superplumes or plume clusters?3. mantle plumes before describing a superplume we should be clear...

Physics of the Earth and Planetary Interiors xxx (2004) xxx–xxx

Superplumes or plume clusters?

G. Schuberta,∗, G. Mastersb, P. Olsonc, P. Tackleyaa Department of Earth and Space Sciences, Institute of Geophysics and Planetary Physics,

University of California, Los Angeles, CA, USAb Institute of Geophysics and Planetary Physics, University of California, San Diego, USA

c Department of Earth and Planetary Sciences, The Johns Hopkins University, USA

Received 28 February 2003; accepted 23 September 2003

Abstract

It is proposed that the broad, seismically slow, mantle structures under Africa and the Pacific, often identified as superplumes,are instead spatial clusters of smaller plumes. Seismic data, including ScS-S differential travel time residuals and tomographicinversions using ScS-S and deep turning S data, show the breakup of so-called superplume regions into smaller structures. Forexample, the superplume under Africa is clearly formed by at least two and possibly three distinct plumes while the superplumeunder the Pacific consists of at least six smaller plumes. Enhanced seismic resolution may reveal even smaller-scale structuresin the superplume regions. Dynamical considerations argue for the plausibility of superplume regions being clusters of smallerplumes whose heads might have merged into a large region of hot and buoyant material. Alternatively, the superplumes maysimply be large, passively upwelling regions that are seismically distinct.© 2004 Elsevier B.V. All rights reserved.

Keywords:Mantle plumes; Mantle convection; Superplumes

1. Introduction

Seismic tomography (Su et al., 1994; Masterset al., 1996; Ritsema et al., 1999; Mégnin andRomanowicz, 2000) has revealed the existence of twobroad (10,000 km across), seismically slow regionsin the lower mantle that some have identified as su-perplumes. The locations of these regions, under thesouth-central Pacific and under Africa, correlate tothe positions of two major geoid highs and to con-centrations of hotspots (Hager et al., 1985). Zones of

∗ Corresponding author. Tel.:+1-310-825-4577;fax: +1-310-825-2779.E-mail addresses:[email protected] (G. Schubert),[email protected] (G. Masters), [email protected] (P. Olson),[email protected] (P. Tackley).

high seismic attenuation in the upper mantle lie ver-tically above the lower mantle low-velocity regionssuggesting the existence of low-velocity structures orsuperplumes that extend continuously throughout themantle from the core-mantle boundary to the litho-sphere (Romanowicz and Gung, 2002) Are theseregions really superplumes? Assuming that they arealso hot, they are probably regions of broad man-tle upwelling (Forte and Mitrovica, 2001), but doesthat make them superplumes? What is a superplumeanyway?

In this paper we explore the idea that the resolu-tion of previous seismic inversions is not adequateto reveal the smaller-scale structure of these regions.We present new seismic data showing the breakup ofthese regions in the lower mantle into at least sev-eral smaller plumes that may in turn consist of even

0031-9201/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.pepi.2003.09.025

2 G. Schubert et al. / Physics of the Earth and Planetary Interiors xxx (2004) xxx–xxx

smaller structures yet invisible to the seismic eye. Weuse dynamical considerations to argue that the regionsare clusters of smaller structures or plumes that origi-nate at the core-mantle boundary (CMB) and perhapsmerge into a more or less continuous agglomerationof plume heads at some distance above the CMB.

2. Seismic evidence of structure withinsuperplumes

Superplumes have been robust features of globaltomographic models for well over a decade (e.g.,Suet al., 1994; Masters et al., 1996). These early modelswere typically parameterized in spherical harmonicstruncated at degree 12 or 16 and convincingly imagedlarge regions of low S velocity in the lower mantleunder Africa and the Pacific. The question of whetherthese regions were really made up of a cluster ofsmaller low-velocity regions could not be addressedwith the data then available. Beginning in about 1994,a rapid expansion of the global seismic network hasnow resulted in sufficiently improved coverage thatwe can begin to address the question of fine-scalestructure.

The inversions described here are whole mantle in-versions which incorporate large datasets of differen-tial travel times (14,000 ScS-S measurements, 28,000SS-S measurements), 70,000 direct S measurements,and Love and Rayleigh wave phase velocity data

Fig. 1. ScS-S differential travel time residuals binned at the bounce point of the ScS phase on the CMB. The color scale is in seconds.

spanning the frequency range 4–15 mHz. In additionto these data, we also include new datasets of SSand S measurements made using an algorithm whichclusters seismic traces based on their similarity andmeasures differential travel times between them. Thisalgorithm allows us to efficiently process data andhas resulted in over 120,000 S times at teleseismicdistances. The inversion follows the method describedby Masters et al. (2000)and uses a simple param-eterization of equal area blocks of dimension 4◦ atthe equator and with a thickness of 200 km in thelower mantle. This block dimension is about twice thewavelength of shear waves at the base of the mantle.

Despite the comprehensive nature of our dataset, thegeometry of sources and receivers means that there areregions of poor coverage near the base of the mantle.As an example, we plot the differential travel times ofScS-S binned by the geographic bounce point of theScS phase (Fig. 1). For this particular dataset, the ge-ometry of sources and receivers means that there aretwo poorly sampled regions both of which are closeto the superplume areas. The “hole” under the Pac-ific is largely filled by the dataset of direct turning Sbut the southern Indian Ocean remains poorly sam-pled. Despite coverage problems,Fig. 1does indicatequite a lot of structure in the superplume region inthe western Pacific and it is clear that there are twoand possibly three distinct slow regions under Africa.

Fig. 2shows the result of formal inversion for S ve-locity perturbation. We plot only the four lowermost

G. Schubert et al. / Physics of the Earth and Planetary Interiors xxx (2004) xxx–xxx 3

Fig. 2. Left column: Shear velocity in the four lowermost layers of a whole mantle model obtained by inverting the datasets described inthe text. Perturbations about a mean 1D model are shown and are in excess of 2% at the base of the mantle. Right column: Checkerboardtests for each of the four layers. The reduced resolution in the southern hemisphere of the lowermost mantle implies that our model is toosmooth and too low in amplitude there. Resolution is much improved in the layers above.

layers of the mantle (left side). On the right is the re-sult of a checkerboard test for each of the layers. Thegrid size of the checkerboard is chosen to be similarto the size of slow features imaged in the model. Notshown is a map of formal model uncertainty (com-puted using a Monte-Carlo technique) which is typi-cally an order of magnitude smaller than the size ofthe slow anomalies imaged here.Fig. 2 does indeedindicate that structure in the lowermost mantle underthe southern Indian Ocean is poorly resolved thoughresolution in the Pacific is adequate. In particular, res-olution improves substantially as we move up in themantle (due principally to the large number of cross-ing SS legs). This improvement in resolution is coin-cident with the Pacific plume region being imaged asseveral separate regions.

In regions of poor coverage, the first-differencesmoothing incorporated in the inversion (seeMasters

et al., 2000) tends to result in laterally smeared struc-ture with correspondingly lowered amplitude. In fact,the lowermost layer checkerboard test results in onlyabout 50% amplitude recovery. We therefore stronglysuspect that the southern hemisphere of the lower-most layer in our S velocity model is too small inamplitude and too smooth. Further improvements indata coverage (for example, by including diffractedphases) may well result in a rougher structure(more similar to the layers above) and with a largeramplitude.

Fig. 3 shows a 3D Cartesian representation of thePacific superplume as viewed from the southwest. Theisovelocity surface encloses velocity perturbationswhich are 1.1% slow or slower. This figure alreadyshows some similarities to the numerical results ofFig. 9 which will likely be enhanced as resolutionimproves.


Fig. 3. Isovelocity surfaces (encompassing negative perturbations of 1.1% or more) of the Pacific superplume.

3. Mantle plumes

Before describing a superplume we should be clearabout what we mean by a plume. We have yet toachieve an unambiguous detection of a mantle plume(cf., Rhodes and Davies, 2001), so our description ofa plume is based on a theoretical picture of one (see,e.g.,Schubert et al., 2001, for a discussion of mantleplumes).

A mantle plume is a buoyant upwelling which,if thermal in origin, results from the instability ofa hot thermal boundary layer. A plume has a headand a tail or trailing conduit of rapidly, upwardlyflowing, low viscosity, light or hot material. Plumeheads may be hundreds to a thousand kilometersacross and plume tails may be tens to a hundredkilometers in diameter. This head and tail structure isconfirmed by various 2D and 3D numerical convec-tion models,Malevsky and Yuen (1993)and Olsonet al. (1993). A cluster of plume tails originatingfrom a hot thermal boundary layer is seen in theresults of the numerical convection model shown inFig. 9.

There is some experimental evidence that not allthermal upwellings have this structure, however. Forexample, laboratory experiments byJellinek et al.(2002) showed upwellings in the form of isolatedthermals with parabolic-shaped heads and no dis-tinguishable tails, such as occur in Rayleigh–Taylorinstabilities. Isolated thermals are known to oc-cur in situations where the instability depletes thethermal boundary layer, leaving no material forthe conduit. The pervasiveness of theD′′-layer ar-gues that material is available there to feed mantleplume conduits. In addition, the longevity of certainhotspots, such as the Hawaiian chain, is hard to rec-oncile with a plume source consisting of a singlethermal.

Plume buoyancy could be compositional as well asthermal in origin. Presumably then a superplume isan oversized version of a plume, with a head thou-sands to ten thousand kilometers across and a tailthat is comparably large. Can such a structure ex-ist? How does it form? Can a boundary layer notmore than about a 100 km thick spawn a super-plume?


4. Boundary layer instability

Considerations of thermal boundary layer stabilityand plume growth argue against the formation of su-perplumes from hot thermal boundary layers and forthe formation of ordinary plumes with the dimensionsquoted above. Instability of a hot thermal boundarylayer leading to mantle plume formation has been ex-tensively investigated using both numerical modelsand laboratory experiments (for example,Whiteheadand Luther, 1975; Griffiths, 1986; Olson et al., 1987;Griffiths and Campbell, 1990; Malevsky and Yuen,1993; Bercovici and Kelly, 1997; Farnetani, 1997;Kellogg, 1997; van Keken, 1997; Davaille et al., 2002;Jellinek and Manga, 2002). The following simplifiedpicture, taken bySchubert et al. (2001)is derived fromthe results of these studies.

The instability occurs when the boundary layerRayleigh numberRaδ exceeds the critical value ofthe Rayleigh numberRacr. This happens after enoughtime tcr has elapsed for the boundary layer to thickenand attain a critical width. The timescaletcr is givenby

tcr = 1

πκ1/3

(νRacr

αgT

)2/3

(1)

where κ is the thermal diffusivity,ν the kinematicviscosity, α the thermal expansivity,g the gravity,and T the temperature drop cross the boundarylayer. We assume values appropriate for the hot ther-mal boundary layer at the base of the lower mantle,κ = 1 × 10−6 m2 s−1, Racr = 1.1 × 103 (appro-priate for a layer with one rigid and one stress-freeboundary),α = 1 × 10−5 K−1, g = 10.5 m s−2.We consider two cases. The first is a large temper-ature increase across a low viscosityD′′-layer, i.e.,ν = 1020 Pa s/5500 kg m−3 and T = 1000 K. Thisgives tcr about 33 Myr. The corresponding criticalboundary layer thicknessδcr = (πκtcr)

1/2 is about57 km. The second case assumes a small tempera-ture increase across a high viscosityD′′-layer, i.e.,ν = 1021 Pa s/5500 kg m−3 and T = 200 K. Thisgives tcr about 450 Myr. The critical boundary layerthickness for this case is about 124 km. Thus, thetendency toward instability is heightened by low vis-cosity, a consequence of the high temperatures in theboundary layer and the strong temperature depen-

dence of mantle viscosity. With low viscosity the hotthermal boundary layer at the CMB does not requiremuch time to reach instability, and is comparativelythin when instability occurs. Even in the high viscos-ity case, the boundary layer thickness at instability ismuch less than superplume dimensions, although theinstability is slow to develop.

Rayleigh–Taylor instability theory predicts that thespacing of incipient diapirs formed from the insta-bility of the hot boundary layer at the base of thelower mantle isδcr(νm/νp)1/3, whereνp is the kine-matic viscosity of the hot boundary layer materialforming the diapir andνm is the kinematic viscosity ofthe mantle just above the boundary layer. This is alsothe spacing of diapirs at separation. Withνm/νp =102 (the first case discussed above), this spacing isabout 265 km. For the second case,νm/νp = 101, andthe predicted spacing is 267 km, about the same. InRayleigh–Taylor instability of a hot thermal boundarylayer with temperature-dependent viscosity, the vis-cosity and temperature effects on the diapir spacingtend to offset each other. Incipient diapirs are onlyabout 100 km across and are separated by only hun-dreds of kilometers.

An alternative way to model plume head formationconsiders the separation of a diapir from a boundarylayer, and equates the speed of buoyant ascent of thediapir (given by the Stokes velocity for a sphericaldiapir) to its growth rate. This model gives

Rs =(

3νmQv

4πg′

)1/4

(2)

ts =(

4π

3Qv

)1/4 (νm

g′

)3/4

(3)

whereRs is the radius at diapir separation,ts the timerequired for the diapir to grow to that size,Qv thevolumetric rate at which the boundary layer suppliesmaterial to the diapir, andg′ = g(ρm − ρp)/ρm (ρpis the density of the diapir andρm the density of theoverlying mantle). WithQv = 13.7 km3 per year (thevolumetric flux for the Hawaiian plume) andνm =1.8×1018 Pa s,Eqs. (2) and (3)giveRs ∼= 208 km andts ∼= 2.75 Myr for g′ = 0.1 m s−2, or Rs ∼= 311 kmandts ∼= 9.2 Myr for g′ = 0.02 m s−2.

The time required for diapir separation from theboundary layer is generally shorter than the time req-uired for the initial instability to develop. The entire


process of plume formation can occur in the hot lowermantle boundary layer within 50 Myr, and within450 Myr if the layer is less heated.Bercovici andKelly (1997) account for the local deflation of theboundary layer by the inflation of the growing diapirand obtain a somewhat different expression forRs(namely,Rs ∼= δcr(νm/νp)

2/9) which givesRs = 160and 210 km for the twoD′′-layer viscosities consid-ered above. These are only slightly smaller than theestimates gotten from the previous model, and wellwithin the uncertainties of either method. The mainpoint of all the above estimates of plume sizes andseparations is that superplumes cannot originate fromthe instability of a hot thermal boundary layer at thebase of the lower mantle. Superplumes are simply toolarge to have formed in this way. Either the so-calledsuperplume regions of the lower mantle have a dif-ferent origin, in which case they should probably bereferred to differently, or the instability of the bound-ary layer must be suppressed, allowing the boundarylayer to thicken toward superplume dimensions. If theboundary layer at the base of the mantle (theD′′-layer)is both compositional and thermal, chemical compo-sition might stabilize it. However, plume dimensionsbasically reflect the boundary layer thickness and theD′′-layer is not more than a few hundred kilometersthick. Other ways to suppress boundary layer instabil-ity or promote diapir growth will be discussed below.

An alternative picture of the lower mantle super-plume regions is suggested by the considerations ofthis section. These regions may be sites of groupsor clusters of large numbers of “normal” plumes andseismic resolution is simply inadequate to discern thisstructure. The plume heads of large numbers of indi-vidual plumes would tend to grow and merge into abroad region of hot upwelling material as the plumesascended through the mantle. Should a region formedin this way be referred to as a superplume? Probablynot, because the dynamical implications of the termplume, described briefly above, would not pertain toa structure formed this way.

5. Mechanisms for the suppression of boundarylayer instability and plume ascent

If boundary layer instability can be suppressed, thena lot of hot material in the boundary layer would have

to pile-up before a buoyant upwelling could form.There are a number of mechanisms that can be thoughtof to accomplish this end. Among them are the ef-fects of: (1) an endothermic phase transition in thedeep lower mantle; (2) compositional gradients in athermo-chemical boundary layer at the base of thelower mantle; (3) a viscosity maximum in the lowermantle; (4) a reduction in thermal expansivity or ther-mal conductivity in the lower mantle.

On Mars, the endothermic spinel to perovskite andmagnesiowüstite phase change might occur just abovethe CMB. This phase change inhibits the ascent of hotupwellings until enough buoyant material accumulatesto penetrate the transition (Schubert et al., 2001). Thepossible occurrence of this phase change just abovethe CMB has been hypothesized to explain the Tharsissuperplume (Weinstein, 1995; Harder and Christensen,1996; Harder, 1998, 2000). While this may work forMars, there is no known endothermic phase change inthe Earth’s lower mantle.

The existence of a stabilizing chemical composi-tional gradient in the mantle boundary layer at theCMB (Montague et al., 1998) would allow the bound-ary layer to be thicker than a purely thermal boundarylayer, but as noted above, theD′′-layer in the mantleis not thick enough to launch a superplume, whateverits thermo-chemical nature. An endmember versionof this effect is the model proposed byKellogget al. (1999), van der Hilst and Kárason (1999)andMontague and Kellogg (2000)in which a composi-tionally distinct thick (O, 103 km) and isolated layerresides at the bottom of the mantle. The lower thermalboundary layer in this model occurs along an undulat-ing surface in the deep lower mantle. But this bound-ary layer is as unstable as a thermal boundary layerat the CMB; the source of “normal” plumes is simplydisplaced upwards from the CMB in this model. Thepile-up of chemically heavy material at the base ofthe lower mantle by large-scale circulation could serveto focus the upwelling above the thickest piles ofheavy material. Such upwellings could be large-scaleif they are passive, i.e., controlled by the large-scalecirculation in the lower mantle. However if they areactive, i.e., positively buoyant and low viscosity, thenour previous dynamical arguments for breakup intosmaller scale plumes should apply to them also.

Any change in a thermal property like thermalexpansivity or thermal conductivity that reduces the


buoyancy of hot material in the lower mantle willlead to larger buoyant structures. Uncertainties inthese thermal properties, however, make it difficult toquantify their effects.

If there is a viscosity maximum in the lower man-tle (van Keken and Yuen, 1995; Forte and Mitrovica,2001), then rising diapirs must inflate by the additionof more light material so their additional buoyancycan overcome the increase in viscous resistance theyexperience in traversing a region of increasing vis-cosity. We evaluate this effect in the next section andshow that any plausible lower mantle viscosity maxi-mum is unable to account for a diapir with superplumedimensions.

5.1. Diapir rise through a region of upwardlyincreasing viscosity

We use a simple model to evaluate how a diapir willevolve as it rises through a region in which viscosityincreases upwards. This simulates what happens to adiapir originating at the CMB and ascending towardthe peak of a lower mantle viscosity maximum. Themodel assumes that a spherical plume head of radiusRrises with the local Stokes velocityus. A trailing con-duit is assumed to supply the plume head with buoyantmaterial at the constant rateQv. The conduit lengthensat the rate at which the plume head is rising. Withinthe circular conduit of areaA, flow is taken to be alaminar, parabolic, buoyantly driven Poiseuille flow.Mantle kinematic viscosityνm increases exponentiallywith heightz above the CMB. This is an extension ofthe model developed byWhitehead and Luther (1975)for the steady rise of a diapir in a mantle with constantkinematic viscosity. In that case, it is straightforwardto show

Qv = AU∞ (4)

A =(

8πνpQv

g′

)1/2

(5)

U∞ =(

g′Qv

8πνp

)1/2

(6)

V∞ = 4π

3(3νm)3/2

(Qv

8πg′νp

)3/4

(7)

whereU∞ is the upward velocity of the plume head,νp and g′ are as defined previously, andV∞ is the

volume of the plume head. WithQv = 2.9 km3 peryear (for the Reunion plume,Schubert et al., 2001)and other parameter values as above, one finds fromEqs. (4)–(7)that U∞ = 0.27 m per year andV∞ =2×108 km3, corresponding to a plume radius of about350 km and a conduit radius of about 60 km.

These are hardly the dimensions of a superplume(certainly the Reunion plume is not a superplume) sowe return to the model of viscosity increasing withheight above the CMB to see if that effect can substan-tially inflate the plume head. In this case, the plumehead will grow as it rises at the rate

dV

dt= Qv − Aus (8)

The local upward velocity of the plume head is givenby the Stokes formula using the local kinematic vis-cosity of the mantle

us = g′R2

3νm(9)

A is still given inEq. (5)andνm is given by

νm = νm0 ez/H (10)

whereνm0 is the kinematic viscosity of the mantle justabove the CMB boundary layer andH is the lengthscale for the viscosity increase.Eqs. (5) and (8)–(10)can be combined and rewritten as

dF

dζ=

{eλζ −

(2γ

3

)1/2

F

}2F−3/2 (11)

where

ζ = z

R(0)= z

(3νm0Qv

4πg′

)−1/4

(12)

F =(

R

R(0)

)2

= R2(

3νm0Qv

4πg′

)−1/2

(13)

γ = νp

νm0

(14)

γ = R(0)

H(15)

andR(0) is the initial radius of the diapir.Eq. (11)isintegrated with the boundary conditionF(0) = 1. Thesquare root ofF gives the normalized radius of the


plume head and the upward speed of the plume headis given by

us

us(0)= F

(νm

νm0

)−1

= F e−λζ (16)

The way in which the plume head rises through thebackground viscosity increase, i.e., the solution ofEq. (11)subject toF(0) = 1 depends only on the twoparametersλ, the ratio of the initial plume head radiusto the viscosity length scale, andγ, the initial ratio ofthe viscosity of the plume material to the viscosity ofthe surrounding mantle.

Figs. 4 and 5show the normalized radius of theplume head and the normalized plume speed as afunction of the normalized distance above the CMBfor γ = 0.1 (plume viscosity one-tenth the mantle vis-cosity just above the boundary layer) andλ = 0.6908,0.4605, and 0.2303. Forλ = 0.6908, mantle viscosityincreases by 103 when the plume head has traveledupward a distance of 10 times its initial radius. Forλ = 0.4605, the viscosity increase is 102 and forλ = 0.2303 it is 10. According toFig. 5, the radius ofthe plume head increases monotonically with distanceabove the CMB, but only by factors of at most 2–6

Fig. 4. Normalized radius of a plume head vs. normalized distance above the CMB for a plume rising through a background viscositythat increases exponentially with normalized distance above the CMB. The parameterλ is the inverse of the normalized scale height forthe viscosity increase. The parameterγ is the ratio of plume viscosity to the viscosity of the mantle at the CMB.

even when the plume has traveled upward more than10 times its initial radius through a viscosity stratifi-cation of factors of 10 to 103. The upward speed ofthe plume head shown inFig. 5 first increases as theplume rises above the CMB, but the plume speed soonreaches a maximum after the plume has traversedabout 1 or 2 times its initial radius. The plume headthen slows down as it moves upward into regions ofincreasingly larger viscosity. The plume head nevermoves upward much faster than its initial speed andit slows down considerably when it encounters largeviscosities.

In the limit γ → 0, small plume viscosity comparedwith mantle viscosity, andλζ = z/H � 1, manymantle viscosity scale heights above the CMB,Eq.(11) has an analytic solution given by

R

R(0)∼

(5νm

λνm0

)1/5

(17)

us

us(0)∼

(5

λ

)2/5 (νm

νm0

)−3/5

(18)

Eq. (17)shows that as the plume head moves upwardsits radius increases asymptotically at the slow rate of


Fig. 5. Similar toFig. 4 for the normalized rise speed of the plume head.

the mantle viscosity to the one-fifth power.Eq. (18)shows that the upward speed of the plume decreasesmore rapidly, with the inverse three-fifths power of themantle viscosity.

The main conclusion of this analysis is that whilea plume would increase in size as it moved upwardtoward a lower mantle viscosity maximum, the plumewould still remain far smaller than the size of a super-plume.

6. Plume clustering

The analysis in the previous section indicates thatindividual mantle plumes, originating as boundarylayer instabilities in theD′′-layer, are likely to bemuch smaller in size than the broad, seismically slowregions of the lower mantle below Africa and thesouth-central Pacific. Here we suggest an alternativeinterpretation for these two regions that is more con-sistent with the dynamical behavior of plumes as seenin laboratory and numerical models. We propose thatthese two regions contain clusters of smaller-scaleplumes, instead of a single large-scale superplumeas sketched inFig. 6. A dense cluster of smallerplumes would appear as a region with lower than

average seismic velocity in a low-resolution tomo-graphic model of the mantle; the individual plumesthat form the cluster would appear only at higherseismic resolution, as discussed later in this paper.

Plume clusters are a common phenomenon in highRayleigh number convection (Manga and Weeraratne,1999), especially in time-dependent convection withvariable viscosity (Davaille and Jaupart, 1993). Clus-ters of plumes often form above variable boundarytopography or variable boundary heat flow (Namikiand Kurita, 2001), and above piles of composition-ally dense material (Olson and Kincaid, 1991; Tackley,1998; Montague and Kellogg, 2000; Davaille et al.,2002; Jellinek and Manga, 2002). All of these areplausible situations in the lower mantle. In addition,plume clusters can occur without any contributionfrom boundary heterogeneity, through the action oflarger-scale, externally driven flows, or by plume en-trainment.

6.1. Plume concentration by external flows

It is well established that boundary layer insta-bilities and plumes are concentrated by externallyimposed larger-scale flows. Both laboratory experi-ments (Kincaid et al., 1996; Jellinek et al., 2003) and


Fig. 6. Sketch of a plume cluster and a superplume.

numerical models (Rabinowicz et al., 1993; Ito et al.,1996) have demonstrated how plumes are focused bylarge-scale upwellings. There is abundant geophys-ical evidence that mantle plume concentrations areaffected by large-scale motions in the mantle, includ-ing the low hotspot concentration near trenches andthe high hotspot concentration near ridges (Weinsteinand Olson, 1989), relative motion of hotspot tracks ondifferent plates (Steinberger and O’Connell, 1998),along-strike variations in mid-ocean ridge structure(Parmentier and Morgan, 1990; Abelson and Agnon,2001) and geochemical variations along ridges and atnearby hotspots (Schilling, 1985; Peate et al., 2001).

The numerical and laboratory studies of plume-ridgeinteraction show that the concentration of plumesbeneath a divergent upper boundary depends on theratio us/um, whereus is the rise velocity of the plume(given here as the Stokes velocity of the plume head,according toEq. (9)) andum is the characteristic ve-locity in the mantle induced by plate motions and sub-duction. For large values of this ratio, the backgroundmantle circulation has little effect on the plumes.In the other extreme, when this ratio is very small,plume formation is suppressed and boundary layerinstabilities are swept directly into the upwelling. Forintermediate values of this ratio, which is the relevantregime for the mantle, the plumes are advected towardthe upwelling by the large-scale flow, but their ownupward motion prevents them from becoming fullycaptured. The result is anomalously high concentra-tion of plumes ascending in the neighborhood of thelarge-scale upwelling, and conversely, anomalouslylow plume concentration near the downwellings, as

seen in the experiments byKincaid et al. (1996)andJellinek et al. (2003).

There is geophysical evidence that plume concen-tration by global-scale flow may be important beneathboth Africa and the south-central Pacific. The anoma-lously high surface topography above each of theseregions is consistent with large-scale upward mantleflows there (Forte and Mitrovica, 2001). In addition,the density of hotspots is higher above these regionsthan the global average (Weinstein and Olson, 1989),even though many of these hotspots, particularly thoseabove the African low-velocity structure, are small inmagnitude (Sleep, 1990).

6.2. Plume concentration by entrainment

Plume clusters can also occur through the ten-dency of isolated groups of plumes to self-organize.The circulation induced by a rising plume includesa strong, inward-directed horizontal flow, sometimesreferred to as the “entrainment wind”. The entrain-ment wind induced by a single vertical plume conduitin a viscous fluid above a free-slip boundary (suchas the core-mantle boundary) is symmetric about theconduit axis, and varies slowly with height abovethe boundary and with distance from the conduit.Neglecting these slow spatial variations, the (inward)entrainment wind velocityue near the base of asemi-infinite vertical plume conduit is (Olson et al.,1993)

ue = g′r2

4νm(19)


Fig. 7. Sketch showing the mutual entrainment of two isolatedplumes.

whereg′ is the buoyancy of fluid in the plume con-duit, r the conduit radius, andνm the viscosity of theexternal fluid, in this case the lower mantle.

Since the entrainment wind decreases slowly withdistance, it tends to draw isolated plumes together,even if the plumes originate some distance apart. Forexample, the approach velocity of the two equal-sizedplumes shown inFig. 7 is 2ue = g′r2/2νm. Using thelower mantle and plume parameters from the previoussection (g′ = 0.1 m s−2 and νm = 1 × 1030 m2 s−1)with r = 120 km,Eq. (19)gives an approach veloc-ity of 2ue = 1.2 cm per year, comparable to the risevelocity of small plumes in the lower mantle.

The entrainment wind causes pairs of isolatedplumes to bend toward each other, as shown schemat-ically in Fig. 7. This effect is often seen in two-dimensional numerical models of mantle convection(Vincent and Yuen, 1989; Balachandar et al., 1993;Balachandar and Yuen, 1994; Hansen and Yuen, 2000;Schubert et al., 2001). Entrainment is nearly as strongbetween the three co-linear plumes shown inFig. 8.In this case the central plume is hardly affected, buteach of the two edge plumes are attracted toward thecentral one with entrainment velocity nearly 2ue. En-trainment winds also affect two-dimensional configu-

Fig. 8. Sketch showing the mutual entrainment of three isolatedplumes.

rations of isolated plumes. For example, each of thefour equal plumes located at the corners of a square areattracted toward the center with velocity(1 + √

2)ue.We note that plumes in the interior of large clustersare not affected in the same way as the plumes onthe edge of the cluster, since the entrainment wind isnearly zero in the cluster interior. This explains whylarge plume clusters (or large arrays of plumes) donot often condense into a single superplume.

Another type of entrainment that contributes toplume clustering is the interaction of plume heads.The flow field around a plume head is dipolar, withflow towards the plume head from below. Thus, thesmaller plume heads emerging from a thermal bound-ary layer after a larger plume tend to get drawn intothe larger plume from below.

6.3. 3D numerical simulation

The physical mechanisms of plume clustering dis-cussed above are apparent in the 3D numerical cal-culation shown inFig. 9. The plume clusters shownin the figure arise from a model with a rheology andother physical properties thought to be realistic for


Fig. 9. Plume clusters in a 3D numerical model. Details of the model are given in the text.

Earth’s lower mantle. The basic compressible, anelas-tic model with depth-dependent thermal expansivity,conductivity, and reference density is similar to thatdescribed byTackley (2002). The rheology is basedon a homologous law

η(T, z) = A exp

(gTm(z)

T

)(20)

with g = 13.5, a reasonable value for the lower mantle(Yamazaki and Karato, 2001). The melting tempera-tureTm(z) in the model (z is the vertical coordinate) isbased on simple fits to the experimental solidii ofZerret al. (1998)in the lower mantle andHerzberg et al.(2000)in the upper mantle. The constant factorA is setsuch that the viscosity for an adiabat with a potentialtemperature of 1600 K is 1022 Pa s at the core-mantleboundary (CMB). The model is configured to studyplumes, with the top of the domain representing thebase of a rigid, isothermal lithosphere with a temper-ature of 1600 K, and the base of the model represent-ing a free-slip, isothermal CMB with a temperatureof 3712 K, giving a superadiabatic temperature rise of

1200 K, all of which occurs over the lower boundarylayer. The initial condition for temperature is a 1600 Kadiabat with an error-function thermal boundary layerat the CMB with thickness 70 km and random per-turbations of peak-to-peak amplitude 60 K. In orderto prevent the build-up of hot material in the upperpart of the domain, temperature deviations from the1600 K adiabat are damped out in the upper 10% ofthe box.

The calculation is performed using the code Stag3D(Tackley, 1996, 2002), but with a new advectionscheme based on upstream tracking and interpolation,similar to characteristics-based methods (Malevskyand Yuen, 1991), thereby minimizing numerical dif-fusion and overshoot. A 128× 128 × 128 grid isutilized, with vertical grid refinement near the CMB.With the above parameters and this grid spacing, tensof thousands of timesteps are necessary to calculaterelatively short geological times (e.g., 100 millionyears).

The system initially undergoes a transient, in whichthe lower boundary layer thickens and develops


Fig. 10. The decay of a superplume into a cluster of nine plumes. In the initial state (upper left), a superplume is produced by the strongincrease of viscosity with pressure. Upon the addition of temperature dependence of the viscosity, the superplume breaks up with time(lower left to upper right to lower right) into the cluster of nine smaller plumes shown in the lower right. From a numerical calculationby Hansen and Yuen (2002).

multiple small-scale instabilities that are swept intotwo large-scale instabilities. Then it settles down intotwo slowly evolving plume conduits, which are sub-sequently added to by three starting plumes, forminga plume cluster. The illustrated time is about 100million years.

Hansen and Yuen (2002)have carried out anothercalculation that illustrates the development of a plumecluster from an initial state of large-scale upwellingthat could be described as a superplume.Fig. 10, fromtheir calculation, shows the breakup of a superplume(top left) into a plume cluster (bottom right). The ini-tial superplume state results from a viscosity that de-pends only on pressure or depth; viscosity increasesstrongly with depth as depth to the fifth power. Thesurface Rayleigh number was 107, and thermal expan-sivity decreased by a factor of 3 with depth. Upon theaddition of an exponential dependence of viscosity ontemperature (viscosity varies by 103 due to temper-ature) the superplume decays into a cluster of nine

smaller plumes. The preferred state for the more re-alistic viscosity dependence on both temperature andpressure is a plume cluster, not a superplume.

7. Summary

We have studied the possibility that the broad,seismically slow structures beneath Africa and thesouth-central Pacific are really under-resolved plumeclusters instead of superplumes. A mantle plume is abuoyant upwelling that forms from the instability ofa hot thermal (or thermo-chemical) boundary layerat the base of the mantle (Schubert et al., 2001). Wereviewed the dynamics of boundary layer instabilityand showed that the thermal boundary layer at thebase of the mantle gives rise to plumes that are onlyO (100 km) across. Superplume regions are too largeto be explained by a single instability of theD′′-layer.Instead, if such broad, hot, upwelling regions of the


mantle have their origin in the instability of a bound-ary layer at the CMB, then the regions must containa large number of ordinary plumes, i.e., they must beplume forests or clusters.

Clusters of plumes are formed by the dynamicsof large-scale flows. Horizontal convergence towardlarge-scale upwelling sweeps plumes into groups.Entrainment by plume-induced flow also promotesthe formation of clusters. We presented a new nu-merical 3D calculation that exemplifies these dynam-ical effects. The locations of hotspots in relation tooceanic ridges supports the concentration of plumesby large-scale upwelling in the mantle. The likeli-hood of large-scale upwelling beneath Africa andthe south-central Pacific favors the accumulation ofplumes in these regions.Johnson and Richards (2003)have proposed that the distribution of coronae onVenus can be understood if coronae are productsof mantle plumes that are gathered into clusters bylarge-scale mantle upwelling.

We investigated whether the rise of a plume into in-creasingly more viscous mantle could broaden plumeheads to superplume size. Upward motion of a plumehead from the CMB toward a lower mantle viscositymaximum would increase the radius of a plume head,but not nearly enough to account for the size of a su-perplume.

In summary, all of these dynamical considerationsindicate that buoyant plumes from theD′′-layer tend toa characteristic size which is far smaller than the ob-served superplume regions. Of course, this still leavesopen the possibility that the superplume regions rep-resent passive upwellings in the large-scale circula-tion of the lower mantle that are nevertheless seismi-cally identifiable. Such passive upwellings would notbe subject to the same instabilities we have discussedhere.

One way to determine if the superplumes beneathAfrica and the south-central Pacific are really plumeclusters is to seismically observe the small-scalestructure characteristic of a cluster. We presented anew S-wave velocity model of the lower mantle thatshows considerable structure near the CMB beneaththe south-central Pacific; the Pacific superplume con-sists of at least six smaller-scale centers of reducedS-wave speed. The model also shows that the Africasuperplume breaks up into at least two and perhapsthree smaller-scale plumes. While seismic resolution

is still inadequate to reveal all the small-scale structureof these regions, the break-up of these superplumesinto concentrations of smaller plumes is a certainty.

Acknowledgements

We thank U. Hansen and D. Yuen for the oppor-tunity to include their figure asFig. 10of this paper.GS acknowledges support from the NASA PlanetaryGeology and Geophysics Program under grant NAG5-1161. GM acknowledges support from grant NSFEAR01-12289.

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superplumes or plume clusters?3. mantle plumes before describing a superplume we should be clear...

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