2.02Seismological Constraints uponMantle CompositionC. R. Bina

Northwestern University, Evanston, IL, USA

2.02.1 INTRODUCTION 392.02.1.1 General Considerations 392.02.1.2 Bulk Sound Velocity 402.02.1.3 Acoustic Methods 40

2.02.2 UPPER-MANTLE BULK COMPOSITION 412.02.2.1 Overview 412.02.2.2 Velocity Contrasts 422.02.2.3 Discontinuity Topography 422.02.2.4 Sharpness 432.02.2.5 Broadening and Bifurcation 43

2.02.3 UPPER-MANTLE HETEROGENEITY 452.02.3.1 Subducted Basalts 452.02.3.2 Plume Origins 46

2.02.4 LOWER-MANTLE BULK COMPOSITION 482.02.4.1 Bulk Fitting 482.02.4.2 Depthwise Fitting 49

2.02.5 LOWER-MANTLE HETEROGENEITY 512.02.5.1 Overview 512.02.5.2 Subducted Oceanic Crust 52

2.02.6 SUMMARY 54

REFERENCES 56

2.02.1 INTRODUCTION

2.02.1.1 General Considerations

Direct sampling of mantle rocks and minerals islimited to tectonic slices emplaced at the surface(see Chapter 2.04), smaller xenoliths transportedupwards by magmatic processes (see Chapter2.05), and still smaller inclusions in such far-traveled natural sample chambers as diamonds(see Chapter 2.05). Because of such limited directaccess to mantle materials, knowledge of mantlestructure, composition, and processes must beaugmented by geophysical remote sensing. Whatcan various seismological observations tell usabout the major-element composition of the uppermantle? How can they constrain possible differ-ences in chemical composition between the upper

and lower mantle? What light can they shed uponthe nature of velocity heterogeneities in both theupper and lower mantle? It is these questions thatwe shall seek to address in this chapter.

Most seismological constraints on mantle com-position are derived by comparison of values ofseismic wave velocities inferred for particularregions within the Earth to the values measured inthe laboratory for particular minerals or mineralassemblages, with such comparisons being madeunder comparable regimes of pressure (P) andtemperature (T ). The primary parameters ofinterest, then, are the compressional (or P-) wavevelocities (VP) and the shear (or S-) wavevelocities ðVSÞ: These wave velocities are simplyrelated to the density (r) and to the two isotropicelastic moduli, the adiabatic bulk modulus (KS)

39

and the shear (or “rigidity”) modulus (G), via V2P ¼

½KS þ ð4=3ÞG�=r and V2S ¼ G=r; respectively.

2.02.1.2 Bulk Sound Velocity

Straightforward measurements of elastic prop-erties of materials can be made via high-pressurestatic compression experiments, in which X-raydiffraction (XRD) is used to measure the molarvolume (V), or equivalently the density (r), of amaterial as a function of pressure (P). Thepressure dependence of volume is expressedby the “incompressibility” or isothermal bulkmodulus (KT), where KT ¼ 2Vð›P=›VÞT :

This isothermal bulk modulus ðKT Þ measured bystatic compression differs slightly from the afore-mentioned adiabatic bulk modulus ðKSÞ definingseismic velocities in that the former ðKT Þ describesresistance to compression at constant temperature,such as is the case in a laboratory device in which asample is slowly compressed in contact with alarge thermal reservoir such as the atmosphere.The latter ðKSÞ; alternatively describes resistanceto compression under adiabatic conditions, such asthose pertaining when passage of a seismic wavecauses compression (and relaxation) on a time-scale that is short compared to that of thermalconduction. Thus, the adiabatic bulk modulusgenerally exceeds the isothermal value (usually bya few percent), because it is more difficult tocompress a material whose temperature rises uponcompression than one which is allowed to conductaway any such excess heat, as described by asimple multiplicative factor KS ¼ KT ð1 þ TagÞ,where a is the volumetric coefficient of thermalexpansion and g is the thermodynamic Gruneisenparameter.

Experimentally, the bulk modulus is thesimplest parameter to measure, but the seismo-logical parameters of primary interest, VP and VS;

both involve the shear modulus as well. It isconvenient, therefore, to define a new parameter,the “bulk sound velocity” (Vf), which eliminatesall dependence upon the shear modulus (G)through a judicious linear combination of thesquares of the two seismic wave velocities: V2

f ¼KS=r ¼ V2

P 2 ð4=3ÞV2S : This new parameter (some-

times thought of as the P-wave velocity of an“equivalent” fluid, for which G ¼ 0) can bedetermined directly from static compressiondata: V2

f ¼ KS=r ¼ ð1 þ TagÞð›P=›rÞT . The bulksound velocity possesses another desirable fea-ture, in that it can also be constrained indirectlythrough chemical equilibrium experiments.Chemical equilibria describe free energy minima;the pressure dependence of free energy isdescribed by the molar volume, and the pressuredependence of volume (or density) is describedby KT and hence Vf. Thus, experimental deter-minations of equilibrium phase boundaries can

provide independent constraints upon Vf (Binaand Helffrich, 1992).

Again, chemical composition in regions ofEarth’s interior is primarily constrained by mappingvalues of seismic velocities in those regions andcomparing the values to those determined forvarious candidate mineral assemblages. The pri-mary observables in the seismological studiesconsist of measured travel times of various P- andS-waves, some of which can in principle constraindensity contrasts (Shearer and Flanagan, 1999) froma large enough set of which values of VP and VS canbe determined through mathematical inversion.Secondary observables include the measured ampli-tudes of various arriving P- and S-waves, some ofwhich can in principle constrain density contrasts(Shearer and Flanagan, 1999) but these are muchmore sensitive to complex properties such asanelasticity than are simple travel times.Seismological observables, then, directly yield VP

and VS; but static compression experiments directlyyield Vf. It is common, therefore, to seek to combineseismological VP and VS models to generate a Vf

model for a region, for comparison to mineralogi-cally constrained Vf values. Such combinatoricprocedures can introduce additional errors, how-ever, in that the VP and VS profiles used may oftenreflect seismic ray paths or frequency bands thatdiffer from one another. Indeed, special source–receiver geometries (such as those whose epicentraldistances are so small as to ensure nearly overlap-ping ray paths) may be necessary to obtain robustestimates of Vf values (Bina and Silver, 1997).Nonetheless, comparisons to Vf, rather than to VP

and VS; are commonly used to constrain compo-sitions in the deep interior, because (as noted below)mineralogical values for G (and hence for VS)become more problematic with increasing depth.

2.02.1.3 Acoustic Methods

Direct laboratory measurements of VP and VS

for materials can be made through acousticmethods, such as Brillouin spectroscopy andultrasonic techniques. Brillouin spectroscopy (or“Brillouin scattering”) determines acoustic velo-cities in a single crystal through measurements ofthe Doppler shifts experienced by visible lightscattering off the faces of a single crystal in whichthermally induced acoustic waves are propaga-ting. Because the technique employs singlecrystals, full elasticity tensors (rather than justisotropic VP and VS) can be determined, which areuseful in studies of velocity anisotropy. Thetechnique requires only small samples, andbecause visible light is employed, the samplesmay be placed in an optically transparentdiamond-anvil cell (DAC) in order to makemeasurements at elevated pressures and tempera-tures. DAC studies yielding VP and VS may be

Seismological Constraints upon Mantle Composition40

combined with XRD analyses yielding r, to allowfor direct determination of KS and G (and henceVf) for single crystals (Zha et al., 1998a).

The second group of acoustic methods, theultrasonic techniques, require larger samples butcan be performed on either single crystals orpolycrystalline aggregates. They require experi-mental measurement (via interferometry) of thetravel times of two consecutive ultrasonic echoesfrom the ends of a shaped sample, combined withmeasurement of the length of the sample. Thesemeasurements directly yield VP and VS; rather thanfull anisotropic elasticity tensors, but this is usuallysufficient (unless patterns of seismic velocityanisotropy are to be used to map strain fields inthe mantle). Samples may be placed in a multi-anvil cell (MAC) to make measurements atelevated pressures and temperatures, and simul-taneous (usually synchrotron) XRD analysis canthen be used to keep track of associated changes insample length. Again, MAC studies yielding VP

and VS may be combined with r measurementsfrom the XRD analyses to directly yield KS and G(and hence Vf) for samples (Li et al., 2001).

The appealing flexibility of acoustic techniquesis leading to rapid expansion of the regime ofpressures and temperatures in which experimentalmeasurements can be made. However, theirpotential utility continues to suffer from onepoorly understood factor. While Brillouin andultrasonic methods determine VP and VS atfrequencies in the MHz–GHz range, seismologi-cal observations constrain VP and VS at frequenciesin the mHz–Hz range. There is ample room for thepoorly understood frequency dependence of thesevelocities (“dispersion”) potentially to confoundpetrological interpretations over these many ordersof magnitude. Unhappily, VS is much more subjectto dispersion than is VP; and the magnitude of sucheffects upon VS (and hence G) only grows withincreasing temperature (and hence depth). Thus,until VS values can be both measured at simul-taneous high P and T and extrapolated from GHz tomHz with confidence (and quantifiable errorbounds), there remain important roles for theparameter Vf. Not only does Vf remain free of thedispersive and thermal complications of G, ifdetermined in part by static compression methodsit also benefits from being constrained bymeasurements near 0 Hz, closer to the seismicfrequency band than acoustic techniques permit.

2.02.2 UPPER-MANTLE BULKCOMPOSITION

2.02.2.1 Overview

Based upon the compositions of mantle rocksemplaced at the surface in large slices (see Chapter2.04) or as small xenoliths (see Chapter 2.05),

the compositions of mantle-derived melts (seeChapter 2.08), various cosmochemical arguments(see Chapters 2.01 and 2.15), and simple geophy-sical considerations, the mineralogy of the uppermantle is commonly concluded to resemble that ofsome sort of peridotite (McDonough and Rudnick,1998). Perhaps the most frequently invoked modelcomposition is that of “pyrolite” (Ringwood,1975, 1989), which contains ,60% olivine byvolume, the depth-varying properties of which aredominated by progressive high-pressure phasetransitions from olivine (a) to wadsleyite (b, alsocalled “modified spinel”) to ringwoodite (g, alsocalled “silicate spinel”) and thence to a mixture ofsilicate perovskite (pv) and magnesiowustite (mw,also called “ferropericlase”). The remaining,nonolivine, components are orthopyroxene(opx), clinopyroxene (cpx), and garnet (gt), andthese undergo more gradual high-pressure tran-sitions as the pyroxenes dissolve into the garnet,with the resulting “garnet–majorite” solid solu-tion (gt–mj) eventually transforming to silicateperovskite as well (Figure 1). While this model ofa peridotitic upper mantle has regularly beenchallenged, the proposed alternatives have

ab

g

opx +

cpx

gt– m

j

mw

(Mg,

Fe)-

pv

Ca-

pv

Volume fraction (%)

P (

GPa

)

29.2

38.2

47.5

56.9

66.5

76.4

86.5

96.8

107.4

118.4

129.8

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

2,400

2,600

2,800

Dep

th (

km)

0 20 40 60 80 100

Figure 1 Depth-varying phase proportions in apyrolite model mantle after the manner of Ringwood(1989), Ita and Stixrude (1992), and Bina (1998b).Phases are: (a) olivine, (b) wadsleyite, (g) ringwoodite,(opx) orthopyroxene, (cpx) clinopyroxene, (gt–mj)garnet–majorite, (mw) magnesiowustite, ((Mg,Fe)-pv)ferromagnesian silicate perovskite, and (Ca-pv) calciumsilicate perovskite. Patterned region at base denotes

likely heterogeneity near core–mantle boundary.

Upper-mantle Bulk Composition 41

evolved over time to accommodate increasingquantities of olivine: from an eclogite containinglittle or no olivine (Anderson, 1979, 1982, 1984),through various “piclogite” models containing16% (Bass and Anderson, 1984), 22% (Andersonand Bass, 1984), 30% (Anderson and Bass, 1986),or 40% (Duffy and Anderson, 1989; Duffy et al.,1995) olivine. Thus, “pyrolite” and “piclogite”represent broad families of mantle compositionsthat are distinguished primarily by the formerhaving .50% olivine by volume and the latterhaving ,50% olivine.

Estimates of a suitable peridotite compositionhave also varied: from 40–70% olivine (Weidner,1986), to 66–74% (Bina and Wood, 1987), to,52% (Bina, 1993), for example. Indeed, forseveral years these two end-member modelsseemed to be converging towards 50% olivine(Ita and Stixrude, 1992; Jeanloz, 1995; Agee,1998; Shearer and Flanagan, 1999). As thearguments hinge upon comparisons of seismicwave velocities in the upper mantle with velocityprofiles computed for candidate mineral assem-blages, firmer constraints upon this numberrequire not only better experimental measure-ments of the simultaneous dependence of theelastic properties of mineral assemblages uponboth temperature and pressure (Sinogeikin et al.,1998; Zha et al., 1998b) but also increasedseismological resolution of the laterally varyingvelocity contrasts at depth within the upper mantle(Melbourne and Helmberger, 1998).

2.02.2.2 Velocity Contrasts

Seismology constrains these contrasts throughobservations of P- and S-wave travel times.Mathematical inversion of large numbers of traveltimes, observed at a variety of distances betweensource (earthquake) and receiver (seismometer),results in velocity profiles that represent thevariation of VP and VS (or Vf) as functions ofdepth. The increase in velocities across seismic“discontinuities” in these models can then becompared to the velocity changes across phasechanges in olivine, as calculated from laboratorydata, in order to estimate mantle olivine content.Unfortunately, seismic velocity profiles deter-mined from such inversions generally are notvery sensitive to, and therefore do not wellconstrain, the magnitudes of velocity discontinu-ities, and this is especially true of globallyaveraged seismic velocity models. Local orregional studies that include travel times of specialseismic arrivals that have interacted directly with(reflected by or undergone P–S conversions at)the seismic discontinuities are best able to providesuch constraints.

Measurements of elastic wave velocities inolivine and wadsleyite at high pressures and

temperatures (Li et al., 2001) generate “remarkableconsistency” between a standard pyrolite modelcontaining ,60% olivine and high-resolutionseismic velocity profiles of the transition zone.Arguments about ^5% olivine aside, we canperhaps safely refer to the upper mantle as aperidotite, as the IUGS classification of ultramaficrocks defines a peridotite as containing 40% ormore olivine.

2.02.2.3 Discontinuity Topography

Perhaps one of the most important conse-quences of a peridotite composition for theupper mantle is that the phase transitions inolivine that are manifested as seismic disconti-nuities should exhibit thermally controlled varia-tions in their depth of occurrence that areconsistent with the measured Clapeyron slopes(Bina and Helffrich, 1994) of the transitions. Inparticular, the olivine–wadsleyite transition at410 km should be deflected upwards in the coldenvironment of subduction zones while thedisproportionation of ringwoodite to silicateperovskite and magnesiowustite at 660 km shouldbe deflected downwards, thereby locally thicken-ing the transition zone. In anomalously warmregions (such as the environs of mantle plumes asdescribed below), the opposite deflections at 410and 660 should locally thin the transitionzone. The seismically observed topography of20–60 km on each of the 410 and 660 is consistentwith lateral thermal anomalies of 700 K or less(Helffrich, 2000; Helffrich and Wood, 2001).

Other consequences of thermally perturbedphase relations in mantle peridotite (Figure 2)are also supported by seismological observations.These include anticorrelation of transition zonethickness and transition zone delay times,whereby positive delays in travel times, whichimply slow velocities (and therefore high tem-peratures), are observed to correlate with negativechanges in (thinning of) transition zone thickness(Gu and Dziewonski, 2002; Lebedev et al., 2002).

Figure 2 Schematic illustration of thermal control ofolivine phase transformations in the transition zone,showing perturbations to transition zone thickness,transition zone seismic velocities (delay times), and

depths of individual phase transformations.

Seismological Constraints upon Mantle Composition42

Similarly, observations of anticorrelation oftransition zone thickness and the depth to the410 km discontinuity are consistent with thermaldeflection of phase boundaries, as a positiveincrease in transition zone thickness (implyinglow temperatures) correlates with a negativechange in depth to (implying uplift of ) the 410(Kind et al., 2002). Furthermore, seismologicalobservations suggest the presence of a thicker(colder) transition zone under continents thanunder (warmer) oceans (Gu and Dziewonski,2002), as well as a thicker transition zone beneath(colder) subduction zones than beneath the(warmer) mid-Pacific (Gu and Dziewonski,2002; Shearer et al., 2002). Although evidencefor the expected anticorrelation of topography onthe 410 and the 660, whereby one may beexpected to deflect upwards in any locale wherethe other deflects downwards, has been less robustthan these other observations (Helffrich, 2000;Shearer et al., 2002), such anticorrelation may beobscured by the dependence of absolute depthestimates upon assumptions about shallowervelocity structures, as discussed later in thecontext of the depths of origin of mantle plumes.Clear anticorrelation of 410 and 660 topographymay also be confounded by frequency-dependenteffects (Helffrich and Bina, 1994; Helffrich,2000): while the 660 may remain sharp in bothcold and warm environments, the 410 should growsharper in warm regions and more diffuse in coldregions, so that these two discontinuities mayrespond differently to seismic waves of differentwavelengths at different temperatures. Overall,however, the bulk of the observational evidenceindicates that topography on seismic discontinu-ities in the transition zone is caused by thermalperturbations of equilibrium phase transforma-tions in a mantle of peridotite composition(Helffrich and Wood, 2001).

2.02.2.4 Sharpness

Other arguments about the composition ofthe transition zone have focused specifically uponthe observed seismic “sharpness” or depth extentof the 410 km discontinuity, which sometimesappears to occur over a narrower depth intervalthan might be expected for the olivine–wadsleyitephase transition. A number of phenomena havebeen invoked to explain apparent variations intransition sharpness. These include kinetic effectson phase transformations (Solomatov and Steven-son, 1994), whereby low-pressure phases persistmetastably for a finite extent before abruptlytransforming to the stable high-pressure phases,thus eliminating what might otherwise be a finitemixed-phase regime. The probable nonlinearity ofmultivariant phase changes is another factor(Helffrich and Bina, 1994; Stixrude, 1997),

whereby a gradual transition appears seismicallyto be sharper because a large fraction of theassociated velocity change is concentrated within aparticular portion of the mixed-phase regime.Differential solubility of water within mineralsacross phase changes (Wood, 1995; Helffrich andWood, 1996; Smyth and Frost, 2002) can alsoaffect transition sharpness, in that small amountsof dissolved H2O should broaden the a ! btransition at 410, while an excess of H2O resultingin a free fluid phase may be expected to sharpen thesame transition. Because the sharpness of the 410may be particularly sensitive to water, some studieshave begun to attempt to map water contents in thetransition zone by examining the manner inwhich its sharpness appears to vary as a functionof the frequency (and hence wavelength) ofthe interacting seismic waves (van der Meijdeet al., 2002).

Studies of multiphase Mg–Fe partitioningbetween coexisting olivine, wadsleyite, pyroxene,and garnet have also suggested that such partition-ing can act to sharpen the a ! b transition at410 (Irifune and Isshiki, 1998; Bina, 1998a). It issomewhat ironic that the nonolivine phases thatexhibit a very broad pyroxene–garnet transitioncan, nonetheless, induce the already sharpolivine–wadsleyite transtition to grow yet sharpersimply by slightly shifting the effective Mg/Feratio in olivine through cation exchange.

2.02.2.5 Broadening and Bifurcation

As noted above, low temperatures alone canserve to broaden the 410 by expanding thedepth extent of aþb mixed-phase stability field(Katsura and Ito, 1989; Bina and Helffrich,1994). Even more confusingly, however, lowtemperatures can give rise to bifurcation of thea ! b transition (Figure 3), resulting in astrongly uplifted a ! aþg transition, whichis seismically diffuse, overlying a less stronglyuplifted aþg ! aþb or aþg ! bþg tran-sition, which is seismically sharp (Green andHouston, 1995; Vacher et al., 1999; Bina,2002). As a result, a still transforms to b(and eventually to g), but it does so by a two-step process, and whether a strongly upliftedbroadened transition or a weakly upliftedsharpened transition is observed may dependupon the frequency of the interacting seismicwaves. While understanding of such sharpeningand broadening processes may be important forresolving fine details of the thermal structure ofthe transition zone, they would seem to haveless bearing upon the overall bulk chemistry ofthe upper mantle, with the possible exception ofconstraints on local volatile contents (Woodet al., 1996).

Upper-mantle Bulk Composition 43

However, within the cold environment ofsubduction zones, the temperature dependence ofphase relations in olivine near depths of 410 kmdoes exhibit particular sensitivity to bulkMg/(MgþFe) ratios. Indeed, the effect on olivinephase relations of iron enrichment is largely ana-logous to that of lower temperatures noted above.For pyrolitic values (Mg/(MgþFe) ¼ 0.90), equi-librium phase relations (Fei et al., 1991) predictuplift and broadening of the sharp a ! btransition in the cold slab, replacement of thesharp a ! b transition by a more diffusea ! aþg transition overlying a sharperaþg ! aþb or a þ g ! bþg transition withinthe colder interior of the slab, and uplift of thebroad b ! bþg ! g transition (Figures 3 and 4);this is equivalent to the bifurcated scenariodiscussed above for low temperatures. Furthermagnesium enrichment (Mg/(MgþFe) ¼ 0.99)would result in smaller uplift of a sharper a ! btransition, little or no replacement of the sharpa ! b transition by a more diffuse a ! aþgtransition within the cold interior of the slab, andan uplifted b ! g transition which is muchsharper within both the slab and the ambientmantle; such sharpening is analogous to the effectof slightly warmer temperatures. This latterscenario would also correspond to a globallysharp 520 km discontinuity, as well as a globallysharp 410 km discontinuity which remainssharp when uplifted (Figure 4). However, ironenrichment (Mg/(MgþFe) ¼ 0.81) would result

in complete replacement of the sharp a ! btransition within both the slab and the ambientmantle by a more diffuse and strongly uplifteda ! aþg transition overlying a sharperaþg ! aþb ! b or aþg ! bþg transition,as well as further broadening of the upliftedb ! bþg ! g transition; this would be equival-ent to the effect of very low temperatures. Such ascenario would correspond to a globally verydiffuse 520 km discontinuity and a 410 kmdiscontinuity consisting of a broad velocitygradient overlying a sharp velocity jump(Figure 4).

Other complexities of transition zone seismicstructure may also indicate thermal or compo-sitional effects. Apparent bifurcation of the 520into superposed 500 km and 550 km discontinu-ities (Deuss and Woodhouse, 2001) may reflectdistinct signatures of the b ! bþg ! g tran-sition and the exsolution of calcium silicate

Figure 3 Effects upon olivine phase equilibria near410 km depth of low temperatures in subduction zones,for mineral thermodynamic parameters of Fei et al.(1991). Dark lines denote boundaries of subductingslab. Phases are: (a) olivine, (b) wadsleyite, (g)ringwoodite, (mw) magnesiowustite, and (pv) ferro-magnesian silicate perovskite. Note that the a ! btransition near 410 km is first uplifted and thenbifurcates into a strongly uplifted diffuse a ! a þ gtransition overlying a weakly uplifted sharp boundary

(after Bina, 2002) (vertical resolution is 1 km).

Figure 4 Effects upon olivine phase equilibria ofvariations in Mg/(Mg þ Fe) for pyrolite (center), Feenrichment (top), and Mg enrichment (bottom) (vertical

resolution is 10 km).

Seismological Constraints upon Mantle Composition44

perovskite from majoritic garnet (Figure 1), andthe offset in depth between these two features mayalso be expected to change with temperature.Furthermore, in colder regions majoritic garnetmay transform to silicate ilmenite (ilm) within the550– 600 km depth range, prior to eventualdisproportionation to silicate perovskite andmagnesiowustite, but this interposed gt ! ilmtransition is unlikely to express a significantseismic velocity signature, at least not withinsubducting slabs (Vacher et al., 1999). Overall,seismological observations of a sharp 410 kmdiscontinuity—which is occasionally broader inplaces, exhibits some topography, and is accom-panied by a sporadic 520 km discontinuity—areprimarily consistent with pyrolitic Mg/(Mg þ Fe)values of 0.90, but local variations certainlycannot be excluded.

2.02.3 UPPER-MANTLE HETEROGENEITY

2.02.3.1 Subducted Basalts

The fate of the basalts and gabbros in theoceanic crust as they are subducted into aperidotite upper mantle (Chapter 2.03) canalso be studied using seismological methods.Anhydrous metabasalts may be expected toundergo equilibrium transformation to an eclogiteassemblage (with growth of garnet at the expenseof plagioclase) around depths of 20–50 km(Wood, 1987; Peacock, 1993; Hacker, 1996).Such eclogites should be ,2% faster thansurrounding pyrolite at depths of ,280 km(Helffrich et al., 1989; Helffrich and Stein,1993). However, most of this velocity contrastarises solely from the temperature contrastbetween cold slab (1,000 8C at 9.6 GPa) andwarmer mantle, with the composition differencealone giving rise to a contrast of only ,0.5%(Helffrich et al., 1989). Consideration of silica-oversaturated basalt compositions can expand thisrange of velocity contrasts somewhat, withanhydrous coesite eclogites being ,2–4% fastand, subsequent to the transition from coesite tostishovite at ,220–240 km depth, stishoviteeclogites being ,4– 6% fast (Connolly andKerrick, 2002). Again, however, it is importantto bear in mind that much of this contrast arisesdue to low slab temperatures alone, so thatthermally equilibrated eclogites lingering longin the upper mantle would appear only slightly(if at all) fast relative to ambient mantle.

In large part, this ability of anhydrous basalticeclogites to seismically blend into an ultramaficmantle arises from the behavior of elastic moduliin pyroxenes. In the shallowest upper mantle,orthopyroxene is ,6% slow in VP relative toolivine and about equal in VS. However, the bulk

modulus of orthopyroxene exhibits a strong andnonlinear increase with pressure, so that there islittle significant difference in either VP or VS

between orthopyroxene and olivine by ,200 kmdepth (Flesch et al., 1998; James et al., 2001).This absence of effective velocity contrastsbetween anhydrous eclogites and mantle perido-tites within most of the upper mantle (Helffrichet al., 1989; Helffrich, 1996) is also evident in theobservation that model upper mantles of bothpyrolite (,60% olivine) and piclogite (,40%olivine) composition exhibit similar velocitiesover the 100–400 km depth range (Vacher et al.,1998).

If anhydrous metabasalts in an eclogite assem-blage can generate only small fast velocityanomalies or no anomalies at all, then a puzzleemerges in understanding subduction zone struc-tures. Seismological observations in Japan,Tonga, Alaska, and other active subductionzones demonstrate the presence of 4–10% slowvelocities in a layer 2–10 km thick along the uppersurfaces of subduction zones in the depth range100–250 km (Helffrich, 1996; Connolly andKerrick, 2002). One explanation that has beenadvanced to explain the presence of such low-velocity layers involves kinetic hindrance in coldslabs. Rather than equilibrium transformation ofslow anhydrous gabbro to fast eclogite at depthsof 20–50 km, a model of metastable persistenceof gabbro into the blueschist and eclogite stabilityfields, perhaps below 100 km depth, has beeninvoked (Hacker, 1996; Connolly and Kerrick,2002). However, it appears that this model ofmetastable anhydrous gabbro may not be appro-priate (Helffrich, 1996), not only because oceanicbasalts commonly are found to be hydrothermallyaltered but also because metastable gabbroappears to be too slow seismically (Connollyand Kerrick, 2002).

Indeed, hydrothermal alteration of basalts maybe the key to understanding the low-velocitylayers in subducting slabs. In hydrous metabasaltsunder subduction zone conditions, lawsoniteblueschist is expected to be the initially dominantfacies (Peacock, 1993). At 65 km depth insubducting basaltic crust, lawsonite blueschistwould be ,7% slower than the overlyingperidotite mantle and ,8% slower than theunderlying garnet harzburgite layer of thesubducting lithosphere, suggesting that hydrousmetabasalts may be the cause of the seismo-logically detected low-velocity layers (Helffrich,1996). As hydrous gabbroic crust subducts beyondthe blueschist regime, the resulting equili-brium lawsonite eclogites should still be 3–7%slow (Connolly and Kerrick, 2002). Withcontinued subduction, garnet increases and law-sonite decreases in abundance, until the coesite–stishovite transition near 220–240 km further

Upper-mantle Heterogeneity 45

destabilizes lawsonite, giving rise to stishoviteeclogites which should be 4–6% fast (Connollyand Kerrick, 2002). Such a change from slowlawsonite eclogites or coesite eclogites to faststishovite eclogites is consistent with the observedtermination of low-velocity layers and, indeed,with the occasional presence of high-velocitylayers, below 250 km depth.

Interestingly, a dominant role for lawsoniteeclogites in subducting oceanic crustal materialmay be echoed in the occurrence of lawsonite (orpseudomorphs thereafter) among the glaucophaneeclogites of the Alpine Sesia zone, a complex ofcontinental provenance presumably exhumedafter subduction to at least 60 km depth (Reinsch,1979; Pognante, 1989). Furthermore, the compo-sitions of majoritic and sodium-rich garnetsoccasionally found as inclusions in diamonds(Chapter 2.05) are also consistent with equili-brium phase relations for basaltic crust which haspenetrated into the transition zone (Ono andYasuda, 1996). Within the transition zone,evidence from seismic tomography suggests thatsome subducting slab material penetrates directlyinto the lower mantle while, in other subductionzones, some is deflected horizontally at depthsshallower than 1,000 km (Takenaka et al., 1999;Fukao et al., 2001). By the time subducted basalticmaterial enters the lower mantle, it should belargely dehydrated and should adopt a simpler,high-pressure perovskitite mineralogy. Theexpected seismic signatures of such basalticmaterial in the lower mantle will be examined ina later section.

2.02.3.2 Plume Origins

While much attention has been focused uponthe seismological properties of subduction zones,in part because of their significant spatial extentand associated mass flux (Chapter 2.11), seismo-logical studies of hotspot areas are also illuminat-ing, particularly with regard to ascertaining thedepth of origin of plume structures. There are twoprimary types of seismic evidence for constrainingthe depth of origin of mantle plumes. The first ofthese consists of seismic tomographic imaging, inwhich one might expect the achievement ofsufficiently fine spatial resolution for imagingnarrow plume conduits to be a significantchallenge. Indeed, this challenge is furtheraggravated by the fact that the resolution of suchmethods tends to decay within the crucial regionof the mantle transition zone.

Nevertheless, seismic tomography has beenemployed in efforts to image the roots of mantleplumes (VanDecar et al., 1995) and to determinewhether or not they arise from deep-seatedsources. An instructive example is the case ofthe Iceland hotspot, which tomographic images

suggest may be connected to a deep-seated plumesource (Wolfe et al., 1997). Such a conclusion isconsistent with the fact that low seismic velocityanomalies appear to extend downward into thetransition zone beneath the hotspot while they donot extend below 150 km beneath the rest of themid-Atlantic ridge (Montagner and Ritsema,2001), an observation supported by both globaland regional tomography (Ritsema et al., 1999;Allen et al., 2002). However, this interpretationhas been challenged. Foulger et al. (2001),claiming tomographic resolution to 450 kmdepth, conclude that the shape of the imagedlow-velocity anomaly changes from cylindrical totabular near the top of the transition zone, and theinvestigators argue on the basis of this apparentchange in morphology that the plume does notextend to deeper levels. Alternatively, Allen et al.(2002), claiming resolution to 400 km depth,report a simple cylindrical morphology at depth.Detailed numerical tests of the spatial resolutionof tomographic imaging under Iceland (Kelleret al., 2000) suggest that a deep-seated plume maynot be required to explain the observed seismicdelay times. In a similar vein, Christiansen et al.(2002) argue that there is a dearth of convincingseismic evidence for a plume extending to depthsbelow 240 km beneath the Yellowstone hotspot.All of this serves to highlight some of thepersistent ambiguities present in interpretation ofseismic tomographic images beneath hotspots,images which remain nonunique results of theapplication of a variety of optimization functionsto different observational data sets.

The second type of seismic evidence used toconstrain the depth of origin of mantle plumesconsists of analyses of boundary-interactionphases. Such phases consist of seismic waveswhich, by interacting with the boundaries generallyknown as seismic “discontinuities,” have under-gone conversion (repartitioning of energy betweenlongitudinal (P) and transverse (S) waves) and/orreflection (repartitioning of energy betweenupgoing and downgoing waves). For the purposesof studying mantle plumes, the crucial measure-ments are differential travel times between thosephases which interact with the 410 discontinuityand those which interact with the 660 discontinu-ity. Such differential times translate (via areference velocity model) into measures of thethickness (depth extent) of the transition zone lyingbetween these two discontinuities.

Given the opposing signs of the Clapeyronslopes of the primary phase transitions associatedwith these seismic discontinuities, any elevatedmantle temperatures associated with thermalplumes may be expected to yield thinning of thetransition zone (Figure 2), via depression of the410 and uplift of 660 (Shen et al., 1998; Bina,1998c; Lebedev et al., 2002). Some global and

Seismological Constraints upon Mantle Composition46

broad regional studies (Vinnik et al., 1997;Chevrot et al., 1999) have detected no clearcorrelation between such estimates of transitionzone thickness and locations of hotspots (Kelleret al., 2000). Since the late 1990s, however, anumber of more localized studies have measuredtransition zone thinning of several tens of kilo-meters, suggesting hot thermal anomalies of a fewhundred degrees, over regions with diameters ofhundreds of kilometers, beneath such presumedthermal plume features as the Snake River plain(Dueker and Sheehan, 1997), Iceland (Shen et al.,1998), Yellowstone (Humphreys et al., 2000),Hawaii (Li et al., 2000), and the Society hotspot(Niu et al., 2002). By contrast, no apparentthinning has been found beneath tectonicallyinactive areas such as the northern North Sea(Helffrich et al., 2003). A straightforwardinterpretation of these results is that the transitionzone beneath plumes is hotter than “normal”mantle, with thermal plumes originating eitherdeep in the lower mantle below the transition zoneor (at the shallowest) in a hot thermal boundarylayer at the base of the transition zone.

The picture grows less simple, however, if weattempt to inquire into how the causes of thistransition zone thinning are distributed between410 and 660. Such inquiry involves estimating theactual absolute depths of these two seismicdiscontinuities beneath plumes. While the use ofdifferential times to estimate thickness requires areference velocity model within the transitionzone, the use of absolute times to estimateindividual depths further requires a (laterallyvarying) reference velocity model from thetransition zone all the way up to the surface. Asimple model of a deep-seated thermal plumesuggests that we should observe a depressed 410with an uplifted 660, which is what seems to beimaged beneath Iceland (Shen et al., 1998).However, we can also find a flat 410 with anuplifted 660 beneath Hawaii (Li et al., 2000), aweakly uplifted 410 with a strongly uplifted 660beneath the Snake River plain (Dueker andSheehan, 1997) and Yellowstone (Humphreyset al., 2000; Christiansen et al., 2002), or adepressed 410 with a flat 660 beneath the Societyhotspot (Niu et al., 2002). Taken at face value, adepressed (hot) 410 with an uplifted (hot) 660suggests a plume origin in the lower mantle (Shenet al., 1998). A flat (normal) 410 with an uplifted(hot) 660 suggests either an origin in the lowermantle (Li et al., 2000) or the presence of athermal boundary layer within the transition zone,as does an uplifted (cold) 410 with an uplifted(hot) 660. A depressed (hot) 410 with a flat(normal) 660 suggests an origin within thetransition zone (Shen et al., 1998). Interestingly,the one combination which would stronglysuggest an origin within the shallow upper-mantle,

a depressed (hot) 410 with a depressed (cold) 660,is not observed. It is complexities such as thesethat have led several investigators to argue againstthe idea of deep-seated plumes in favor of thedominance of upper-mantle processes in theorigins of hotspots (Anderson, 1994, 2001; Saltzerand Humphreys, 1997; Christiansen et al., 2002),including such detailed proposals as “propagatingconvective rolls organized by the sense of shearacross the aesthenosphere” (Humphreys et al.,2000). This latter proposal would explain a cold410 overlying a hot 660 (and underlying anotherhot region near 200 km depth), e.g., throughlocalized convection at depths shallower than400 km (Humphreys et al., 2000).

There are a range of other possible explanationsfor these seeming complexities, however, aprimary factor being the aforementioned relianceof absolute depth estimates for seismic disconti-nuities upon accurate models of shallow velocitystructures (Walck, 1984; Helffrich, 2000; Niuet al., 2002). If absolute depth estimates are sosensitive to assumptions about shallower struc-tures, then these various and seemingly para-doxical combinations of apparent deflectionsmay arise simply from inaccurate representationsof structure outside of the regions of study.Conclusions drawn from differential times,which are free of such dependence upon assump-tions about distal regions, may be judged morerobust. Such a stance also renders more tractablean understanding of the magnitudes of the impliedthermal anomalies. If all of the observed thinningof the transition zone were caused by deflection ofeither the 410 or 660 alone, then hot temperatureanomalies of ,400 K would be required, but thesize of the requirement falls to ,200 K if thethinning is shared between anticorrelated 410 and660 deflections (Helffrich, 2000; Niu et al., 2002).

Another factor to consider is an inherentseismological bias toward underestimatingtopography. For example, the “Fresnel zones”that describe the regions of the discontinuities thatare sampled by boundary-interaction phases canbe both large in extent and irregular in shape(Helffrich, 2000; Niu et al., 2002), so that themeasured travel times incorporate entwined inter-actions with both deflected and undeflectedportions of a given discontinuity. Moreover,such seismological biases can yield greater under-estimates of topography at 410 than at 660 (Neeleet al., 1997; Helffrich, 2000), which is consistentwith the apparent “cold 410” puzzle noted above.Indeed, some topography simply may not beclearly visible. While the a ! a þ b ! b tran-sition should grow sharper at high temperatures aswell as being depressed, any small-scale topo-graphy on or “roughening” of discontinuitysurfaces can render undetectable the very P-to-Sconversions which indicate the presence of

Upper-mantle Heterogeneity 47

topography (van der Lee et al., 1994; Helffrichet al., 2003). Again, such effects may be moresignificant near 410, where the magnitudes ofClapeyron slopes and hence of topography may belarger (Bina and Helffrich, 1994), but they mayalso be significant near 660 (van der Lee et al.,1994). Furthermore, the apparent magnitude ofdiscontinuity topography will vary with thefrequency of the seismic waves used to probe it(Helffrich, 2000).

Finally, there is yet another possible contributorto the apparent “cold 660” puzzle noted above. It isthe negative Clapeyron slope of the g ! pv þ mwtransition that predicts uplift of the 660 in hotplumes. The g ! pv þ mw transition, however,may be replaced by a b ! pv þ mw transition athigh temperatures, the latter exhibiting a positiveClapeyron slope and so allowing 660 depressioninstead of uplift (Liu, 1994). However,b ! pv þ mw appears to succeed g ! pv þ mwonly in pure Mg2SiO4 compositions, so thisparticular mechanism is unlikely to operate inreal multicomponent mantle compositions (Binaand Liu, 1995; Niu et al., 2002).

The primary point of this discussion, then, isthat estimates of lateral variations in transitionzone thicknesses from differential seismic traveltimes are more robust than estimates of lateralvariations in the absolute depths of discontinuitiesfrom absolute travel times. There are manyfactors, largely unrelated to plumes, that maycause some underestimation of the former butwhich induce serious complications in the latter.Certainly, it is possible that the overall tecto-nic system, including some hotspot-designatedvolcanic chains, may be controlled to a signifi-cant extent from above via the lithosphere ratherthan from below via the deep mantle (Anderson,2001). However, the simplest interpreta-tions consistent with observations of transitionzone thinning, despite some apparent inconsisten-cies in estimates of absolute depths of disconti-nuities, strongly suggest that some hotspots areassociated with plume-like thermal anomalies thatpenetrate the transition zone. Given the greatdisparities in heat and mass flux among differenthotspots, however, there is certainly room fordiversity in the family of thermal plumes, and itwould not be surprising ultimately to discovervarious classes of plumes associated with differentdepths of origin (Kerr, 2003).

2.02.4 LOWER-MANTLE BULKCOMPOSITION

2.02.4.1 Bulk Fitting

Given that the properties of the 660 km seismicdiscontinuity are in excellent agreement with

the predicted behavior of an isochemical phasetransformation, it might seem reasonable to assumethat the lower mantle below this depth possesseslargely the same bulk composition as the uppermantle above. This assumption has been regularlychallenged, however, based largely upon cosmo-chemical concerns (Anderson, 1989; Bina, 1998b),upon estimates of mass fluxes between geo-chemical reservoirs (Helffrich and Wood, 2001),or upon driving forces for chemical differentiationacross phase transitions (Garlick, 1969; Kumazawaet al., 1974; Walker and Agee, 1989; Bina andKumazawa, 1993; Liu and Agren, 1995). Concernhas focused primarily upon whether the lowermantle might be enriched in iron and/or siliconrelative to the upper mantle.

A simple way to address this question is tocompute profiles of density and bulk soundvelocity (thereby avoiding the large uncertai-nities associated with extrapolating shearmoduli), along plausible lower-mantle adiabats,for a variety of candidate lower-mantle compo-sitions and to compare these model profiles to areference seismological model such as ak135(Kennett et al., 1995). Examination of the r.m.s.misfit between such models over the entire lowermantle quickly reveals several important prin-ciples. Density (Figure 5) is primarily sensitiveto Mg/(Mg þ Fe) but not to silica content.Velocity (Figure 5) sensitivity, alternatively,exhibits a trade-off between Mg/(Mg þ Fe) andSi/(Mg þ Fe). This suborthogonal nature ofdensity and velocity sensitivities allows thetwo together (Figures 5 and 6) to constrainlower-mantle composition via the intersection oftheir respective misfit minima. The resultingfamily of allowable lower-mantle bulk compo-sitions (Figure 6) includes a pyrolite mantlecomposition. While some uncertainty in siliconcontent remains, there is no evidence for ironenrichment of the lower mantle (Figure 6). Theextent to which silicon enrichment of the lowermantle can be accommodated by the seismo-logical constraints increases as the assumedtemperature (at the root of the adiabat) of thelower mantle is increased (Figure 7). Theseschematic results are for a simple lower mantlemineralogy limited to ferromagnesian silicateperovskite (Fiquet et al., 2000), magnesiowustite(Fei et al., 1992), and stishovite (Li et al., 1996).Effects of other components (e.g., calcium,aluminum, sodium) have been neglected, and adepth-varying Mg–Fe partitioning coefficientbetween perovskite and magnesiowustite (Maoet al., 1997) has been employed. However,repetition of these analyses with the inclusion ofcalcium-silicate perovskite (Wang et al., 1996)or the use of a depth-invariant partitioningcoefficient (Kesson et al., 1998) results in onlyvery minor perturbations.

Seismological Constraints upon Mantle Composition48

2.02.4.2 Depthwise Fitting

A different way of examining these relation-ships is to plot the best-fitting lower-mantlecompositions within 10 km thick depth slices.Again, it is apparent (Figure 8) that densityconstrains only Mg/(Mg þ Fe) while both densityand velocity together are required to constrainSi/(Mg þ Fe). Bulk sound velocity alone, asshown by the unstable oscillations in best-fittingcompositions (Figure 8), does not effectivelyconstrain either compositional parameter withinsuch small depth slices. Throughout the bulk ofthe lower mantle, there is no evidence for ironenrichment, and the deviation from a pyrolitecomposition, in terms of both Mg/(Mg þ Fe) and

Si/(Mg þ Fe), falls within the overall 1% r.m.s.misfit contour (Figure 7). Indeed, the onlystatistically significant deviations of the best-fitting composition from pyrolite occur in the top,300 km of the lower mantle and in the bottom,200 km. For the former region, this deviation isnot surprising, as we probably have not fullyincorporated the appropriate mineralogy. Whilethe g ! pv þ mw transition in the olivine com-ponent occurs at 660 km depth, the attendantgt ! pv transition in the majorite component maynot achieve completion until 100 km deeper ormore, due to the solubility of aluminum and ferriciron in both garnet–majorite and silicate perovs-kite (Wood and Rubie, 1996; McCammon, 1997).Thus, the anomalous best-fitting compositions in

Figure 5 Contours of r.m.s misfit (%) to seismological reference model ak135 of density (red) and bulk soundvelocity (green) for candidate lower-mantle compositions, parametrized in terms of Mg/(Mg þ Fe) (¼ XMg) andSi/(Mg þ Fe)(¼ XPv), over the entirety of the lower mantle. Shaded region at XPv . 1 indicates free silica. Triangledenotes pyrolite. Plus signs denote minima of r.m.s. misfit. Root of lower-mantle adiabat is 2,000 K at 660 km depth.

Figure 6 Contours of joint (blue) r.m.s. misfit (%) to seismological reference model ak135 of density and bulksound velocity for candidate lower-mantle compositions, parametrized in terms of Mg/(Mg þ Fe)(¼Xmg)and Si/(Mg þ Fe)(¼XPv), over the entirety of the lower mantle. Shaded region at XPv . 1 indicates free silica.Triangle denotes pyrolite. Plus sign denotes minimum of r.m.s. misfit. Root of lower-mantle adiabat is 2,000 K at

660 km depth.

Lower-mantle Bulk Composition 49

Figure 8 Depthwise best-fit compositions to seismological reference model ak135 for density alone (red), bulksound velocity alone (green), and both density and bulk sound velocity jointly (blue), with compositions parametrizedin terms of Mg/(Mg þ Fe) (XMg) and Si/(Mg þ Fe) (XPv), in 10 km depth slices through the lower mantle. Shadedregion at XPv . 1 indicates free silica. Dotted lines (at XPv ¼ 0:67 and XMg ¼ 0:89) denote pyrolite. Root of lower-

mantle adiabat is 2,000 K at 660 km depth.

Figure 7 Contours of joint r.m.s. misfit (1%) to seismological reference model ak135 of density and bulksound velocity for candidate lower-mantle compositions, parametrized in terms of Mg/(Mg þ Fe)(¼XMg) andSi/(Mg þ Fe)(¼XPv), over the entirety of the lower mantle. Shaded region at XPv . 1 indicates free silica. Triangledenotes pyrolite. Plus signs denote minima of r.m.s. misfit. Roots of lower-mantle adiabats are 1,800 K (red), 2,000 K

(green), and 2,200 K (blue) at 660 km depth.

Seismological Constraints upon Mantle Composition50

the top 200–300 km of the lower mantle probablyarise simply from our omission of garnet from themodel mineralogy. The situation in the bottom,200 km of the lower mantle is more intriguing.Certainly, extrapolation of mineral properties aremost uncertain in this region, and a globallyaveraged seismological model such as ak135 maynot accurately reflect details of structure near thecore–mantle boundary. However, it is interestingto note that the implied iron enrichment andpresence of free silica (Figures 8 and 9) are notinconsistent with what one might expect frominteractions between silicate lower mantle andmetallic core or from accumulation of subductedbasaltic material at the core–mantle boundary.

Aside from the core–mantle boundary region, apyrolite lower-mantle composition appears to beconsistent with seismological constraints. Silicaenrichment of the lower mantle can be accommo-dated if the lower mantle is hotter than expectedfor a simple adiabat rooted at the 660 kmg ! pv þ mw transition (Figure 9). Because anychemical boundary layer between the upper andlower mantle would be accompanied by a corre-sponding thermal boundary layer, such a model

of a chemically distinct and hot lower mantle is alsointernally consistent. This trade-off has beenevident for decades (Birch, 1952; Jackson, 1983,1998; Jeanloz and Knittle, 1989; Bina and Silver,1990, 1997; Stixrude et al., 1992; Zhao andAnderson, 1994). However, the seismologicalevidence (discussed above) that the transitionzone capping the lower mantle behaves like a setof thermally governed isochemical phase trans-formations, coupled with the absence of seismicevidence (e.g., a globally sharp seismic reflectordisplaying hundreds of kilometers of dynamicallyinduced topographic undulations) for a chemicalboundary in the lower mantle, lends considerablesupport to the minimalist assumption that thebulk composition of the lower mantle greatlyresembles that of upper-mantle peridotite.

2.02.5 LOWER-MANTLE HETEROGENEITY

2.02.5.1 Overview

Seismic velocity heterogeneity in the mantle,e.g., as revealed by seismic tomography, is often

Figure 9 Depthwise best-fit compositions to seismological reference model ak135 for both density and bulk soundvelocity jointly, with compositions parametrized in terms of Mg/(Mg þ Fe) (XMg) and Si/(Mg þ Fe) (XPv), in 10 kmdepth slices through the lower mantle. Shaded region at XPv . 1 indicates free silica. Dotted lines (at XPv ¼ 0:67 andXMg ¼ 0:89) denote pyrolite. Roots of lower-mantle adiabats are 1,800 K (red), 2,000 K (green), and 2,200 K (blue)

at 660 km depth.

Lower-mantle Heterogeneity 51

interpreted in terms of strictly thermal origins.However, lateral variations in seismic velocitywithin the lower mantle (Hedlin et al., 1997; Niuand Kawakatsu, 1997; Castle and Creager, 1999;Deuss and Woodhouse, 2002) may arise from anumber of sources, including temperatureanomalies (d T ), local phase changes (dXf), andchemical heterogeneity (dXi), and they should beaccompanied by associated density anomalies.Thus, lower-mantle seismic velocity anomaliesmay reflect local heterogeneity in chemical1 com-position, such as variations in iron–magnesiumratio and silica content, rather than simplyvariations in temperature. Together, thermal andchemical variations may jointly explain the mannerin which the r.m.s. amplitudes of seismic velocityanomalies appear to vary with depth (Bina andWood, 2000). The distinction is important becausevelocity anomalies arising from compositionaldifferences are not subject to the same temporaldecay as those due to thermal perturbations, due todifferent timescales for chemical diffusion andthermal conduction.

Temperature anomalies may arise due to lowtemperatures within cold subducted slab material,but such thermal anomalies will decay with time(and hence depth of penetration into the mantle) asthe slab is thermally assimilated into the warmermantle. Local phase changes are unlikely to occuron significant scales below transition zone depths,except perhaps in exotic compositions containingfree oxides (Bina, 1998b). Chemical heterogeneitythus seems a reasonable candidate as a source ofseismic velocity heterogeneity in the lowermantle, and an obvious source of major-elementchemical heterogeneity is subducted slab materialthat retains the chemical differentiation acquiredduring its formation at spreading ridges.

2.02.5.2 Subducted Oceanic Crust

Formation of oceanic lithosphere involveschemical differentiation (by partial melting) ofmantle lherzolite parent material (see Chapter 2.03and Chapter 2.08). The complex structure ofoceanic lithosphere closely approximates a simplemodel of a basaltic–gabbroic crustal layer over-lying a depleted harzburgite layer, which in turnoverlies lherzolitic peridotite mantle material.During subduction, these layers undergo phasetransformations to denser phase assemblages withincreasing depth of penetration into the mantle. Forexample, the basalt and gabbro componentsprogressively transform to eclogite in the uppermantle, to garnetite in the transition zone, and toperovskitite in the lower mantle (Vacher et al.,1998; Kesson et al., 1998; Hirose et al., 1999).Upon deep subduction, all of the components of apetrologically layered slab should transform to a

lower-mantle mineralogy, consisting of some sub-set of the phases (Mg, Fe, Al)SiO3 ferromagnesiansilicate perovskite, (Fe, Mg)O magnesiowustite,CaSiO3 calcium silicate perovskite, and SiO2

stishovite, along with minor amounts of sodium-bearing and other phases. The seismic velocitiesand densities of these layers will differ due, e.g., tothe coupled effects of silicon enrichment andmagnesium depletion of the basaltic melt relativeto the parent mantle.

Let us represent a subducting slab using asimple three-layered slab model (Helffrich andStein, 1993), consisting of a basaltic crustal layeroverlying a harzburgite layer overlying lherzolitemantle material. To represent the range of possiblecompositions of the basaltic crustal layer, we testboth the “eclogite” of Helffrich et al. (1989) andthe “gabbro” of Helffrich and Stein (1993), thelatter being significantly richer in silicon andmagnesium (Table 1). For the harzburgite layer,we adopt the “harzburgite” composition ofHelffrich et al. (1989). For the mantle layer, wetest both the “lherzolite” of Helffrich et al. (1989)and the “peridotite” of Helffrich and Stein (1993),the latter being slightly richer in silicon and iron(Table 1). We transform each of these bulkcompositions into its stoichiometrically equival-ent lower-mantle mineralogy (Table 2).

To isolate compositional and thermal effects,we calculate elastic properties for the various bulkcompositions along adiabats rooted at a tempera-ture of 2,000 K at 665 km depth (Bina, 1998b),using equations of state for (Mg, Fe)SiO3 per-ovskite (Fiquet et al., 2000), (Fe, Mg)O magne-siowustite (Fei et al., 1992), CaSiO3 perovskite(Wang et al., 1996), and SiO2 stishovite (Li et al.,1996; Liu et al., 1996). We calculate Voigt–Reuss–Hill-averaged bulk sound velocities, toavoid the large uncertainties associated withextrapolating shear moduli to lower-mantle con-ditions. In these simple calculations, we haveneglected the role of Al2O3 in silicate perovskite(Wood and Rubie, 1996; Wood, 2000), butthe effects of this component upon the elasticproperties—depressed bulk moduli (Zhang andWeidner, 1999)—are expected to be importantonly in the shallowest part of the lower mantle(Brodholt, 2000). Furthermore, we have assumedthat any free silica is present as stishovite, rather

Table 1 Molar bulk compositions for model slabcomponents.

Mg/(Mg þ Fe) Si/(Mg þ Fe)

Eclogite 0.57 1.65Gabbro 0.64 2.58Harzburgite 0.92 0.66Lherzolite 0.90 0.68Peridotite 0.89 0.69

Seismological Constraints upon Mantle Composition52

than as higher-pressure SiO2 polymorphs such asthose with CaCl2 and a-PbO2 structures (Karkiet al., 1997), so that our calculated velocities forthe silica-oversaturated basaltic crustal com-ponents will represent conservative lower bounds.

The temperature dependence of the bulk soundvelocity (›V/›T) for all of the compositions in thelayered slab falls from below 0.2% per 100 K at thetop of the lower mantle to below 0.1% per 100 K atthe base of the lower mantle (Figure 10). As themagnitude of thermal anomalies associated withcold slab material will also fall with increasingdepth as slabs thermally assimilate, this behaviorsuggests that it will be difficult to explain any largevelocity anomalies at depth in terms of temperaturealone. Indeed, even if thermal anomalies ,100 Kwere to somehow survive down to the base of

the lower mantle, they would only give rise tovelocity anomalies ,0.1%.

Alternatively, the composition dependence ofbulk sound velocity (›V/›Xi) is significantlygreater (Figure 11), and bulk chemical anomaliesshould not change significantly with depth. Thevelocities for the two representative models ofthe underlying mantle layer, the “lherzolite”(Helffrich et al., 1989) and “peridotite” (Helffrichand Stein, 1993) compositions, are virtuallyidentical. Relative to the “peridotite” composition,the “harzburgite” (Helffrich et al., 1989) layer isless than 0.5% fast. However, the basaltic crustalcompositions yield significantly fast velocityanomalies, and anomaly magnitudes increasewith depth. The “eclogite” (Helffrich et al.,1989) rises from below 2.4% fast near 660 km

Table 2 Molar quantities at 665 km depth for model slab components.

pv-MgSiO3 pv-FeSiO3 mw-MgO mw-FeO st-SiO2

Eclogite 0.57 0.43 0.00 0.00 0.65Gabbro 0.64 0.36 0.00 0.00 1.58Harzburgite 0.63 0.03 0.29 0.05 0.00Lherzolite 0.64 0.04 0.26 0.06 0.00Peridotite 0.65 0.04 0.24 0.07 0.00

Figure 10 Temperature dependence of the bulk soundvelocity versus depth in the lower mantle, for candidatebulk compositions for the basaltic layer (red), theunderlying harzburgite layer (green), and the basallherzolite (blue). Note that temperature sensitivity falls

with increasing depth.

Figure 11 Bulk sound velocity anomalies relative toperidotite mantle versus depth in the lower mantle(blue); for candidate bulk compositions for the basalticlayer (red); and the underlying harzburgite layer(green). Note that the basaltic layer is fast and grows

faster with increasing depth.

Lower-mantle Heterogeneity 53

depth to above 2.6% fast near 2,890 km depth,and the more silica-rich “gabbro” (Helffrich andStein, 1993) rises from ,7.0% fast to ,7.8% fast.Hence, it should be easier to generate largevelocity anomalies through compositional varia-tions, such as those associated with subductedslabs.

Thus, for temperature effects only, velocityanomalies should be small and decay withincreasing depth. This effect would occur evenfor depth-invariant temperature anomalies, but itwill be even more pronounced in the case of coldsubducting material whose temperature anomaliesshould decay with increasing depth due to thermalassimilation. Even for large temperature ano-malies, in the range of hundreds of degrees,velocity anomalies remain below 1%. For com-positional effects, however, velocity anomaliesdue to chemical contrasts between basaltic/gabbroic material and peridotitic mantle shouldbe large and grow with increasing depth. Suchvelocity anomalies should fall in the range 2–8%or greater.

Similar results have been reported byMattern et al. (2002), using more recent equationsof state for lower-mantle minerals and incorpora-ting the solubility of alumina in silicate perovskite.They also used a three-layered slab model (mid-ocean ridge basalt (MORB) over harzburgiteover pyrolite), but with a MORB composition(Si/(Mg þ Fe) ¼ 2.29) intermediate between ourextreme end-members of the Helffrich et al.(1989) “eclogite” (1.65) and the Helffrich andStein (1993) “gabbro” (2.58).

The high velocities in the basaltic material ariselargely from the presence of free silica. As wehave assumed that all free silica is in the form ofstishovite, rather than as higher-pressure SiO2

polymorphs, actual lower-mantle velocity pertur-bations arising from basaltic crustal material maybe even larger than the values calculated here.Free silica in the former crustal material, however,should react with magnesiowustite in the sur-rounding lower-mantle material to form silicateperovskite. Thus, survival of free silica in thelower mantle may require formation of perovskiterinds to preserve the free silica from reaction withmagnesiowustite, just as porphyroblasts canprotect inclusions (which would otherwisebecome reactants) to form “armored relics” inmore familiar metamorphic rocks.

Damping and smearing arising from regulariza-tion in seismic tomography typically causenarrow, intense anomalies to be imaged asbroader, more subdued anomalies (Garnero,2000). Thus, layers of basaltic/gabbroic material,10 km thick that are ,5% fast, e.g., mightperhaps appear as ,0.5% velocity anomaliesdistributed over 100 km thick slabs. If this is thecase, then one might seek frequency-dependent

effects in seismological observations, in which theapparent magnitude of velocity anomalies riseswith the spatial resolving power of the seismicprobe. Studies of lower-mantle seismic scatterershave suggested that bodies of 100 km or less insize exhibit velocity anomalies of several percent(Kaneshima and Helffrich, 1998; Garnero, 2000),especially near subduction zones. Some studiesfind evidence of 0.8–2.0% lower-mantle P-wavevelocity heterogeneities at length scales of lessthan 8 km (Hedlin et al., 1997), as well as lower-mantle S-wave velocity structures that are either.4% slow and ,8 km thick or .8% fast(Kaneshima and Helffrich, 1999). Such narrowbut fast velocity anomalies are consistent with ourmodel of lower-mantle velocity anomalies insubducted oceanic lithosphere.

Of course, we have calculated only bulk soundvelocities here. Detailed comparison with seismo-logical observations will require computation ofP- and S-wave velocities, which in turn mustawait better constraints on the pressure andtemperature dependence of the shear moduli oflower-mantle mineral phases. Furthermore, thevelocity perturbations that we have calculated toarise from thermal and compositional anomalieswill be accompanied by associated densityanomalies. While the harzburgite is ,1% lessdense than mantle peridotite, basaltic crustalmaterial should be 1–7% denser than peridotiteunder lower-mantle conditions (Figure 12). Themagnitude of this latter density anomaly shouldfall with increasing depth (Figure 12), as shouldthe density consequences of thermal anomalies(Figure 13). These extrapolations suggest thatmetagabbros should remain denser than perioditethroughout the lower mantle, as do others whichadditionally incorporate the affects of calciumand aluminum (Mattern et al., 2002). (A contraryprediction by Ono et al. (2001), that metagabbroshould attain neutral buoyancy deep in the lowermantle, seems to depend upon the large amountof low-density, calcium-ferritic-structured, sodicaluminous phase incorporated in their modelmineralogy. Thus, although the common mappingof fast-velocity anomalies into low temperaturesappears to be a serious oversimplification, inview of the large potential for compositionalsources, the usual mapping of fast anomaliesinto positive density (i.e., negative buoyancy)anomalies does appear to survive in the presenceof chemical differentiation.

2.02.6 SUMMARY

The properties of upper-mantle seismic reflec-tors, especially the observed lateral variations inthe seismological properties of the mantle tran-sition zone, indicate that the upper mantlepossesses a peridotite composition, approaching

Seismological Constraints upon Mantle Composition54

that of the pyrolite model, whose seismiccharacter is largely controlled by thermal pertur-bations of phase transformations in olivine.Response of seismic character to temperature inthe upper mantle may be complicated by localvariations in water content or minor variability inMg/Fe ratios. The role of pyroxene and garnetcomponents in defining seismic character issecondary to that of olivine polymorphs: e.g.,dissolution of pyroxene into garnet occurs gradu-ally over more than 100 km, and exsolution ofcalcium silicate perovskite from garnet–majoritesolid solution between 410 km and 660 km depthmay overlap with the b ! bþg ! g transform-ation in olivine.

Subducted basaltic crust is chemically distinctfrom its surrounding peridotite upper mantle.However, aside from a small signature arisingsolely from temperature gradients, anhydrousbasalt should rapidly become seismically invisibleas it sinks below 100–200 km depth. Featuresexhibiting low seismic velocities in associationwith the upper surfaces of subducting slabs inthe 100–250 km depth range probably arise fromhydrous (lawsonite-bearing) metabasalts in theblueschist and eclogite metamorphic regimes.The disappearance of such slow features, and the

occasional appearance of fast velocity anomalies,below 250 km may arise from the passageof silica-saturated eclogites into the stishovitestability field.

The use of seismic tomography to determine thedepth of origin of mantle plumes yields conflictingresults. Analyses of travel times of seismicboundary-interaction phases, in terms of lateralchanges in the absolute depths to the 410 km and660 km seismic discontinuities, also give rise toseeming inconsistencies, perhaps in part becauseof the dependence of such methods upon laterallyheterogenous models of shallow mantle structure.The use of (more robust) differential travel times,however, to assess lateral changes in the verticaldistance between the 410 km and 660 km seismicdiscontinuities (i.e., the thickness of the transitionzone), suggests that at least some hotspots areassociated with thermal plumes which penetratethe entire transition zone.

Densities and bulk sound velocities in the lowermantle are also consistent with the high-pressuremineralogy of a bulk composition approximatingan upper-mantle peridotite, such as pyrolite.Seismic constraints provide no support for ironenrichment of the lower mantle relative to such anupper mantle. Silica enrichment of the lower

Figure 13 Temperature dependence of density versusdepth in the lower mantle: for candidate bulk compo-sitions for the basaltic layer (red); the underlyingharzburgite layer (green); and the basal lherzolite(blue). Note that temperature sensitivity falls with

increasing depth.

Figure 12 Density anomalies relative to peridotitemantle versus depth: in the lower mantle (blue); forcandidate bulk compositions for the basaltic layer (red);and the underlying harzburgite layer (green). Note thatthe basaltic layer is denser but grows less so with

increasing depth.

Summary 55

mantle can be accommodated if the lower mantleis anomalously hot, as would be consistent with athermal boundary layer of several hundreddegrees across a chemical boundary layer. How-ever, silica enrichment alone is unlikely togenerate an intrinsic density contrast sufficient tostabilize a chemical boundary layer againstconvective rehomogenization. Failure to observethe expected seismic signature of such a chemicalboundary, in the form of a globally sharp seismicreflector exhibiting significant dynamic topogra-phy (.100 km) in the lower mantle, confirms thata peridotite whole mantle that is largely homo-genous in its major element chemistry is mostconsistent with seismological observations.

Seismic scatterers within the lower mantle aremore likely to represent chemical than thermalheterogeneities, with subducted slab material(especially the basaltic crustal component thereof)constituting a likely candidate. The very base ofthe mantle, nearest the core–mantle boundary,may also be characterized by significant major-element chemical heterogeneity.

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