Earth and Planetary Science Letters 366 (2013) 99–111

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Earth and Planetary Science Letters

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New observational and experimental evidence for a plume-fedasthenosphere boundary layer in mantle convection

J.P. Morgan a,b,n, J. Hasenclever c,d, C. Shi e,b

a Earth Sciences Department, Royal Holloway University of London, Runnymede, UKb EAS Department, Cornell University, Ithaca, NY, USAc Hamburg Institute of Geophysics, Hamburg, Germanyd Future Oceans, GEOMAR, Kiel, Germanye Hess Corporation, Houston, TX, USA

a r t i c l e i n f o

Article history:

Received 21 September 2011

Received in revised form

17 January 2013

Accepted 3 February 2013

Editor: P. Shearerfed asthenosphere is a thermal and density inversion with cooler underlying average-temperature

Available online 19 March 2013

Keywords:

mantle convection

mantle plume

asthenosphere

mantle seismology

1X/$ - see front matter & 2013 Elsevier B.V.

x.doi.org/10.1016/j.epsl.2013.02.001

esponding author at: Earth Sciences Departm

ity of London, Runnymede, UK. Tel.: þ44 178

ail address: jason.morgan@rhul.ac.uk (J.P. Mo

a b s t r a c t

The textbook view is that the asthenosphere is the place beneath the tectonic plates where competing

temperature and pressure effects on mantle rheology result in the lowest viscosity region of Earth’s

mantle. We think the sub-oceanic asthenosphere exists for a different reason, that instead it is where

rising plumes of hot mantle stall and spread out beneath the strong tectonic plates. Below this plume-

mantle. Here we show several recent seismic studies that are consistent with a plume-fed astheno-

sphere. These include the seismic inferences that asthenosphere appears to resist being dragged down

at subduction zones, that a sub-oceanic thermal inversion �250–350 km deep is needed to explain the

seismic velocity gradient there for an isochemical mantle, that a fast ‘halo’ of shear-wave travel-times

surrounds the Hawaiian plume conduit, and that an apparent seismic reflector is found �300 km

beneath Pacific seafloor near Hawaii. We also present 2D axisymmetric and 3D numerical experiments

that demonstrate these effects in internally consistent models with a plume-fed asthenosphere. If

confirmed, the existence of a plume-fed asthenosphere will change our understanding of the dynamics

of mantle convection and melting, and the links between surface plate motions and mantle convection.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The Earth’s mantle underneath the tectonic plates, commonlyreferred to as asthenosphere, is known to be the lowest viscosityregion of the upper mantle. Several potential mechanisms have beensuggested to be responsible for this low viscosity zone. Thesemechanisms, each further discussed in Karato (2008a, 2008b, 2012)and Yamamoto et al. (2007) include: (1) the temperature andpressure dependence of the mantle rheology may lead to a viscosityminimum between 70 and 200 km depth; (2) a small and immobilefraction of partial melts may weaken the mantle; (3) wet mantlebelow its dry solidus (deeper than about 70 km) would be expectedto be weaker than shallower mantle that dehydrated during partialmelting at mid-ocean ridges (MOR) (Hirth and Kohlstedt, 1996;Morgan, 1994, 1997)—but this mechanism does not explain thephysical origin for the base of the asthenosphere; (4) a reduction inmantle grain size within the asthenosphere. Here we investigate analternative view that the sub-oceanic asthenosphere forms because itis the ‘‘graveyard’’ for rising (i.e. hotter-than-average mantle) plumes(Deffeyes, 1972; Kumagai et al., 2008) (cf. Fig. 1b–d). In this view,

All rights reserved.

ent, Royal Holloway

4 443606.

rgan).

below the plate-age-dependent �60–100 km-thick oceanic litho-sphere there exists a pool of hot plume material that has risen asfar as the overlying thermal and/or compositional lithosphere (Hirthand Kohlstedt, 1996; Morgan, 1994, 1997) will allow. At the base ofthis pool of hotter-than-average mantle corresponding to the base ofthe seismic low-velocity zone (LVZ), there would be a negativevertical gradient in density and potential temperature (potentialtemperature is temperature corrected for adiabatic effects). Thisdensity inversion may be augmented by the density reductionassociated with partial melting where this has also occurred. Such athermally and compositionally buoyant asthenosphere offers a parti-cularly simple explanation for a set of recent seismic observationsthat are otherwise difficult to explain. The conceptual scenario of aPFA and its geodynamic predictions have been discussed elsewhere(Morgan et al., 1995b; Yamamoto et al., 2007), where previousobservational hints for the effects of a plume-fed asthenosphere(PFA) on patterns in seismic anisotropy, geoid, dynamic topography,and ocean island basalt/mid-ocean ridge basalt geochemistry wereevaluated. Here we will focus on several new observations (cf. Figs.2–4) and interpret these in Section 2 in the context of the PFAscenario as well as in the context of alternative views (see above). InSection 3 we will present results from 2D axisymmetric and 3Dnumerical experiments on the PFA scenario that predict mantle flowand thermal structures consistent with these new observations.

Lithosphere

Asthenosphere

Mesosphere

a

b

c

d

Fig. 1. Cartoons of flow patterns in conventional asthenosphere and plume-fed

asthenosphere. (a) Schematic of conventional view of upper mantle convection.

(b) Schematic of flow structures in a convecting mantle that includes a plume-fed

asthenosphere (PFA). (c) Schematic of 3D flow characteristics within the PFA.

(d) Schematic showing how buoyant asthenosphere resists slab dragdown at

trenches, consistent with recent global seismic patterns mapped by Long and

Silver (2008, 2009).

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111100

2. New observations supporting a plume-fed asthenosphere

2.1. Seismic and mineral physics inversions for upper mantle

temperature profiles

One new line of seismic evidence is direct inversions of longperiod seismic waveforms for mantle temperature along verticalprofiles in a global upper mantle wavespeed model that aims tomatch 3D travel time data and attenuation (Cammarano and

Romanowicz, 2007). While Cammarano and Romanowicz (2007)assumed a homogeneous pyrolitic mantle composition andinverted only for best-fitting vertical temperature profiles, theinversion study by Cammarano et al. (2009) tested differentvertical compositional profiles to obtain best-fitting thermoche-mical models. These studies find that globally a strong positivegradient in shear-wave velocity is required between 250 and350 km depths. If thermal in origin, it implies negative tempera-ture gradients at 250 km depths beneath ocean basins but notcontinental cratons, and if compositional in origin it implies agradual enrichment into a more garnet–pyroxene rich composi-tion with depth beneath ocean basins. We will show that the PFAmodel is able to explain either possibility and in fact favors acombination of the two.

Inverting for temperature variations alone results in theseismically-inferred geotherms shown in Fig. 2a (Cammaranoand Romanowicz, 2007). Note that Fig. 2a shows inverted in-situ temperatures rather than potential temperatures correctedfor the adiabatic depth-dependent increase in temperature whichare shown in Fig. 2b. Beneath continental cratons—solid lines inFig. 2b—the inferred temperature is consistent with the thermalstructure for a 40 mW/m2 surface heatflow, and reaches an in-situtemperature of �1300 1C at �250 km corresponding to a poten-tial temperature of �1200 1C at �250 km when corrected for atypical mantle adiabatic temperature gradient of �0.33 1C/km. Incontrast, sub-oceanic upper mantle (dashed lines in Fig. 2b and c)follows a strikingly different geotherm that reaches in-situtemperatures of �1475 1C (potential temperatures of �1400 1C)at �225 km before decreasing to in-situ temperatures of�1250 1C (potential temperature of �1150 1C) at �325 km,identical to the sub-cratonic temperatures at this depth. Between�225 and 325 km, however, the potential temperatures in theoceanic asthenosphere are about 200 1C hotter than those inferredbelow cratons. Cammarano et al. (2009, 2011) pointed out that thethermal profiles are nonunique, but depend on the mantle composi-tion assumed for the inversion. In fact Cammarano et al. (2009) referto the negative temperature gradient as being ‘‘unrealistic’’ and prefermodels in which compositional variations with depth lead to tem-perature profiles without this intriguing feature. Here we offer analternative explanation, that the negative thermal gradient impliedfor a near-uniform mantle composition may be real and physicallyreasonable.

If mantle plumes are hotter than average mantle and feed asub-oceanic pool of asthenosphere, while temperatures at depthsgreater than 325 km more closely reflect average mantle tem-peratures, then the temperature contrast discussed above wouldbe anticipated between a PFA being well-developed beneathrelatively thin sub-oceanic asthenosphere and poorly-developedor absent beneath the much thicker continental cratons. Thisargument has been further discussed for better-constrained NorthAmerican seismic data in Reston and Morgan (2004). In the PFAscenario (Morgan et al., 1995b; Reston and Morgan, 2004;Yamamoto et al., 2007), a continental craton will only be under-lain by hotter-than-average plume material when passing directlyover a plume that then drains laterally towards the adjacentocean basin (cf. Fig. 1b) or when lying over a regional ‘superswell’such as present-day S. Africa.

Attributing all or even a part of the strong positive gradient inshear-wave velocity between 250 and 350 km depth to a changein mantle composition, as suggested by Cammarano et al. (2009),requires a geochemical or fluid dynamical mechanism for thegradual increase of mantle enrichment with depth. Melt extrac-tion at mid ocean ridges is an efficient mechanism to removeenriched mantle components (e.g. eclogite, pyroxenite) andthereby leave a residue that is less dense and richer in depletedharzburgites. However, mantle will not extensively melt at ambient

oceanic lith.craton lith.

S

N

oceanic lith.craton lith.

potential

0.33°C/km

adiabat

10 12 14 16 18 20 22 24 26 28 30

200

300

400

500

600

700

800

900

1000

1100

S NLatitude (°)

Dep

th(k

m)

Asth Bottom?

‘410km disc.’

‘520km disc.’

‘660km disc.’

Fig. 2. Seismic geotherms and �300 km-discontinuity reflections consistent with the PFA scenario of mantle convection. (a) Seismically-inferred in-situ geotherms

(Cammarano and Romanowicz, 2007) for selected sub-cratonic (solid line/box) and sub-oceanic (dashed line/box) regions. (b) Same geotherms as in (a) but corrected for an

adiabatic temperature increase of 0.33 1C/km (i.e. potential temperatures). Each colored geotherm in (a,b) is for the corresponding colored location in (c). Note that sub-

oceanic geotherms in the depth interval �100–250 km are 200 1C hotter than underlying mesosphere at 330 km. This type of thermal anomaly is expected for a PFA. Also

note all sub-cratonic and sub-oceanic seismic geotherms in (a) converge at depths between �300–350 km to �1250 1C—i.e. to a cool mesosphere potential temperature of

1150 1C. (d) Generalized Radon Transform imaging (Cao et al., 2010) of the upper mantle along the profile S–N at 1601W in panel (a). This profile around Hawaii shows a

strong reflector at �330 km. Could this reflector be the base of the PFA near Hawaii? (see also Fig. 4). (For interpretation of the references to color in this figure legend, the

reader is referred to the web version of this article.)

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111 101

pressures corresponding to 250 km depths—this region is simplytoo deep for a significant volume-fraction of enriched pyroxeniticcomponents to be removed by partial melting (Petermann andHirschmann, 2003). Furthermore, there is no phase transitionassociated with significant changes in mantle density and visc-osity known for this depth so that mantle material should be ableto cross this depth range without much resistance. Hence thereshould be efficient mixing of all mantle material above the 410-km depth of the transition zone, which would be inconsistentwith a global change in mantle composition at �250–350 kmdepths in an isothermal mantle. However, if some of the shear-wave anomaly were due to a negative thermal gradient at 250–300 km depth as predicted by the PFA scenario, the shallowermantle would be both hotter thus both less viscous and lessdense, which would significantly resist vertical flow across thisdepth interval. Vertical flow would instead be limited to regionsof stronger lateral temperature contrasts, i.e. subduction zonesand regions where mantle plumes feed the asthenosphere.

In Yamamoto et al. (2007) and Morgan et al. (2007)we also discuss in more detail alternative suggestions (e.g.changes in average grain size, partial melt, fluids) for the originof the seismic low-velocity zone (LVZ) beneath the ocean basins.In the discussion section of this paper we will briefly revisit someof these other potential mechanisms, which have also beenreexamined by Yang et al. (2007), whose preferred scenarioappears to be consistent with a sub-oceanic PFA, and by Karato(2012).

2.2. Underside reflectors at �250–350 km depths beneath ocean

basins

Another line of evidence is recent observations of undersidereflections from a �250–350 km-deep reflector in ocean basinswhere no continental craton could possibly be linked to thesereflections. Cao et al. (2010) have recently applied the GeneralizedRadon Transform seismic inversion technique to remotely probethe reflectivity structure of the upper mantle beneath selectedoceanic regions. Fortunately, the region around Hawaii is well-located for this land-station-based imaging technique. An exam-ple of their preliminary results is shown in Fig. 2d; it shows notonly clear ‘410 km’ and ‘660 km’ seismic discontinuities but alsoshows an equally strong mystery reflector at �330 km depths.Could this reflector be due to a sharp change in anisotropy at thebase of a plume-fed sub-oceanic asthenosphere? This would beentirely consistent with observed lateral variations in shear-wavetravel-time delays around Hawaii shown in Fig. 4 (Wolfe et al.,2009). Using a different processing technique, Thomas et al.(2008) found a reflector at similar depths beneath seafloor located�500 km seaward from the Kurile Trench. This ‘X-discontinuity’(Revenaugh and Jordan, 1991) reflector was first recognized as afeature of the 1D horizontally averaged reflectivity structurealong a path between Tonga EQs and Hawaii receivers byRevenaugh and Jordan (1991). Further evidence for a variable-depth X-discontinuity was later found in SS precursor studies(Deuss and Woodhouse, 2002, 2004), and similar path-average 1D

S-wave variation relative to PREM in %

m of dynamic topograpahy

Fig. 3. (a) Long and Silver’s (Long and Silver, 2008, 2009) subslab shearwave split-delay measurements imply to Long and Silver that near-trench asthenosphere is resisting

slab dragdown everywhere. (Fig. 1c and d illustrate the PFA mechanism for resistance to slab dragdown and possible implications for patterns of global asthenosphere

flow). (b) Predicted global PFA flow (Yamamoto et al., 2007) determined from boundary layer theory (lubrication theory). If the asthenosphere viscosity is non-Newtonian,

trench-parallel flow is likely to be even more enhanced. (c) Global shear anisotropy model at 100 km depth (Debayle et al., 2005). Note evidence for trench-parallel flow

near Tonga and Indonesia that is consistent with PFA-flow prediction in panel (b) and the shear-wave splitting observations in panel (a).

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111102

reflectivity studies (Bagley and Revenaugh, 2008) in several otherlocations beneath the Pacific, Indian and Atlantic oceans. A keyfeature of the X-discontinuity is that it has lateral variations indepth of more than 70 km between �260 and 330 km depths(Deuss and Woodhouse, 2002; Bagley and Revenaugh, 2008;Jacobsen et al., 2010). If due to a phase change such as coesite–stishovite in an eclogite-rich mantle composition (Williams andRevenaugh, 2005), such 470 km depth variations would implylateral temperature variations at this depth of 4800 1C, which is

difficult to imagine in a convecting upper mantle (Jacobsen et al.,2010). The observation that the upper mantle sampled by theglobal spreading center system has lateral variations o300 1C isanother argument against lateral asthenosphere temperaturevariations of order 4800 1C (see discussion in Yamamoto et al.(2007), in particular in their reply to the comment by DonAnderson). However, this scale of lateral depth variability to thebase of a plume-fed asthenosphere would be a natural character-istic if relief at the base of a buoyant layer is caused by dynamic

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111 103

compensation of the lateral pressure variations linked to lateralpressure-driven flow within the asthenosphere (Yamamoto et al.,2007; Morgan et al., 2007). This type of stress-supported reliefwould be analogous to dynamic topography arising at Earth’ssurface or the core–mantle boundary in response to stressesassociated with viscous mantle flow. A closely related form ofdynamic relief compensating the viscous stresses induced by thebuoyancy within subasthenospheric plume conduits will be dis-cussed below. Jacobsen et al. (2010) have also proposed analternative possible explanation for this relief caused by relativelysmall lateral variations in the trace water content of the uppermantle.

2.3. Limited slab entrainment and trench-parallel asthenosphere flow

Subduction zones also have intriguing new observations con-sistent with a plume-fed asthenosphere. A particular character-istic of a plume-fed asthenosphere is that a subducting slab canonly drag down a �10–20 km thick sheet of asthenosphere whenit descends (cf. Fig. 1b, c and 5c; and Morgan et al. (2007)) so thatthe bulk of the asthenosphere will resist being dragged down atthe subduction zone. The formation of this thin entrained bound-ary layer at the sides of the subducting slab has several geody-namic consequences. One consequence is that it would lead topartial asthenospheric counterflow, and in many cases to trench-parallel asthenospheric flow. The latter is driven by trench-parallel pressure gradients, which often arise in 3D subductiongeometries such as that along the west coast of S. America. Forexample, see the predicted first-order global asthenospheric flowpattern shown in Fig. 3b, where Tonga and Indonesia are bothpredicted to have trench parallel asthenosphere flow that isconsistent with the patterns of seismic anisotropy in these areas(Fig. 3c). While there are several potential mechanisms causingseismic anisotropy—and not always are fast directions fromshear-wave splitting an unambiguous indicator for the directionof present day mantle flow (e.g. Kaminski and Ribe, 2001,2002)—it is remarkable that predicted asthenosphere flow andanisotropy pattern coincide so well. Trench parallel flow is alsothe preferred interpretation for the shear-wave splitting measure-ments in these areas (Fig. 3a) (Long and Silver, 2008, 2009), and itis consistent with patterns in global inversions for azimuthalanisotropy (Debayle et al., 2005; Montagner, 2007). Long andSilver (2008, 2009) even interpreted their observations as imply-ing that the asthenosphere was resisting dragdown by subductingslabs—an interpretation completely compatible with a buoyantplume-fed asthenosphere.

2.4. Underside slab reflectors

The sheets of low viscosity asthenosphere that sheath thesubducting slab could be potential seismic reflectors due to theintense strain accumulated within them. Kito et al. (2008) haverecently imaged an intriguing and widely-distributed undersidereflector underlying mid-mantle portions of the subducted Far-allon slab. Kito et al.’s suggestion for this underside reflector wasthat it supported the hypothesis of a thin downdragged sheet ofasthenosphere along the base of the subducting slab (Morganet al., 2007).

2.5. The ‘‘Fast Halo’’ imaged by the Hawaiian PLUME experiment

Another striking recent observation is the lateral variations inshear-wave arrival times that were mapped around Hawaii by thePLUME ocean bottom experiment (Wolfe et al., 2009). The PLUMEanalysis (Wolfe et al., 2009) inverted for lateral shear velocityvariations beneath the lithosphere, after removing the assumed

1D model velocity structure IASP91 (Kennett and Engdahl, 1991).They found that a slow plume-conduit extends to at least1200 km below the Hawaiian hotspot. In this inversion the slowplume conduit is—quite surprisingly—surrounded by a �1% fastwavespeed halo that appears to extend, in their inversion,between depths of �100 and 400 km (Fig. 4a). In their supple-mentary material, they show the data is fit equally well by a 2%fast halo extending over a smaller depth range of 200 km (Fig. 4b),which we interpret to indicate that they actually have limitedvertical resolution in the uppermost �400 km of their inversionvolume. A fast halo is impossible to explain as a thermal haloaround the plume; this should lead to a slow wavespeed halo fornear-vertical raypaths, not a fast one. Similarly, plume-flow-related S-wave anisotropy cannot simply explain this pattern.For example, simple vertical strain around a plume conduit wouldresult in an anisotropic slow shear-wavespeed halo, not a fasthalo. While vertical-strain-related anisotropy would lead to theopposite apparent wavespeed anomalies for P- and S-waveinversions, a subsequent P-wave inversion (cf. Fig. 9 of Wolfeet al. (2011)) shows similar, but more poorly resolved, long-wavelength features to those discussed above. Therefore seismicanisotropy is not a good candidate to explain this ‘fast halo’ effect.

Is a plume related dynamic uplift of the mantle underlying theasthenosphere the cause of this fast halo? If the asthenosphere isplume-fed, hence more buoyant than underlying mantle, thenthere can be a simple explanation for this pattern. The seismicanomaly would be due to faster traveltimes resulting fromdynamic relief at the asthenosphere–underlying mantle (‘‘meso-sphere’’) interface; uplift of the colder (i.e. denser) mesosphere bythe buoyancy of the rising plume increases the distance a wavetravels through faster mantle and reduces the distance though theslower asthenosphere (Fig. 4f and g). This effect can only happenif the asthenosphere is more buoyant than underlyingmantle—and is therefore direct evidence that a buoyant PFAexists around Hawaii. Note that this ‘bump’ of dynamic relief atthe base of a buoyant asthenosphere naturally arose in our initial3D experiments on the dynamics of a plume-fed asthenosphere(Fig. 5d, Supplemental Fig. 1b), and is a robust feature insubsequent 2D axisymmetric experiments (Figs. 4g, 5,Supplemental Fig. 2). With this interpretation, we would estimatethat the Hawaiian plume ‘bump’ is a �40–70 km high, �200 km-wide dynamic uplift of the base of the asthenosphere thatsurrounds a plume stem of radius �100 km.

This relief can be directly estimated by combining the PLUMEresults with the well-measured average �6–10% reduction inshear velocity between the Pacific asthenosphere/LVZ and itsunderlying mantle (Dziewonski and Anderson, 1981; Gahertyet al., 1999; Nettles and Dziewonski, 2008) (also see Box 1). Tomake this estimate, we equate the fast travel time anomaly(h/Va)�(h/Vm) created by passing through faster mantle (wave-speed Vm) within an uplifted ‘bump’ of mesosphere of height h tothe PLUME (Wolfe et al., 2009) travel-time anomaly (L/Vc)�(L/Vm)due to near vertical ascent through faster mantle ðVc�VmÞ for adistance L¼200 km. The thickness of the inverted high-amplitudelayer in Fig. S9b of Wolfe et al. (2011) is shown in Fig. 4b here.(Fig. 4e and f shows definitions of L, Vc , Vm, Va). The resultingestimate of bump relief h is h¼ LðVa=VcÞððVm�VcÞ=ðVm�VaÞÞCLð½dVc=Vm�VmÞ=ð½dVa=Vm�VmÞ � Lð2%=ð6�10%ÞÞ. For the measured‘halo’ wavespeed anomaly of þ2% seen in Fig. 4b, and a near-vertical pathlength through the high-wavespeed anomalyL¼200 km, this estimate indicates that �40–70 km of dynamicplume-conduit-buoyancy-induced relief on the base of the sub-Hawaiian asthenosphere is consistent with the seismic anomalypattern in Fig. 4b. Relief of �40–70 km over a radial distanceof �100–350 km are also the amplitude and wavelengthof the plume bump predicted to surround a �150 km diameter

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111104

Hawaiian plume conduit (Fig. 4f and g). Numerical experiments(cf. Fig. 5b) show that the relief of the plume bump at the base of aPFA is most sensitive to the diameter and buoyancy of the plumeconduit within the upper mantle—e.g. to the plume conduit’sintegrated upper mantle buoyancy anomaly.

Even though the PLUME analysis by Wolfe et al. (2009)vertically integrates and conflates seismic wavespeed anomaliesacross a wide depth interval, we can see by comparison with thesurface wave analysis of Laske et al. (2011) that a ‘fast-halo’

Lateral Vs scenario

(Wolfe et al., 2009)vs. Relief at base of asth

L plume

Normalpath

Fastpath

Slowpath

fast

Asthenosphere

Mesosphere

LithosphereLithosphere

Actual Vspattern

slow

(faster Vs)

Fastpath

Slowpath

(slow Vs)

slow

plume

Vs anomaly1-D modelswell root

fast

Mesosphere

(faster Vs)

Plume Stem(300-800+ km

depths)

-6%

Plume Bump~300 km depth

40-70 kmrelief

Swel~50-1

+ +

Travel time signal≈ -6% x 500+ km

Travel time≈ -4% x 10

Travel time equivalent≈ +2% x 200 km

-4%

similar between 50-250kmif inversion forced to 50-250km.

similar anomalies within100-400km depth interval.

PLUME S-wave velocity anomalies

Longitude West

dVs/Vs [%]dVs/Vs [%]

Longitude West

Latit

ude

16

18

20

22

24

26

16

18

20

22

24

26location of panel c

162160 158156 154 152 150148 162160 158156 154 152 150148

structure will persist even after we better correct for shallowerhotspot-swell-related wavespeed anomalies. For example, panel4c taken from Laske et al. (2011) shows a horizontal slice from thesurface-wave inversion beneath this region. Similar wavespeedstructures are found in the �40–140 km depth interval (seepanels 1–6 of Fig. 11 of Laske et al. (2011)). The hotspot swell(dashed line) is underlain by �3–4.5% slower-than-averageshear-wave anomalies within this �100-km-thick interval. Thiseffect would be enough to counteract a ‘fast-halo’ effect of

.

Normalpath

}h(r)

with removed

Lithosphere

l-root50 km depths

=

signal0 km

net PLUMEpattern

similar between 60-140km.(Rayleigh wave inversion)

Latit

ude

Longitude West

Latit

ude

dVs/Vs [%]

Vs=4.23 km/s

120 km

16

18

20

22

24

26

160 158 156 154 152 150

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111 105

a �1.5–2% fast (�200 km-thick) halo-region to the NW of theHawaiian plume conduit, which is exactly the magnitude of theeffect seen in Fig. 4b where the fast halo disappears to a near-zerolevel within the quadrant covered by the Hawaiian swell-root.Fig. 4d and f sketch our preferred scenario in which the totalPLUME anomalies are due to a vertical integration of the wave-speed effects of a 4300 km deep plume stem, �300 km deepplume bump relief, and shallow �50–150 km deep hotspot swelleffects. In this interpretation, the fast wavespeed plume bumpsignal should be visible everywhere except in the NW quadrantwhere it is masked by the slow wavespeed effects of the Hawaiianswell-root. Furthermore, the surface wave inversion showsthat 40–140 km depth anomalies away from the swell are only�0–0.5% faster-than-average and hence contribute only a smallamount (�10%) to the total fast-halo signal.

3. Numerical exploration of a PFA

The idea of a plume-fed asthenosphere is almost as old as themantle plume theory; Deffeyes (1972) was the first to suggest thisimplication of hot mantle plumes. However, numerical experi-ments of mantle flow were not able to capture this flow structureuntil very recently, and are not able to capture the proper physicsof a buoyant and low-viscosity asthenosphere unless they canwell resolve both the downdragging of thin sheets of astheno-sphere around subducting slabs, and the proper magnitude ofbuoyant upwelling in narrow low-viscosity mantle plumes. Theinsidious difficulty of these two technical issues is that impro-perly resolved numerical experiments will look ‘plausible’, but beboth qualitatively and quantitatively wrong in their predictedstructures and flowrates of large-scale mantle circulation.

3.1. Necessary grid resolution to create PFA-like structures in mantle

flow simulations

The technical issue of the grid resolution needed to resolveasthenosphere downdragging by sinking slabs is the easier one toaddress, because it can be isolated and explored with 2D numer-ical experiments. We have done this (Morgan et al., 2007), andfound that the buoyant downdragged sheet is anticipatedto be of order �10–20 km thick for a 1018–1019 Pa-s buoyantasthenosphere. A code must be able to resolve boundary layer flowat this scale near the slab, flow that occurs in an environment withsharp and strong (up to 1000-fold) variations in viscosity. If the

Fig. 4. Reinterpretation of the PLUME experiment’s (Wolfe et al., 2009) inversion fo

inversion for Vs structure beneath Hawaii. This cross-section is quite similar to all oth

surrounding the central plume conduit anomaly, while only the central slow plume con

et al. (2009) for further information. (b) PLUME two-step inversion for Vs structure with

We think this inversion produces amplitudes closer to the magnitude of the true she

mantle. It is also easier to determine from this figure the portion of the wavespeed an

where the basal relief is induced by buoyancy forces within the underlying buoyant p

resolution are tending to smear anomalies throughout the upper mantle and transition

(50–660 km)-thick interval will lead to more reasonable inferences for wavespeed a

�310 km-deep base of the asthenosphere. (e.g. the plume conduit would only exist in

(c) Surface shear wavespeed inversion of PLUME network data at a cross-section for 120

from 60 km to 140 km (Laske et al., 2011). For reference the location of the Hawaiia

information. (d) Map-view sketch of our preferred interpretation for the PLUME experim

through these three horizontal slices. (e) Lateral Vs scenario assumed in the PLUME

wavespeed plume conduit. Note that this effect cannot be easily explained by shearwave

halo effect. (f) The pattern of relief at the base of a buoyant PFA that would be induce

produce a fast travel-time halo in the regions where the base is uplifted by the buoya

vertical averaging distance L�200 km, �2%-fast Vs from panel (b) (from inversion as

anomalies shown in Panel b), and 6–10% PFA-mesophere Vs contrast (consistent with

Dziewonski, 2008); and the Hawaiian plume Vs anomaly in (b)) would imply that �40–

within the Hawaiian plume conduit. This relief has the similar amplitude and spatia

�100–150 km-diameter plume conduits. (see also Fig. 5b and Supplemental Fig. 2) (g) T

also shown by the solid red line in panel 5c. Similar scale relief is also seen in fully 3D

grid does not include of order �4 km grid resolution in this region,the result will be that too much asthenosphere is downdraggedwith the slab, resulting in the absence of partial asthenosphericreturn flow from the trench. The grid resolution needed toproperly model the physics of ascending low-viscosity mantleplumes is less well known, but likely to be less critical as long asplume conduits are more than �100 km in diameter, with velocityerrors o0.7% for 3D experiments of variable-viscosity plumeupwelling (See Fig. A1 and Appendix). Apart from the need forwell-resolved 3D experiments, a further difficulty is that it isunclear if many aspects of the large-scale influence of plume flowand slab entrainment can be studied in isolation from D0 0 andasthenospheric flow. Some boundary layer theories have alreadybeen explored to study plume upwelling (e.g. Liu and Chase, 1990;Loper and Stacey, 1983; Sleep, 1992).

3.2. A PFA does spontaneously form in experiments with sufficient

numerical resolution

We are beginning to explore the dynamics of a PFA in self-consistent 3D numerical experiments which include a thermalplume that rises from a low-viscosity D0 0 to a low viscosity PFA(Shi and Morgan, 2009; Shi et al., 2008). The numerical experi-ments build on numerical techniques developed by Hasenclever(2010) during his Ph.D. work. They use an unstructured finiteelement mesh that is designed to accurately resolve downdrag-ging of a thin asthenosphere sheath around the subducting slaband upwelling within the buoyant and low-viscosity plumeconduit. Fig. 5d (and Supplemental Fig. 1) shows the results ofan initial numerical experiment. This idealized experiment showsmany features that are consistent with the above observations ofPFA-related dynamics: (1) Here too asthenosphere resists beingpulled down by the subducting slab which results in partialasthenosphere counterflow from the trench; (2) a thin sheet ofasthenosphere is downdragged below the subducting slab;(3) there is a plume conduit ‘bump’ of relief at the base of thebuoyant asthenosphere, and (4) there is an inversion in potentialtemperature between hotter asthenosphere and cooler under-lying mantle.

4. Discussion

We hope that this review of these recent seismic observationshas made a compelling case that it is time to at least seriously

r lateral seismic shearwave variations beneath Hawaii. (a) PLUME (their Fig 2b)

ers between 100 and 400 km depths that all show a similar fast wavespeed halo

duit anomaly is seen on deeper depth-slices between 500 and 1200 km. See Wolfe

as much structure as possible forced to lie between 50 and 250 km (their Fig. S9b).

ar wavespeed anomalies between the Hawaiian plume conduit and surrounding

omalies actually associated with relief at the base of the buoyant asthenosphere,

lume conduit—see panel 4f for details. If inversion smoothing and lack of vertical

zone as we suspect is occurring here, then a �200 km-thick instead of a 610 km

nomalies because, in our interpretation, the plume conduit only lies below the

the �350 km interval between �310 and 660 km depths as sketched in panel 4f.)

km depth. Similar anomalies are seen on horizontal depth slices spanning depths

n hotspot swell is shown by the dashed line. See Laske et al. (2011) for further

ent’s observed shearwave anomaly pattern. Panel 4f shows a vertical cross-section

inversion—which implausibly would imply that a ‘fast’ halo surrounds the slow

anisotropy as vertical stretching near the conduit would lead to a slow shearwave

d by the buoyancy within the underlying plume conduit. This dynamic relief will

ncy within the underlying plume conduit. Using the equation in the text with a

suming L¼200 km, e.g. the 200 km thick-layer assumed to have the wavespeed

PREM (Dziewonski and Anderson, 1981); Nettles and Dziewonski (Nettles and

70 km of ‘dynamic’ relief at the base of the PFA is being induced by the buoyancy

l variation to that predicted by our 2D axisymmetric and 3D PFA models with

he plume bump predicted by one of the 2D axisymmetric numerical experiments,

PFA experiments (cf. Fig. 5d, Supplemental Fig. 1b).

Ridge Axis

Trench/Slab

Distance from plume center (km)

Dep

th (k

m)

0 50 100 150 200 250 300 350 400 450 500

150

200

250

300

350

400

insulating +no slip (u=w=0)

asthenosphere

stress free outflow

insulating +free slip (u=0)

insulating + free slip (w=0)w(r)prescribed inflow velocity w(r) and inflow temperature T(r)

T(r)

free

slip

(axi

s of

sym

met

ry)

plum

e co

ndui

tρ= ρ(T)

mesosphere

z, w

r, u

0 50 100 150 200 250 300 350 400 450 500-400

-350

-300

-250

-200

-150

Distance from plume center (km)

Dep

th (k

m)

Lines show 1020 Pa-s interface

Lines show 1020 Pa-s interface

Fig. 5. Examples of 2D axisymmetric and 3D numerical experiments that spontaneously generated ‘‘Plume Bump’’ relief around the plume inlet to a PFA. (a) The

idealization and boundary conditions used in the 2D axisymmetric experiments to explore the factors shaping the amplitude and wavelength of the dynamic ‘plume bump’

relief at the base of the plume-fed asthenosphere surrounding the inlet to an underlying mantle plume. We use a top velocity boundary condition that treats the base of the

lithosphere as the top of the computational region (i.e. insulating and no slip). (b) Examples of several axisymmetric experiments where the plume flux and plume

viscosity have been covaried to generate the same diameter plume conduit. Plume density contrast was 1%, mantle viscosity was 1021 Pa-s, and no thermal diffusion effects

were included in these experiments. Each dashed vs. solid line pair has the same diameter of their steady-state plume conduit, each pair also shows almost exactly the

same plume bump relief. (c) Examples of several axisymmetric experiments where mantle density and viscosity are temperature dependent (thermal expansion coefficient

a¼3�10�5 K�1, thermal diffusivity k¼10�6 m2/s, activation energy Ea¼500 kJ/mol). Basal plume flux and plume inflow temperature are shown in the legend. Note the

strong similarity of these patterns to those in 5b that more directly show the guiding physics of the ‘plume bump’ effect. (d) Snapshot from a 3D experiment that includes

both a high-resolution boundary-layer region of slab-dragdown and a high-resolution low viscosity plume conduit within a numerical experiment containing all elements

of mantle flow from ridge accretion to slab subduction. This experiment developed a stable PFA. The relief at the base of the PFA (shown by the 1310 1C isosurface) is

contoured in depth (km). A plume bump, the depression of the PFA near the trench, and uplift near the ridge axis are clearly visible. Note that, for clarity, this figure does

not show the overlying accreting and moving lithosphere (cf. Shi (2012) and Supplemental). In this experiment, oceanic lithosphere moves at 100 km/Ma, so the plate is

60 My old when it enters the trench, with a thermal boundary layer thickness of �80 km. Additional information on the boundary conditions, mesh resolution, and the

unstructured mesh used in this calculation are given in Supplemental Fig. 1. The message we want to stress with this panel is that the plume bump effect is also evident in

more complex and realistic numerical experiments that include a ridge, trench, and moving, accreting oceanic lithosphere. (For interpretation of the references to color in

this figure, the reader is referred to the web version of this article.)

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111106

consider the possibility that the Earth has an inversion in itspotential temperature at the base of the sub-oceanic astheno-sphere, as long as the asthenosphere’s source is coming fromhotter-than-average parts of the mantle (plumes), while theunderlying mantle has a cooler temperature closer to theaverage temperature of the mantle. Note that the key observablefor a plume-fed asthenosphere is not the top lithosphere–asthenosphere boundary that should exist in both a PFA andother hypotheses for the origin of the asthenosphere, but, instead,significant internal flow layering associated with the base of thePFA. Note that a simple lithosphere–asthenosphere conductive

temperature profile can fit the depth-dependence of wavespeedvariations across the lithosphere–asthenosphere boundary (Stixrudeand Lithgow-Bertelloni, 2005)—excepting perhaps near mid-oceanridges, the presence of partial melt is not required to explain theseismic wavespeed variations across the lithosphere–asthenosphereboundary. In contrast, the seismic wavespeed gradients between�225 and 325 km below the oceanic lithosphere are simplytoo large to be consistent with mineral physics observationsfor an isochemical mantle with an adiabatic temperature gradient(Stixrude and Lithgow-Bertelloni, 2005)—yet would be expectedif the asthenosphere were indeed plume-fed.

Box 1–Shear wavespeed contrast between the sub-Pacific astheno-sphere and underlying mantle.

The 1D PREM model (Dziewonski and Anderson, 1981) andGaherty et al.’s (1999) 1D model for Tonga–Hawaii uppermantle shear wavespeeds predict a �6% reduction betweenthe asthenosphere and underlying mesosphere, while Nettlesand Dziewonski (2008) invert for as much as a �10% reductionbeneath the Pacific. Note that a �46% contrast beneath theHawaiian plume-fed asthenosphere and underlying mantle isalso directly seen in PLUME (Wolfe et al., 2009) results, if wesay that their measured Hawaiian-plume-to-mesospherecontrast (6% in Fig. 4b) is a reliable measure of the localHawaiian plume-fed-asthenosphere (PFA)-to-underlying me-sosphere variation in wavespeed. Their observed lateraltravel-time anomalies probably imply a 46% variation, sincethe inversion assumes a strong lateral plume-to-outside-plume variation within the �100–300 km asthenosphereinterval (shown in Fig. 4e) that would not exist in the simplestPFA scenario.

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111 107

Of course individual arguments can and have been crafted tointerpret many of the above observations. In fact, the conven-tional scenario for the asthenosphere is a compendium of specialeffects; the seismic low-velocity zone is presumed to be due tothe presence of partial melt in the asthenosphere but not deeper(Anderson, 1989), the strong change in seismic attenuationbetween asthenosphere and underlying mantle is presumed tobe related to a sharp increase in grain-size below the astheno-sphere (Faul and Jackson, 2005), and the viscosity increase belowthe asthenosphere is presumed to be due to a change betweendislocation creep within the asthenosphere and diffusion creepbelow the asthenosphere (Karato and Wu, 1993). But all can besimply explained—in our opinion, more simply explained—by thesingle unifying hypothesis that these observations reflect naturalcharacteristics of a plume-fed asthenosphere that has a higherpotential temperature than underlying mesosphere.

The only type of observation that apparently contradicts thePFA hypothesis are petrological observations (Putirka, 2005;Herzberg et al., 2007) suggesting that Hawaii and Iceland have�150–2001 higher potential temperatures than the mid-oceanridge basalt (MORB) source. In the PFA hypothesis, the initialpotential temperatures of the MORB and plume sources might bethought to differ only due to the latent heat consumed by plumemelting. Below we show how there could be a systematic biaswhere the hottest plume material is most likely to be draggedaway by the overriding plate as it becomes a hotspot swell-rootthat is a part of the compositional lithosphere (cf. Morgan et al.,1995a). The hottest material is hence least likely to replenish thePFA. Before discussing this mechanism is detail, note that it ispossible that Putirka’s (2005) and Herzberg et al.’s (2007) resultsare incorrect, since they differ significantly from Falloon et al.’s(2007) results based upon a similar petrological technique—thesemeasurements can have spurious high-T artifacts if olivine fromentrained xenocrystals of mantle wallrock is included within acompositional measurement. However, assuming they are cor-rect, we interpret this observation as follows—with an argumentthat simultaneously explains the existence of a hotspot swellaround Hawaii (Morgan et al., 1995a; Yamamoto and Morgan,2009). Thermal plumes are likely to have a hot core and coolerrim. Earlier, we proposed that the hot core melts enough beneathHawaii (and Iceland) to generate a desiccated and strong restiteroot of ‘plume core material’ that viscously couples to the litho-sphere, where it spreads out to form the sublithospheric restiteroot to the Hawaiian swell (Morgan et al., 1995a; Yamamoto andMorgan, 2009) and Iceland platform, just as shallower melting

and melt-extraction beneath a mid-ocean ridge generates therestite root forming the ‘compositional lithosphere’ (Hirth andKohlstedt, 1996; Morgan, 1994, 1997). In contrast, the coolerouter regions of the Hawaiian plume do not melt enough beneathHawaii to desiccate and increase its viscosity, and it is this coolerfraction of plume material that preferentially replenishes theasthenosphere around Hawaii. Perhaps the average temperatureof asthenosphere leaving the Hawaiian plume towards the EastPacific Rise (EPR) is still �50 1C higher than the average MORB-source temperature, but during its migration from plume to EPR,it loses heat to overlying lithosphere and underlying mesosphere tocool by �50 1C. At on-ridge plumes like Iceland (and the Galapagos,etc.), the asthenosphere from the plume-rim is already at the ridge,hence does not have time to cool, and the melting of this seemingly‘anomalously hot MORB source’ produces the �50 1C hotterenhanced melting and crustal production that characterizes ridgesegments near on-ridge plumes.

5. Conclusion

If a plume-fed asthenosphere indeed exists, this would havesignificant consequences for the dynamics of mantle convectionand melting, and the links between surface plate motions andmantle convection. Since this asthenosphere is replenished byupwelling plumes and consumed by accretion into eventualsubducting slabs and dragdown alongside subducting slabs, flowwithin the PFA will be strongly shaped by plume feeding, platemotions, the spatial distribution of accretion into overlying litho-sphere, and slab dragdown effects (Morgan et al., 2007, 1995b;Yamamoto et al., 2007). The PFA would form a decoupling layerbetween deeper ‘‘mesosphere’’ and overlying plate motions(Morgan et al., 1995b). Cratons and subducting slabs would bethe only places where plates strongly couple to the viscousmesosphere (Morgan et al., 1995b), as perhaps is reflected inthe striking contrasts in seismic wavespeed and seismic aniso-tropy beneath cratons and oceanic lithosphere (Gung et al., 2003).The presence or absence of PFA beneath a rifting continent couldlead to either a rifting-related continental flood basalt or theformation of a non-volcanic rifted margin, respectively (Restonand Morgan, 2004). The geochemical evolution of the Earth wouldbe changed by the two-stage melting process where upwellingplume material typically first melts a small amount at the plume-related hotspot, then a larger amount when this asthenospherematerial later upwells beneath a mid-ocean ridge (Morgan andMorgan, 1999). Time-variations in the global plume flux wouldlead to global variations in the thickness of the PFA, potentiallychanging the drag-resistance to plate motions, hence plate speeds(Morgan et al., 1995b). If we conclude that the above observationsare indeed strong support for the existence of a PFA, this will leadto a dramatic change in our understanding of the roles of mantleplumes and of the asthenosphere and D0 0 boundary layers inEarth’s mantle convection.

Acknowledgment

Joerg Hasenclever was supported by DFG funding Ho1411 17-1, 2.

Appendix A

A.1. Governing equations and tests of the numerical methods

The numerical experiments presented in this paper have beenconducted using 2D axisymmetric and fully 3D numerical models

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111108

for viscous flow and thermal evolution of the mantle. Next, thegoverning equations and the numerical methods are brieflydiscussed. The 2D axisymmetric flow solutions follow the FiniteElement approach described in Hughes (2000), with quadraticvelocity–linear pressure P2–P1 Taylor-Hood elements. This is nowa fairly routine approach to solve for 2D variable viscosity slowviscous flow (Dabrowski et al., 2008). The 3D elements usea tetrahedral version of the P2P1 element combined with aniterative solution technique that is briefly summarized below. Forfurther details the reader is referred to the Ph.D. thesis byHasenclever (2010) and to Hasenclever et al. (2011).

We idealize the mantle as an incompressible, viscous fluidwith infinite Prandtl number and apply the Boussinesq approx-imation. Using index notation with the Einstein summationconvention, the equations for viscous Stokes Flow and the energyequation can be written:

@ui

@xi¼ 0 ðA:1Þ

@p

@xi¼@tij

@xj�rgi ðA:2Þ

tij ¼ Z@ui

@xjþ@uj

@xi

� �ðA:3Þ

@T

@t¼ k @

2T

@x2i

�ui@T

@xiðA:4Þ

respectively, with (A.1) satisfying conservation of mass by impos-ing incompressibility, (A.2) describing the force balance to ensureconservation of momentum, (A.3) being the constitutive law, and(A.4) conserving thermal energy. Here tij denotes the deviatoricstress tensor, Z dynamic viscosity, ui individual velocity compo-nents, xi physical coordinates, p pressure, gi the components ofgravitational acceleration (here only non-zero in the vertical x3

direction), r density, T temperature, k thermal diffusivity, and t

time. Buoyancy-driven flow is caused by density variations thatarise from temperature differences:

r¼ r0ð1�aðT�T0ÞÞ ðA:5Þ

where a¼3�10�5 K�1 is the thermal expansion coefficient, T is thetemperature of the mantle, and r0¼3300 kg m�3 and T0¼1200 1Care reference density and reference temperature of the mantle,respectively. We consider a temperature dependent mantle rheologythat can be described by an Arrhenius-type relation:

ZðTÞ ¼ Z0expEA

RT½K�

� �ðA:6Þ

where EA ¼ 500 kJ=mol is the activation energy, R the universal gasconstant, T[K] the mantle temperature in degrees Kelvin, and Z0

the reference viscosity. For simplicity, the pressure- and stress-dependence of mantle viscosity is neglected here.

Eqs. (A.1)–(A.4) are solved numerically using 2D and 3Dnumerical codes for parallel computing clusters developed byHasenclever (2010) that are coded in MATLAB (http://www.mathworks.com). The equations defining the velocity–pressure pro-blem (A.1)–(A.3) are discretized using the Galerkin finite elementmethod with triangular (in 2D) and tetrahedral (in 3D) P2–P1Taylor-Hood elements with continuous quadratic velocity andlinear pressure interpolation functions. The 2D code is very similarto the ‘‘MILAMIN’’ code presented in Dabrowski et al. (2008);velocity–pressure equations are decoupled using a standard tech-nique known as the consistent penalty method that is described inintroductory Finite Element texts (e.g. Hughes, 2001) and alsosummarized by Hasenclever (2010). The only slight novelty in 2Dis that we perform the consistent penalty method on a continuous

pressure formulation. This results in the incorporation of theinverse of the full mass matrix during the creation of theconsistent penalty stiffness matrix, rather than the element-wisemass-matrix inversion that is possible for a discontinuous pres-sure formulation. While the resulting matrix equations for con-tinuous and discontinuous pressure formulations look the same inalgebraic notation, the continuous pressure code implementationis slightly different because the pressure mass matrix is first fullyassembled, before its inverse is determined to become a term inthe consistent penalty stiffness matrix (cf. Hasenclever, 2010). In2D, we use a Cholesky direct solver to solve the resulting matrixequations. In 3D, a different method is chosen, because the largermatrix problem size requires an iterative solution technique thatperforms much poorer in combination with the consistent penaltymethod. Instead, in 3D the equations for velocity and pressure aredecoupled using a Schur complement formulation (Maday andPatera, 1989), and a multigrid-preconditioned conjugate gradientalgorithm is used to solve the resulting matrix equations (seeHasenclever (2010) and Hasenclever et al. (2011)). The 3D codewas parallelized using the MPI-wrapper routines in MATLAB’sParallel Computing Toolbox.

The advection–diffusion Eq. (A.4) is solved using operatorsplitting (cf. Hasenclever, 2010). The diffusion part is discretizedusing a Galerkin finite element formulation based on the samequadratic-order elements that are used for the velocity problem.An implicit time approximation scheme is used for its stability.The resulting matrix equations are solved using a direct Choleskysolver and a conjugate gradient algorithm in 2D and 3D, respec-tively. Advection of temperature is done by a Semi-Lagrangeadvection scheme with second-order accurate Predictor–Correctorback tracking in combination with a cubic smooth interpolationon unstructured 2D and 3D meshes (Shi, 2012) that significantlyreduces artificial interpolation-related numerical diffusion in theupwind direction.

The unstructured finite element meshes were generated using thecommercial software GiD (http://gid.cimne.upc, Version 8, 2007).

Numerical accuracy and resolution tests

Here we assess the accuracy of both the 2D axisymmetric and3D codes by solving for buoyancy driven viscous flow in anelongated cylindrical pipe. For the isoviscous case, the 2D axisym-metric and 3D solutions are compared against the analyticalsolution for Poiseuille flow (e.g. Turcotte and Schubert, 2002,p. 232). The results are shown in Fig. A1. To verify the numericalmethod for a pipe flow with temperature-dependent viscosity wedissect the channel into thin shells of constant viscosity and use afourth-order Runge–Kutta scheme (RK4) to solve for the velocityprofile (Turcotte and Schubert, 2002, p. 232):

du

dr¼

r

2Zdp

dz

� �ðA:7Þ

where r is the radial direction, Z dynamic viscosity, p pressure,and z the vertical coordinate parallel to the pipe’s central axis. Weapply the boundary condition u¼0 at the pipe walls r¼rmax. Weuse this semi-analytical RK4 solution as the ‘‘exact’’ solution forthe variable viscosity tests. Note that a uniform density-contrast(i.e. no temperature dependent density) is used here because (A.7)is only valid for dp=dr¼ 0. The results are shown in Fig. A1c and d.

For the isoviscous case, the error in the 2D solution is on theorder of 10�14%. This is because the dynamic pressure solution ofthis problem is zero. In addition, with the same zero dynamicpressure starting condition, no pressure iterations are needed sothat the final solution is reached after a single Cholesky solution.The same would be true for the 3D solution with a smoothdiscretization of the cylindrical plume conduit. However, because

0 10 20 30 40 50 60 70 80 90 1000

500

1000

1500

2000

2500

3000

Distance from pipe center (km)

analytical solution2D axis−symmetric3D

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

Distance from pipe center (km)

2D axis−symmetric3D

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Distance from pipe center (km)

2D axis−symmetric3D

0 10 20 30 40 50 60 70 80 90 1000

1000

2000

Distance from pipe center (km)

0 10 20 30 40 50 60 70 80 90 1001e18

1e19

1e20

1e21

1e22

Vis

cosi

ty(P

a−s)

RK4 solution2D axis−symmetric3Dviscosity profile

Vel

ocity

err

or (%

)

d

Ver

tical

vel

ocity

(mm

/yr)

a

Ver

tical

vel

ocity

(mm

/yr)

cV

eloc

ity e

rror

(%)

b

Fig. A1. Numerical tests to verify the potential accuracy of the 2D axisymmetric and 3D numerical models of flow in a plume conduit. (a) Test problem 1: Buoyancy-driven

viscous flow through a 400 km long cylindrical pipe with radius 100 km. Nodal vertical velocity components of the 2D (red dots) and 3D solution (blue squares) are

compared against an analytical solution (cf. section 6–15 of Turcotte and Schubert (2002)) for Poiseuille flow (black line). (b) Error of the vertical velocity components in

the 2D axisymmetric and 3D solutions. (c) Test problem 2: Flow through the same pipe but with viscosity varying as a function of pipe radius (viscosity variation shown by

the dashed black line). The viscosity profile was calculated using Eq. A6 and a Gaussian-shaped temperature profile mimicking a mantle plume with hot core temperature.

A semi-analytic solution was derived using a fourth-order Runge–Kutta method to solve Eq. A7. (d) Error of the vertical velocity components in the 2D axisymmetric and

3D solutions. In all cases, both the 2D and 3D numerical solutions predict velocities within 0.7% of the analytical or semi-analytical solution. The 2D and 3D numerical

experiments discussed in the text all have numerical grid resolution comparable to that in these numerical tests. (For interpretation of the references to color in this figure

legend, the reader is referred to the web version of this article.)

Distance from plume center (km)

Dep

th (k

m)

0 50 100 150 200 250 300 350 400 450 500

150

200

250

300

350

400

1400°C 6.3km3/yr1400°C 25.1km3/yr1600°C 6.3km3/yr1600°C 25.1km3/yr

solid : high resolution (~5 km in plume conduit, ~3 km near ‘bump’)dashed: low resolution (~7km in plume conduit, ~15 km near ‘bump’)

Lines show 1020Pa-s interface

Fig. A2. Resolution test to verify the ‘plume bump’ amplitude and wavelength. Predictions of lower resolution experiments (dashed lines) are compared against higher

resolution experiments (solid lines). Differences between runs of different resolution are mainly caused by poorly resolved mantle flow in narrow plume conduits, which

then leads to incorrect viscous stresses on the surrounding mantle. Nonetheless, the topography at the base of the PFA is clearly visible in all calculations. The high-

resolution mesh (�5 km within the plume conduit, �3 km near the ‘bump’) has been used for all 2D axisymmetric calculations presented in this study. (For interpretation

of the references to color in this figure, the reader is referred to the web version of this article.)

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111 109

J.P. Morgan et al. / Earth and Planetary Science Letters 366 (2013) 99–111110

we use elements with straight faces the discretized pipe boundaryis not a perfect cylinder but instead composed of piecewise planarsegments. Consequently the numerical and analytical solutionsdiffer slightly near the pipe walls (cf. Fig. A1b). Nonetheless, themaximum errors are always less than �1%.

For the variable viscosity tests the highest velocities occur inthe central low viscosity region of the pipe away from the walls,so that the face-segmented 3D pipe geometry has a smallerinfluence on the solution. The largest 3D errors are less than0.7% and the 2D axisymmetric solutions have errors always lessthan 0.2%.

We also conducted several resolution tests to make sure thatthe ‘‘plume bump’’ is a well-resolved numerical feature. Fig. A2compares 2D axisymmetric experiments with different numericalresolutions for four parameter combinations. If flow in the plumeconduit is well resolved (e.g. green and blue curves), both experi-ments predict the same plume bump amplitude and wavelength.Differences arise if the plume conduit is too narrow (i.e. low plumeflux and low viscosity plume material), in which case the plumeflux itself and consequently the viscous stresses acting on themantle surrounding the conduit are numerically inaccurate. Thisexplains the larger deviations for experiments with a narrowplume conduit (red and black lines), however, even in these casesthe differences are still small compared to the amplitude andwavelength of the ‘plume bump’. Note that the high-resolutionmesh was used for all 2D experiments presented in this study.

Appendix B. Supplementary materials

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.epsl.2013.02.001.

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