forourpurposes, thissimplifica-coolinganda smalleroverallrangein viscosityvaluesin the tionis reasonable because the threshold r/.,,/r/0is thedominant uppermostmantle,respectively. modelisthe parameter inourmantle viscosity models, andourmodels arenot Theuppermantlethermalprofileforourisotropic resultof half-space coolingof an isotropic mediumwitha unisensitive tothedetailsof r/.,.h (e) forsmallstrains. formthermal diffusivity of 10-6 m2/s.Thusit is comparable to Anisotropic ModelsWith ShearHeating simplethermalmodelsfromwhichmanyoceanbasindepthand heatflow estimateshavebeenobtainedand discussed (e.g., Davis
Shearheatingproduces heatat a rateof
andLister[! 974];half-space coolingexampleof SteinandSte#z [1992]). Like otherhalf-space coolingmodels,ourisotropic reference model predicts ocean basin depths which match whereA is heatproductionperunit volume. A increases with an A = or. 2•
(6)
to an age of about80 Ma, after whichdepthslevel increase in minimumasthenosphere viscositybecause of resulting observations off with age. By 150 Ma, ourreferencemodeloverpredicts ocean highshear stresses. To account for shearheating, we calculate temperature by modifyingour heatdiffusion modeling with a basindepthby about1.5 kin. Our referencemodel,like other half-spacemodels[e.g., Stein sourceterm to accountfor the additionof shearheat and Stein,1992],alsounderpredicts heatflow (Qo) at the surface 3T
32T
A
= r -bT'z +
(7)
in old ocean floor. Surface heat flow measurements [Louden,
1989;SteinandAbbott, 1991] showthat at 100 and 150 Ma, Qo is
40-75 and50-60mW/m2, respectively. Our isotropic model where weassume heatcapacity % to be 1.17kJ/kgK anddensity yieldsQovalues of 51 and41 mW/m 2 at theseages.Wecould
p is3300kg/m 3 (seeTable2). During eachtimestep,wefirst
increaseour Qo estimates(without changing•c) by assuminga calculate temperatures assumingconductivecoolingandthenadd higherheatcapacity(andthereforea higherthermalconductivity theshearheatingterm. K), but such tinkering is not necessarysince these values are given primarilyto comparewith Qo estimatesfrom anisotropic Results
mantle models.
In this section,we presentand discussthe resultsof our isotropicandanisotropicmantlemodels. We focuson resultsthat canbe relatedto observations (suchas constraints on lithosphere thickness, the thicknessof the depthintervalwith well-deve!oped LPO,oceanbasindepth,andheatflow) and on resultswhichare of dynamicsignificance(suchas viscositiesand shearstresses). For simplicity,we considerthe asthenosphere to be the depth
Models With r Anisotropy
In this section,we discussthe effect of r anisotropyon temperaturesin the uppermantleand,in turn, on otheroceanicupper mantleproperties. Models with r=g(e). Thermal diffusivity anisotropyraises temperatures in the lower lithosphereand asthenosphere relative to an isotropic r model, regardless of •?.•,(•). Maximum temperaintervalin whichstrainratesexceed10-14S-1, andwe usethis ture increasein the asthenosphere attainsabout80øCby about50 strainratevalueto definethebaseof the lithosphere.The zoneof Ma (Plate 2). Plate 2 also showsthat the depthintervalwith welldeveloped LPO is definedasthedepthintervalwith e > 2. anisotropy-related temperatureincreasesgrowswith time. TemWe usetemperature profilesproducedby our modelsto estiperatureincreasesdue to r anisotropyare not observablydepenmateoceanbasindepthsandheatflow at the lithosphere surface, dent on the choiceof r/.•.h(e).Figure 3 showsthat anisotropic andcompare thesewith the existingdata[e.g.,SteinandAbbott, producesoceanbasinsthat are shallowerat all agesthan for the 1991;Louden,1989]. 'Becausea significantproportion of heat isotropic•' case,regardless of the choiceof r/.,,(e). After 150 Ma, fluxthrough thesurfaceof youngoceanlithosphere is attributed the effect of anisotropicr is to reduceestimatedbasindepthsby to hydrothermalcirculation[Steinand Stein, 1994], we estimate about600 m, buta distinctflatteningof the oceanbasindepth-age heatfluxfor lithosphere 50 Ma or olden Thisis approximately curveafter 80-100 Ma is not observed.The anisotropicr model
theestimated "sealing age"(ageat whichhydrothermal heatflow yieldsQ0values of 57 and46 mW/m 2 in 100and150Ma ocean becomes negligible)of 65+10Myr obtainedby SteinandStein floor (Figure 3), about 10% higher than the isotropicmodelQ0 [1994]forthePacific,Atlantic,andIndianOceans. values(40 and32 mW/m2) but still lowerthanmostmeasured values[e.g., Stein and Abbott, 1991; Louden, 1989]. Qo is not observablyaffectedby the choiceof In Plate !, we illustratehaw the referencemodellithosphere, Unlike the thermal parameters(basin depthsand heat flow), asthenosphere, and depthintervalwith well developed LPO the distributionof strain, and hence modeled lithosphereand thicknesses, is sensitiveto thedegreeof weakening evolve.The lithosphere is 10-20km thicknearthemid-ocean asthenosphere or strengthening (?l.,.h/rlo) (Figure 4). As expected,dynamicvariridgeandthickens asthesquare rootof timeto 180km after150 Ma.Thisisgreater thanthemaximum seismically inferred thick- ables(e.g., r/.,,,shownon Figure4) scalewith the choiceof r/(e). nessof 110km [e.g.,Nishbnuraand Forsyth,1989]. The seismi- Thicknessesand dynamicvariablesare not as sensitiveto the rate as they are to the threshold callyinferredlithosphere thickness is expected to be somewhatof weakeningor strengthening
Isotropic ReferenceModel
thinner thanthatof our modelsbecause the minortemperaturevalue becausethe thresholdstrainswe examine (1-10) are low relvariations at thebaseof our simulated lithosphere wouldnotbe ative to typical strainsexperiencedby oceanicupper mantle resolved seismically.Secondary convection [Richter,1973] or greaterthanabout10 Myr in age(Figure4). Sincethe dynamic mantlethermalanomalies[Andersonet al., 1992] may also and thicknessquantitieswe estimatedo not dependstronglyon the choiceof thresholdstrain(e,,,,r), we simplifythe discussion reduce lithosphere thickness beneath theoceans.
Themodeled asthenosphere thickness is40-50kmattheridge. of tl anisotropyby referringonly to the degreeof weakeningor Theasthenosphere broadens anddeepens withtime,andthemini- strengthening.
11,948
HEARNET AL.' OCEANICUPPERMANTLEANISOTROPY
Etotal 90
lOO
2O0 50
300 400 5OO 600
o
0
50
100
150
Plate Age (MY)
• (/s) 0
100
5X10 -14 '
200 '"" 300
2.5x10 -14
ca 400 5OO
600
0
0
50
100
150
Plate Age (MY) Plate 1. (top) Simulated•:,,,,,,/and (bottom)g in theuppermantle,assuming isotropic•,-and r/and a constant,: of
10-6m2/s (reference model) The left marginsrepresent the mid-ocean ridge,andage(distance fromthe ridge) increases towardtheright. For illustration,LPO is assumed to be well developedwhere s,,,,,/>2, andwe definethe
asthenosphere asthezonein whichg> 10-•4s -•. Whitedashed linesrepresent these limits.Notethatthissimple half-spacecoolingmodel overestimates the lithospherethickness.
In general, the lithosphereand the asthenosphereare thinner
for anisotropic•--modelsthantbr conaparable isotropicw models (incorporating the same/1.,.h/qo functions)because• anisotropy produceshotter geotherrns(Plate 2). The proportionaldifference in lithosphereand asthenosphere thicknesses is independentof 71.,.Jq(, becausevariation in the thicknessof the low •5, interval (which is controlled by rl.,.h!•h)) has no observableeffect on the geotherm(Plate 2).
The •- anisotropythinsthe lithosphereby only 20-30 km alter 150 Ma, and thereforemay not be observablewith surfacewave studies.Asthenosphere thinningdue to •,-anisotropy is evenless significant.Relativeto the isotropicreferencemodel,the slowed downwardpropagationof the asthenosphere with distancefrom
the ridge(resultingfromtemperature increases) resultsin onlya 10% thinner LPO zone thicknesses after 150 Ma.
Dynamicvariablessuchas minimumasthenosphere viscosity andshearstressare affectedsignificantly by •canisotropy. After 150 Ma, the hottergeothermsof modelswith •- anisotropycause
a 60% reductionin mininmmviscosityandbasalplatetractions
compared to modelswith isotropic •-. For example, Figure4 showsthatthe minimumviscosityfor 150Ma old oceanastheno-
sphere is40% of itsvaluefor comparable modelswithisotropic for all /1.,.•,/q(). Minimum•1.,.•, valuesfor all r/.,.•,(s) functions (,Figure4) showthat for thisgroupof ]'nodels, minimum•l.,.h is proportional to the thresholdvalueof
Modelswith •' anisotropyand shear heating. Thermal,
HEARNETAL.'OCEANIC UPPER MANTLE ANISOTROPY
turesthat exceedreasonableuppermantle temperatureestimates (compare1400øCat a depthof 400 km [Akaokiet al., 1989]) over considerabledepthintervals,thoughthere is considerableuncertaintyin all suchmantletemperature estimates.We concludethat increasing•l.,.h(e)functionsare not tenable for the uppermantle (unlesscomplexities suchasa very high radiativecomponentto •at high temperaturesor onsetof convectionremovesthis shearproducedheat). This is true even when a lower plate velocity is assumed;for a platerate of 3 cm/yr, maximum uppermantletemperaturesill 150 Ma prolilcsare 1400øCand 1450øCfor q.,./,/q() of I and 10.respectively (seesensitivityanalysis). Basindepth-agecuxvesfor modelswith shearheatingtendto flattenrelativeto curvespredictedby half-spacecooling(Figure 3). The basindepth-agecurvesare shalloweroverall in models
50
100
-
'•\•.•
\%\ .
150 Ma "\N reference model '\,,
\
150
anisøtrøpic • mødels_ .......
2OO
............
Wqo=o.3
........
q/qo= 1O0
•,•t
with shearheatingand may be approximated by plateor (up to someage limit) half-spacecoolingof mantle with reduced•,-values.
1
anisotropic•c models 250
11,949
7000
withshear heating
6000 5000 1500
4000
Temperature
C
3000
Plate2. Geotherms for anisotropic•- and q models,showing how•- anisotropy andshearheatingelevateuppermantletemperatures.The colorsblack(to gray),blue,andredrepresent 10,50,
2000
and150 Ma uppermantle,respectively.Thin, dashedlinesshow uppermantle geothermx,predictedby the isotropicreference
0
model.Heavy,darklinesrepresent modelswith x anisotropy but noshearheating(the differentll.,. h(œ)casesare indistinguishable at this scale). Heavy light colored lines representthe same anisotropic•- and /1 models,includingthe effectsof shearheat-
ing.Dashed, solid,anddottedlinesrepresent threeanisotropic r/ cases:strengthening (•l.,.h (max)hlo= 10), isotropic•1,and weak-
ening(•l.,.h (min)/qo=0.3). Thisfigureillustrates that •c'(•)plays a keyrole in elevatingmantlegeotherms beneathoceanbasins (especially thoseof youngto moderate age)andthatsomemodels withshearheatingresultin unreasonably highshallowupper
50
100
15O
Age MY 90
E 80 E 7O
• 60
mantletemperatures. :i: 50
dynamic, andthickness parameters areall sensitive to thechoice of •l.,.h(S) functionwhenshearheatingis considered. Figure5 illustratesthat model resultsare not sensitiveto the rate of viscos-
40
50
100
150
Ago MY
itychange, however, andwemayagainsimplify thediscussion by Figure3. (top)Basindepthsversusageand(bottom)heatflow versusagefox'mantlemodelswith •' anisotropy andthreecases only referringto the degreeof weakeningor strengthening of anisotropic r/evolution. Theheavysolidlinerepresents models imposed by/?sh(œ). with ,: anisotropy andno shearheating(thedifferentviscosity Temperature profilesfor modelswithshearheating areshown casesare indistinguishable). The heavygraylinesrepresent the on Plate2. As expected,temperatures in the lithosphere and samemodelswith shearheatingadded;dashed,solid, anddotted uppermantleare elevatedin all of the shearheatingmodels(rela- linesrepresent weakening(tl.,.•, (min)/qo=0.3), isotropic•?,and tivetocomparable models withoutshearheating), andthelargest strengthening (q.,,(max)/qo= 10),respectively. The r anisotropy of basin temperature increasesoccur in modelswith large threshold resultsill shallowerbasinsandcausesa slightflattening curvesrelativeto thosepredicted assuming half-space •?.,.dq(). Theeffectsof shearheating alsoincrease dramatically as depth-age
cooling (thin dashed line), and these effects are accentuatedin theasthenosphere cools.Shearheating results in unreasonably shearheating.A basindepth-age curverephightemperatures in oldocean uppermantle forourmodels with modelsincorporating resenting half-space coolingwith •-=7.0x 10-7m2/s approxistrengthening •?.,.h(œ) functions.For modelswith q.,.hhh} of I (the
matestile anisotropic•,- basindepth-agecurve(top figure,thin
isotropic case) and10,tilemaximum upper mantle temperatures solidline), thoughit fiattellslesswith age.This figurealsoillusin 150Ma profiles are 1450øC and 1500øC, respectively, and tratesthatthechoiceof/l.,.h(s) functiononlyaffectsbasindepths occurat a depthof 160 to 170kin. Both modelssuggesttempera- andQ,, whenwe modelshearheating.
HEARN ET AL.: OCEANIC UPPER MANTLE ANISOTROPY
MinimumViscosity- 50 MY
102i 2b, ',22
'
+
102
MinimumViscosity- 150 MY
1 .be+22
2e+23
1 e+22 o
.....
le+23
5e+21
101
o
•'10 o
5e+22
10-1 10
œchar
o
10'•
•"!0 0
10-1
102
11,951
6
10
8
char
LithosphereThickness- 50 MY
LithosphereThickness - 150 MY
102 .........
104
o
101
(all 100 km)
•'10 o
½'10ø169 •
10-1•
•
!•
8..char
•
10
;•
•,
161
•
F__, char
8
10
Figure4. (top)Minimum asthenosphere shearviscosity and(bottom) lithosphere thickness for 50 and150Ma upper mantle profiles withanisotropic r anda variety of rL,. h(e)functions. Thehorizontal axesarethethreshold e (e•.h,,r) fortherampr/.,,(e) functions, andthevertical axesaremaximum orminimum rL,,/r/oforstrengthening or weakening r/.,,(e)functions, respectively. These plotsshow thatlithosphere thickness andminimum r/aresensitive to maximumor minimumhsh/hobutnotto rateof viscosity changewithstrain.Sincetheotherparameters (thick-
nesses, shearstresses, heatflowandbasindepths) alsoareinsensitive to therateof r/changein our r/.,,(e) functions,we discuss r/(e) effectsin termsonlyof maximum orminimumrl(e)h7o.
ing,andisotropicr/.,,. It is importantto evaluatethemodel'ssen- flow and estimatedbasindepths(an integratedmeasureof upper sitivityto E* and V* becauseof uncertaintyin thesevaluesfor mantletemperature)arevirtuallyunaffectedby changesto V*. A changeto E* scalesall viscositiesbeneaththe lithosphereby dislocation creepin the uppermantle [Karatoand Wu, 1993]. Furthermore, bothE* and V* appearin the exponential termin a constant(seeequation(4)), but aiterslithosphere,LPO zone, thicknesses only slightly. A 50% changein E* theshearviscosity equation(equation(4)), sosmallvariations can andasthenosphere thicknessby lessthan 10%andchangesLPO causelargeviscosityvariations.We examineda lowerplaterate changeslithosphere thicknessesby less than 30%. Ocean (3 cm/yr)to covera rangeof realisticplateratesandto illustrate zone and asthenosphere howstrongly shearheatingis tiedto plateratein ourmodel.We basindepthsand Qo are similarly insensitiveto changesin E*. alsoran modelswith severaldifferentmantler values(or func- Viscosity and shear stressare strongly affectedby E* variation in viscosityapproximately followequation(4) for tions),includinga casein whichonly the conductive partof r anddecreases' decreased E*. For increasedE*, viscosityincreases departfrom wasanisotropic, becauseof uncertaintybothin thebulk mantler
valueandthedegree of anisotropy of theradiative r component. the predictionof equation(4) becauseshearheatingbecomes In all cases,changes to modelresultsarein accordance with important. The effectof usinga lower plate rate (uo = 3 cm/yr) in our simple reason, anddonotchange thegeneralconclusions found modelis to reduceestimated shearheatingin the above.Thatis,changes to theseparameters donotinfluence the anisotropic doesnotsigdevelopment of LPO relatedeffects,andtheexactchoicesof E*, uppermantle.Fortheslowplatecase,shearheating elevate geotherms in profileslessthan50 Myr old,and V*,uo,andr arenot.important tothepoints made inthispaper. nificantly asthenosphere, and LPO zonethickSensitivity to V*, E*, and Uo. We ran simulations with V* its effect on lithosphere, valuesof 10-5 and 2 x 10-5 m3/mo!to bracketthe value of V*
nesses,as well as oceanbasin depthsand Qo, is negligible.
viscosity increase relativeto the (1.5x 10-5m3/mol) weusein ourmodel.Lowering V* increasesAlthougha slightasthenosphere seoccurs in oIderuppermantleprofiles (duetolack lithosphere thickness, asthenosphere thickness, andthe depth fasterplateca. interval withwell-developed LPOandincreases minimum viscos- of shearheat),thelowerplaterateresultsin lowerstrainrates,so sheartractionsandthe totalforcerequiredto movethe platedo ity. RaisingV* reduces lithosphere thickness, asthenosphere significantly relativeto theirvaluesfor the faster thickness, andthickness of theintervalwithwell-developed LPO not increase andreduces minimumviscosity. Exceptin veryyoungprofiles, platemodel. allthicknesses anddynamic variables change byaboutthesame The influenceof r anisotropyon the uppermantlegeotherm to suchproperties as lithosphere thickness, basin percentage asthe changein assumed V* (or less).Surface heat (andtherefore
11,952
HEARN ET AL.: OCEANIC UPPER MANTLE ANISOTROPY
MinimumViscosity- 50 MY
102
o
..............
MinimumViscosity- 150 MY
102
101
'
o
10•
½-
½-100
•10ø
5e+ 19
4e+19
..
ap.4.1".q
-
•
2e+19
10-1_ ,
5•+19
•
2
E,char
102 ,
4.5e+
10-1
....
LithosphereThickness- 50 MY
.,
102
•.101
o104
• 0o ½-1
o• ø •'10
10-1;• •' E-,char •, •
10
10-•
4
6 •--char
3.5e+19_.... 8
10
LithosphereThickness - 150 MY
......
145
"•
•' ;F--char6
•
8 10
Figure5. (top)Minimum asthenosphere shear viscosity and(bottom) lithosphere thickness for50 and150Ma upper mantle profiles withanisotropic r, shear heating, andavariety of •.$.h (œ)functions. These plots (likeFigure 4)show thatlithosphere thickness andminimum r/aresensitive tomaximum orminimum r/.,.h/r/o (vertical axis)but nottorateofviscosity change withstrain (horizontal axis).Ther/.,.• (e)effects onmodels withr anisotropy and shear heating canbeevaluated interms ofmaximum orminimum rh•/r•o.
depths, andQo)is thesameasfor thefasterplatecase,butshear
Changes to bulk•chavea smalleffectonlithosphere, asthenoheating is lessimportant. In theoldestuppermantleprofilewe sphere,LPO zonethicknesses, anddynamicparameters, butthe examine(150 Ma), shearheatingaccounts for about75% of the percentage change to theseparameters is lessthanthepercentage reduction in minimum viscosity relativeto anisotropic reference changeto r. The maineffectof a changein •- is to raiseorlower modelwitha platerateof 3 crn/yr(andnoshear heating), butit geotherms, whichin turncontrolestimated oceanbasindepths. onlycontributes slightly(10-20%)to lithosphere, LPOzone,and Thiseffectis smallbutnotnegligible; a 50% change to r alters asthenosphere thinning.Thedepthpredicted by theslowplate estimatedbasindepthsby up to 20%. The influenceof r variamodel for 150 Ma oceanbasinsis about 750 m shallowerthan tiononQ0is strong(upto a 40% change fora 50%change tor),
thatpredietedby the isotropicreferencemodelandabout500 m of thedifference is dueto r anisotropy (thesamecontribution as forouranisotropic modelwitha platerateof 10cm/yr).Thusold oceanbasindepthsestimated by ourslowplatemodelareseveral hundredmetersgreaterthanobservations indicate[cf. Steinand
partlybecause Q0 is directlyproportional to •- nearthesurface.
(The departure from proportiona!ity betweenQ0 andr arises from the differentsurfacetemperature gradients resulting from differentr cases.)
Because theSchatz andSimmons [1972]r(P, T) values areon
Stein,1992].Theeffectof shear heating onQ0in theslowplate averagehigherthan the constantr valueof 10-6 m2/swe used modelis negligiblefor profilesof all ages. For modelswith above(Figure2), themodeled mantlecoolsfaster,resulting in •l.,.h/rh) = 1 and10, maximumestimated temperatures in theoldest slightly greater lithosphere, asthenosphere, andLPOzonethickuppermantleprofilesexceed1400øCand 1450øC,respectively nesses, aswell asgreater viscosities. Results arecomparable to (assuming anadiabatic gradient of 0.3øC/km). Thelattertemperatureexceeds uppermantleestimates (compare 1400øCat400km [Akaokiet aI., 1989]). This suggests thatevenwe asumea low u0,a largeincrease to uppermantler/as a functionof strain(i.e., r/.,.h/rh) > 10)is unlikely. Sensitivityto to. We ran modelswith constantr valuesof
those fromthe•c=1.5x 10-6 m2/ssensitivity run,except that
estimated ocean basindepths are700m shallower (5.9kmversus
6.6kmafter150Myr),andestimated Q0is30%greater. A shallowerocean basin(i.e.,hotuppermantle) is estimated because of lowr (and•cv)in thedepthintervals whereshearheatis gener-
2). HighQo(74mW/m 3after150Myr)iscaused by 5x 10-?m2/s and1.5x 10-6 m2/sto evaluate thesensitivity of ated(Figure ourmodelto bulkmantle' r. Simulations usingtheSchatz and bothhighr nearthesurface andtheelevated near-surface temperSimmons[1972] mantler functionwere alsorun to examinethe aturegradient duetotherapiddecline in r(P, T) withdepth.Our effectof P andT dependencies (especially therapiddecline in r observation thatmantlemodels withr(P, T) produce shallower withdepth nearthesurface (Figure 2)) onestimated upper mantle basins andhigherheatflowthanconstant r modelsstands regardtemperatures andotherproperties andto showthatr anisotropy lessof theextent(or presence) of anisotropy, andis consistent alsoinfluencesthe resultsof suchmodels. withthefindings of Schubert et al. [1976],whose upper mantle
HEARNET AL.:OCEANICUPPERMANTLEANISOTROPY a.)
11,953
b.)
200
300
..
250
c • 200
/
._9.
•100 I'
cx 50 I ' 00
õ 100
N
o
50
5'0 100 150
c.)
o
AgeMY
10
10
&. 0:,•
o d.)
5'0 lOO AgeMY
150
x 10•
8
.• 1 ._• 1 >
,•
.........
]
• 1019 ._.E ._.q
:• 01 s 1
0
50
100
150
Age MY
50
100
150
Age MY
Figure6. Resultsof anisotropic uppermantlemodels including shearhehting, compared with reference model results.(a) Lithosphere thicknessversusprofileage,(b) LPO zonethickness versusprofileage,(c) minimumviscosity versusprofileage,and (d) total forcerequiredto movethe plateversusplateage. On eachplot, threecasesof anisotropic r/ evolutionare shown:onewith a weakeningr/.,.h (e) functionthat yieldsr/.,.h (min)hl,,=O.3 (dashed line);onewith isotropicr/(solid line);andonewith a strengthening r/.,.h (s) functionthatleadsto r/.,.h (max)hlo= 10 (dottedline), andreferencemodelresultsare plottedwith a thin dashedline. Strengtheningr/., (s) thinsthe lithosphereand asthenosphere becauseof the increased roleof shearheating.Minimumviscositybeneathold ocean basinsandtotalforcerequiredto movetheplatescalewithr/., hl,, thoughlargedepartures from valuespredictedby theisotropicret•rencemodelaremainlydueto shearheating.
modelincorporatesthe Schatzand Simmonsr(T) relationand shear heating.
estimatesare moderatelysensitiveto changesto parametersand to •' anisotropy.Minimum viscosityand shearstressare moderSensitivity to •canisotropy.Because of uncertainty aboutthe atelysensitiveto V*, uo,and•candhighly sensitiveto E*. extentof radiative•c anisotropy in the uppermantle,we ran a Shear heating reducesthe sensitivity of viscosityto •, V*, or u0by preventinglarge viscositieswhen thesevaluesare modelin which the radiativecomponent of •' was assumed r/.,4,/r/o, isotropic.The model predictsnearlythe samelithosphere,increased.Changesto parameters which resultin strongerupper asthenosphere, andLPO zonethicknesses asourfully anisotropic mantle(i.e., increasedr, E*, or V*) tendto increasethe imporr model,aswell as small(15%) increases in minimumviscosities tanceof shearheating,while changesthatweakenthe uppermanand sheartractions.For the fully anisotropic r model,r tle (i.e., lowerr, E*, or V*) reduceits importance.A slowerplate
anisotropy isresponsible forreducing thedepthestimate fora 150 rate also reduces shear tractions and the influence of shear heatMaocean basinby about500m relative to theisotropic reference ing. Even assuminga slowplaterate, the magnitudeof viscosity modelestimate.This valueis 300 m whentheradiativecompo- increaseat very high strainsis boundedbecausesuchmodelsprohightemperatures in theuppermantle. nentof •- is assumed isotropic, thoughin bothcases, mostof the duceinappropriately
departure in basindepths fromestimates madeassuming simple halfspace cooling isduetoshear heating. Qovalues arereduced Discussion byabout5% whenradiative •cis assumed isotropic, buttheyare stillupto !0%greater thanisotropic reference model estimates. Eitherthermaldiffusivityanisotropy, whichis a consequence Sensitivity summary.The effectsof r anisotropy arenot of observed LPO in theoceanicuppermantle,or shearheating influenced bythechoice of E*, V*, Uo,or meanr. Compared to cankeepoceanlithosphere anduppermantlehotterthaninferred models withisotropic •c,models with•canisotropy predict weaker froma simplehalf-spacecoolingmodelusingaccepted parameter asthenosphere, thinner asthenosphere andLPOzone,greater heat values(Table2). Geotherms predicted by a modelincorporating flow,andshallower oceanbasins.In all models, lithospherebothr anisotropy andshearheatingare similarto thoseof a plate
thickness does notscale significantly withparameter values andis model with an isothermalbottom boundarycondition and a notstrongly influenced by r anisotropy. Oceanbasindepths, sur- diminishedplate •- value. Hotter upper mantle in turn affects
faceheatflow(Qo),andLPOzoneandasthenosphere thicknessoceanbasindepths,heat flow, lithosphereand LPO zone thick-
11,954
HEARN ETAL.:OCEANIC UPPER MANTLE ANISOTROPY
ness,and properties controllingplatedynamics, suchas basal Nishimura andForsyth [1989]reportthatazimuthal anisotropy tractions.
OceanBasinDepthsand Heat Flow
existsat depthsup to -200 km in youngoceanmantle(lessthan
80Ma). The200km valueis consistent witha shear wavesplit
time of about1.2-2.4 s, dependingon the degreeto whichLPOis Ocean basindepths areproportional to thesquare rootof the developed.In older mantle,the seismicmodel of Nishimuraand
[1989]indicates noanisotropy belowabout50km.They seafloor ageuntilabout 50-I00Ma,afterwhich basindepths tend Forsyth to increase moreslowlywith time [Davisand Lister,1974]. attributethis lack of significantanisotropyin older profilesto interferencebetween depth intervals with differing LPO direcattributed to shearheating[Schubert et al., I976], smallscale tions that tend to cancel azimuthal velocity variations. This is convection [Richter,1973],radiogenic heat[Crough,1977],or consistentwith our model, where changingplate motiondirec-
Departure fromhalf-space cooling inolder ocean basins hasbeen
theformer LPOorientation inthethickening mantle plumes [cf.Heestand andCrough, 1981; Anderson etaL, tionswouldpreserve 1992]andis oftenrepresented by platemodelswitha constant lithosphere. Shearwave split timesare a functionof the thickness of the temperature orheatflowbasalboundary condition. We find that the elevationof the geothermresultingfrom •'
depthinterval with well developedazimuthalanisotropy, which
anisotropy reduces basin depths. Thiseffect doesnotexplain the increasesaway from the mid-oceanridge (seePlatesI and3). distinctflattening of old oceanbasins(Figure3), thoughthe The rate of thickeningis controlledby shearheatingandthermal
resulting basin depth-age curve mayappear tomatch a4•-curve diffusivity anisotropyin our anisotropicmodels, and estimated for a reduced r value. Models with shear heating but no •'
shearwavesplittimesareup to 30% lessthanthosepredicted by
anisotropy alsoelevate oldocean basins andproduce basindepth theisotropicreferencemodelfor all profileages(Figure6b). For agecurves whichareshallow relative tothatproduced bytheref- instance, for 50 Ma ocean floor, the reference model and the
erencemodel,and modelswith higherviscosities resultin more anisotropicr model with shearheatingpredict maximumshear assuming a P velocity flattening withage.Neithershearheating norr anisotropy indi- wavesplitsof 1.05 and0.9 s, respectively, viduallyreduces basindepths or flattenoldoceanbasins suffi- anisotropyof 4.5%. For 150 Ma oceanbasins,thesevaluesare
cientlyto beconsistent withobserved basindepths (summarized1.7 and 1.2 s. bySteinandStein[1992]).Modelswithbothshearheating and•' anisotropy produce basindepthssimilarto observations (Figure Plate Dynamics 3). Contriving a modelwith slightlyhigherr valuesand a All of our models indicate that the asthenosphere migrates strongly increasing shearviscosity function, we couldimprove downward, broadens,and strengthenswith time, thoughthese thematchto basindepthdata,butsucha modelwouldproduce trends are reducedin models incorporatingr anisotropyand untenablyhighasthenosphere temperatures.
eithershearheatingor a weakeningr/sh(e ) function. For ourref-
Bothplateandhalf-space coolingmodelsunderestimate heat erence model, the minimum viscosityincreasesfrom the ridge flowthrough theoceanfloorby about20%at timesgreater than value(5x 10•a Pa s) to 1022Pa s after 150 Myr. When about65 Ma, leadingSteinand Stein[1992, 1994] to suggest a
anisotropy is included,theminimumasthenosphere viscosity after
thin(95km)plateanda highbasaltemperature (1450øC).Figure 150Myr is I02• to 3.8 x 1023Pas, witha lineardependence on 3 showsthat r anisotropy and shearheating(and no viscosity the thresholdr/.,h(e)value;for the isotropic71case,the valueis anisotropy) elevates surface heatflowby 10-15%,whilemaintain- 4.0x I02• Pa s. Shearheatingfurtherreduces viscosities bya
ingupper mantle temperatures thatarelessextreme thanthose of factorof 25 or more,with the degreeof weakeningdepending on SteinandStein. Q0 increases with •c anisotropy because LPO the choiceof rL.h(e); as a result,the rangeof minimumviscosities reducesvertical •' in the lower lithosphereand asthenosphere,after!50Myrissmall(4to6 x 1029 Pas). causing a stepincrease in verticalr nearthe surface.Even The temperatureincrease that results from anisotropic greaterQ0 valuesareattained in modelsin whichr decreasesreducessheartractionsactingon an old (150 Ma) oceanicplate. withtemperature [cf.Schatz andSimmons, 1972].Withoutshear Basal sheartractionsare 600 and 130 MPa, respectively, for heating, r anisotropy elevates Qorelative toanisotropic modelby isotropicand anisotropicr models(assumingisotropicr/). Shear almostthe sameamount(exceptwhenextremestrengthening of heatingfurtherreducesthe basalsheartractionfor 150 Ma plate 71.,.• withstrainis assumed), indicating thatsurface heatflowis to 3.7 MPa. We estimatethe Ibrce requiredto movean oceanic increased more.byr anisotropy thanby shearheating in ourmod- plateby integratingthebasalsheartractionoverthe lengthof the
els (Figure3). Anisotropic r quitenaturally increases surface platenormalto theridge.Fora 150Ma platemovingat 10crn/yr, heatflow with no needto appealto externalmechanisms. modelswith anisotropic r requirehalf the force predicted by isotropic•' models. Shearheatingfurtherreducesthe force
Seismic Anisotropy
required, though thedegree of decoupling is sensitive to
Shear wave splitting, surface wave, and Pn studies[e.g., andtheplaterate. Forrapidplatemotion, shearheating reduces Nishimuraand Forsyth,1989; Farra and lhnik, 1994;Kuo and theforce required forplatemotion farmorethanr anisotropy for Forsyth,1992;Hess, 1964]showseismicanisotropy beneaththe all O.,.h(e) functions (Figure6d). oceans. Estimatesof the thicknessof the anisotropiczonemay be obtainedfrom shearwave splittingand surfacewave studies.S
Conclusions
wavesplittingexperiments havefoundsplittimesof up to 1 s Ourmodeling shows thatthermal diffusivity andviscosity [Farraand Vinnik,1994;KuoandForsyth,1992]. Thisis consishave effects ontheevolution ofoceanic upper mantle tentwith an anisotropic zoneabout70-150km thickfor perfectly anisotropy Thermaldiffusivity anisotropy in alignedolivine and perid9titewith 4.5% P wave anisotropy,thatshouldnotbe overlooked.
appears tohavethermal andmechanical ramifications respectively [Christensen, 1984]. Sincetheseseismic observa-particular fortheoceanic lithosphere. tionsare from islandsassociatedwith mantlehot spots,theymay thatarelikelyto beimportant of olivineandpyroxene crystals, whichhave measure splittimeswhereLPOhasbeenmodified andtheresult- Alignment thermal diffusivities, causes temperatures in theupper ingsplittimesmaynotbe representative of undisturbed mantle. anisotropic
HEARNETAL.:OCEANIC UPPER MANTLEANISOTROPY
11,955
mantle to exceedisotropichalf-space coolinggeotherm tempera- Christensen, N. I., The magnitude, symmetry,andorigin of uppermantle anisotropy basedon fabric analyses of ultramafictectonites,Geophys. tures calculated with an isotropicbulk thermaldiffusivityvalue. J. R. Astern. Soc., 76, 89-111, 1984. Asa result,the anisotropicr model predictsshallowerocean Christensen, U. R., Somegeodynamical effectsof anisotropic viscosity, basindepths,higherheatflow,andweakerasthenosphere than Geophys.J. R. Astron.Soc.,91, 711-736, 1987. does a comparable isotropicmodelusingbulk •- for mantleperi- Cordcry,M., andJ. PhippsMorgan,Convectionandmeltingat mid-ocean dotitc.When shearheatingis also considered, the resulting ridges,J. Geophys. Res.,98, 19477-19503, 1993. Crough,S. T., Approximate solutions for the formationof the lithosphere, model predicts significantly thinnerlithosphere andasthenosphere thanthe isotropicreferencemodel. Shearheatingalsoraisesthe
geotherm, resulting in evenshallower ocean basins andweaker asthenosphere thanresultfromr anisotropy alone,buthasonlya minoreffect on surfaceheat flow. The magnitudeof shearheat-
ingeffects onmodelresults is greatest in highviscosity mantle models (i.e., thosewith viscositythatincreases with strain). Esti-
mating isotropic •' by fittinghalf-space or platecoolingmodel basindepthpredictions to basindepth-agecurveswill yield a valueof r that is too low.
A modelwith r anisotropyandshearheating(andisotropic
predicts lithosphere thickness, LPO zonethickness, andsurface
Phys.Earth Planet. Inter., 14, 365-377, 1977. Davis,E. E., andC. R. B. Lister,Fundamentalsof ridgecresttopography, Earth Planet. Sci. Lett., 21, 405--413, I974.
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Acknowledgments. Wewouldliketo thankKenDucker forhelpful suggestions andcomments earlyin thisstudy.We alsothankAndreas
Ribe, N.M., and Y. Yu, A theory for plastic deformationand textural evolutionof olivine polycrystals, J. Geophys.Res., 96, 8325-8335, 1991.
Kronenberg, Adolphe Nicolas, andtwoanonymous reviewers for their Richter,F. M., Convectionandthelarge-scalecirculationof themantle,J. suggestions during thereview process. Thisresearch wasfunded under NSF grantsEAR-9405547 and EAR-9628474.
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