Localization of dislocation creep in the lower mantle ...mcnamara.asu.edu/content/publications/pdfs/Mcnamara_et...Localization of dislocation creep in the lower mantle: implications

Localization of dislocation creep in the lower mantle:implications for the origin of seismic anisotropy

Allen K. McNamara a;*, Shun-Ichiro Karato b, Peter E. van Keken a

a Department of Geological Sciences, 2534 C.C. Little Building, University of Michigan, Ann Arbor, MI 48109-1063, USAb Department of Geology and Geophysics, 108 Pillsbury Hall, University of Minnesota, Minneapolis, MN 55455, USA

Received 26 March 2001; received in revised form 15 June 2001; accepted 19 June 2001

Abstract

Recent seismological observations reveal the presence of seismic anisotropy in localized regions at the base of themantle within an otherwise isotropic lower mantle. These regions can be placed in a tectonic context, corresponding tolocations of paleosubduction and plume upwelling. This project works toward determining whether the observedseismic anisotropy may be explained by the development of a mineral fabric by lattice-preferred orientation (LPO).Numerical modeling is used to explore whether the conditions at the base of upwelling and downwelling regions areconsistent with those required for fabric development. Specifically, we examine whether dislocation creep dominatesthese regions within a background mantle that flows primarily by diffusion creep. The key to our study is the use of acomposite rheology that includes both mechanisms of diffusion and dislocation creep and is based on mineral physicsexperiments. Results show that it is possible to produce a localization of dislocation creep near slabs within abackground mantle dominated by diffusion creep. In contrast, upwelling regions are characterized by a domination ofdiffusion creep. These results indicate that LPO may be the cause of lowermost mantle seismic anisotropy nearpaleoslabs, but other mechanisms such as shape-preferred orientation may be required to produce the anisotropyobserved near upwellings. ß 2001 Elsevier Science B.V. All rights reserved.

Keywords: mantle; convection; anisotropy; dislocation creep; core^mantle boundary

1. Introduction

A more detailed study of the lowermost mantleis needed to better understand the dynamical pro-cesses occurring at the core^mantle boundary

(CMB) region. This region is particularly impor-tant because it likely includes a thermal boundarylayer and may be a source of chemical heteroge-neity as well (e.g. [1,2]). An improved understand-ing of the dynamics of this boundary region willallow us to work toward answering many funda-mental questions regarding the dominant creepmechanisms in and near slabs and plumes, plumeformation, slab deformation, the possible meltdistribution, and the presence of chemical hetero-geneity.

Recent improvements in seismic observations of

0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 4 0 5 - 8

* Corresponding author. Tel. : +1-734-764-1435;Fax: +1-734-763-4690.

E-mail addresses: [email protected] (A.K. McNamara),[email protected] (S.-I. Karato), [email protected] (P.E.van Keken).

EPSL 5911 13-8-01 Cyaan Magenta Geel Zwart

Earth and Planetary Science Letters 191 (2001) 85^99

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the CMB region (e.g. [3]) now allow additionalconstraints to be placed on geodynamical models.The focus of this project is to provide a ¢rst stepin identifying the cause of the seismic anisotropyobserved at the base of the mantle. Here, we in-vestigate whether the observed anisotropy may beexplained by the development of a mineral fabriccaused by lattice-preferred orientation (LPO). Westart by using numerical modeling to explorewhether mantle conditions at upwelling anddownwelling regions in the lowermost mantleare consistent with those required to develop afabric. Speci¢cally, we examine the degree of lo-calization of dislocation creep near upwelling anddownwelling regions in our models. Before discus-sing the details of the modeling, we will review thethe seismic observations of and the mineralphysics background on the mechanisms for theformation of seismic anisotropy.

1.1. Seismic observations

The bulk of the lower mantle is seismically iso-tropic except for some portions of DQ [4,5]. Theobservation of seismic anisotropy in the deepestmantle is important as it may be related tochanges in mantle £ow mechanisms or £ow ori-entation. For example, seismic anisotropy in theupper mantle is generally considered to be due toLPO caused by dislocation creep in olivine [6].

Excellent summaries of the nature of DQ aniso-tropy are given in [3,7,8]. Studies of shear wavesplitting have revealed the presence of anisotropyin patches of DQ beneath Alaska [9], the Carib-bean [10], and the Indian Ocean [11] that can beinterpreted as transverse isotropy with VSH sVSV

although the bias of source^receiver locationsmakes it di¤cult to rule out azimuthal anisotropy.A shear wave discontinuity 200^350 km above theCMB marks the onset of anisotropy in these re-gions, and there is evidence for a lack of aniso-tropy at shallower depths provided by the absenceof shear wave splitting for source^receiver spac-ings at slightly smaller epicentral distances. More-over, the magnitude of anisotropy decreases withdepth, and becomes isotropic near the CMB. Fur-thermore, these regions are characterized by faster

than average wave velocities, hinting that theyconsist of paleosubducted slabs [12].

The pattern of anisotropy in the central Paci¢cis strikingly di¡erent. Seismic observations indi-cate a high degree of lateral variability with sub-regions exhibiting VSV sVSH, VSH sVSV, or nomeasurable anisotropy at all [13^17]. In contrastto the circum-Paci¢c regions, the anisotropy ofthe central Paci¢c appears to be deeper, justabove the CMB, and there is no convincing evi-dence for a shear wave discontinuity. The pres-ence of strong negative velocity gradients in thelowermost mantle, lower-than-average wavespeeds regionally, a thick (V40 km) ultralow-ve-locity zone (ULVZ), and a dense hotspot distri-bution at the surface all lead to the likelihood ofthis region being related to the source of mantleupwelling.

1.2. Causes of seismic anisotropy

The possible causes of seismic anisotropy at thebase of the mantle are extensively summarized in[3,7,8,10,18^20].

Mantle anisotropy may be caused by eithershape-preferred orientation (SPO) or LPO. SPOmay be a result of either aligned melt inclusionsor laminated solid materials with contrasting elas-tic properties. LPO is caused by an alignment ofcrystallographic axes of anisotropic minerals.Mineral physics studies have shown that the twomain lower-mantle minerals, (Mg,Fe)SiO3 andMgO, have a high degree of intrinsic anisotropy[20]. The development of LPO is closely linked tothe creep mechanisms controlling £ow. Di¡usioncreep dominates under low stress and/or smallgrain size and leads to a random distribution ofmineral grain orientations resulting in an e¡ec-tively isotropic aggregate. The observation thatthe bulk of the lower mantle is seismically iso-tropic is used to infer that di¡usion creep is theprimary £ow mechanism operating [21].

On the other hand, dislocation creep occurs athigh stresses and/or large grain sizes and leads toan alignment of mineral grains. The resulting ag-gregate is seismically anisotropic, the degree ofwhich is dependent on the amount of strain.


A.K. McNamara et al. / Earth and Planetary Science Letters 191 (2001) 85^9986

2. Problem formulation

We are interested in determining the cause oflowermost mantle seismic anisotropy associatedwith upwellings and downwellings. We initiallywant to determine whether the anisotropy canbe explained by the formation of a fabric byLPO. As a ¢rst step toward that goal, we inves-tigate whether the conditions are appropriate forLPO development in upwelling and downwellingregions near the CMB by determining whetherdislocation creep (LPO enhancing) or di¡usioncreep (LPO reducing) dominates in speci¢c re-gions. To achieve this goal, we employ a compo-site rheology that includes components of di¡u-sion and dislocation creep. We produce mapsillustrating the relative in£uence of each compo-nent on the overall viscosity. Conditions are con-sidered appropriate for fabric development if thedislocation creep component dominates the vis-cosity. We predict that regions dominated by dis-location creep have the potential to form a min-eral fabric strong enough to produce the observedseismic anisotropy.

Since di¡usion and dislocation creep are inde-pendent mechanisms, we utilize a compositerheology expressed as:

_O � _O diff � _O disl �1�

where _O diff and _O disl are the e¡ective strain ratesfor di¡usion creep and dislocation creep, respec-tively, and are expressed as:

_O diff � A0diffbd

� �m exp 3

gdiff Tm

Tdim

� �cW

�2�

_O disl � A0disl exp 3gdisl Tm

Tdim

� �cW

� �n �3�

where APdiff and APdisl are prefactors, W and b arereference values for the rigidity and Burgers vec-tor, gdiff and gdisl are activation coe¤cients, Tm isthe dimensional melting temperature, d is thegrain size, c is the stress, and m and n are con-stants. Because c=R _O , these may be rearranged

to yield:

R � 1R diff

� 1R disl

� �31 �4�

where:

R diff � WA0diff

db

� �m exp

gdiff Tm

Tdim

� ��5�

R disl � WA0disl

expgdisl Tm

Tdim

� �cW

� �13n �6�

where R is the e¡ective viscosity, and Rdiff andRdisl are the viscosities for the respective creepmechanisms.

The transition stress, ct, is de¢ned as the stressat which the material £ows equally by di¡usionand dislocation creep:

c t �"

A0disl

A0diff

� �db

� �m W �13n� exp

Tm

T�gdiff3gdisl�

� �# 113n �7�

We employ an olivine rheology for the uppermantle (gdiff = 17, gdisl = 31). Rheological parame-ters for lower-mantle materials have large uncer-tainties; however, di¡usion creep parameters arenow relatively well constrained through direct ex-perimental studies on MgO, (Mg,Fe)O, andMgSiO3 perovskite [22]. Both materials have arelatively small activation coe¤cient for di¡usioncreep (gdiff is between 10 and 14). We use thelower value throughout (gdiff = 10). The activationcoe¤cient for dislocation creep is less well con-strained, and we have explored a range of thisparameter from 10 to 18 [23].

The melting temperatures for both materials areparameterized as:

Tm �

2100� 1:4848z35:00U1034 z2 �upper mantle��8�


A.K. McNamara et al. / Earth and Planetary Science Letters 191 (2001) 85^99 87

Tm �2916� 1:2500z3165U1034 z2 �lower mantle�

�9�

where T is in Kelvin and z is the depth in km [22].The viscosity prefactors, and consequently the

transition stress, are not well known. We con-strain these by choosing a set of prefactors thatresults in a background lower mantle dominatedby di¡usion creep, consistent with seismologicalobservations. We also insist that the magnitudeof average mantle viscosity is consistent with ge-oid and post-glacial rebound constraints [23]. Inaddition, experimental work on oxides limits theratio of non-dimensional prefactors APdisl/APdiff

between 1038 and 10310 [24].In order to simulate subduction of cold litho-

spheric slabs, we need a mechanism to break therigid lid produced by the temperature-dependentrheology. We choose a method that utilizes amaximum yield stress in the topmost region ofour model which is similar to that of [25]. In theupper 300 km of our model, the viscosity is ad-justed in order not to exceed a critical yield stress,cc which is a function of depth. cc includes twocomponents, a constant ductile yield stress, cd,and a depth-dependent brittle yield stress that isde¢ned by a brittle stress gradient, cPb.

c c � min�c d; c 0bz� �10�

where z is the depth. The e¡ective viscosity isde¢ned as:

R eff � min R �T ;Tm; _O �; c c

_O

� ��11�

cd and cPb are related such that they are equal ata depth of 75 km. This implies that the brittleregime dominates near the surface and the ductileregime dominates at depth. Trial and error wasused to pick appropriate values of cd that e¡ec-tively produced slab-like features. We do notclaim to adequately model the physical mecha-nisms occurring in the Earth's lithosphere, andwe only use this method as a quasi-self-consistentmethod to break the rigid lid.

The list of ¢xed parameters used in this study isgiven in Table 1. Each run is started from a pre-vious solution pro¢le and is given enough time toreach a new quasi-equilibrium state. A successfulmodel run must satisfy the constraint that thebulk of the lower-mantle £ows primarily by dif-fusion creep. We attempt to meet the observatio-nal constraints of velocity, viscosity [23], and heat£ow [26].

2.1. Model setup

The numerical calculations are performed bysolving the non-dimensional conservation equa-tions of mass, momentum, and energy in the ex-tended Boussinesq approximation [27]. The equa-tion for mass conservation in incompressible £owis:

9Wu � 0 �12�

where u is the velocity vector. The momentumequation is:

9P� 9W�R _O � � KRaT r̂ �13�

where rª is the radial unit vector directed towardthe center, P is the dynamic pressure, R is thee¡ective viscosity, _O is the deviatoric strain ratetensor, K is the non-dimensional thermal expan-sivity, Ra is the Rayleigh number, and T is thetemperature. The energy equation includes vis-cous dissipation and adiabatic (de)compression:

DTDt� �uW9�T � K

Tdim

vTDiw � 9�kW9T� � Di

Rac ij

Dui

Dxj

�14�

where t is time, Tdim is the dimensional temper-ature, k is the non-dimensional thermal conduc-tivity, vT is the temperature contrast across themodel, Di is the dissipation number, w is the ra-dial component of velocity, cij are components ofthe stress tensor, and ui and xi indicate the ithcomponent of the velocity and location vectors,respectively. The strain rate components are:

_O ij � Dui

Dxj� Duj

Dxi�15�



The second invariant of the strain rate tensor isthe e¡ective strain rate and is represented as:

_O � �124 _O ij _O ij�12 �16�

The Rayleigh number is given as:

Ra � b 0gK 0vTh3

U 0R 0�17�

where b0, K0, U0, and R0 are reference values ofdensity, thermal expansivity, thermal di¡usivity,and viscosity. h is the reference length scale cor-responding to the depth of the mantle.

The non-dimensional viscosity is determined bydividing by the reference viscosity, R0, which isde¢ned as the di¡usion creep viscosity of the oli-vine layer at Tdim = 1500 K and z = 140 km. Thedissipation number is given as:

Di � KghCp

�18�

We use depth-dependent values of thermal con-ductivity and thermal expansivity of the non-di-mensional form:

k � bGb f

� �3 �19�

K � 1b 2 �20�

where b is the non-dimensional density given by:

b � expDiQ

z0� �

�21�

where Q is the Gru«neisen parameter (set equal to1) and zP is the non-dimensional depth [28]. Notethat the expression for variable density is onlyused in the speci¢cation of K and k. This param-eterization is similar to that used in [29].

The equations are solved in a 2-D cylindricalgeometry, and the model domain is a quarter cyl-inder. The radii of the bottom boundary, lower^upper-mantle interface, and top boundary are setto maintain the volume ratios of the Earth. Our

models are bottom-heated in order to exaggeratethe production of upwellings for study. The veloc-ity boundary conditions are free slip.

The equations are solved with the ¢nite elementtoolbox SEPRAN (http://dutita0.twi.tudelft.nl/sepran/sepran.html). The model domain is discre-tized into 21 356 nodal points. The momentumequation is solved on quadratic triangular ele-ments using a penalty-function method [30]. Thestrain rate dependence of viscosity necessitatessolving the momentum and viscosity equationsiteratively until viscosity and velocity are consis-tent. In most cases a relaxation between successivevelocity solutions is required. We do a pointwiseiteration to determine stress in the viscosity calcu-lation. A predictor^corrector method with up-winding is used to solve for temperature on lineartriangular elements nested within the quadraticelements.

3. Results

Due to the uncertainty in the rheological pa-rameters, we vary the lower-mantle dislocationcreep activation coe¤cient, the magnitude of vis-cosity, and the transition stress. We also study thee¡ect of weak slabs in the lower mantle.

Results are displayed as snapshots in time forparticular model runs. Table 2 displays speci¢cparameters used and output results for each pre-sented run. Fig. 1 illustrates results from a modelrun which incorporates identical values of g forboth di¡usion and dislocation in the lower man-tle. As a consequence, the transition stress for thelower mantle is independent of temperature anddepth (Eq. 7). This run will be considered as areference case that the other runs are comparedto. The transition stress for this case is 70.7 MPa.The temperature ¢eld, shown in Fig. 1a, indicatesthe presence of upwelling jets of hot material atthe edges as well as a cold slab penetrating intothe lower mantle. Fig. 1b shows the correspond-ing viscosity ¢eld. The temperature-dependentrheology produces a slab that is much sti¡erthan the background mantle. The stress ¢eld,shown in Fig. 1c, indicates that regions of highstress are associated with the downwelling slab as



well as the £anks of the upwellings. The logarithmof non-Newtonian (dislocation creep) viscosityover Newtonian (di¡usion creep) viscosity is illus-trated in Fig. 1d. Note that positive values repre-sent regions of di¡usion creep-dominated rhe-ology whereas negative values represent regionswhere dislocation creep dominates. Dislocationcreep dominates the upper mantle except forslab itself. The reason for a switch to di¡usioncreep in the upper mantle portion of the slab isthat gdisl s gdiff in the olivine rheology which re-sults in an increased transition stress at lower tem-peratures (Eq. 7). In the lower mantle, di¡usioncreep dominates the background whereas disloca-tion creep is localized in and near the slab. In the

thin space between the slab and the CMB, £ow isdominated by di¡usion creep, likely due to thefree slip lower boundary condition and the lowthermally activated viscosity which both in turnproduce lower stresses. There are also smallerzones of dislocation creep-dominated rheologynear the £anks of the upwellings.

We also investigated the e¡ect of varying thetransition stress while maintaining gdiff = gdisl.We performed runs with transition stresses of32, 100, and 225 MPa. The case with ct = 32MPa results in a slab that undergoes more intensedislocation creep-dominated £ow. In addition, alarge proportion (about half) of the lower mantleis dominated by dislocation creep. As the transi-

Table 1Fixed parameters

Parameter Description Value Units

vT Temperature drop across mantle 3000 KK0 reference thermal expansivity 3U1035 K31

b0 reference density 4500 kg m33

Cp speci¢c heat 1250 J kg31 K31

h mantle thickness 2.8U106 mk0 reference thermal conductivity 5.6 W m31 K31

g gravitational constant 9.8 m s32

U0 reference thermal di¡usivity k0 b310 C31

pDi dissipation number 0.5dum grain size 2.0 mmdlm grain size 1.0 mmmum grain size index 2.5mlm grain size index 2.5num power-law index 3.0nlm power-law index 3.0APdiffÿum olivine di¡usion prefactora 2.25U1014 s31

APdislÿum olivine dislocation prefactora 1.28U1022 s31

APdiffÿlm lower-mantle di¡usion prefactora 1.06U1014 s31

W reference rigidity 300 GPab Burgers vector 5.0U1037 mmgdiffÿum olivine di¡usion activation coe¤cient 17gdislÿum olivine dislocation activation coe¤cient 31gdiffÿlm lower-mantle di¡usion activation coe¤cient 10cd ductile yield stress 400 MPacPb brittle yield stress gradient 5.33 MPa km31

Rsurface non-dimensional surface radius 1.67813Rbottom non-dimensional bottom radius 0.67813Rinterface non-dimensional upper^lower-mantle interface radius 1.42Rmax non-dimensional viscosity maximum 1.0Rmin non-dimensional viscosity minimum 1036

Upper- and lower-mantle values are denoted by um and lm, respectively. The above radii are non-dimensionalized by dividing bythe length scale, h.aFor the higher Rayleigh number case, APdiffÿum = 9.01U1014 s31, APdislÿum = 5.11U1022 s31, and APdiffÿlm = 4.22U1014 s31.



tion stress is increased, both the magnitude andthe areal extent of dislocation creep domination isreduced. The case with ct = 225 MPa results in athin sliver of dislocation creep-dominated behav-ior within the slab and near its base. In all cases,the base of upwelling regions remains in the dif-fusion creep regime.

Because of the uncertainty associated with theactivation coe¤cient of the dislocation compo-nent of the lower-mantle rheology we have variedthe value of gdisl. For unequal values of gdiff andgdisl, the transition stress depends on temperatureand depth (Eq. 7). First, we varied gdisl whilemaintaining the prefactor ratio, APdiff /APdisl, usedin the reference case. As gdisl was increased, theslab region became increasingly dominated by dif-fusion creep. With gdisl = 12, only tendrils of dis-location creep-dominated material remained nearthe slab. Greater values of gdisl resulted in £owthat is entirely dominated by di¡usion creepalthough in all cases, stress values remain similarto the reference case. The reason for this is thatthe transition stress (Eq. 7) increases greatly forsmall increases in gdisl. We reduced the prefactorratio to provide lower transition stresses (Table2). Temperature and viscosity ratio ¢elds areshown in Figs. 2 and 3 for cases in which gdisl isincreased and the prefactor ratio is decreased. Inall cases we maintain the value of gdiff at 10. Theconsequence of gdisl s gdiff is an increase in tran-sition stress for decreasing temperature. Fig. 2aillustrates the temperature ¢eld for a case in whichgdisl is set to 14. Compared to the reference case(Fig. 1), the style of convection is similar, but theviscosity ratio ¢eld (Fig. 2b) is markedly di¡erent.

The colder, central portion of the slab primarilyundergoes di¡usion creep, and dislocation creep isconcentrated along the slab boundaries. In addi-tion, dislocation creep is concentrated along thebending portion of the slab at the CMB, but asbefore, there is a thin gap between the CMB andthe slab that £ows mainly by di¡usion creep. Fig.3 shows results for a case in which gdisl is in-creased to 18. The temperature ¢eld is shown inFig. 3a and the viscosity ratio ¢eld is shown inFig. 3b. In this case, the cooler slab is almostentirely Newtonian, and localization of disloca-tion creep occurs mainly below the slab. In addi-tion, the high-temperature dependence of disloca-tion creep has signi¢cantly decreased thetransition stress in hot regions near the CMBand the upwellings, so £ow is primarily non-New-tonian in these regions. Note however, the base ofthe upwelling regions remains dominated by dif-fusion creep.

Of some interest is the e¡ect of reducing thesti¡ness of the slab in the lower mantle. As ma-terial passes through the transition zone into thelower mantle, recrystallization occurs. Karato etal. [31] have suggested that grain size is a functionof temperature as it passes through the transitionzone, so colder material will have a smaller grainsize which acts to reduce viscosity. Fig. 4 illus-trates results in which we have reduced the max-imum viscosity cuto¡ by a factor of 10. The tem-perature and viscosity ¢elds are shown in Fig.4a,b, respectively. Note the sharp decrease in vis-cosity as the slab passes into the lower mantle.Examination of the viscosity ratio in Fig. 4cshows that regions where dislocation creep domi-

Table 2Variable parameters and results

APdisl (APdisl/APdiff ) gdiffÿum gdislÿum gdiffÿlm gdislÿlm heat £ow GRflog cT related ¢gure(s31) (mW m32) (Pa s) (MPa)

3.36U105 3.18U1039 17 31 10 10 53 1.8U1023 70.7 Fig. 11.68U109 1.59U1035 17 31 10 14 50 1.9U1023 197.2 Fig. 21.68U1014 1.59U100 17 31 10 18 65 3.0U1023 123.0 Fig. 33.36U105a 3.18U1039 17 31 10 10 58 1.4U1023 70.7 Fig. 41.34U106b 3.18U1039 17 31 10 10 85 1.2U1023 70.7 Fig. 5

APdisl, (APdisl/APdiff ), gdisl, GRflog, and cT , are lower-mantle values. GRflog is the logarithmic average of viscosity. cT is evaluated atT = 1800 K and depth = 2000 km.aCase in which the lower-mantle viscosity maximum is reduced to 0.1.bCase in which the Rayleigh number is increased.



nates are more widespread compared to the pre-vious cases. Again, there is a thin band of di¡u-sion dominated material directly above the CMB.We performed runs with a further reduction in theviscosity maximum and found similar results.

We performed a case at a higher convectivevigor in order to examine the e¡ect of lower over-

all viscosity. We did this by uniformly decreasingthe viscosity prefactors. Temperature and viscos-ity ratio ¢elds are shown in Fig. 5a,b, respectivelyfor one case. This more vigorous case results in anoscillatory migration of the subduction site, lead-ing to the presence of a folded slab in the lowermantle. It is observed that the presence of a dis-

Fig. 1. Snapshot of a model run with gdiff = gdisl = 10 in the lower mantle, resulting in a transition stress that is independent ofdepth and temperature. (a) The temperature ¢eld shown in non-dimensional units. (b) The logarithm of dimensional viscosity inPa s. (c) The logarithm of dimensional stress in Pa. (d) The logarithm of the ratio of non-Newtonian viscosity over Newtonianviscosity. Positive values (blue) re£ect a domination of di¡usion creep, and negative values (red) indicate a domination of disloca-tion creep.



Fig. 2. Snapshot of a model run with gdiff = 10 and gdisl = 14 in the lower mantle. The transition stress increases with decreasingtemperature. (a) The temperature ¢eld shown in non-dimensional units. (b) The logarithm of the ratio of non-Newtonian viscos-ity over Newtonian viscosity. Positive values (blue) re£ect a domination of di¡usion creep, and negative values (red) indicate adomination of dislocation creep.



Fig. 3. Snapshot of a model run with gdiff = 10 and gdisl = 18 in the lower mantle. The transition stress increases with decreasingtemperature. (a) The temperature ¢eld shown in non-dimensional units. (b) The logarithm of the ratio of non-Newtonian viscos-ity over Newtonian viscosity. Positive values (blue) re£ect a domination of di¡usion creep, and negative values (red) indicate adomination of dislocation creep.



location creep-dominated region near the slab ispreserved at higher convective vigor.

4. Discussion

The goal of this project was to use numerical

modeling to determine if the conditions for fabricdevelopment by LPO are met near upwellings anddownwellings at the base of the mantle under con-straints of mineral physics, seismology, and sur-face observations such as heat £ow, velocity, andviscosity. In essence, we were looking for high-stress regions that will allow a localization of dis-

Fig. 4. Snapshot of a model run in which the maximum viscosity of the lower mantle has been reduced. gdiff = gdisl = 10 in thelower mantle. (a) The temperature ¢eld shown in non-dimensional units. (b) The logarithm of dimensional viscosity in Pa s. (c)The logarithm of the ratio of non-Newtonian viscosity over Newtonian viscosity. Positive values (blue) re£ect a domination ofdi¡usion creep, and negative values (red) indicate a domination of dislocation creep.



Fig. 5. Snapshot of a model run in which the viscosity prefactors have been uniformly decreased, resulting in a greater convectivevigor. gdiff = gdisl = 10 in the lower mantle. (a) The temperature ¢eld shown in non-dimensional units. (b) The logarithm of the ra-tio of non-Newtonian viscosity over Newtonian viscosity. Positive values (blue) re£ect a domination of di¡usion creep, and nega-tive values (red) indicate a domination of dislocation creep.



location creep in an otherwise di¡usion creep-dominated mantle. Our results consistently revealthat slabs provide the highest stress regions in thelower mantle, leading to a localization of disloca-tion creep near downwellings. Therefore, condi-tions are right for the development of LPO inthese regions and may provide the source of theobserved seismic anisotropy. Interestingly, thiswas not observed at the base of upwellings. Ourresults show that hot upwelling regions are pri-marily Newtonian unless we signi¢cantly increasegdisl. Even under high gdisl values, only the plumeconduits exhibit non-Newtonian £ow, and thebases of the upwellings remain in the Newtonianregime. This result indicates that the conditionsfor LPO development are not right at the baseof upwellings which is inconsistent with seismo-logical observations [7] and leads to the possibilitythat SPO is the primary source of the observedanisotropy in these regions. These results indicatethat it is important to look at stress regimes whenusing a temperature-dependent rheology ratherthan intuitively assuming fabric development inregions of high strain rate (e.g. [7]).

One point of consideration is how our resultscompare with the observation that seismic aniso-tropy ceases directly above DQ. Most of our re-sults reveal cases in which a domination of dislo-cation creep extends a considerable distance upthe slab. Seismic observations are more robustnear the CMB than other portions of the lowermantle, so a likely possibility is that seismology isinsensitive to fabric development in much of theslab. Another possibility relates to the uncertaintyin transition stress. Most of our model results in-dicate stress is greatest at the lowermost extent ofthe slab. If the transition stress is increased, it isconceivable that results with only a sliver of dis-location creep-dominated material will exist at thebase of the mantle. An additional possibility isthat the magnitude and direction of strain is notconsistent with signi¢cant fabric developmentalong the shallower portions of the slab. Prelimi-nary calculations using model strain rates withinthe slab regions indicate that it takes approxi-mately 1000 km of slab descent to produce100% strain, an amount needed for the formationof a detectable fabric.

It is important to note that uncertainty in theratio of rheological prefactors and the grain sizeof lower-mantle minerals allow for di¡erent volu-metric extents of dislocation creep-dominated re-gions. We ¢nd that a larger APdisl/APdiff ratio orlarger grain size extends the region exhibiting dis-location creep. Conversely, a smaller ratio orsmaller grain size decreases the extent of disloca-tion creep-dominated regions. We consistently¢nd that slabs provide the highest stress regionsin our models and that the bases of upwellings arecharacterized by low stress. Di¡usion creep is al-ways the dominant £ow mechanism at the base ofupwellings, and dislocation creep dominates slabregions for transition stresses on the order of 250MPa and less.

Our results show that localization of dislocationcreep occurs in downwelling regions regardless ofslab sti¡ness. To produce weak slabs we simplycut the maximum viscosity, but we admit that thismay not be entirely appropriate. If the reasoningfor weak slabs is smaller grain size, an increase intransition stress is expected. This may produceresults more similar to those in which gdisl s gdiff . gNevertheless, computational limitations make itcomputationally expensive to track a grain size¢eld through the convection calculations.

We have shown that conditions are right for thedevelopment of LPO near slabs but not for up-wellings. Future work which tracks the strainmagnitude and direction is necessary for furtherconstraining the degree of fabric developmentnear slabs.

5. Conclusions

We used numerical modeling to examinewhether conditions are appropriate for the devel-opment of LPO in upwelling and downwellingregions of the lower mantle. Speci¢cally, welooked at whether mineral physics constraints onmantle rheology allow for regions of dislocationcreep localization within a lower mantle that £owsprimarily by di¡usion creep. Under a variation ofthe rheological parameters, we consistently ob-serve slabs forming the highest stress regions,therefore, localization centers for dislocation



creep. In contrast, we observe hot upwelling re-gions to be dominated by di¡usion creep. Ourresults indicate that the conditions are appropri-ate for the development of LPO in and near slabs.Our work also shows that it is unlikely that LPOis occurring in upwelling regions, and other mech-anisms such as SPO may be required to explainthe seismic anisotropy.

Acknowledgements

We thank Lars Stixrude, Carolina Lithgow-Bertelloni, Rob van der Voo, Charlie Doering,and Boris Kiefer for constructive discussions.We also thank Scott King, Thorne Lay, and ananonymous reviewer for thoughtful reviews. Thisresearch was supported by Grant CSEDI EAR9905601.[SK]

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