The influence of olivine metastability on deep subduction

Ž .Physics of the Earth and Planetary Interiors 120 2000 29–38www.elsevier.comrlocaterpepi

The influence of olivine metastability on deep subduction ofoceanic lithosphere

M. Tetzlaff ), H. SchmelingInstitut fur Meteorologie und Geophysik, UniÕersity of Frankfurt, Feldbergstr. 47, 60323 Frankfurt, Germany¨

Received 28 May 1999; received in revised form 19 November 1999; accepted 21 January 2000

Abstract

The dynamics of subduction of oceanic lithosphere is mainly controlled by thermal buoyancy forces and mineralogy. InŽ .self-consistent models, the influence of metastable olivine MO on the dynamics and evolution of subducting oceanic

Ž . Ž . Ž .lithosphere is investigated. We consider both phase boundaries — olivine Ol to spinel Sp 410 km and Sp to perovskiteŽ . Ž . Ž .Pv qmagnesiowustite Mw 660 km — treating the kinetics of the phase transition in a simplified way. While models do¨not allow the formation of MO penetrate straight into the lower mantle, slabs with a sufficient amount of MO flatten out atthe 660-km boundary before penetrating at a later stage. Furthermore, our models show that the effect of MO to slow downsubduction velocities within the transition zone is rather moderate. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Metastable olivine; Subduction; Numerical modeling

1. Introduction

Tomographic images indicate that some slabspenetrate straight into the lower mantle, whereasothers flatten and stagnate within the transition zoneŽ .van der Hilst et al., 1991 . Recent results suggestthat in the Northern Tonga subduction zone, the slab

Ždeflects in the transition zone between about 400-.and 700-km depth before continuing into the lower

Ž .mantle van der Hilst, 1995 . The dynamics of coldsubducting slabs are mainly controlled by negativethermal buoyancy forces and by buoyancy anomaliesstemming from slab mineralogy because of the den-

) Corresponding author.E-mail address: [email protected]

Ž .M. Tetzlaff .

sity contrasts of the different mineralogical phases.Ž .The transition of the abundant mineral Mg,Fe SiO2 4Ž .in the upper mantle from the a-phase olivine to the

Ž . Žb-phase wadsleyite and to the g-phase ring-.woodite may be kinetically inhibited because of the

low temperature conditions in the subducting litho-Žsphere Sung and Burns, 1976; Rubie and Ross,

.1994 . Under equilibrium conditions the phaseboundaries of the exothermic transitions a™b™g

are elevated in a cold slab resulting to negativebuoyancy forces. If a-olivine persists as a metastablephase in the high-pressure stability fields, positivebuoyancy forces will reduce, or even overcome,these negative buoyancy forces. Sufficient volumes

Ž .of metastable olivine MO may be expected to in-Žhibit further penetration into the lower mantle Okal

.and Kirby, 1998 , in addition to the positive buoy-

0031-9201r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0031-9201 00 00139-4

( )M. Tetzlaff, H. SchmelingrPhysics of the Earth and Planetary Interiors 120 2000 29–3830

ancy forces stemming from the endothermic transi-Ž .tion of the g-phase to perovskite Pv and magne-

Ž .siowustite Mw . Thus, the investigation of the influ-¨ence of MO on the shapes and the dynamics of slabssubducting through the transition zone and, eventu-ally, into the lower mantle is of particular interest.

Ž .Schmeling et al. 1999 considered the behaviourof a self-consistent subducting slab penetrating theupper mantle and observed an increasing influenceof the MO on the dynamics with lithospheric age.They found that the MO formed in slabs with agesgreater than approximately 70 Ma and that a signifi-cant slowing down of subduction velocity occurs forages greater than 100 Ma. The metastable wedge of

Žolivine acted as a low-density ‘‘parachute’’ Kirby etal., 1996; Marton et al., 1999; Schmeling et al.,

.1999 . The maximum depth of MO did not exceed550 km in their models, partly because no slabpenetration beneath 660 km has been allowed.

In contrast to these former models, we will in-Ž .clude both phase boundaries — olivine Ol ™spinel

Ž . Ž . Ž .Sp 410 km and Sp™PvqMw 660 km . Wewill investigate the influence of the MO wedge andthe behaviour of the subducting oceanic lithospherenear the boundary between the upper and the lowermantle with particular emphasis on the questionwhether the MO could retard or prevent slabs frompenetrating into the lower mantle.

2. Model

The system of equations for thermal convection— conversation of mass, momentum and energy —is solved in two dimensions in the extended Boussi-nesq and infinite Prandtl number approximation.

The nondimensional momentum equation in thestream function formulation is given in two dimen-sions:

E2 E2 E2c E2c E2 E2cy h y q4 h2 2 2 2ž / ž / ExEz ExEzEx Ez Ex Ez

ET Eb EbSp PvsRa yRc yRc 1Ž .Sp Pv

Ex Ex Ex

with the buoyancy terms on the right-hand side ofthe equation. x, z are the coordinates, c is the

Ž .stream function Õ sEcrEz, Õ syEcrEx ; Õ , Õx z x z

are the velocities in horizontal and vertical direction;Ž 3. Ž .Ras ar gDTh r kh is the thermal, Rc s0 0 Sp

Ž 3. Ž . Ž 3. Ž .D r gh r kh and Rc s D r gh r khSp 0 Pv Pv 0

are the compositional Rayleigh numbers of the sim-plified Ol™Sp and Sp™PvqMw phase transi-

Ž y1 .tions, respectively; a s3.7ey5 K is the ther-Ž 3. Žmal expansivity; r s3.4e3 kgrm , D r s1810 Sp

3. Ž 3.kgrm and D r s173 kgrm are the referencePv

densities and the Ol–Sp and Sp–PvqMw densityconstrasts, respectively; g is the gravity acceleration;DT is the scaling temperature; h is the total layer

Ž 2 .thickness; k s1.0ey6 m rs is the thermal diffu-sivity, h is the reference viscosity; b and b are0 Sp Pv

the fractions of the Sp and PvqMw phases, respec-tively. The density contrasts have been chosen, as-

Ž .suming that only the olivine component 60% of themantle material undergoes the phase transformations,and are in general agreement with recent data based

Žon seismological observations Shearer and Flana-.gan, 1999 . The dynamic viscosity: h s

wŽ .Ž . �Ž . 4 1yn x1rh 1r2A exp E q PV rRT s , is as-0 a a

sumed to be temperature-, pressure- and stress-de-Žpendent, according to a power-law rheology Chopra

. 4.46 yn y1and Paterson, 1984 , where As10 MPa s ,E s535 kJrmol, z is the depth, V s1.3ey5a a

m3rmol, T is the absolute temperature, s is thesecond invariant of the stress tensor, ns3.6. Therange of viscosity variation in our model is restrictedto 1021 to 1027 Pa s. The rheology law we used is anoversimplification, particularly in the transition zoneand in the lower mantle. The rheology of spinel and

Žmodified spinel is very poorly constrained Karato,.1996; Riedel and Karato, 1997 . Subducted slabs are

likely to have complicated rheological structures inthe transition zone due to combined effects of crystalstructure, grain size and temperature on rheologyŽ .Karato, 1996 . Recent geodynamical observationssuggest that the subducted slabs are rather weak and

Ž .highly deformable. Karato 1996 showed viscosityprofiles of subducting slabs with different tempera-ture profiles and different subducting velocities inwhich the effect of grain-size reduction due to theOl–Sp phase transformation is considered. In thesemodels, the viscosity inside the subducting litho-sphere is found to vary between 1023 and 1028 Pa s.The rheology of the lower mantle minerals is onlypoorly known due to the lack of direct experimental

( )M. Tetzlaff, H. SchmelingrPhysics of the Earth and Planetary Interiors 120 2000 29–38 31

studies under high pressures and temperatures. It hasbeen argued that the lower mantle rheology dependsstrongly on whether Pv or Mw controls the rheology,because the rheology of the two materials is likely tobe very different at the same homologous tempera-

Ž .ture Karato, 1989 .Because of this lack of knowledge of rheological

properties of mantle minerals at greater depths, weused a simplified rheological law that is based onlaboratory data for the upper mantle, but is con-

Žtrolled by additional parameters truncation viscosi-.ties and an activation volume to match other geo-

physical observations. The formation of a highlyviscous slab is allowed; too high viscosities areavoided by an upper truncation viscosity. The lowervalue of 1021 Pa s has been chosen to represent theaverage upper mantle viscosity, according to theanalyses of the postglacial rebound data. The activa-tion volume was adjusted to result in an appropriateviscosity increase in the lower mantle, as required

Žfrom dynamic inversions of geoid data e.g., Hager,.1984, 1991 or from matching hot spot tracks by

Ž .advecting plumes Steinberger and O’Connell, 1998 .The nondimensional heat equation is given by:

ET™™1q l qÕ= TŽ .T ž /Et

Di EÕi2s= TyÕ DiTq l q s , 2Ž . Ž .z z i jRa Ex j

w Ž .where l s 1rc L Eb rET q LT p Ol™ Sp Sp Sp™ PvŽ .x w ŽEb rET and l s hrc DT L Eb rPv z p Ol™ Sp Sp. Ž .xEz qL Eb rEz with the latent heat termsSp™ Pv Pv

Ž . ŽL s60.3 kJrkg and L sy63.9Ol™ Sp Sp™ Pv.kJrkg of the Ol™Sp and the Sp™PvqMw tran-

sitions. t is the time, Disa ghrc is the dissipationpŽ .number, c s1.3e 3 JrK kg is the heat capacityp

and s is the stress tensor.i jŽUsing a finite difference code see, e.g., Schmel-

.ing and Marquart, 1991 , the equations are solvedwith a spatial resolution of 11 km for the streamfunction, viscosity and phase fractions and with afour times higher resolution for the temperature.

Our model is 1320 km deep with an aspect ratioof 3. The boundary conditions are free slip at allboundaries, thermally insulated sides and a bottom

heat flux of 20 mWrm2. The initial temperatureŽfield of the model is divided into two parts accord-

.ing to Christensen, 1996 . In the left part of the boxŽ .0 kmFxF2244 km , we have superimposed a coldlayer, representing the lithosphere with a conductivetemperature gradient, with a typical mantle adiabat.In the right part of the box, the adiabatic temperature

Žprofile is continued to the surface cf. Schmeling et.al., 1999 . We are interested on the evolution of the

slab after the phase transition. Thus, we neglect theeffects of an overriding plate, which we assume to besmall in comparison to the slab pull forces. Further-more, back-arc basins produce only very thin litho-spheres. The thickness of the cold layer correspondsto the initial ages of 33, 49, 90, 111, 131 and 165Ma, applying the cooling half-space model.

Our simplified phase diagram for the compositionŽ .of Mg , Fe SiO is based on thermodynamic0.9 0.1 2 4

Ž .data of Akaogi et al. 1989 . We approximate bothŽ .the exothermic transitions of olivine a to modified

Ž . Ž .spinel b to spinel g by one single transitionregime in which the spinel fraction increases linearly

Ž .Fig. 1. Simplified disequilibrium kinetic phase diagram of theolivine–spinel and spinel–perovskite transition. Lines of 1% to99% spinel and perovskite fraction are shown, respectively. Bothtransitions are assumed to increase linearly with depth. The verti-cal segments of the lines show the conditions required for trans-formation at low temperature and are consistent with MO persist-ing at T -6008C. Arrows indicate typical temperature profiles inthe normal mantle and in a downgoing slab.


Ž .Fig. 2. Evolution of a subducting slab initial thickness corresponds to a 131-Ma-old lithosphere with time. Shown are the temperature fieldand the contour lines of the olivine to spinel and spinel to perovskite transition.


with depth within the depth range of about 130 kmŽcf. the isolines of 1% to 99% degree of transition,

. Ž .Fig. 1 . The Ol™Sp a™b ,b™g and the Sp™PvqMw transitions are represented by two sets ofcontour lines. The subhorizontal part of the Ol™Sptransition represents the equilibrium transition. The

Ž .vertical part which is met only within the slabmimics the kinetic transition of MO into Sp in thefollowing way: we included the results of extrapola-

Žtions of high-pressure experiments Rubie et al.,.1990 , which suggest that below a temperature T ,1

the transition of Ol™Sp is kinetically delayed and

will not take place on the subduction time scale,while between T and T , the transformation takes1 2

place but is still kinetically delayed. For tempera-tures greater than T , the transformation takes place2

under equilibrium conditions. Here, we choose 6008Cand 7008C for T and T , respectively. Below T ,1 2 2

the MO transforms into Sp by a disequlibrium trans-formation that could be described by a kinetic equa-tion, suggesting an exponential increase of the Sp-fraction. We simplified this equation by assuming alinear increase of the Sp-fraction in the temperaturerange between T and T , shown in the phase dia-1 2

Ž . Ž .Fig. 3. Close-ups of subducting slabs with different initial ages of 165 Ma top and 49 Ma bottom after the same relative amount ofmaterial is subducted.


gram by vertical isolines representing 1% to 99%transition degree. The endothermic phase transitionof Sp™PvqMw is approximated by a linear in-crease of the PvqMw-fraction with depth. Thekinetics of the endothermic phase transition of Sp™PvqMw are not known. Therefore, we assume anequilibrium transition that may be approximated by alinear increase of the PvqMw-fraction with depthwithin the depth interval as indicated in Fig. 1. Incase of MO entering the PvqMw-field, it is as-sumed that Ol first transforms into Sp via the kineti-cally delayed transition as described above, but theresulting Sp immediately transforms into PvqMw,assuming equilibrium transition. This kind of be-haviour has also been implicitly assumed in previous

Žslab models with a metastable wedge e.g., Okal and.Kirby, 1998 .

3. Results

In Fig. 2, the typical evolution of subduction isshown for a 131-Ma-old lithosphere, which corre-sponds to an initial thickness of 110 km. After about10 Ma, we observe a first uplift of the Ol–Sp phase

boundary, which adds negative buoyancy to the slaband accelerates the rate of subduction. As a conse-quence, the part of the slab between the surface andthe Ol–Sp phase boundary undergoes some exten-sion and thinning. Because of the cold inner part of

Ž .the lithosphere less than 6008C , the phase transitionfrom Ol to Sp is kinetically inhibited and a growingMO wedge is formed as can be seen by the down-ward deflection of the Ol–Sp contour lines withinthe slab. The resulting positive buoyancy force slowsdown the velocity of the slab. This effect is in-creased, as the slab reaches the endothermic Sp–Pv

Ž .qMw phase boundary 660 km . As a result, theslab flattens out at the Sp–PvqMw phase boundaryand further penetration into the lower mantle isdelayed. Thinning and extension of the upper part ofthe slab is reduced. Due to conductive heating of theinner part of the slab, the amount of MO decreasesand the total positive buoyancy force is reduced. Thethinned part of the lithosphere loses most of its MOfirst, and bends into the lower mantle. The frontalpart of the slab is still fixed at the Sp–PvqMwphase boundary mainly because of the remainingvolume of the MO. Only after 32 Ma did the MOvanish and the frontal part continue to subduct intothe lower mantle.

Ž .Fig. 4. Close-up of a subducting slab with initial age of 131 Ma without MO. The model time is the same as in Fig. 2 third from top .


To test whether this subduction evolution is simi-lar for lithospheres with different ages and, respec-tively, thicknesses, we calculated models with differ-ent initial ages. Significantly different behaviour is

Ž .observed in the relatively young F50 Ma andŽ .older G150 Ma lithospheres, depending on the

amount of MO. For example, large amounts of MOŽ .in an old, thick lithosphere 165 Ma, 120 km result

in strong positive buoyancy forces, which make pen-etration into the lower mantle impossible for at least

Ž .as long as 19 Ma Fig. 3 . In contrast, a lithosphereŽ .with an initial thickness below 70 km 49 Ma

penetrates straight into the lower mantle only be-cause of small amounts of MO. The positive buoy-

Žancy forces of the endothermic phase transition Sp.™PvqMw are not strong enough, in this case, to

completely inhibit the penetration into the lowermantle; it only slows down subduction and leads toupwards bending of the slab.

Comparing models with and without allowing forthe formation of MO shows that all slabs withoutMO slow down when they encounter the Sp–PvqMw boundary, but even the thickest continue topenetrate directly into the lower mantle. As an exam-ple, Fig. 4 shows a snap shot of the same model as inFig. 2, only without allowing for MO. It has sunkmore than 300 km deep into the lower mantle, while

Ž .the counterpart with MO Fig. 2, third from top stillrests on top of the Sp–PvqMw boundary.

To quantify the influence of MO on the rate ofsubduction, we determined the root-mean-square ve-locity of the models and averaged them over time.The time window for averaging has been chosenstarting from the first appearance of MO up to thetime of the strongest slowing down of the slab. Atthat stage, the slab has reached the Sp–PvqMwboundary, but penetration into the lower mantle hasnot yet started. For different initial lithospheric ages,these velocities are shown for models with and with-out allowing for MO in Fig. 5A. The increase ofvelocities with lithospheric age is reduced for themodels with MO; the oldest lithospheres are slowerby up to 20%.

The absolute peak values of velocity of a charac-teristic tracer within the slab with an initial position

Ž .at xs1584 km i.e., 660 km left of the slab edge isshown in Fig. 5B for different lithospheric thick-nesses. For each model, this tracer represents the

Ž .Fig. 5. A Root-mean-square velocities averaged over time andŽ .B absolute velocity of a tracer within the downgoing part of aslab. Initial position of the tracer is 660 km left of the front of theslab in the middle of the lithosphere. Diamonds represent modelsin which metastable olivine may be formed, crosses show modelsin which metastable olivine is not allowed to form. The age at thetrench is taken as the initial age plus the model time until first MOappears.

subducting part of a slab during a second phase ofŽ .acceleration e.g., Fig. 2, second from the top . At

that time, the lower part of the slab moves towardsthe right-hand side upon the Sp–PvqMw phaseboundary, while the trench migrates towards the left.Sinking velocities at this stage are of the order of11–15 cmryear in the models in which MO ispresented and increasing up to 20 cmryear in mod-els without MO. As already shown by the root-

Ž .mean-square velocities Fig. 5A , thick and coldslabs are slowed down by about 20% compared toslabs of the same age but without MO.


4. Discussion and conclusion

Our models show that the slab penetration into thelower mantle is significantly influenced by the exis-tence of MO. As long as slabs contain considerableamounts of MO, they bend upwards and rest on topof the 660-km boundary. Further subduction is de-layed until the slab is heated to temperatures aboveT to T . As our models show, conductive heating of1 2

thick slabs, enhanced by heating due to release oflatent heat, and subsequent transformation of MOinto Sp, may take as long as 8 Ma. Given averagedsubduction rates of 10 to 15 cmryear, this wouldlead to subhorizontal slab sections of 800- to 1200-km

Ž .length near the 660-km boundary cf. Figs. 2 and 3 .Based on tomographic observations and seismicity, asimilar slab piece of about 700 km has been ob-served in the Tonga subduction zone, where the slabis 110-Ma-old, while the 90-Ma-old slab at the Ker-madec trench seems to penetrate directly into the

Ž .lower mantle van der Hilst, 1995 .Our models may somewhat overestimate the max-

Ž .imum depth of MO 850 km in Fig. 2 and the totalamount of MO near the 660-km boundary becausewe neglected the depth dependence of the latent heat.Consideration of the depth-dependent latent heatterm, together with solving the exact kinetic equa-tions, will lead to a runaway effect and an overexpo-nential increase in Sp-fraction at certain critical

Ždepths and temperatures Rubie and Ross, 1994;.Devaux et al., 1997 . Two conditions are necessary

Ž .to initiate this runaway process: 1 the release ofŽ .latent heat i.e., the transformation of Ol into Sp

must have started, which requires that the tempera-Ž .ture has to exceed T ; and 2 the temperature must1

be greater than T minus dT , where dT is the total2

temperature increase due to latent heat. The secondcondition ensures that enough latent heat is availableto heat up the transforming Ol to a temperature equalor higher than T . Taking into consideration the2

Ž .parameters given by Rubie and Ross 1994 , dT isabout 508C near the 410-km depth and increases to1008C at 535 km or to 1508C near the 660-kmdiscontinuity. With T yT s1008C as assumed2 1

here, we expect the runaway process to work atdepths greater than 535 km, essentially transformingall Ol with T)T almost immediately into Sp. Thus,1

we expect that the MO will only remain in those

regions, whose temperatures are still below T . A1

further reduction of size of these regions is expecteddue to enhanced conductive heating as a result ofsteeper temperature gradients close to the runawayregions. Taking together these effects, the rims ofour MO-regions may have already transformed intoSp at depths greater than 535 km, resulting to some-what, but probably not significantly, smaller MO-re-gions. The expected differences in the total MOvolumes are small and we believe that the generalbehaviour of our models is not affected by theneglection of the temperature dependence of latentheat.

To study the influence of the upper limit of theviscosity and to obtain some idea about the effect of

Žthe slab rheology on our results see the chapter.Model , we varied the upper limit of viscosity in a

few models. Starting at a stage with well-establishedsubduction, the upper truncation viscosity was variedbetween y s1023 Pa s and y s1032 Pa s,max max

while all other parameters were kept equal to thoseof the model shown in Fig. 2. In the models withy less than 1024 Pa s, the slabs are weak enoughmax

so that deformation is facilitated and they flatten outand rest on the 660-km boundary for about 11 Ma.Increasing the upper limit to y s1029 Pa s, themax

slabs show a similar evolution, i.e., until the timethey sink into the lower mantle, reduced to about 8Ma. Only in the models where viscosities greaterthan 1030 Pa s are allowed did the evolution of thesubducting lithosphere change significantly. Theslabs are too stiff to flatten out on the 660-kmboundary and penetrate directly into the lower man-tle. From these tests, we conclude that within certainlimits, a wide range of viscosities leads to essentiallya similar penetration behaviour, and we feel that ourresults are also applicable to cases with more com-plex rheologies.

An important observation from some of our mod-els is the thinning and extension of the slab during

Ž .subduction see also Houseman and Gubbins, 1997 .In a thinned slab, the MO may be transformed fasterdue to enhanced conductive heating. Such a thinninghas not been observed or included in previous mod-

Ž .els by Schmeling et al. 1999 , who used a strongerŽ .olivine rheology, or by Marton et al. 1999 , who

used spatially constant subduction velocities. Furtherslab deformation might be expected to be caused by


rheological weakening due to grain-size reductionŽassociated with the transformation Riedel and

.Karato, 1997 . Because the concept of the thermalŽ .parameter e.g., Kirby et al., 1996 is based on

steady state subduction with constant velocity, itsapplication to thinned and deforming slabs as well astime-dependent subduction might be problematic;thus, we did not apply this concept here.

In our experiments, we observed a trench roll-back, depending on the thicknesses of the litho-spheres and the amount of MO. The rates of thisroll-back increase from 1 cmryear in models with a

Ž .thin lithosphere 55 km to about 4.5 cmryear inŽ .those with a thick lithosphere 120 km . In models

with a significant amount of MO, the rate of trenchroll-back is about 14% larger than in the models withthe same thicknesses, but without allowing for theformation of MO. The MO causes a flattening of theslab on the 660-km phase boundary, resulting to astronger trench roll-back.

In our models, we found that metastable wedgesof olivine slow down slabs by as much as 20% byincreasing positive buoyancies. This is in general

Ž . Ž .agreement a with Marton et al. 1999 , who founda decrease of up to 20% in their thermokinematicmodels by balancing buoyancy and drag forces, andŽ . Ž .b with Schmeling et al. 1999 , who found a de-crease of up to 30% in their dynamical models thatwere confined to the upper mantle only. In contrast

Ž . Ž .to Schmeling et al. 1999 and Marton et al. 1999 ,the velocities for slabs with MO in our models arestill increasing with the age of the slab. We believe

Ž .that this is due to the fact that a our models includeŽ .the full convective flow field, and b the slabs are

Ž .weaker and return flow within the lower mantle isallowed. To answer the question whether velocities

Žof slabs with MO decrease with age Schmeling et. Žal., 1999 , become independent of age or thermal. Ž .parameter Marton et al., 1999 or increase with age

Ž .this study requires a better knowledge of the rheol-ogy of the slab and mantle.

In conclusion, our models show that olivinemetastability may strongly influence subduction byinhibiting and delaying subduction into the lowermantle. Slabs with MO flatten out at the 660-kmboundary, and penetration into the lower mantleoccurs only after all MO has been transformed. Onthe other hand, our models show that the effect of

MO to slow down subduction velocities within theŽ .transition zone is rather moderate cf. Fig. 5 .

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The influence of olivine metastability on deep subduction