MANTLE CONVECTION IN TERRESTRIAL PLANETS …...Mantle convection is the dominant mech-anism by which...

MANTLE CONVECTION IN TERRESTRIALPLANETS

Elvira Mulyukova & David BercoviciDepartment of Geology & GeophysicsYale UniversityNew Haven, Connecticut 06520-8109, USAE-mail: [email protected]

May 15, 2019

Summary

All the rocky planets in our Solar System, in-cluding the Earth, initially formed much hot-ter than their surroundings and have since beencooling to space for billions of years. The result-ing heat released from planetary interiors pow-ers convective flow in the mantle. The man-tle is often the most voluminous and/or stiffestpart of a planet, and therefore acts as the bottle-neck for heat transport, thus dictating the rate atwhich a planet cools. Mantle flow drives geo-logical activity that modifies planetary surfacesthrough processes such as volcanism, orogene-sis, and rifting. On Earth, the major convectivecurrents in the mantle are identified as hot up-wellings like mantle plumes, cold sinking slabsand the motion of tectonic plates at the surface.On other terrestrial planets in our Solar System,mantle flow is mostly concealed beneath a rockysurface that remains stagnant for relatively longperiods of time. Even though such planetary

surfaces do not participate in convective circu-lation, they deform in response to the underly-ing mantle currents, forming geological featuressuch as coronae, volcanic lava flows and wrin-kle ridges. Moreover, the exchange of mate-rial between the interior and surface, for exam-ple through melting and volcanism, is a conse-quence of mantle circulation, and continuouslymodifies the composition of the mantle and theoverlying crust. Mantle convection governs thegeological activity and the thermal and chemicalevolution of terrestrial planets, and understand-ing the physical processes of convection helpsus reconstruct histories of planets over billionsof years after their formation.

Keywords

Mantle convection, terrestrial planets, planetaryevolution, plate tectonics, volcanism

1

Oxford Research Encyclopedia of Planetary Science Mantle Convection

Mantle Convection

The interiors of terrestrial planets are comprisedof three main layers: a metallic core at thecenter, overlain by a rocky mantle, whichis in turn enveloped by a rocky crust. Theexact compositions and thicknesses of theselayers, and their thermal and chemical evolu-tion through time, vary from planet to planet,depending on their size, distance from the sun,formation history, etc. However, common to allthe terrestrial planets in our Solar System, andeven to some of its larger moons, is that theirmantles undergo convective motions, whereinhot buoyant material rises from the deep interiorand the heavy cold material near the surfacesinks.

Mantle convection is the dominant mech-anism by which planets cool and undergochemical segregation. The flow of the mantleinduces motion in the overlying crust, whichcan lead to such phenomena as volcanoes,earthquakes and, uniquely for Earth, plate tec-tonics. Ultimately, mantle convection governsthe evolution of planetary surfaces and interiors.

The fundamental features of any convectivesystem include cold and hot boundaries (suchas the outer and inner boundaries of the mantle,respectively), and a fluid between the twoboundaries on which gravity acts to move hotand cold material. Hot upwelling and colddownwelling vertical currents are connectedalong the horizontal boundaries by the hotand cold thermal boundary layers (TBLs): ahot TBL at the bottom, and a cold TBL at thetop. The TBLs are where heat is conductedrapidly across the boundaries into or out of theconvectively stirred mantle. The large thermalgradients across the TBLs, compared to if thetemperature increased gradually from top tobottom, is what makes thermal convection suchan efficient mechanism for heat transfer.

In planetary mantles, the convective currentscan deform and chemically modify the top andbottom boundaries; their effect on the planetarysurfaces is of particular interest, since thatpart can be most readily observed and usedto interpret the workings of the underlyingmantle. For example, hot upwelling mantlecurrents can generate surface uplift, seen astopographic highs, or induce volcanic activity,when hot material melts and erupts whileapproaching the surface. Extruded lavas onplanetary surfaces record the presence andevolution of hot mantle regions, and can beused to infer mantle temperature, chemistryand flow velocity. Similarly, the downwellingcurrents can give rise to topographic lows, asthe sinking mantle material pulls the surfacedown from below. In the possibly unique caseof the Earth, the top cold thermal boundarylayer is subdivided into tectonic plates, whichare moving relative to each other and sink intothe mantle at subduction zones. The rate atwhich a planet recycles cold material into themantle largely determines its cooling rate.

Naturally, more observations are available forthe Earth’s surface and mantle than for otherplanets. Thus, our understanding of planetaryinteriors, and their surface manifestations, islargely shaped by what is known about ourhome planet, as well as by our understanding ofthe fundamental processes that govern mantleconvection, such as the physics of heat transportand rock deformation.

In what follows, the different components ofconvective mantle flow on Earth are described,tracking the material trajectory as it forms tec-tonic plates traversing the Earth’s surface, whichthen sink into the mantle as cold subductingslabs, that eventually impinge on and flow lat-erally along the core-mantle boundary; some ofthis material ascends across the mantle again asmantle plumes, while most of it ascends broadlyas part of the global tectonic circulation, thus

2


closing the loop. The convective currents onother terrestrial planets are discussed as well,albeit our understanding of these is less certaindue to fewer observational constraints. We willthen survey the underlying physics of convec-tion, which forms the basis for understandinghow mantle convection is both similar to anddifferent from classical theories of convectiveflow, and how this physics lets us infer mantledynamics on Earth and other terrestrial planets.

Mantle Top to Bottom

One of the greatest challenges in the studiesof planetary mantles is their inaccessibilityfor direct observations. The structure andphysical properties of planetary interiors haveto be inferred from indirect measurements suchas satellite observations of gravity, surfacetopography and magnetic fields [Phillips andIvins, 1979], see Sohl and Schubert [2015]for a recent review. In addition, analysis ofmeteorites collected at the Earth’s surfaceconstrain the chemistry of some other planets,as well as the building blocks of our ownplanet. Earth is special in this sense, because, inaddition to the remote measurements, scientistshave access to a wealth of geological samplesand can perform seismological observationsof the interior. Most of what we know aboutEarth’s interior is obtained indirectly from theanalysis of seismic waves, which are triggeredby powerful earthquakes and propagate throughthe mantle and core. Seismic waves travel fasterthrough rocks that are stiffer. In the mantle, therocks become denser, and therefore stiffer, whenthey are exposed to higher pressures at greaterdepths. The resulting increase with depth of themeasured seismic velocities can thus be used toinfer mantle’s density structure. When seismicwaves pass through sharp changes in materialproperties (e.g., density), such as the boundariesbetween the felsic crust and the mafic mantle,or the silicate mantle and the metallic core,

they get partially reflected, and these reflectedsignals allow to determine the boundaries of themain layers that make up the Earth’s interior.Furthermore, hot rock is typically softer andmore easily compressed, hence seismic wavesare slower passing through such material;the opposite is true for cold rocks which arestiffer. The resulting seismic wave travel timevariations can be used to infer pictures of themantle showing “hot” (seismically slow) and“cold” (fast) regions, appearing much like anultrasound of the mantle.

The distance to the center of the Earth isapproximately 6400 km, of which the mantlecomprises about 2900 km, sandwiched betweenthe thin crust (average thickness of about 20km: 7 km in the ocean and 40 km in continents)and iron core (about 3500 km radius). Althoughthe core is thicker, the mantle envelops it andthus the mantle constitutes about 80% of ourplanet’s volume (Figure 3). The similar sizeand density of Earth and Venus, which hasa total radius of about 6100 km, makes itlikely that the thicknesses of the venusian coreand mantle are similar to those of Earth. Atabour 3400 km total radius, Mars is the thirdlargest terrestrial body in the Solar system. Thecombined measurements of the martian mass,moment of inertia (i.e., inertial resistance tobeing spun), and chemical analysis of martianmeteorites, constrain the radius of the martiancore to be about 1400 km, leaving about 1900km to be taken up by the mantle, and 100 kmby the crust [Harder, 1998]. The radial massdistribution of Mercury is unusual, comparedto other terrestrial bodies, in that most of it isoccupied by a dense metallic core, which isabout 2020 km in in radius, overlain by a 400km thick mantle [Hauck et al., 2013] and a 50km thick crust [Smith et al., 2012].

While the metallic cores likely separatedout of the mantles early in planetary histories,i.e., within the first few tens of Myr of the life

3


EarthVenus

MarsMercury

Figure 1: Cutaway views of the interiors of four terrestrial planets in the Solar System. Reproduced fromhttp://solarviews.com/cap/index/cutawaymodels1.html

of the Solar System [Kleine et al., 2002], thesegregation of the crust out of the mantle is stillongoing, as evident in recent volcanism, seenon all terrestrial planets except for Mercury,where global magmatic activity appears to haveceased about 3.5 Gyr ago [Namur and Charlier,2017]. Mantle melting at shallow depths (withthe exact depth depending on temperature andcomposition) is induced by decompression,and leads to magmatism that forms the mafic(or silica poor) crust (such as the oceanic cruston Earth). Specifically, as upwelling mantlematerial approaches the surface, towards lowerpressure, its own temperature changes little(decreasing slightly by “adiabatic” decompres-sion, further explained in the Section “Basicsof Thermal Convection”), but the temperatureat which it melts decreases more rapidly (inessence, decreasing the confining pressuremakes it easier for molecules to mobilize intoa melt). At a certain depth (usually between afew 10s to 100 km, depending on temperature)the upwelling mantle’s temperature exceeds themelting temperature and undergoes melting.The mantle is made up of different chemicalcomponents and each have their own specificmelting temperatures. The material that canmelt at higher pressures (usually more silica richmaterial with lower melting temperature) meltsfirst, freezes last and is typically chemically lessdense, and thus comes to the surface as lighter

crust. The more refractory mantle material(i.e., harder to melt, silica poor and heaviermaterial) may melt little if at all and much ofit stays in the mantle. Such ‘pressure release’melting in hot vertical currents, such as mantleplumes arising from the deeper mantle, or bypassive upwelling beneath mid-ocean-ridges(presently only known to occur on Earth), isvital for chemical segregation of the mantle anddevelopment of oceanic crust (and possibly thefirst kernels of proto-continental crust early inEarth’s history).

Melting at subduction zones (which isalso only known to occur on Earth) is morecomplicated than melting at mid-ocean ridgesor at hotspots, but is responsible for most ofthe production of continental crust [see alsoStein and Ben-Avraham, 2015]. For subductionzones, melting is facilitated by water. Tectonicplates entering a subduction zone have typicallybeen submerged under water for hundreds ofmillions of years. When the first basalts areextruded at mid-ocean ridges they react withwater and make hydrous minerals, such asamphibole and serpentine. Sediments washedoff continents and islands into the ocean arealso usually hydrated. When a plate reachessubduction zone, many of its hydrated mineralsare entrained with the slab into the mantle(though many sediments remain at the surface

4

http://solarviews.com/cap/index/cutawaymodels1.html


Earth

Venus

Mars

Mercury

Figu

re2:

Glo

balt

opog

raph

y(t

opro

w),

and

the

tota

lgra

vita

tiona

lano

mal

y(b

otto

mro

w)o

fthe

four

terr

estr

ialp

lane

tsin

the

Sola

rSys

tem

[mod

ified

from

Wie

czor

ek,

2015

].T

heto

pogr

aphy

isre

fere

nced

toth

ege

oid,

whi

chis

aneq

uipo

tent

ial

surf

ace

onw

hich

the

sum

ofth

egr

avita

tiona

lan

dce

ntri

fuga

lpot

entia

lene

rgie

sha

sth

esa

me

valu

e,an

dw

hich

onE

arth

wou

ldco

rres

pond

toth

ese

ale

vel.

to form accretionary prisms). Once the en-trained minerals reach about 100 km or more,they are unstable at the higher temperature andpressure conditions, and they release their waterinto the mantle wedge above the slab, whichin turn gets modestly hydrated. The hydratedmantle rock melts more readily than dry man-tle rock (hydrogen replacement weakens themineral bonds), and so even at the ‘moderate’mantle temperatures next to a cold slab, thedamp mantle material will partially melt, andthe melt phase percolates to the surface. Thisoriginal melt phase is basaltic (as typical ofmantle melts), but cooler than plume-derivedbasalts. Thus, when this cool/damp melt comesinto contact with crustal rocks (which formedby prior melting events), it remelts silica richminerals, which are the easiest to melt, butnot the more refractory silica-poor or ‘mafic’ones (e.g. dry basalt). The remelted silica richrocks are separated and ascend to produce, forexample, granitic magmas. Indeed, granitetends to be the final product of such repeatedmelting, and it is the primary component ofcontinental crust.

Except for the very small portions of themantle where melting takes place, most terres-trial mantles are currently comprised of solidrock, in spite of their fluid-like mechanicalbehavior over geological time scales. Thelarge thicknesses of these mantles (with theexception of Mercury) means that their con-stituent materials experience a large range oftemperature and pressure conditions with depth.For example, the mantles pressure on Earth(and likely similar on Venus) increases from topto bottom by about 140 GPa (about 1.4 millionatmospheres of pressure), and temperatureby 3500 K (probably less by a few hundredKelvin on Venus, due to its higher surfacetemperature); martian pressure and temperatureincrease by about 23 GPa and 2800 K acrossthe mantle [Schubert and Spohn, 1990; Harder,1998]; these extreme conditions strongly affect

5


the physical properties of rocks, including theirmineralogical structure, density, viscosity, etc.

Viscosity is the material’s resistance to de-formation under an applied force or stress. Thehigher the viscosity, the higher the resistance toflow. For example, the viscosity of water is onthe order of 10−3 Pa s and that of honey is about1 − 10 Pa s, both at room temperature, whilethat of the mantle ranges between 1019 − 1023

Pa s. Mantle viscosity varies with pressure,temperature and composition. While thereremains uncertainty about the compositionalvariations in the mantle, the depth-profiles ofpressure and temperature, at least for the Earth,are relatively well constrained. The viscosity ofmantle rocks increases with increasing pressure,but decreases with increasing temperature. Gen-erally, the strongest effect on viscosity is that oftemperature, which allows for many orders ofmagnitude variations in viscosity. However, formost of the mantle depth (excluding the TBLsin the top and bottom few hundreds of kilome-ters), temperature varies only gradually alongan adiabatic profile. Thus, the depth-profile ofviscosity is dominated by pressure-variations[Steinberger and Calderwood, 2006; Stein-berger et al., 2010]. For Earth, the combinedeffects of increasing pressure with depth withmineralogical phase transitions (discussed next)cause the viscosity to increase by up to threeorders of magnitude across the mantle.

Mantle minerals may have different geome-tries of atomic arrangement (crystal structures)at different pressures and temperatures. Chang-ing from one atomic arrangement to anotheris called a phase transition, or, commonlyfor the mantle, a solid-solid phase transition,since the material remains in a solid stateas it transforms to another phase. Thus, amaterial may have one crystal structure (orphase) at low pressures, but once the pressurereaches some critically high value, the materialorganizes into a more compact, higher density

state, which then has greater resistance tocompression. The first major phase changein the Earth’s mantle occurs at 410 km depth,where olivine (which is the major componentmineral of the upper mantle) transitions tothe same material with a wadsleyite structure[Katsura et al., 2004], and which involves amoderate 5 − 8% density increase [Dziewonskiand Anderson, 1981]. Wadsleyite changes toringwoodite at 520km depth [Ita and Stixrude,1992], with an associated 1 − 2% densityincrease [Dziewonski and Anderson, 1981]. Thelargest phase change occurs from ringwooditeto perovskite/magnesiowustite at 660km depth[Katsura et al., 2003], with a density increase of10−11% [Dziewonski and Anderson, 1981] andinvolves a viscosity increase by about a factorof 30 [Hager, 1984; Ricard et al., 1984]. The410km and 660km phase changes are the twomost remarkable, globally contiguous phasechanges in the Earth’s mantle, and the regionbetween them is called the Transition Zone,since it is where most of the mineralologicaltransitions occur, over a relatively narrowregion [Ringwood, 1991]. The mantle abovethe Transition Zone is typically identified as theUpper Mantle (although in some papers andbooks Upper Mantle includes the TransitionZone), and that below is the Lower Mantle.The temperature and pressure profiles, which,together with the composition, determinethe depth at which the phase transitions oc-cur, are more uncertain for the interiors ofthe other terrestrial planets. Nonetheless, ithas been estimated that the olivine to wads-leyite transition occurs around 450-580 and1000-1500 km depth on Venus and Mars,respectively, while the ringwoodite-perovskitetransition occurs at about 710 and 1910 kmdepth on Venus and Mars, respectively [Itoand Takahashi, 1989; Harder, 1998; Katsuraet al., 2004]. The mantle of Mercury appears tobe too thin for it to sustain any phase transitions.

There is seismological evidence for other

6


phase changes in the Earth’s mantle, althoughthese are less well resolved, and in some in-stances do not appear to be global, thus theireffect on mantle convection will only be men-tioned briefly.

Mantle’s Heat BudgetThe ultimate driver of mantle flow is thatplanets cool to space as they inexorably cometo equilibrium with the rest of the much colderuniverse. A major source of heat within themantle is the kinetic energy delivered to theplanetary interiors by the impacts of planetes-imals during accretion, and the gravitationalenergy released upon the segregation of themetallic core from the silicate mantle, knowncollectively as primordial heat sources. Anothersource of heat arises from radioactive decayof unstable isotopes, mostly uranium ( 238U),thorium ( 232Th) and potassium ( 40K), whichare collectively termed radiogenic heat sources.The total rate that heat is flowing out of theEarth is approximately 46 TW [Jaupart et al.,2015], as measured by heat-flow gauges incontinents and oceans [see Turcotte and Schu-bert, 2014]. About 20-30% of the Earth’s totalmantle heating is thought to come from thecore [Jaupart et al., 2015]. The relatively lowendogenic heat flow emanating from withinterrestrial planets, compared to radiative releaseof incident solar heating, makes surface heatflows measurements challenging, and even so,such observations are available only for theEarth and the Moon.

Most radioactive elements in the mantle areincompatible, meaning that if their host rockundergoes partial melting, they tend to dissolveor “partition” into the liquid phase. Thus, inthe process of crust formation through mantlemelting, the incompatible radioactive elementspartition towards and concentrate in the crust,which has two competing consequences for the

mantle heat budget. On the one hand, forminga crust depletes the mantle of heat producingelements. On the other hand, a radiogenicallyheated crust acts as a warm blanket that impedesheat flow out of the mantle. Whether the neteffect of crustal production is to help or impedemantle cooling remains a matter for furtherinvestigation [Rolf et al., 2012].

Earth’s continental crust, which is inevitablyextracted from the early mantle by melting andremelting, acquired an especially high concen-tration of incompatible radioactive elements,and thus produces a significant fraction of thenet heat output through the surface. Subtractingthe contribution to surface heat flow from thecontinental crust leaves approximately 38 TWemanating from the mantle and core [Jaupartet al., 2015].

It is not currently known exactly how muchof the heat output from the mantle (and core) isdue to primordial heat, and how much of it isdue to the heating by radioactive elements. Themantle’s abundance of radiogenic sources canpotentially be constrained using the measuredconcentrations of U, Th and K in chondriticmeteorites, which are thought to represent theoriginal building blocks of terrestrial planets.However, to what degree the chondritic con-centrations (not to mention which families ofchondrites) are representative of those for thebulk Earth is still an active area of debate.Complicating the issue is the large uncertaintyin the efficiency of heat transport throughoutEarth’s history, with different proposed mod-els spanning more efficient and less efficientcooling rates on early Earth. There is a tradeoff between what is assumed for the budgetof radioactive elements, and the efficiency ofmantle heat transport through time. Chondriticconcentrations of radioactive elements requirethe mantle to have released heat less efficientlyin the past [Korenaga, 2008]. Alternatively,if the present heat transport mechanism is

7


Figure 3: Graphic rendition of cutaway view of Earth’s structure showing crust, convecting mantle andcore. The relevant dimensions are that the Earth’s average radius is 6371 km; the depth of the base of theoceanic crust is about 7 km and continental crust about 35 km; the base of the lithosphere varies from 0 atmid-ocean ridges to about 100 km near subduction zones; the base of the upper mantle is at 410 km depth,the Transition Zone sits between 410 km and 660 km depths; the depth of the base of the mantle (the core-mantle boundary) is 2890 km; and the inner core-out core boundary is at a depth of 5150km. Reproducedfrom Lamb and Sington [1998].

representative of that on early Earth, thenthe mantle’s radiogenic sources must be super-chondritic, and would also imply that the mantleholds a reservoir of heat-producing elementsthat are not sampled by plate tectonics (sincewe don’t see these heat-producing elements inMORB) [Schubert et al., 1980; Jaupart et al.,2015].

The question about the efficiency of mantleconvection through Earth’s history, as well asits characteristics on other planets, requires un-derstanding how mantle dynamics changes withvarying temperature, planet size, etc.; this issuewill be revisited later, after the basic physics ofconvection has been discussed.

Mantle’s Cold ThermalBoundary Layer

The outer portion of a planet, its crust and litho-sphere, makes up the cold thermal boundarylayer (TBL), which is the layer across whichheat escapes from the interior to space; the heattransfer across the cold TBL happens mainly byconduction, but is also helped by the volcanictransport of hot material to the surface. On mostterrestrial planets (that is, all except Earth),mantle convection occurs beneath the surface;while the surface may get deformed and havevolcanic lavas emplaced on top of it, it remainsin place for periods of time that are much longerthan the characteristic timescale of mantle over-turn. This mode of convective cooling is termedstagnant lid convection, with the lid being theportion of the TBL that does not participatein convective mantle flow, and planets cooling

8


in this mode are termed one-plate planets.The lid can thicken over time due to cooling,compression in response to underlying mantlecurrents, or burial under the lavas emplaced ontop of it [Moore et al., 2017]. Thickening of thebasaltic crust may push its lowermost portioninto depths where it transitions to eclogite. OnEarth, Venus, Mars and Mercury the basalt-eclogite transition occurs at about 45, 50, 65and 100 km depth, respectively, with the exactdepth being dependent on temperature [Arndtand Goldstein, 1989; Spohn, 1991; Babeykoand Zharkov, 2000]. Eclogite is denser thanthe underlying mantle material, and is thereforegravitationally unstable and prone to sink intothe mantle, a process known as delamination.On one-plate planets, episodes of lithosphericdelamination possibly act to thin the stagnantlid, or even remove it entirely, and are oftenfollowed by extensive volcanic activity thateffectively renew the surface [Turcotte, 1989;Spohn, 1991; Parmentier and Hess, 1992;Morschhauser et al., 2011; Ogawa and Yanag-isawa, 2011]. There is a growing evidencefor a mobile Venusian lithosphere (rather thana stagnant one, as was previously believed).Some of the observed topographic featureson Venus, in particular in the vicinity of largecoronae, resemble trenches, possibly indicativeof subduction [Schubert and Sandwell, 1995;Davaille et al., 2017]. Furthermore, some ofthe radar imagery of Venus has been interpretedas folds and faults, all indicative of lateralsurface motion, although this type of geologicalstructures can be generated by the stresses ofthe underlying convective mantle, even if thelithosphere does not circulate into the mantle[Harris and Bedard, 2014].

The surface of planet Earth is unique in thatmost of it, namely the oceanic crust (whichmakes up about 60% of the surface area), is con-tinuously renewed through the process of platetectonics. Instead of a largely stagnant top TBLcommon for other terrestrials, the cold TBL of

Earth is mobile, moving laterally along the plan-etary surface at a rate dictated by that of man-tle overturn. The resulting high rate of surfacerejuvenation, as reflected in the young ages ofthe oceanic crust, typically less than 200 Myr[Condie, 1997], allows for efficient convectivecooling of the planet. The theory and observa-tion of plate tectonics on Earth, including its linkto mantle flow, has revolutionized our under-standing of planetary dynamics and evolution,and we discuss it in more detail in the follow-ing.

Plate Tectonics - The Unique Case ofPlanet Earth

The Earth’s surface, its crust and lithosphere, issubdivided into 12 major tectonic plates and anumber of minor plates or microplates (Figure4). Some plates consist entirely of the oceaniclithosphere, while others incorporate continentsas well. The plates move relative to each other,and their movement away from, towards orlaterally past each other, characterizes theirboundaries as divergent, convergent or trans-form (or, alternatively, strike-slip), respectively.New tectonic plate material is formed at themid-ocean ridges (MORs), which constitutethe divergent plate boundaries; specifically, hotmantle material partially melts and the resultingmagma ascends to drive ridge volcanism andform new oceanic crust. The residual unmeltedmaterial remains in the mantle as the thindepleted portion of the lithosphere. As theplates move away from MORs they cool, andthe lithosphere of which they are comprisedthickens as a thermal boundary layer, becomesheavier and eventually sinks back into the man-tle at subduction zones, which constitute theconvergent plate boundaries. The divergent andconvergent motion of the plates is the surfacemanifestation of the upwards and downwardsmotion associated with convective currentsin the underlying mantle, which is often also

9


referred to as the poloidal component of mantleflow [Hager and O’Connell, 1981; Bercoviciet al., 2015]. The plate-motion that is notdirectly associated with spreading or subductionis associated with strike-slip shear or platespin, and is also referred to as the toroidalcomponent of flow. Such motion has no directenergy source (such as gravitational energyrelease for poloidal flow), which points to theimportant effect of non-linear rock rheology(i.e., the way a rock responds to stress throughdeformation, or strain rate) to indirectly coupleit to convective motion [Kaula, 1980; Bercoviciet al., 2015].

One of the first to recognize the mobilityof the Earth’s surface was Alfred Wegenerin his theory of Continental Drift, largelymotivated by the striking correlation in thegeometry of the margins of different continents[Wegener, 1924]. Wegener’s theory, however,lacked a physically plausible mechanism thatwould provide a sufficient driving force forthe continents to move through oceanic crust,which is why it was criticized and discredited.Decades later the accumulation of sea-floorsounding and magnetic data during and afterWar World II provided compelling evidencefor sea-floor spreading [Hess, 1962; Vine andMatthews, 1963; Morley and Larochelle, 1964],see Tivey [2007], which marked the start of thePlate Tectonics revolution. The theory of platetectonics, in which the plates comprise a mosaicof contiguous rafts blanketing the mantle, butall moving as solid blocks around their ownrotation or Euler poles, was articulated by 1968independently by McKenzie and Parker [1967]and Morgan [1968]. Plate tectonics differsfrom Continental drift in that the continentsare passive riders on the backs of the plates,rather than plowing through oceanic lithosphereas Wegener assumed. Meanwhile, the theorythat the mantle is convecting in order to getrid of its heat had become more physicallysound, generating testable predictions of flow

velocity and stress, which compared favorablyto the Earth’s gravity, geoid, and topographymeasurements [Holmes, 1931; Pekeris, 1935;Hales, 1936; Runcorn, 1962a,b], see Bercovici[2015].

Tectonic plates constitute the cold thermalboundary layer of the convective mantle system,i.e., the conductively cooled surface layer, madeup of the differentiated mantle (crust and de-pleted lithosphere) in the uppermost part, andthe undifferentiated cold lithospheric mantle atthe bottom. It is generally understood that platetectonics is the surface manifestation of man-tle convection. Complicating this picture is thefact that the mantle material behaves very dif-ferently when it is at depth (at higher pressuresand temperatures) compared to when it is nearthe surface. Prior to becoming a plate, the man-tle acts as a highly viscous fluid, with its de-formation distributed over tens or hundreds ofkilometers. In contrast, the cold tectonic platesappear to be strong, nearly rigid, in their inte-rior, with most of their deformation confined tothe weak and narrow plate boundaries. In fact,the strength of the plates appears to be so highthat they shouldn’t be able to bend and sink intothe mantle, given the available convective forc-ing [Cloetingh et al., 1989; Solomatov, 1995].The physical mechanism responsible for weak-ening of crustal and lithospheric rocks, whichultimately allows for the formation of tectonicplate boundaries, are still debated, with plasticyielding, percolation of fluids and grain size re-duction being some of the leading theories. Nev-ertheless, understanding how the nearly discon-tinuous motion of plates self-consistently arisesfrom the convective flow of the mantle, andhow the strong plates bend and sink into themantle, remains a major goal in geodynamics[Bercovici, 1995; Tackley, 2000a,b; van Heckand Tackley, 2008; Foley and Becker, 2009;Bercovici et al., 2015].

10


60˚S 60˚S

0˚ 0˚

60˚N 60˚N

Africa

Antarctic

Arabia

Australia

Caribbean

Cocos

Eurasia

Indian

Juan de Fuca

Nazca

N. America

Pacific

Philippine

Scotia

S. America

Figure 4: The present day tectonic plates on Earth. The names of the major plates are given, where arrowson some of the largest plates indicate their direction of motion. (Modified from a figure compliments of PalWessel, University of Hawaii at Manoa.)

Mantle’s Cold DownwellingFlow

Unless cold mantle downwellings entrainsurface material, as in the case of plate tectonicson Earth, their presence is largely hidden fromdirect observation. However, the motion ofcold dense material in the mantle generatestopography and a measurable signal in thesurface gravity field. For example, anomalouslydense material in the mantle (such as fromcold downwelling currents) induces a positiveanomaly in the gravitational field (i.e., a gravityhigh), albeit some, or all, of that positive signalmay be offset by the flow-induced downwarddeflection of the surface, which effectivelygenerates a negative mass anomaly. For theEarth, the seismic anomalies can be imagedindependently using seismic tomography,which can then be combined with the topog-raphy and gravity measurements to constrainmantle structure [Hager, 1984; Ricard et al.,1984; Steinberger et al., 2010]. Combiningobservations of topography, volcanism and

gravitational anomalies, and using Earth as areference for mantle rock properties, it has beendemonstrated that there exist large-scale densityanomalies, likely induced by vertical convectivecurrents, in the mantles of Earth, Mars andVenus [Steinberger et al., 2010].

The cold downwelling mantle flow on Earthis linked to the subduction zones at the surface,which we discuss next.

Subduction on EarthAs oceanic lithosphere migrates away from aspreading center (mid-ocean ridge), it becomesdenser and heavier. The resulting thermallyinduced negative buoyancy causes the plate toeventually sink into the mantle. Oceanic platesbend and flow downwards at subduction zones,forming trenches, which are the deepest partsof the Earth’s surface, like the Marianas trench.While most subduction zones are locatedalong continental margins where oceanic andcontinental plates meet, there exist examplesof intraoceanic subduction as well (e.g., the

11


Izu-Bonin-Mariana arc system along the easternmargin of the Philippine plate). The ages ofsubducting plates vary from 0 (i.e., subductingridges) to roughly 200 Myr. In all cases, thedownwelling is asymmetric, with one platesinking underneath the other, rather than twoplates converging and sinking together [seeWada and King, 2015].

Convective mantle flow is extremely slow andlaminar (i.e., there is no turbulent eddy transportof momentum), because of the high mantle vis-cosity. Therefore, the velocity of sinking slabsis well approximated by their terminal velocity,at which the gravitational force pulling the slabsdownward is balanced by viscous resistance totheir motion. The terminal slab velocity canbe estimated from a slab’s thermally inducedbuoyancy, and the viscosity of the mantle [seeDavies and Richards, 1992].The result of thisrelatively simple approximation is in goodagreement with the observations of tectonicplate velocities, especially for oceanic platesattached to appreciable slabs, which move atspeeds on the order of 10 cm/yr [Forsyth andUyeda, 1975].

Seismic tomography reveals that someslabs appear to stagnate and become deflectedhorizontally at around 660 km depth, whichcorresponds to the olivine-wadsleyite phasetransition. Other slabs appear to traverse theentire depth of the mantle, with little deflection.The increasing mantle viscosity with depthcauses the slabs to thicken as they descend, asindicated in seismic tomography models; inprinciple this occurs because the slab experi-ences more viscous resistance and slows down,causing it to effectively inflate or buckle, thusappearing thicker. An additional effect is thatof thermal diffusion, where the deeper portionsof the slab have had more time to cool thesurrounding mantle. It is also worth noting thatthe resolution of tomography models is poorin the mid mantle, such that at least some of

the broadening may be an imaging artifact [seeWada and King, 2015, and references therein].

Although in total a subducting slab is coldand heavy, it is also compositionally strati-fied: its top layer is basalt, which makes upthe oceanic crust, underlain by harzburgite,which makes up the depleted portion of thelithosphere, and finally lherzolite at the bottom,which is the undifferentiated part of the mantle[see review by Wada and King, 2015, andreferences therein]. The intrinsic densities ofbasalt and harzburgite are lower than that of theupper mantle, which partially offsets the plate’sgrowing negative thermal buoyancy. However,once the plate sinks and becomes a slab, thesechemical effects are counter-acted by the tran-sitions to intrinsically denser phases that occurat greater depths (most notably the transitionfrom basalt to eclogite at about 60 km depth),rendering the net effect of lithospheric compo-sitional stratification on subduction negligible[Bercovici et al., 2015]. However, once theslab reaches the core-mantle boundary (CMB),which acts as an impenetrable boundary, theslab stalls, heats up, softens, and potentiallysegregates into different paths of the convectiveflow. Slab segregation is hypothesized to be oneof the primary sources for compositional het-erogeneity in the mantle [Hofmann and White,1982; Coltice and Ricard, 1999; Mulyukovaet al., 2015]. Whether the resulting hetero-geneity can form large scale compositionalanomalies, as detected by seismic tomography,or whether the different slab components getstirred by the convective flow and mechanicallyhomogenized remains an active area of research.

When a slab sinking into the lower mantle im-pinges on the impermeable CMB, it is deflectedhorizontally and induces flow parallel to theCMB. The slab-induced flow can displace thematerial already residing at the CMB, and if thatmaterial happens to be compositionally anoma-lous, it may get swept up into large piles of seis-

12


mically detectable anomalies, such as the largelow shear velocity provinces [Tan et al., 2011;Bower et al., 2013]. Furthermore, as the slabpushes material along the CMB, it causes thehot thermal boundary layer to thicken ahead ofthe slab; this process has been hypothesized totrigger plume-formation [Weinstein and Olson,1989; Steinberger and Torsvik, 2012; Dannbergand Gassmoller, 2018], discussed in the nextSection. If that is the case, then the flow alongthe CMB provides an important link betweenplate tectonics, which is mainly driven by thesubducting slabs, and the intraplate volcanismgenerated by plumes, which otherwise appearsto be decoupled from surface plate motions.

Core-Mantle Boundary and theMantle’s Hot Thermal Bound-ary LayerThe bottom of the mantle is defined by thecore-mantle boundary (CMB), which separatesthe silicate mantle material from the underlyingmolten metallic core. The efficiency of heattransport across the CMB is the determiningfactor for the generation of planetary dynamos:in order to sustain a dynamo, the electricallyconductive core material needs to move atsufficiently high velocities, which in turn aredictated by the convective flow velocities andthus the rate of core cooling. In addition tothermal convection, an even more effectiveway to generate a dynamo is by chemicalconvection, whereby as the core cools below themelting temperature and freezes, it expels itslight elements, such as sulfur and silicon, whichthen buoyantly rise up to the CMB, inducingflow [Stevenson et al., 1983; Braginsky andRoberts, 1995]. The rate of core freezing is,again, controlled by the rate of heat transportacross the CMB, which in turn is limited bythe convective heat transport across the mantle.Observations of intrinsic magnetic fields of

terrestrial planets can thus provide importantinsight into their thermal histories and presentstates. For example, the apparent absence ofmagnetic field on Mars [Acuna et al., 1998] islinked to its relatively cold interior, possibly in-dicating that its mantle is too cold to efficientlyconvect heat out of the core. Venus does notseem to feature a measurable magnetic fieldeither [Russell and Elphic, 1979], which hasbeen linked to its relatively hot interior, with themantle and the core being so hot that the coreis not crystallizing [Stevenson et al., 1983] (atleast presently, albeit it may have undergonesome freezing in the past). In contrast, Earthand Mercury possess substantial magneticfields, indicating rapid heat transport across themantle [Ness et al., 1974; Connerney and Ness,1988; Anderson et al., 2011]. Better constraintson the composition and interior structure ofthe Earth’s deep interior, thanks to seismictomography and mineral physics data, provide amore detailed picture of the nature of the CMB.

Earth’s Core-Mantle BoundaryThe CMB is a natural place where denseheterogeneities accumulate: material that isheavier than the ambient mantle but lighter thanthe outer core can linger here. Moreover, sincethe core only exchanges heat with the mantleby conduction, leading to a 200− 300 km thickhot thermal boundary layer, across which thetemperature increases with depth by about 1000K, from the ambient temperature profile ofabout 2500 K in the lower mantle to about 4000K at the CMB [Calderwood, 1999; Kawai andTsuchiya, 2009].

Seismic studies of the deep interior use thecompressional and shear wave velocities andthe bulk sound speed, which are related to thematerial’s bulk modulus (incompressibility),rigidity and density [Masters et al., 2000]. Forexample, the correlation between anomalies

13


in the shear wave velocity and the bulk soundspeed can be used to infer the physical causesfor an observed anomaly. If the anomaly isdue to the variations in temperature, then theshear velocity and bulk sound speed should becorrelated (i.e., both positive or both negative),while an anti-correlation (anomalies of oppositesign) is indicative of compositional variations.There is abundant evidence for the heteroge-neous nature of the lowermost mantle fromseismological observations, which indicate thepresence of both thermal and compositionalvariations (Figure 5) [Ishii and Tromp, 1999;Garnero, 2004; Garnero and McNamara, 2008;Ritsema et al., 2011]. The main observationalfeatures of the CMB region include the D”discontinuity, the large low shear velocityprovinces (LLSVPs) and the ultralow velocityzones (ULVZs) [Lay et al., 1998; Thorne andGarnero, 2004]. The D” discontinuity is seenas a sharp increase in shear-wave velocity withdepth occurring several hundred kilometersabove the CMB. The part of the mantle betweenthe D” discontinuity and the CMB is commonlyreferred to as the D” layer. The D” varies inthickness and even appears to to be absent insome regions, which suggests that it is not aglobal phase transition, unlike, for example,the 410km and 660km discontinuities boundingthe transition zone; [see also Hernlund andMcNamara, 2015]. A possible cause for theD” is the solid-solid phase transition fromperovskite (Pv) to postperovskite (PPv) [Mu-rakami et al., 2004], which would only occurat deep mantle pressures in sufficiently coldregions, such as in the vicinity of newly arrivedslabs. Postperovskite is slightly denser (by1 − 2%) and less viscous (by up to an orderof magnitude) than the perovskite phase, andthus can act to mildly destabilize the lowermostmantle material, making convection slightlymore vigorous [Tackley et al., 2007; Nakagawaand Tackley, 2011].

The two major LLSVPs appear as two large

scale heterogeneities in seismic tomography[Garnero and McNamara, 2008; Dziewonskiet al., 2010; Ritsema et al., 2011]: one of themlies beneath Africa and the other beneath thePacific Ocean. LLSVPs have irregular shapesand can measure up to 1000 km in height andwidth; they cover nearly 20% of the CMB andoccupy about 2% of the mantles total volume[Burke et al., 2008].The negative correlationbetween the bulk sound and shear velocitywithin the LLSVPs suggests that they are ofchemical origin [Masters et al., 2000; Trampertet al., 2004; Steinberger and Holme, 2008].Moreover, the material that makes up theLLSVPs appears to be intrinsically denser thanthe ambient mantle [Ishii and Tromp, 2004].There is yet no consensus on the origin ofthis compositional anomaly, with the proposedscenarios falling within two main categories: aprimordial layer that formed early in the Earth’shistory [e.g. Lee et al., 2010; Nomura et al.,2011], and accumulation of a dense eclogiticcomponent from the subducted MORB thatsegregates at the CMB [Hofmann and White,1982; Christensen and Hofmann, 1994; Tackley,2011; Mulyukova et al., 2015]; [see also reviewby Hernlund and McNamara, 2015].

The ULVZs are localized structures thatare much smaller in size than the LLSVPs,extending around 1-10 km above the CMBand 50-100 km laterally [Thorne and Garnero,2004; McNamara et al., 2010]. However,ULVZ’s have a large seismic velocity reduction,10% for P-waves and 10-30% for S-waves[Garnero and Helmberger, 1996], and a 10%density increase relative to the ambient mantle.Mechanisms for producing the ULVZs are stilla matter of debate, with some of the candidatesincluding partially molten and/or iron-enrichedmaterial, possibly formed early in Earth’shistory when the mantle was much hotter andlargely molten [Williams and Garnero, 1996;Labrosse et al., 2007], outer core materialleaking into the lower mantle due to chemical

14


Figure 5: A simplified sketch of a possible interpretation of the seismically observed structures in theEarth’s lower mantle. LLSVP and ULVZ stand for Large Low Shear wave Velocity Province and Ultra-Low Velocity Zone, respectively. See Section “Earth’s Core-Mantle Boundary” for their possible formationscenarios and the proposed thermal and chemical properties. Adapted from Deschamps et al. [2015].

disequilibrium or morphological instability[Otsuka and Karato, 2012], and subduction andgravitational settling of banded-iron formations[Dobson and Brodholt, 2005].

The compositionally anomalous nature of thedeep mantle has important implications for man-tle convection and hence Earth’s thermal evo-lution. In particular, the presence of composi-tionally dense material at the CMB reduces theamount of heat that flows from the core into themantle, which is one of the energy sources forconvective flow. This effective blanketing of theCMB has implications for the rate at which themantle has been cooling since core formation.In addition, as discussed previously, the heatflow across the CMB controls the rate at whichthe Earth’s core cools and freezes, and thus thehistory of the geodynamo.

Mantle’s Hot Upwelling Flow

As heat is conducted from the core into themantle, it creates a hot thermal boundarylayer (TBL) at the bottom of the mantle.The hot TBL material thermally expands and

becomes buoyantly unstable. When the TBLis sufficiently thickened and buoyant to risethrough the overlying viscous mantle, it can riseupwards in the form of hot mantle currents, alsocalled mantle plumes, and potentially reach thesurface. Arrival of plume material at the surfacecan generate volcanic activity or a hotspot anddeflect the surface upwards, generating a hightopography or a hotspot swell. Hot plumematerial will also undergo melting when it as-cends to lower pressures and induce volcanism;the resulting lava flows may serve as anothersurface signature of the underlying convectivemantle currents. For example, the large volcanicrises Themis, Eastern Eistla and Central Eistlaon Venus [Smrekar and Stofan, 1999] and theTharsis rise on Mars [Wenzel et al., 2004] havebeen interpreted as manifestations of underly-ing plume activity [see Steinberger et al., 2010].

Plume geometry is hypothesized to bemushroom-like, with a plume-head spanning afew hundred kilometers across, followed by acylindrical plume-tail that can be as long as thedepth of the mantle, and a 100 km or less indiameter [Whitehead and Luther, 1975; Whiteand McKenzie, 1989; Olson, 1990; Sleep, 2006];

15


[see review by Ballmer et al., 2015]. Theplume-tails are relatively narrow and, in thecase of the Earth, until recently have been dif-ficult to resolve seismologically [Montelli et al.,2004; French and Romanowicz, 2015]. More-over, planetary mantles are heated both frombelow (by the core) and from within (by pri-mordial heat and radioactive elements); thestrength of the plumes (i.e., their size and ther-mal anomaly) decreases with the decreasingcontribution from bottom heating, since that’swhat controls the size and temperature of theTBL. Thus, plume detection, both through grav-ity measurements, seismology and volcanism,is challenging in planets that are predominantlyheated from within, as seems to be the case forthe terrestrial planets in our Solar System.

Plumes and Mid-Ocean Ridges onEarth

When a new starting plume head first reachesthe surface of the Earth, it is thought to initiallygenerate extensive volcanic activity, oftenreferred to as flood-basalt volcanism, leadingto large igneous provinces (e.g., Ontong-JavaPlateau, Columbia River Basalts, the DeccanTraps and the Siberian Trapps). This initialeruption is associated with a massive floodbasalt volcanism and is ostensibly followedby continuous hotspot activity, supplied bythe narrow plume-tail [Richards et al., 1989;Ballmer et al., 2015]. This ongoing hotspotvolcanism can sometimes be seen as a chainof volcanic islands (typically on the sea floorwhere the plume material can readily penetratethe thinner lithosphere); in particular, thestationary plume conduit emplaces lava onto thesurface of a tectonic plate that is moving relativeto it, thus forming a chain of volcanoes with acharacteristic age progression, the archetypicalexample of which is the Hawaiian-Emperorhotspot chain that extends across the North Pa-cific sea-floor. In contrast to the more common

forms of volcanism, which occur at mid-oceanridges and subduction-related volcanic arcs,hotspots often occur in plate interiors and arenot generally associated with plate boundaryprocesses.

The classical view of mantle plumes as purelythermal upwelling currents has been challengedin recent years, due to the large kilometerscale topographic uplift that is predicted for athermal plume impinging on the lithosphere[White and McKenzie, 1989], but that is notalways observed [Czamanske et al., 1998;Korenaga, 2005; Sun et al., 2010]. One ofthe proposed resolutions to this inconsistencyare compositionally anomalous plumes (alsocalled thermochemical plumes), whose mantle-material is enriched in heavier elements and isthus intrinsically dense relative to the ‘normal’mantle (but, of course, still positively buoyantdue to their high temperature) [Dannberg andSobolev, 2015]. The thermochemical plumesare less buoyant than the classical purely ther-mal plumes, and therefore rise more slowly andgenerate less dynamic topography, in agreementwith the observations. Thermochemical plumessimultaneously explain another feature ofplume-volcanism, namely their geochemicallydistinct basaltic lavas, in terms of trace elementsand isotopes, relative to basaltic lavas derivedfrom mid-ocean ridges [Hofmann and White,1982; Zindler and Hart, 1986; Kobayashi et al.,2004; Jellinek and Manga, 2004; Sobolev et al.,2005; Jackson and Dasgupta, 2008; Sobolevet al., 2011]. The distinct geochemistry ofhotspot-lavas is one of the arguments for whythey are thought to be extracted from a mantle-region that is deep-seated and that is at leastpartly decoupled from the large tectonic scalemantle circulation. Furthermore, the spatialcorrelation of plume-derived lavas at the surfaceand their projection down to the LLSVPs andULVZs at the CMB provides further supportiveevidence for their deep origin [Torsvik et al.,2006; Burke et al., 2008; Dziewonski et al.,

16


2010; Steinberger and Torsvik, 2012].

The vertical flow of hot mantle upwellingsinduces lateral flow along the CMB, due to a dy-namic low-pressure that is created at the plumesbase. As the ambient material gets sucked intothe rising plume, it drags the underlying, pos-sibly compositionally heterogeneous materialalong with it. This is the process by whichplumes can potentially bring the chemicallydistinct material from the deep mantle all theway up to the surface, producing geochemicallydistinct lavas. As such, plume-derived lavasare a window into the chemical structure of thedeep mantle.

Another component of the upwelling flow,which is associated with plate tectonics and isthus unique for the Earth, is the return flow ofthe mantle that compensates for, or gets dis-placed by, the downward motion of the slabs.The material that makes up the return flow even-tually ends up becoming the bottom-most un-differentiated part of the tectonic plates, ac-counting for their thickening as they grow older.As opposed to the actively upwelling plumes,MOR volcanism is not associated with the ex-cess buoyancy of hot material, but rather with itspassive rising in response to lithospheric spread-ing motion; this is for example evident in theEast Pacific Rise, which is the fastest spreadingridge on Earth, and which is devoid of a grav-ity anomaly or deep seismic structure [Forsythet al., 1998], implying that it is isostatically sup-ported and is not being lifted up by any deep up-welling current [Runcorn, 1963; Davies, 1988].MORs constitute the divergent plate boundarieswhere tectonic plates are first formed. Manyridges initiate as rift zones during continentalbreak up, eventually becoming sites of sea floorspreading that separate the continents; these pro-cesses are an integral part of the classical Wilsoncycle, involving repeated closing and opening ofoceans [Wilson, 1968].

The mantle region that undergoes fractional

melting beneath a ridge is several hundredkilometers wide [Forsyth, 1998]. However,as the melt migrates to the surface, it focuseswithin just a few kilometers of the spreadingaxis, creating narrow regions where the oceaniccrust is emplaced and where the deformationis localized [Morgan, 1987; Spiegelman andMcKenzie, 1987; Parmentier, 2015]. The phys-ical explanation for why MOR-volcanism isfocused into narrow ridges-structures is relatedto, and is as enigmatic as, the cause for strongplates and weak plate boundaries. The ridgeorientation typically mirrors the subductionzones that they eventually feed, implying thatthey may initiate as a strain localization, suchas a self-focusing necking instability [Ricardand Froidevaux, 1986]. Such mechanisms areplausible if the stresses in the lithosphere dueto the pull of slabs can be guided considerabledistances. The cause for ridge formation andgeometry remain an active area of research.

The lavas produced at MORs and hotspots areknown as Mid-Ocean Ridge Basalts (MORB)and Ocean-Island Basalts (OIB), respectively.Being direct samples of the mantle, theirpetrological composition, and trace-elementchemistry is of great interest for understandingmantle dynamics and structure [Hofmann, 1997,2003; van Keken et al., 2002; Tackley, 2015].For example, the distinct features of MORB andOIB implies that they originate from differentsource regions in the mantle with limitedmaterial exchange between them. Geochemicalmeasurements of trace elements, in particularincompatible elements (which dissolve morereadily in a rock’s melt than its solid duringpartial melting), such as uranium, thorium andhelium, show that MORB and OIB are measur-ably distinct: MORBs appear to be significantlydepleted in such trace elements relative toOIB, which implies that the MORB sourceregion has undergone previous melting anddepletion, compared to that of OIB [Hofmannand White, 1982; Zindler and Hart, 1986]. The

17


emerging model of upwelling mantle flow hasthe MORB source confined to an area in theupper mantle, which has been cycled repeatedlythrough the plate tectonic process of mid-oceanridge melting and separation of oceanic crustand trace elements from the mantle. OIB, onthe other hand, ostensibly come from a partof the mantle that has seen little if any of thismelt processing, and hence would be isolatedpresumably at depth from the upper mantleand the plate-tectonic cycling [Allegre, 1982;Tackley, 2015, and references therein].

Mantle layering is also implied by a putativeheat flow paradox. Specifically, if the mantlewere composed entirely of MORB-sourcematerial, which is depleted in U, Th and K, thenits radioactive heating would not be sufficient toaccount for the observed mantle heat outflow of38 TW. This inconsistency can be resolved byassuming a higher concentration of radioactiveelements in the lower mantle, which then alsoimplies that the mantle is not well-stirred andthere is at least some decoupling of convectiveflow between the upper and lower mantle.However, if the contribution from primordialheat to the net mantle heat output is equal toor larger than the radiogenic source, then theobserved heat flow can be reconciled withthe low concentration of radioactive elements,thus resolving this so-called heat-flow para-dox [Christensen, 1985; Korenaga, 2003, 2008].

Another geochemical argument for limitedexchange between lower and upper mantlecomes from taking the “bulk silicate earth”composition (i.e., with the mantle and crustcombined) and assuming that the continentalcrust was removed from it uniformly. Themantle residue left behind from this thoughtexperiment is too enriched in incompatibleelements, compared to the MORB-source.However, extracting the continental crust fromonly the top 1/3 to 1/2 of the mantle causessufficient depletion to reproduce MORB-source

composition [see van Keken et al., 2002]. Astratified mantle, with a shallow portion ofthe mantle that has segregated to form thecontinental crust, leaving a complementary un-depleted region in the deeper mantle, makes fora geochemically plausible mantle compositionmodel. It is worth noting that the total volumeof the two major LLSVPs or even the entire D”layer, is not enough to hold all of the unseg-regated portion of the mantle, and thus cannotsingle-handedly account for all of the enrichedmantle material. A 1000 km thick layer at thebase of the mantle would potentially be bigenough to serve as a storage of unsegregatedmaterial [Kellogg et al., 1999], however, suchlayer has never been seismologically observed.

There remains a contradiction between geo-chemical and geophysical inferences of layeredvs whole mantle convection: while there is com-pelling evidence from seismic tomography mod-els for material exchange between the lower andupper mantle, with subducting slabs extendinginto the lower mantle [van der Hilst et al., 1997;Grand et al., 1997], as well as mantle plumestraversing the transition zone [Montelli et al.,2004; Wolfe et al., 2009; French and Romanow-icz, 2015], the geochemical data appears to ar-gue for a layered mantle with an isolated and un-depleted mantle at depth. Some of the attemptsto reconcile these observations circumvent theproblem of layered convection, which is not ob-served, by instead invoking differential melting.For example, one model envisions the mantleas a plum-pudding, where ‘plums’ are scatteredregions that are enriched in volatile elements,while the rest of the mantle is a depleted ‘pud-ding’ [Morgan and Morgan, 1999; Becker et al.,1999; Tackley, 2000c]. The size of the plumsand their degree of relative enrichment of in-compatible and radiogenic elements depends ontheir assumed origin and the history of mantlestirring, both of which are highly uncertain. Theenriched domains can melt at higher pressures,while the depleted ones require lower pressures

18


to melt. One of the proposed scenarios envisionsthat a mantle plume impinging on the base of a100 km thick lithosphere would mostly melt the‘plum’ material (OIB-source), while the part ofthe mantle that rises to lower pressures at ridgesmelts additional depleted ‘pudding’-component(MORB-source), resulting in MORB that ap-pears depleted relative to OIB [Ito and Ma-honey, 2005a,b]. Another model argues forwhole-mantle convection, but takes into accountthe different abilities of mantle minerals to ab-sorb water, in particular transition zone mate-rials absorb water more readily than the up-per mantle. As mantle material passively up-wells through the transition zone (as part ofthe slab-driven return flow) and enters the up-per mantle at the 410 km boundary, it becomescloser to water-saturation and more likely tomelt. Melting at 410 km depth strips, or filters,the upwelling mantle from the incompatible ele-ments, which forms the depleted MORB-source.Mantle plumes, on the other hand, traverse thetransition zone too fast to become hydrated,which limits the amount of melting and volatile-filtering they can undergo as they cross the 410km boundary. Thus, the lavas sourced by theplume material, the OIBs, would appear to comefrom an enriched mantle [Bercovici and Karato,2003]. The prediction of a melting site at 410km depth inferred by this model, known as theTransition Zone Water Filter model, has beensupported by some seismological studies [Reve-naugh and Sipkin, 1994; Tauzin et al., 2010].However, there still exists relatively large uncer-tainty regarding the melting properties and thesolubilities of incompatible elements, which re-quire further constraints to test the models thatinvoke differential melting. In summary, theconflicting geochemical and geophysical infer-ence of layered vs whole mantle convection re-mains an unsolved problem.

Basics of Thermal Convection

To understand the origin and mechanics ofthe important features of mantle convectionsurveyed above, it is necessary to review thebasic physics of thermal convection. Forexample, tectonic plates, slabs, lithosphericdrips and mantle plumes are all forms ofthermal boundary layers, which are common toconvection in any fluid system. The simplestform of thermal convection is referred to asRayleigh-Benard convection, named after theFrench experimentalist Henri Benard, whorecognized the onset of convective motion influids from a static conductive state and theformation of regular flow patterns in a convect-ing layer [Benard, 1900, 1901], and the Britishtheoretical physicist and mathematician LordRayleigh (William John Strutt), who providedthe theoretical framework to explain Benard’sexperimental results [Strutt, 1916].

The Rayleigh-Benard system is an idealizedmodel of a fluid layer that has a finite thickness,but is infinite in all horizontal directions. Thelayer is heated uniformly from below andcooled from above by applying fixed highand low temperatures at the bottom and topboundaries, respectively. As the bottom part ofthe layer heats up, it thermally expands, whichlowers its density and makes it buoyant relativeto the overlying colder material (analogously,the material at the top cools, contracts andbecomes negatively buoyant). The resultingdensity stratification, with low density materialunderlying high density material, is gravita-tionally unstable and can lead to fluid flow thatoverturns the layer, bringing hot material upand cold material down. Of course, because thetemperature at the boundaries remains fixed, thecycle continues with the newly arriving materialat the bottom heating up and rising, while thematerial at the top cools and sinks. Eventually,the system reaches a dynamic equilibrium withlaterally alternating regions of upwelling and

19


Figure 6: Result of a numerical simulation of Rayleigh-Benard convection in a two-dimensional plane-layer at Ra = 105. Black and white represent cold and hot fluid, respectively. Modified from Bercoviciet al. [2015].

downwelling currents.

Convective fluid flow is a form of heat trans-port that is activated when thermal conduction isnot efficient enough to accommodate heat flow.For example, if the layer is thin enough, it canconduct heat diffusively through molecular vi-brations, thus the fluid can remain static and ob-tain a conductive temperature profile across itsdepth. Convective motion emerges when ther-mally induced density anomalies induce flowthat is sufficiently vigorous to withstand the sta-bilizing effects of thermal diffusion. In addition,while the thermal contrast across the layer sup-plies buoyancy to drive the flow, the viscous re-sistance of the fluid opposes it. The competi-tion between forcing by thermal buoyancy, anddamping by viscosity and thermal diffusion, ischaracterized by a dimensionless ratio called theRayleigh number

Ra =ρgα∆Td3

µκ(1)

where ρ is fluid density, g is gravity, α is thermalexpansivity, ∆T is the difference in temperaturebetween the bottom and top boundaries, d isthe layer thickness, µ is fluid viscosity and κ isfluid thermal diffusivity. The higher the valueof Ra, the higher the propensity for convectiveoverturn. Ra needs to exceed a certain value,called the critical Rayleigh number Rac, in or-

der to excite convective flow. The value of Racis typically on the order of 1000, with the exactvalue depending on the thermal and mechanicalproperties of the horizontal boundaries, (e.g.,whether the boundary is rigid or open to the airor space, see Chandrasekhar [1961]).

The characteristic physical properties of theEarth’s mantle entering the Rayleigh num-ber are ρ ≈ 4000 kg/m3, g = 10 m/s2,α = 3 × 10−5 K−1, ∆T ≈ 3000 K,d = 2900 km, µ = 1022 Pa s (dominatedby the lower mantle), and κ = 10−6 m2/s [seeSchubert et al., 2001]. According to (1), theselead to a Rayleigh number of approximately107, which is well beyond supercritical. Thus, inspite of the extremely high viscosity of the solidrock that makes up the Earth’s mantle, the man-tle spans a large depth and is subject to a highthermal contrast, and hence convects vigorously.

While the properties of other terrestrial plan-ets are less well known than for Earth, there arereasonable constraints on their gravitational ac-celeration, mantle thickness and surface temper-ature (Table 1). Assuming their material prop-erties are similar to Earth’s, we can estimate theRayleigh numbers for the mantles of other ter-restrial planets: 104 for Mercury, 107 for Venus,and 106 for Mars. With the exception of Mer-cury, whoseRa is at most an order of magnitude

20


above critical, the mantle of the rocky planets inthe Solar System appear to be cooling predomi-nantly by convection.

In a convecting system, heat that is beingtransported by the upwellings and downwellingsfirst enters the fluid layer through the horizon-tal boundaries by conduction across thermalboundary layers (TBLs). TBLs are the portionsof the fluid that, once sufficiently heated orcooled, become unstable and rise as upwellingsor sink as downwellings, respectively. Thelonger time it takes for thermal diffusion toinduce enough buoyancy and destabilize theTBLs, the thicker they get prior to overturning,and thus the broader the vertical currents thatthey form. The lower the Rayleigh number,the longer the time that it takes for TBLs togo unstable. In fact, another way to view asystem at subcritical Ra is that by the time theTBLs would be thick enough to overturn, theyalready span the entire layer depth, which iswhy the layer remains stable. On the oppositeend, at Ra-values way above supercritical,only thin TBLs manage to develop beforeundergoing gravitational instability. As the hotbottom TBL starts to rise, the region it used tooccupy gets replenished by the newly arrivingcold material, and analogous for the cold topTBL. Meanwhile, the material in betweenthe laterally moving TBLs and the verticallymoving upwellings and downwellings is simplymoved around by the viscous drag from theambient flow, and eventually equilibrates totheir average temperature. (In fact, if thelayer is deep enough such that the pressuresare comparable to fluid incompressibility, thefluid in-between the TBLs is not isothermalbut adiabatic). An adiabatic profile is causedby material moving up or down through largeenough pressure changes to induce compressionor decompression, but fast enough so that thematerial has little time to exchange heat with itssurroundings. Material that rises and expandsfrom decompression must increase its mechan-ical or ”reversible” internal energy (essentially

pressure times volume change), and to do thisit uses its own thermal internal energy, whichresults in the material ”cooling” (although theonly exchange of energy is with itself). Thusrising material has an adiabatic temperature de-crease. Likewise, sinking, compressing materialrelinquishes its mechanical energy to thermalenergy, causing it to apparently ”heat up”,which leads to a temperature increase for sink-ing material. The average cooling and heatingadiabatic temperature profiles appear as a meanadiabat. A typical temperature-profile acrossthe depth of a vigorously convecting layer hasnarrow regions (TBLs) at the top and bottomthat accommodate most of the temperature jumpacross the layer, with most of the layer in theinterior being isothermal or adiabatic (Figure 7).

The heat flow (power output per unit area)out of the convecting layer is essentiallygiven by the heat that is conducted across theTBLs, given by k∆T/δ where k is thermalconductivity (units of W K−1m−1), ∆T/2 isthe temperature drop from the isothermal (oradiabatic) interior to the surface and δ/2 is thethickness of the TBL. By comparison, the ther-mal conduction across a static non-convectinglayer is k∆T/d. The ratio of heat flow inthe convecting layer to the purely conductivelayer is thus d/δ, which is called the Nusseltnumber Nu (named after the German engineer,Wilhelm Nusselt 1882-1957). The relationbetween Nu and convective vigor parameter-ized by Ra is important for understanding theefficiency of convective cooling of planetarybodies. Convective heat transport is oftenwritten as Nu(k∆T/d), and in consideringthis relation, Howard [1966] argued that heattransport across the depth of the vigorouslyconvecting fluid layer is so fast that the layerthickness is not a rate limiting factor in re-leasing heat, and thus heat flow should beindependent of fluid depth d; this implies thatsince Ra ∼ d3 then Nu ∼ Ra1/3, which yieldsa convective heat flow Nu(k∆T/d) that is

21


Property Mercury 1 Venus 2 Earth 3 Mars 4

Density [kg m−3] 3500 4000 4000 3500

Surface Temperature [K] 440 730 285 220

CMB Temperature [K] 3000 3500 3500 3000

Mantle Thickness [km] 400 2900 2900 2000

Gravity [m s−2] 3.7 10 10 3.5

Table 1: Some Properties of Terrestrial Planets and the Moon Relevant to MantleConvection Studies1 [Hauck et al., 2013; Tosi et al., 2013]2 [Kaula, 1990]3 [Schubert et al., 2001]2 [Schubert and Spohn, 1990; Harder, 1998]

independent of d. In general, since the fluidis conductive for Ra ≤ Rac, one often writesthat Nu = (Ra/Rac)

1/3 (although Nu = 1for Ra ≤ Rac), which is a reasonably accuraterelationship born out by simple experimentsand computer modeling [Schubert et al., 2001;Ricard, 2015]. This relationship also impliesthat the ratio of thermal boundary width to fluidlayer depth is δ/d ∼ Ra−1/3, which showsthat the TBLs become increasingly thin asconvection becomes more vigorous.

While the average TBL thickness is wellapproximated by δ ∼ Ra−1/3, it is worth notingthat the TBL thickness varies laterally: forexample, as the fluid in the top boundary layermoves from an upwelling to a downwelling, itcools and the boundary layer thickens as more

material cools next to the cold surface. Thethickening depends on the thermal diffusivity κand the residence time or time t since leavingthe upwelling. With regard to convectionin the Earth’s mantle, the top cold thermalboundary layer is typically associated withthe lithosphere, the layer of cold stiff mantlerock that is nominally divided into tectonicplates and reaches thickness of 100km or so.Simple dimensional considerations show thatthe boundary layer thickness goes as

√κt; this

corresponds to the well known√

age law forsubsidence of ocean sea floor with age sinceformation at mid-ocean ridges, implying thatsea-floor gets deeper because of the coolingand thickening of the lithosphere [e.g., Parsonsand Sclater, 1977; Sclater et al., 1980; Steinand Stein, 1992; Turcotte and Schubert, 2014];

22


temperature

he

igh

t

convection

conduction

temperaturetemperature

all bottom heated

he

igh

t add internalheating

Figure 7: Sketch of temperature profiles, showing how convective mixing homongenizes the conductivemean temperature into a nearly isothermal state (if the fuid is incompressible) with thermal boundary layersconnecting it to the cold surface and hot base (top frame). With no internal heating the interior meantemperature is the average of the top and bottom temperatures; the effect of adding internal heating (bottomframes) is to increase the interior mean temperature and thus change the relative size and temperature dropacross the top and bottom thermal boundary layers.

this emphasizes that the oceanic lithosphere isprimarily a convective thermal boundary layer.

A simple analysis of the heat transported byslabs demonstrates that slabs and plates are anintegral part of mantle convection [Bercovici,2003]. The energy flux Q associated with a slabsinking at velocity vsink is given by

Q = vsinkAρcp∆T (2)

where ∆T ≈ 700 K, ρ ≈ 3500 kg m−3

and cp = 1000 J kg K−1 are the slabs thermal

anomaly, density and heat capacity, respectively.A ≈ 2πRδ is the effective global cross-sectionalarea of all slabs crossing the depth at which theenergy flux is being estimated, with δ ≈ 100km being a typical slab thickness, and usingthe Earth’s circumference with R ≈ 6000 kmto approximate the net horizontal length of allslabs (since most slabs occur in a nearly largecircle around the Pacific basin). Assuming thatthe sinking slabs account for about 80% of themantles surface heat flow through the oceanfloor (the other 20% coming from the plumes),

23


such that Q = 0.8 ∗ 38 TW, and solving (2) forvsink yields a slab velocity vsink ≈ 10 cm year−1.This is in good agreement with the observedvelocity of tectonic plates, especially the oneswith an appreciable slab attached to them, suchthat slab-pull is particularly significant. Theagreement between the observed plate kinemat-ics and the measured heat flow at the Earth’ssurface is one of the major accomplishments ofmantle dynamics theory. In fact, the matchingconvective fluid velocities and plate velocitieshave also been inferred using gravity andheat-flow measurements [Pekeris, 1935; Hales,1936], as well as simple dynamical models ofthe force balance on sinking slabs [e.g., Daviesand Richards, 1992].

Understanding the dynamics of mantleconvection using the classical Rayleigh-Benard model is complicated by the fact thatthe mantle rocks are far from a simple fluid,with the most notable distinction being thatthe viscosity of rocks is extremely sensitiveto temperature. A drop in temperature bya few hundred degrees Kelvin - a plausibletemperature difference across planetary TBLs- can raise the viscosity by several orders ofmagnitude, as will be described in detail in thefollowing section. The dynamical consequenceof such thermal stiffening is that as the rocksget colder and denser, and thus more prone tosink, they also become increasingly resistantto deformation and flow, making it harderfor them to sink. Depending on the degreeof thermal stiffening of the cold TBL, thereare three possible modes of terrestrial mantleconvection [Solomatov, 1995; Solomatov andMoresi, 1997]. When the ratio of the maximum(coldest) to minimum (warmest) viscosity ismoderate, say less than about one order ofmagnitude, the cold TBL fully participatesin convective circulation. This mode may bethe most applicable to Earth, which featurescontinuous downwelling of its surface at sub-duction zones. Thermal stiffening of the Earth’s

lithosphere, however, is by significantly morethan one order of magnitude, suggesting thatthere exists a weakening mechanism (unique toEarth, as discussed later) that offsets the thermaleffect. At moderate viscosity ratios of abouttwo to four orders of magnitude, the flow of thecold TBL is significantly impeded, meaning itflows much more sluggishly than the underlyingmantle. Finally, at viscosity ratios more thanfour orders of magnitude, most of the cold TBLbecomes immobile. The deeper softest portionsof the TBL may participate in the convectivemantle flow; however, the shallower coldestportions act as a rigid boundary condition to theunderlying convective mantle layer. This so-called stagnant lid regime appears to take placeon Mars and Mercury (if Mercury’s mantle at allconvects). The failure to entrain the uppermostportion of the lithosphere effectively lowers thetemperature difference that drives convection,∆T in (1), since the temperature drop acrossthe lower, softer, mobile part of the cold TBL issmaller than for the drop across the entire TBL.The smaller effective TBL temperature contrastand the greater resistance of the rigid upperboundary act to lower the Ra of the so-calledsingle-plate planets, making them convect andcool less efficiently than the Earth does. Whilethe cold TBL may not get recycled into themantle, the surface of planets that are in thestagnant lid regime may still get renewed byvolcanism, as has been proposed for planetsexhibiting heat pipe behavior [Spohn, 1991;Moore et al., 2017], or as a consequence oflithospheric delamination, described in Section“Mantle’s Cold Thermal Boundary Layer”.

The dynamics of the hot TBL at the base of aplanetary mantle is affected by the temperature-dependence of viscosity as well. Specifically,for the onset of a new hot upwelling, since thehotter material is less viscous, it is less capa-ble of displacing the colder and stiffer ambi-ent mantle in order to rise through it. Fluidin the bottom TBL lingers at the CMB as it

24


gathers enough buoyancy to overcome the vis-cous resistance of the overlying mantle. Oncethe fluid has accumulated enough thermal buoy-ancy, it starts rising rapidly through the mantle,first forming a diapiric plume [Whitehead andLuther, 1975], which efficiently drains the re-maining low-viscosity hot TBL from the bot-tom [Bercovici and Kelly, 1997]. The efficientsupply of hot material from the bottom of themantle further propels the plumes ascent. Thesetwo stages of plume formation are responsiblefor its mushroom shape - the initial gathering ofhot material forms the large plume head, and thesubsequent rapid draining of the hot TBL uponascent forms the narrow plume tail [Campbelland Griffiths, 1990].

Another contrast between mantle convectionand the idealized Rayleigh-Benard model is thatthe planetary mantles are heated not just by thebottom boundary, referred to as ‘basal heating’,but also by the release of both radiogenic andprimordial heat distributed through the volumeof the fluid, termed ‘internal heating’. Addingthe effect of internal heating to the model of aconvecting layer raises the temperature of itsinterior, bringing it closer to the temperature ofthe bottom boundary (instead of the mean of thetwo boundary temperatures, as is the case in theclassical symmetric Rayleigh-Benard model).While this makes the temperature jump acrossthe bottom TBL smaller, the jump across thetop TBL becomes larger, since the top boundarynow must conduct out heat injected through thebottom, plus heat generated from the interior(Figure 7). As a result, the top TBL in an inter-nally heated system is more negatively buoyantand forms stronger downwellings, while theupwelling currents are smaller and weaker,compared to a system that is entirely basallyheated. The strong temperature-dependence ofviscosity of mantle rocks further adds to thisasymmetry, with the thermally stiffened colddownwellings having to acquire more thermalbuoyancy in order to overcome their ownviscous resistance and sink. The convective

currents on Earth do, indeed, feature large coldslabs with large thermal anomalies (of the orderof 700 K) and smaller plumes with weakerthermal anomalies (on the order of 200 K).

Convective currents also self-organize in sucha way that the horizontal spacing between theupwellings and the downwellings is optimized:not too small, so that they don’t exert too muchviscous drag on each other and/or don’t loseheat too rapidly to each other, and not too big,so that they don’t have to roll too much mass be-tween them. In addition, the separation distancebetween the vertical currents is determined bythe time it takes for the material that arrives toand moves laterally along the boundary to con-duct enough heat so as to become convectivelyunstable. The convective instability theorypredicts that the horizontal spacing between theupwellings and the downwellings is approxi-mately equal to the layer depth d (a bit larger atthe onset of convection, but identically d as Rabecomes very large). Applying this theoreticalprediction to the mantle is complicated by thefeatures of the mantle materials that tend tobreak the symmetry of flow observed in theidealized Rayleigh-Benard model. In particular,the strongly temperature-dependent viscositymeans that the cold TBL has to spend longertime near the surface, and thus travel furtherlaterally, before it is heavy enough to sinkagainst its own viscous resistance, resulting inconvection cells that are wider than the depth ofthe mantle [Weinstein and Christensen, 1991].Notably, if the degree of thermal stiffening putsconvection in a stagnant lid regime, then theaspect ratio of the convective part of the layerapproaches unity. In addition, mantle viscosityincreases with depth due to the effect of pres-sure [Sammis et al., 1977], and the resultingimpediment to vertical flow also acts to increasethe width of the convective cells [Christensenand Harder, 1991; Bunge et al., 1996]. ForEarth, the characteristic length scale of mantleconvection, with most downwellings occurring

25


in a torus along the planet’s circumference,and upwelling flow focused in the two regionson the either side of the torus (one beneathAfrica and the other beneath the Pacific, whereperhaps not coincidentally the LLSVPs reside),or what is know as spherical harmonic degree-2convection pattern, is indeed larger than thedepth of the mantle. Another example, albeitless well constrained, is the proposed degree-1convection pattern on Mars, in which a singleupwelling in the southern hemisphere, broadlybeneath the Tharsis Bulge, has been invoked toexplain the gravity anomaly and the observedtopographic dichotomy [Zhong and Zuber,2001; Roberts and Zhong, 2006; Keller andTackley, 2009]. For a martian mantle thicknessthat is between 0.4-0.6 of the planetary radius[depending on the assumed core-compositionand density, see Harder, 1998], a degree-1 pat-tern implies a characteristic convective lengthscale that is much larger than the mantle depth.Thus, the temperature- and depth-dependentviscosity may serve to explain the large aspectratio of convection cells of mantle convection,compared to that predicted by the Rayleigh-Benard system. The three large volcanic riseson Venus, which are arguably produced bydeep-rooted mantle plumes [Stofan et al., 1991;Smrekar and Stofan, 1999], may also indicate alow-degree convective pattern, although the re-mote measurements of gravity and topographyhave not been able to confirm such planform ofconvection for the venusian mantle [Steinbergeret al., 2010]. Whether the mantle of Mercuryis presently convecting is unclear, since thereare no indications of volcanism taking placesince about 3.5 Gyr ago [Namur and Charlier,2017], and its predicted Rayleigh number isonly modestly supercritical.

The presence of phase transitions in plane-tary mantles affects the convective pattern aswell. For example, the Earth’s endothermicwadsleyite-to-perovskite transition at 660 kmdepth impedes the vertical convective flow, with

its effect being stronger for the smaller scalestructures, as has been shown by analyticaland numerical studies [Bercovici et al., 1993;Tackley et al., 1993, 1994; Tackley, 1996].Thus, the 660-km transition for Earth [or the710-km for Venus, Ito and Takahashi, 1989]acts as a low-pass filter, effectively increasingthe characteristic length scale of convectiveflow. This phase transition on Mars is thoughtto be much deeper, at about 1910 km depth[Harder, 1998], which puts it very close to themartian CMB. Furthermore, the presence of alow viscosity asthenosphere on Earth lowersthe horizontal drag on convective flow andacts to increase the size of the convection cells[Lenardic et al., 2006]. The absence of an as-thenosphere on Venus precludes the same effect[Kaula, 1990], but has been speculated to occuron Mars and further support the large scale(degree-1) convection pattern of the martianmantle [Harder and Christensen, 1996; Harder,2000; Zhong and Zuber, 2001]. The mantlethickness on Mercury is arguably too small toexperience any solid-state phase transitions.

The 3-D convection pattern in fluids withtemperature-dependent viscosity has also beenobserved in experiments [White, 1988] and nu-merical models [Ratcliff et al., 1997; Schubertet al., 2001] to exhibit upwellings in the form ofcylindrical plumes at the center of a canopy ofsheet-like downwellings; this is crudely applica-ble to mantle convection on Earth, with the sheetlike slabs forming the downwelling flow and thecylindrical upwelling plumes forming the oceanislands, manifested as intraplate volcanism atthe surface. At more modest viscosity ratios, forexample due to a smaller temperature contrastacross the mantle, as may be the case for Marsand Venus, the upwelling flow may organizeinto linear structures, possibly explaining thebands of volcanic highlands observed on Venusor the chain of volcanoes in the Tharsis regionon Mars [Ratcliff et al., 1997; Schubert et al.,2001; Breuer and Moore, 2015]. While Earth’s

26


mid-ocean ridges or spreading centers are alsolinear, they primarily involve shallow upwelling,best explained as being pulled passively by adistant force (ostensibly slabs), rather than in-volving a deep convective upwelling that priesthem open. The features of mantle convectionthat are not readily explained by the classicalRayleigh-Benard model mainly arise becauseof the peculiar flow properties of the rock thatmakes up the mantle, which we discuss next.

How Can Rock Flow?Viscous flow of the solid rock that makes upthe mantle (also called solid-state creep) isgoverned by a number of complex processes,or rock rheologies, a full survey of which isbeyond the scope of this essay [see Ranalli,1995; Karato, 2008]. However, a brief outlineof the dominant mechanisms that accommodatemantle flow, namely diffusion and dislocationcreep, can help illustrate why the mantle is not asimple fluid, and explain some of its main flowfeatures.

Deformation by solid-state creep dependson the statistical-mechanical probability of anatom in a crystal lattice to leave the potentialwell of its lattice site. The potential-well itselfis defined by electrostatic or chemical bondsinhibiting escape, and Pauli-exclusion pressurepreventing molecules squeezing too closely toeach other. The mobility of atoms is determinedby a Boltzman distribution, which measuresthe probability of having sufficient energy toovercome the lattice potential well barrier,which is often called the activation energy (orallowing instead for pressure variations, theactivation enthalpy). This probability dependson the Arrhenius factor e−Ea/RT where Ea is theactivation energy (J/mol), R is the gas constant(J/K/mol) and T is temperature; RT representsthe thermal excitation energy of the molecule inthe well. As T goes to infinity, the probability

of escaping the well goes to 1, while as T goesto 0 the probability of escape goes to 0.

When there is stress acting on the mate-rial, the potential wells of the crystal changeshape, with the walls on the side of the wellunder compression getting steeper (squeezingmolecules closer makes Coulomb’s attraction inthe chemical bonds stronger), while the wallson the side of the well under tension becomeshallower (separating molecules weakens thebonds). Thus, the probability of atoms to escapetheir wells is higher in the direction of tension,with the lower activation barrier and away fromcompression, causing the medium to deform inthe tensile direction by solid-state diffusion ofatoms.

The accommodation of deformation bydiffusion of atoms is known as diffusion creep.For the deformation to occur, the atoms have todiffuse through mineral grains or along the grainboundaries. The smaller the grains, the smallerthe distance that an atom has to migrate beforeencountering a grain boundary, where the moredisordered atomic arrangement (compared tothat of the bulk of the grain) makes it easier forthe atom to move. Thus, the diffusion creepviscosity depends on grain size, wherein thesmaller the grains the weaker the material.

When the material deforms by disloca-tion creep, the strain is accommodated bythe propagation of dislocations through thegrain. Dislocations are linear lattice defects,where a whole row of atoms can be out oforder, displaced or missing. It requires moreenergy to displace a dislocation, compared toa single atom as in diffusion creep, but oncea dislocation is mobilized, it accommodatesstrain more efficiently than diffusion creep(unless the grains are sufficiently small). As thematerial creeps, new dislocations are nucleated,displaced or annihilated, so that the dislocationdensity of the material evolves and eventually

27


reaches a steady state that is determined pre-dominantly by stress. Due to the relatively largesize of the dislocations, they can interact witheach other through the induced long-rangingstress fields, which makes their velocity dependon dislocation density, which is itself stress-dependent. Thus both the dislocation densityand velocity depend on stress, and this makesfor a non-linear dislocation creep rheology, i.e.,viscosity depends on stress to some power.

The viscosities for diffusion and dislocationcreep mechanisms can be written as

µ =

{Bame

EaRT for diffusion creep

Aσ1−neE′a

RT for dislocation creep(3)

where A and B are proportionality constants,a is grain size, σ is stress (in fact, since stressis a tensor, σ2 is the scalar second invariant ofthe stress tensor), and m and n are exponents,typical values of which are 2 < m < 3 and3 < n < 5. The activation energies are differentfor diffusion and dislocation creep, with, for ex-ample, typical values for olivine (most abundantmineral in the upper mantle) being Ea = 375kJ mol−1 and E ′a = 530 kJ mol−1, respectively[Hirth and Kohlstedt, 2003]; however, thesevalues may be different for other minerals.Diffusion and dislocation creep are thought tooccur independently of each other dependingon stress and grain size: for a given stress,dislocation creep dominates for large grains anddiffusion creep for small grains; likewise, fora given grain-size, dislocation creep dominatesfor large stress and diffusion creep for smallstress (Figure 8).

The temperature-dependence of rheologyenables thermal variations to induce manyorders of magnitude changes in viscosity. Itseffect is most profound in the lithosphere. Forexample, a plausible temperature drop of 1500K across the martian lithosphere [Harder, 1998;Plesa and Breuer, 2014], assuming 500 and

2000 K at the top (about 100 km depth) andbottom (about 300 km depth) of the lithosphere,respectively, would increase the dislocationcreep viscosity by a factor of 1041, or the diffu-sion creep viscosity by a factor of 1029 (usingthe activation energy values for olivine fromthe previous paragraph for the lack of bettermineralogical constraints). It is unsurprising,then, that the thermally stiffened part of themartian lithosphere does not participate in theconvective mantle flow, rendering it in thestagnant lid regime. A more modest thermalcontrast across the venusian lithosphere, withabout 1200 and 1500 K at the top and bottom,respectively (assuming, crudely, the samethermal conditions as on Earth, but with a400 K hotter surface temperature), yields anincrease in the dislocation creep viscosity by afactor of 104, or the diffusion creep viscosityby a factor of 103. A modest thermal stiffeningof the lithosphere on Venus makes it morepliable to deformation by mantle flow, possiblyexplaining the episodic recycling of its surface,as witnessed by its relatively young 500 Myrold surface.

Cooling from the the Earth’s upper mantletemperature of 1500 K to 800 K at the top ofits lithosphere (about 10 km depth) would in-crease the dislocation creep viscosity by a fac-tor of 1016, or the diffusion creep viscosity by afactor of 1011 (using the activation energy val-ues for olivine from the previous paragraph). Inthis case, the viscous resistance to deform andsubduct a slab would require a force that is muchin excess of what is available from buoyancy,thus disallowing convective motion. However,Earth’s surface is clearly deforming, as is ev-idenced in plate tectonics, and so some otherphysical mechanism must exist that induces rhe-ological weakening and allows for the litho-sphere to deform. Dislocation creep allows formoderate softening as stress increases. How-ever, for the above example for a typical litho-spheric temperature drop, an unrealistic increase

28


Figure 8: Deformation map of stress-temperature space, including different creep mechanisms. Modifiedfrom Bercovici et al. [2015].

in stress by a factor of 108 would be requiredto offset thermal stiffening. Diffusion creep po-tentially allows for significant softening if thegrain size is reduced, and for the above exam-ple a grain size reduction by a factor of 10−3

would suffice to mobilize a plate and/or or al-low a slab to sink. Geological examples of grainsize reduction in the lithosphere by three and po-tentially more orders of magnitude in stronglydeformed regions abound (more on this in Sec-tion “Forming Tectonic Plates”). Understandingthe physical mechanisms responsible for rheo-logical weakening in the lithosphere that offsetsthermal stiffening and allows for plate-like de-formation is an active area of research.

Forming Tectonic PlatesThe plate-like character of the mantle’s coldthermal boundary layer, or the lithosphere, can

be described as large areas of strong barelydeforming plate interiors, separated by weakand narrow plate boundaries that undergointense deformation [with a few exceptions,such as broad diffuse plate boundaries, forexample in the Indian Ocean Gordon et al.,1998]. Understanding the physical mechanismsresponsible for such plate-like motion, whichrequire some form of rheological weakeningand strain localization in the lithosphere, is oneof the biggest questions in the geodynamics[see Bercovici et al., 2015, for a recent review].The proposed solutions include complex defor-mational behavior, such as plastic, brittle, orgrain size dependent rheologies.

Brittle deformation is one of the most extremecases of strain localization, where the materialbreaks along narrow faults that remain weakeven after the deformation ceases. However,

29


brittle rheology is not active for most of thedepth of oceanic lithosphere, giving way tosemiductile and eventually ductile behavior atdepths greater than about 10 km [Kohlstedtet al., 1995].

Another candidate for shear localization inthe lithosphere is viscoplasticity, which dictatesthat the material acts as a strong viscous fluidat low stresses, but once the stress exceeds ayield stress, the viscosity drops or in an extremecase the resistance to flow remains small nomatter the rate of deformation. Viscoplasticrheologies can be successful at generatingplate-like motion [Moresi and Solomatov, 1998;Trompert and Hansen, 1998; Tackley, 2000b;van Heck and Tackley, 2008; Foley and Becker,2009], but are difficult to reconcile with otherimportant observations. For example, whileplastic yielding is known to occur in rocks,laboratory experiments on rock deformationinfer a much higher yield stress than what isused in geodynamic models. Moreover, weakzones formed as a result of plastic yieldingare only active as long as the deformation isongoing, and vanish, or regain their strength,once deformation ceases. In contrast, tectonicplate boundaries are known to be long-livedfeatures, which remain weak for some timeeven without being deformed, and can betransported with the material and get reactivatedat a later time [Toth and Gurnis, 1998; Gurniset al., 2000]. In fact, dormant plate boundaries(e.g., sutures and inactive fracture zones) canretain their deformation memory in the form ofintrinsic weak zones over timescales that aremuch longer than the typical convective mantleoverturn time. In other words, the deformation-history dependent strength of the lithospherecannot be explained with an instanteneous-typeviscoplastic rheology.

For strain localization to occur, there needsto be a positive feedback mechanism in whichdeformation itself causes weakening, the weak

zones subsequently concentrate deformation,which causes further weakening, and so on.One example of such dynamic self-weakeningis the coupling of temperature-dependent vis-cosity and viscous heating: deformation causesfrictional heating, which makes the materialwarmer and weaker, and thus more readilydeformed, causing the deformation to focuson the weak zone, leading to more heatingand weakening, and so forth. Because thermalanomalies take time to dissipate away, the warmweak zones can be retained for some timeand allow for some history dependence of thematerial strength. However, for lithospheric andmantle material, thermal diffusion is relativelyfast and the memory of induced weaknessonly lasts a few million years, which is lessthan what is needed to explain long-lived plateboundaries. There are other limitations for thethermal self-softening mechanism in explainingthe localized lithospheric deformation. For ex-ample, the diffusive nature of thermal anomaliesonly allows for weak localization and toroidalmotion. While not sufficient on its own, thethermal self-softening might still assist in strainlocalization [Kameyama et al., 1997; Foley,2018].

Fluids in the lithosphere, such as water, inthe form of pores or hydrous mineral phases,can serve as a long-lived weakening agents.In this case, weakening can occur due to thereduction of friction through pore pressure,or through lubrication of plate boundaries byintroduction of sediments at subduction zonesor serpentinization along faults. The longevityof the potential weak zones over geologicaltime scales is ensured by the slow chemicaldiffusivity of hydrogen in minerals, as opposedto, for example, much faster thermal diffusionrates. One of the main difficulties with invokingwater for lithospheric-scale weakening is that itseffects are likely to be limited to shallow depths.Specifically, the frictional reduction by porepressure aids brittle failure and frictional slid-

30


ing, which are only relevant in the top roughly10-20 km depth. Ingesting water to greaterdepths, say to the bottom of a plate boundary atabout 100 km depth, would require pushing thefluid against a very large lithospheric pressuregradient and then preventing it from escaping(e.g., by invoking negligible permeabilities).While there are mechanisms, such as thermalcracking [Korenaga, 2007] or creating voidsand microcracks through deformation dam-age [Bercovici, 1998; Bercovici and Ricard,2003; Landuyt and Bercovici, 2009b], that canpotentially allow for the water to penetrateand serpentinize the uppermost few tens ofkilometers of the plate, there are no knownmechanisms that would allow it to weaken thedeepest, and potentially strongest, portion of thelithosphere.

An important clue to understanding thephysics of lithospheric weakening, and therebythe formation of tectonic plate boundaries,comes from the observed microstructure of thedeformed rocks, specifically the mineral grainsize and the density of intragranular defects.The exposed plate boundaries at the Earth’ssurface (i.e., in ophiolites and lithosphericshear zones), as well as samples from rockdeformation experiments, show that parts of therock that have undergone extreme deformationexhibit a substantial degree of recrystallizationand grain size reduction. Grain size evolution,including the processes of grain growth bydiffusion and grain shrinkage by dynamicrecrystallization, is governed by atomic scaleprocesses, the thermodynamics of which isdescribed by grain damage theory [Bercoviciand Ricard, 2005; Austin and Evans, 2007;Ricard and Bercovici, 2009; Rozel et al., 2011].Grain damage theory postulates that whilemost of the deformational work is dissipated asheat and irrecoverable viscous deformation, asmall fraction of work goes towards recoverableenergy, which is stored in the form of graindefects and new grain boundary area (i.e., by

splitting the same volume of material into alarger number of grains). Grain damage caninduce shear-localizing feedback through theinteraction of grain-size sensitive rheology(such as diffusion creep or grain-boundarysliding [Hirth and Kohlstedt, 2003]) and grainsize reduction via dynamic recrystallization[Karato et al., 1980; Derby and Ashby, 1987]:smaller grain size makes the material weaker,which thus deforms more readily, increasing theamount of deformational work available to driverecrystallization and grain damage, reducingthe grain size further, etc [Braun et al., 1999;Kameyama et al., 1997; Bercovici and Ricard,2005; Ricard and Bercovici, 2009; Rozel et al.,2011]. In monomineralic materials, recrys-tallization takes place so long as the materialdeforms by dislocation creep, which dominatesat high stresses and large grain sizes. Once thegrains shrink to sizes at which the grain sizedependent rheologies set in, recrystallizationprocess becomes limited, and so does the self-weakening localization feedback [De Bresseret al., 2001]. However, lithospheric rocksare polymineralic (with olivine and pyroxenebeing the most abundant minerals, or phases),and the grain size evolution of each phase isstrongly affected by the presence of the other.First of all, the rate of grain coarsening, whichoccurs independent of whether the material isdeforming or not, and which generally makesthe material stronger, is significantly impededby the secondary phase; this happens becausegrains grow by atomic diffusion, and it is dif-ficult to exchange atoms between grains whichare separated by another mineral. Thus, thegrain growth becomes effectively blocked bythe secondary phase, an effect known as Zenerpinning. Second, as the grains of each phasedeform to accommodate strain, be it in diffusionor dislocation creep, they are forced to movearound the grains of the other phase, resultingin stronger distortion of the grain boundariesthan if it was a single phase material; thisincreases the internal energy of the grain and

31


lowers the amount of energy needed for it torecrystallize and split into smaller grains. Thus,the presence of the secondary phase facilitatesgrain damage and induces grain size reductioneven when the material deforms in the grainsize sensitive diffusion creep regime, therebyenabling self-weakening feedback by graindamage [Bercovici and Ricard, 2012]. Indeed,the geological examples of peridotitic mylonitesand ultramylonites, where large strains correlatewith extreme grain size reduction, and whichhave been observed at all types of plate bound-aries, typically feature polymineralic rocks,often embedded in a matrix of coarse-grainedsingle-phase material [Warren and Hirth,2006; Herwegh et al., 2011; Linckens et al.,2011, 2015]. Moreover, the slowing of thegrain growth due to pinning in polymineralicmaterials promotes longevity of the damagedweak zones even after the deformation ceases,thus allowing for long-lived dormant plateboundaries [Bercovici and Ricard, 2014].

Geodynamic models featuring damage rhe-ology have successfully reproduced some ofthe plate-like features of the lithospheric mo-tion, including toroidal motion, strongly local-ized plate boundaries and observed microstruc-ture [Bercovici and Ricard, 2005; Landuyt et al.,2008; Landuyt and Bercovici, 2009b; Foleyet al., 2012; Bercovici and Ricard, 2013, 2014;Foley and Bercovici, 2014; Bercovici and Ri-card, 2016; Bercovici and Mulyukova, 2018;Mulyukova and Bercovici, 2017, 2018] gener-ated at stresses and temperatures typical for tec-tonic plates, and is a promising venue for fur-ther testing in global mantle convection models.While grain damage and pinning is potentiallyan important plate generation mechanism, es-pecially in the deepest cold and ductile portionof the lithosphere, it is likely that the effects ofbrittle deformation, lubrication by fluids and po-tentially other processes play an important roleat shallower depths [Lenardic and Kaula, 1994,1996; Korenaga, 2007; Bercovici et al., 2015].

Mantle Convection on EarlyEarth

Solid state mantle convection likely started afew tens or hundreds of millions of years afterthe Earth experienced its last major impact,which happened about 4.5 Gyr ago and led tothe formation of the moon [Canup and Asphaug,2001]. The energy released by the impact likelyleft the planet largely molten (although it couldvery well have been molten before the impactalso), a part of the Earth’s history referred to asmagma ocean [Elkins-Tanton, 2008; Solomatov,2015]. It would take about 10 Myr or more(depending on the model) for nearly all of themagma ocean to crystallize, differentiate, andfor solid state mantle convection to set in [seeFoley et al., 2014, and references therein]. Un-derstanding the nature of this early convectiveflow, i.e., its heat transport efficiency and itsability to mobilize and deform the surface, arecrucial for reconstructing the Earth’s dynamichistory and evolution, as well as for interpretingits present state.

The geological record becomes increasinglysparse in the Earth’s deep past. However, anumber of safe assumptions can be made aboutthe early physical state of the planet based onsome theoretical considerations. First of all,Earth’s size, or mass, has probably remainedmore or less the same after the last giant moon-forming impact. Second, the Earth’s interiorhas been getting colder for a significant portionof its history, although the rate of cooling ofits different layers (core, mantle and evolvingcrust) may vary, depending on their concen-trations of heat-producing elements, and theirability to exchange heat with one another (e.g.,thermal conduction across the CMB, or flow ofcold downwellings and hot upwellings acrossthe transition zone). The thermal history of themantle is governed by the competition betweeninternal heating by radioactive elements and

32


surface heat loss by convection. The mainuncertainty of the former is in the abundancesof radiogenic elements in the mantle; while theirhalf-lives are known, their initial concentrationand thus their net contribution is unknown. Byfar the largest uncertainty about mantle thermalhistory, however, comes from the assumedrate of convective cooling through time, and inparticular the initiation and rate of subduction,which is the dominant mechanism by which themantle cools [van Hunen and van den Berg,2008; van Hunen and Moyen, 2012]. Coolingof the mantle for at least the last 3 Gyr isconstrained by the measured temperatures ofthe mantle source that formed lavas at mid-ocean ridges, which appear to get progressivelycolder the younger they are: from 1500-1600◦C 2.5-3 Gyr ago to 1350 ◦C today [Herzberget al., 2010]. In addition, the existence of theinner core, which is the product of a coolingand crystallizing liquid outer core, implies thatthe Earth’s deep interior is cooling through time.

The rate at which heat can escape from man-tle to space depends on the temperature dropacross the Earth’s top thermal boundary layer,and thus on surface temperature, which in turnis controlled by the thermally insulating effectof the atmosphere (the greenhouse effect), aswell as the amount of incident solar energy. Thegreenhouse effect helps to keep the temperatureof the atmosphere relatively stable, and thusone can assume that for most of the Earth’shistory the temperature difference across thelithosphere has been controlled by the mantlesinternal temperature [Sleep and Zahnle, 2001;Lenardic et al., 2008].

Another important difference between theyoung and the modern Earth is the presence andvolume of the continents. Continents have aninsulating effect, which impedes surface heatflow due to their large thickness (compared tothe oceanic plates) and a higher concentration ofradiogenic elements. Heat flow measurements

on modern Earth support this notion: after cor-recting for the radioactive heating, the mantleheat flow is about one order of magnitude lowerat the surface of the continents than for oceanseafloor [Stein and Stein, 1992; Jaupart et al.,2015, and references therein]. The role of con-tinents as thermal insulators, and the resultinganomalously hot and buoyant mantle beneaththem, has been invoked as a mechanism fordriving continental dispersal and the subsequentsupercontinent reorganization - a key part of theWilson cycle [Gurnis, 1988; Rolf et al., 2012].However, whether the thermal insulation effectis sufficient to move the continents aroundremains subject to debate [Lenardic et al., 2005,2011; Heron and Lowman, 2011; Bercoviciand Long, 2014]. The junction between thestrong continental and the much weaker oceaniclithospheres helps to localize stresses thereand may serve as zones of heterogeneity andweakness where new plate boundaries can form[Kemp and Stevenson, 1996; Schubert andZhang, 1997; Regenauer-Lieb et al., 2001; Rolfand Tackley, 2011; Mulyukova and Bercovici,2018].

Modelling mantle dynamics on early Earthentails understanding mantle convection athigher internal temperatures. Using the theoret-ical framework outlined in, we can characterizemantle dynamics through time using theRayleigh number, which describes the vigorof convection, and the thermally induced vis-cosity difference across the lithosphere, whichpresents the biggest impediment to convectiveflow through stiffening of the cold thermalboundary layer.

It can be speculated that a hotter mantlein the past might have been convecting morevigorously, or at a higher Rayleigh number,due to the lower viscosity of mantle rocks,which is extremely sensitive to tempera-ture. Some mathematical formulations oftemperature-dependence of viscosity (e.g., the

33


Frank-Kamenetskii parametrization) suggestthat, for a given temperature jump, the thermallyinduced viscosity difference is smaller at highertemperatures. Thus, a weaker mantle and litho-sphere, compared to those on modern Earth,would make convection and plate tectonicsmore efficient in the past. Using some parame-terization of this positive relationship betweenmantle temperature and convective heat flow(i.e., such as the canonical canonical Nusseltnumber Rayleigh number relationship presentedin Section “Basics of Thermal Convection”),together with the rate of internal heating forsome plausible abundances of radioactive ele-ments, it is possible to extrapolate the internaltemperature of the mantle back in time frompresent day value. Depending on the detailsof this parametrization, such as the modernvalue assumed for the ratio of internal heatingto convective heat flux, called Urey ratio [seeChristensen, 1985], there is a range of possiblethermal evolution models [Korenaga, 2006;Silver and Behn, 2008]. The possible scenariosinclude the paradoxical thermal catastrophecase [Christensen, 1985], obtained for a lowvalue of present day Urey ratio (about 0.3),where the temperature of the mantle exceedsvalues that are well beyond uncertainty (mantletemperature quickly rises and diverges towardunrealistically high values before reaching 2Ga). To avoid the thermal catastrophe, onecould assume a higher value of modern Ureyratio, for example a value of 0.7 results in areasonable thermal evolution model. However,such high Urey ratio implies a much higherconcentration of radioactive elements in themantle, which is difficult to reconcile with therange provided by the cosmogenic analysis. Analternative solution is to assume that the mantleheat flow is less sensitive to the temperatureof the interior than what is predicted by theRayleigh-Benard model (i.e., Nu ∼ Rab,where in simple Rayleigh-Benard b = 1/3,but b < 1/3 for less temperature-dependentheat flow). In particular, factors other than

temperature may play a role in the complexrheology of the lithosphere may need to betaken into account [Korenaga, 2006, 2007,2013].

The mantle’s cold top thermal boundary layerdiffers from the rest of the mantle not just by itsconductive thermal profile, but also by its com-position, since it undergoes melting-assisteddifferentiation (i.e., segregation by fractionalmelting and melt-migration, which separatesthe crust and the depleted lithosphere). Meltingat higher temperatures leads to a more dehy-drated lithosphere. It is even more difficultfor a lithosphere that is drier, and thus stiffer,to founder under its own negative buoyancy[Conrad and Hager, 2001; Korenaga, 2006].Moreover, a higher degree of melting producesmore of the chemically buoyant basaltic crust,which further reduces the ability of the litho-sphere to sink [Davies, 2009]. Thus, platetectonics might have been less likely to occuron a hotter younger Earth. If the lithospherecannot subduct, mantle convection may proceedin a different regime, in which heat transportfrom the interior to the surface is restricted toconduction across a thick immobile layer [e.g.,stagnant lid mode, Solomatov and Moresi,1997] and volcanism [e.g., heat pipe mode,Spohn, 1991; Moore et al., 2017; Lourencoet al., 2018], and is thus relatively inefficient;this would mean that the rate of planetarycooling was slower in the past. How and whensubduction, and more generally plate tectonics,started is a question of formidable importancein the Earth evolution models, but the answer isobscured by our currently limited understandingof the physical mechanisms responsible for theformation of plate boundaries, as well as thepaucity of geological samples and data in theEarth’s deep history, which we discuss next.

There are no rock samples preserved from thefirst few hundred million years after the freezingof the magma ocean; the only geological data

34


available to elucidate this early stage of theEarth’s history are mineral inclusions in zircons[Mojzsis et al., 2001; Valley et al., 2002].Geochemical analysis of this sparse datasetshows evidence for melting of sediments andformation of granites, which may imply thatsubduction may have operated already at thisearly stage [Hopkins et al., 2010]. However, ap-plication of the extremely sparse zircons-dataset(in terms of their temporal and spatial distribu-tion) to infer the global tectonic regime bearssignificant uncertainty with it [Korenaga, 2013].

One of the key features of plate tectonics isthe continuous production and destruction ofthe oceanic lithosphere. Thus, the geologicalindicators of a mobilized lithosphere have tocome from the more indirect markers, expectedto be left behind on the fraction of the Earth’ssurface that is less prone to destruction [Condieand Kroner, 2008]. For example, when the seafloor is consumed by subduction, the continentson either side of it collide and form synchronousorogens, which can then be preserved even afterthe continents split up again. Earth’s surfaceappears to have gone through several episodesof continental assembly and dispersal, knownas the Wilson cycle, in some cases formingsupercontinents, where virtually all of the conti-nents come together. The oldest supercontinentis thought to be Kenorland, which assembledabout 2.7 Gyr ago. The need to close multipleoceans in order to form a supercontinent pro-vides a compelling evidence that global scaleplate tectonics was occurring already at thattime.

Furthermore, there exist examples of rocksthat have arguably formed in geological settingscharacteristic of plate tectonics and that areolder than 3 Gyr. Examples include 3 Gyr oldxenoliths from Kaapvaal craton, whose oxygenisotopic signature show that they may originatefrom subducted oceanic crust; a 3.6 Gyr oldsuture zone and a 3.8 Gyr old accretionary com-

plex, both in Greenland, are some of the oldestgeological structures indicative of convergenttectonics. However, it remains controversialas to whether the processes that formed theserocks are representative of the global state ofthe planetary surface; in addition, there existother explanations for how to form them, whichdon’t involve tectonic processes, adding to theuncertainty of interpreting these samples [Stern,2004, 2005; Condie and Kroner, 2008; Palinand White, 2016; Condie, 2018].

The absence of rock samples that are ex-pected to form if tectonics is widespread hasbeen invoked as evidence for the absence ofplate tectonics. For example, the lack of evi-dence for high-pressure and ultra-high pressuremetamorphism earlier than about 1Gyr, such asblueschists and eclogites, which are expectedto form in subduction zone environments, hasbeen suggested to indicate that subductiondidn’t start until about 1 Gyr ago [Stern, 2005].However, other studies caution that the absenceof preserved high-pressure rocks at the surfacedoesn’t preclude the operation of subduction onearlier Earth, it may instead indicate that theprocesses required for the exhumation of previ-ously subducted rocks were limited, or that thehigh-pressure phases formed upon subductionof the hotter, thicker and more magnesium-richoceanic lithosphere would be different than, forexample, the blueschist-facies typically formedin modern-day subduction zones [Brown, 2006;Korenaga, 2013; Palin and White, 2016].

The initiation of subduction remains an ex-tremely challenging issue in geodynamics to-day [Stern, 2004; Condie and Kroner, 2008;Wada and King, 2015]. The physical mech-anisms that allow for the lithosphere to over-come its thermal stiffening and spontaneouslyinitiate subduction are hotly debated, with theproposed models including weakening by rift-ing [Kemp and Stevenson, 1996; Schubert andZhang, 1997], sediment loading and water injec-

35


tion [Regenauer-Lieb et al., 2001], re-activationof pre-existing fault-zones [Toth and Gurnis,1998; Hall et al., 2003], or the weak zonesformed by accumulation of lithospheric dam-age from proto-subduction [Bercovici and Ri-card, 2014], collapse of passive margins [e.g.,Stern, 2004; Mulyukova and Bercovici, 2018]or at an active transform plate boundary [Caseyand Dewey, 1984] and plume-induced subduc-tion initiation [Gerya et al., 2015]. A better un-derstanding of the rock physics, as well as fur-ther interrogation of the geological, geochemi-cal and petrological record of the early Earth dy-namics continue to be fruitful areas of research.

Mantle Convection on OtherTerrestrial Planets

The rocky planets of the solar system exhibit alarge variation in their observed features, includ-ing size, gravity anomalies, topography, mag-netic field, atmosphere, distance from the sun,etc, all of which affect their interior dynamics.The heat sources available to drive mantle flowand convective cooling (with the possible excep-tion of Mercury, whose mantle may cool by con-duction), including the primordial as well as theradioactive heat sources, are finite and are notbeing replenished, which is why planetary activ-ity driven by mantle convection, such as volcan-ism and crust production, become weaker andeventually die out with time. The rate at whicha planet cools is determined by its initial heatbudget, as well as the efficiency at which it canrelease heat. For example, smaller planets haveless primordial heat, as they have experiencedfewer impacts upon accretion and the differenti-ation of their metallic cores had a smaller grav-itational energy release associated with it. Asfor the heat transport out of the planetary inte-riors, plate tectonics is the most efficient mech-anism (as on Earth), followed by the sluggishand stagnant lid convection regimes (for Venus

and Mars), and finally by the conductive cool-ing (possibly for Mercury). In our Solar Sys-tem, Earth is the largest terrestrial body, withthe largest amount of heat to dissipate away, andwhose mantle is, at least at present, convectivelytransporting heat most efficiently. Importantly,none of the known terrestrial planets, besidesEarth, appear to have surface rejuvenation byplate tectonics.

VenusVenus is arguably the most similar to our ownplanet, at least in terms of its size (which deter-mines internal depth, or pressure, structure) anddistance from the Sun (which determines theamount of surface heating by solar radiation).The Venusian surface appears to be young,dry and wrapped in a thick, dense and opaqueatmosphere, which makes remote observationsparticularly challenging. At about 460 ◦C,the surface of Venus is hundreds of degreeshotter than that of Earth, which some studieshave attributed to the runaway greenhouseeffect and the eventual loss of water [Kasting,1988]: liquid water is an important player inthe geological carbon cycle, which on Earthdrew down most of the carbon into carbonaterocks and allows for a temperate climate, whileon Venus the dry conditions fail to allow thesurface to extract the greenhouse gases fromthe atmosphere, thus keeping the surface hot[Driscoll and Bercovici, 2013]. The Venusianmantle temperature is likely higher than that onEarth, because it appears to be in a less efficientconvection regime [i.e., stagnant or mobile lidregime, Solomatov and Moresi, 1997; Moresiand Solomatov, 1998] which, along with ahotter surface, would make the heat flow out ofthe interior slower.

The relatively young age of the crust onVenus, inferred to be about 500 Myr old bycrater counting [Strom et al., 1994], points toglobal surface rejuvenation events, presumably

36


by extensive volcanism or lithospheric founder-ing [Turcotte, 1993; Turcotte et al., 1999]. De-pending on the chosen thermal evolution model,including the rate at which the cooled surfacecan be recycled into the mantle, the mantle tem-perature of Venus might be about 200 ◦C hotterthan that of Earth [Lenardic et al., 2008; Lan-duyt and Bercovici, 2009a]. A hotter surface andpossibly interior makes Venus a popular ana-logue of the early Earth, and some of the reason-ing of early Earth geodynamics can be appliedto understand the dynamics of Venus and viceversa. For example, it has been speculated thatthe hotter conditions on Venus is the reason whyit doesn’t have plate tectonics. One of the argu-ments is that a hotter surface, but a similar man-tle temperature on Venus compared to Earth, re-duces the temperature contrast across the Venu-sian lithosphere, and thus the amount of negativebuoyancy available to deform and potentiallymobilize it [Lenardic et al., 2008]. Another ar-gument is that if grain damage is responsiblefor the formation of plate boundaries on Earth,which requires a high enough ratio between therates of grain growth and grain size reduction,then the hotter surface temperature on Venuswould make the grain growth faster, potentiallyinhibiting the formation of fine-grained local-ized shear zones, or zones of weakness wherenew plate boundaries can form [Landuyt andBercovici, 2009a; Foley et al., 2012; Bercoviciand Ricard, 2014]. A potentially important dif-ference between Earth and Venus is that, in spiteof their similar size, Venus appears to not havea low-viscosity upper mantle, or asthenosphere;this has been inferred by numerical modelingstudies of mantle convection on Venus, con-strained by the observed surface topography,volcanism and geoid [Huang et al., 2013]. Theconvective stress acting on the Venusian litho-sphere is thus presumably smaller, comparedto that on Earth [Hoink et al., 2012]. Further-more, it has been argued that the Venusian litho-sphere and mantle lack water, which is an impor-tant weakening agent, and are therefore stiffer

than the Earth’s [Nimmo and McKenzie, 1998;Hirth and Kohlstedt, 1996], making the mobi-lization of the Venusian surface even more dif-ficult. Strictly speaking, the observational ev-idence for dry conditions on Venus only ex-ists for its atmosphere, and not for its interior.However, water is an incompatible element, andtherefore gets preferentially extracted from theinterior in the process of melting and volcanism,and there is no obvious mechanism on Venusby which water would be returned to the mantle(i.e., as is done by subduction on Earth). Thus,even if the mantles of Venus and Earth startedoff with similar compositions, the water mayhave been lost from the Venusian mantle, first toits surface, then to its atmosphere, and inevitablyto space [Donahue and Hodges, 1992; Nimmoand McKenzie, 1998]. These and other struc-tural differences between Earth (or early Earth)and Venus prompt some caution in comparingthe two planets.

MarsMars is the next largest terrestrial body in thesolar system after Earth and Venus, although atits 3390 km radius is still much smaller than theother two, and is thus likely to cool much fasterto space. In addition, the possible presence ofwater in the Martian mantle [within the range of73-290 ppm H2O, which is comparable to thatof Earth, McCubbin et al., 2012], as well as itshigh iron content [Martian olivines contain FeO∼ 18 wt%, compared to Earth’s FeO ∼ 8 wt%Zhao et al., 2009], act to lower the mantle vis-cosity, facilitating convection and efficient heattransport. The rapid cooling of Mars constrainsthe time-window for when its interior is hotenough to induce melting and to produce crust.Indeed, it appears that most of the Martian crustformed early in its history - in the first fewhundred million years after accretion [Nimmoand Tanaka, 2005]. At present, Mars is likely tohave a colder and less active interior, comparedto Earth, possibly explaining the absence of an

37


internal magnetic field on Mars [Acuna et al.,1998]. The strongly magnetized martian crust,however, suggests that the surface and interiorof Mars may have undergone extensive activityin the past, in particular within the first billionyears after solar system formation. Mars’ssurface may have deformed similarly to platetectonics on Earth, according to maps of mar-tian crustal remanent magnetization obtainedfrom spacecraft missions: the quasi-parallelmagnetic lines of alternating magnetic polarity[Connerney et al., 1999], as well as offsets inmagnetic field contours that identify transformfaults [Connerney et al., 2005], are similar tothe magnetic features associated with sea floorspreading on Earth. In addition, geologicalstructures interpreted from the satellite data,such as rifting and strike-slip faulting, mayalso be indicative of plate-tectonic like surfacedeformation [Yin, 2012].

Another curious feature of the Mars’s sur-face is its crustal dichotomy, with a 20-30 kmthick primordial crust in its northern hemisphere[Grott et al., 2013] and a much thicker, 30-80km, and presumably younger crust in its south-ern hemisphere [Solomon et al., 2005], with thesurface age difference of about one billion yearsbetween the two hemispheres. One of the pro-posed explanations for the martian crustal di-chotomy posits that it reflects the underlyingmantle convection pattern. Numerical simula-tions of Martian interior dynamics obtain mantleflow pattern with a single hot upwelling on onehemisphere, and thus predict enhanced crustalproduction in the region over mantle upwelling[Harder and Christensen, 1996; Harder, 2000;Keller and Tackley, 2009]. The presence of ex-tensive low-conducting crustal layer on Mars isthought to have thermally insulated the mantleso as to suppress its cooling rate and to pro-long its history of volcanic activity [Plesa andBreuer, 2014]. The high resolution images ofthe martian surface reveal that its has been ge-ologically active, albeit at a declining rate, for

at least the last 3.8 billion years, with recordsof volcanism on the Tharsis edifices as young astwo million years [Neukum et al., 2004]. Suchrecent volcanic activity on Mars may suggestthat its volcanoes may even erupt in the future,and that its mantle is not yet geodynamicallydead.

MercuryMercury is the smallest rocky planet in oursolar system (about 2440 km in radius) and theone that is the closest to the Sun. The strikinglylarge mean density of Mercury implies that it ismuch more iron-rich than the other terrestrialplanets, or has the largest ratio of metallic coreto silicate mantle, with the size of the core in-ferred to be over 2000 km in radius [Harder andSchubert, 2001]. The remaining few hundredkilometers thick (400 km typically used in mod-eling studies) mantle shell is likely convectingin the stagnant lid regime for seemingly all of itsgeologically recorded past, as indicated by theextremely well preserved cratering history onits surface [Watters et al., 2016]. A prolongedslow cooling of the planet’s interior appears tohave left lobate scarps on Mercury’s surface[Watters et al., 1998], interpreted to be thrustfaults that record the ancient pattern of mantleconvection, in addition to global contraction[King, 2008]. Most recent observations of thescarps crosscuting the impact craters indicatethat they are relatively young, less than 50Myr, implying that Mercury is probably stilltectonically active at present day [Watters et al.,2016]. The mineralogy of Mercury’s volcaniccrust, inferred from the geochemical data fromrecent space missions, records the history of itscooling mantle: the fractional melting by whichthe crust was produced occurred at shallowerdepth and lower temperature with time, fromabout 1900 K and 360 km 4.2 Gyr ago, toabout 1700 K and 160 km 3.5 Gyr ago, withthe magmatic activity terminating about 3.5Gyr ago as the mantle became too cold to melt

38


[Spohn, 1991; Namur and Charlier, 2017].Although Mercury’s mantle is not generatingany volcanic activity at present, its cooling mustnonetheless be very efficient, since it is ableto transport heat away from the core at highenough rate to support the internally generateddynamo [Ness et al., 1974; Connerney andNess, 1988]. Numerical models of Mercury’sinternal dynamics have been able to reconcile itsmagnetic and thermochemical evolution, withthe possible planforms of mantle convectionranging from numerous small-scale cells toa single upwelling, and including scenarioswhere the mercurian mantle convection ceasesaltogether after 3-4 Gyr [Heimpel et al., 2005;Tosi et al., 2013].

Comparing the observations made on differ-ent terrestrial planets is a powerful tool for teas-ing out the general physics that govern plane-tary evolution. Of course, the currently availabledataset is relatively sparse, but it is growing withthe increased number of space missions. In ad-dition, with the advent of extra-solar planet dis-covery, there is hope to find other planets withplate-like mantle dynamics, which would elu-cidate the peculiar tectonic regime of our ownplanet [e.g., Valencia et al., 2007; Sotin et al.,2010; Korenaga, 2010; van Heck and Tackley,2011; Foley et al., 2012].

ConclusionMantle convection governs the thermal andchemical evolution of the Earth and otherterrestrial planets in our solar system, dictatingthe dynamics of planetary interiors and drivinggeological motions at the surface. The ultimatedriver for convective mantle flow is that planetscool to space, releasing the heat acquired inthe course of their accretion, as well as theradiogenic internal heating. Thermal convectiontheory itself is a well established physicaltheory rooted in classical fluid dynamics and

thermodynamics. The theoretical predictions offlow velocities, establishment of thermal bound-ary layers and the convective pattern of slab-likedownwellings and plume-like upwellings go farin describing circulation and structure in theEarth’s mantle. However, the solid rock thatmakes up the mantle flows and deforms in waysthat are not easily captured by the propertiesof simple fluids on which classical convectiontheory is based. For instance, the manifestationof mantle convection as discrete tectonic platesat the surface, with strong and broad plateinteriors separated by weak and narrow plateboundaries, remains one of the most puzzlingphenomenons in geoscience. Much of theprogress in explaining how and why the Earth’smantle convects in the form of plate tectonics,unlike any other known terrestrial planet, comesfrom the studies of the rheologies of rocks thatmake up planetary mantles, including their de-pendence on temperature, stress, chemistry andmineral grain size. Understanding the physicsthat govern the geodynamics of modern Earthis essential to reconstructing the thermal andchemical history of our planet. For example, itremains problematic to explain how the Earthis stirred by deep subducting slabs, but stillappears unmixed when producing melts at mid-ocean ridges and ocean-islands. To unravel thehistory mantle stirring, a better understandingof melting, chemical segregation and mixing inthe mantle are needed.

The theory of mantle convection successfullyexplains many of the key features of planetaryinterior and surface dynamics, unifying thegeoscientific observations with the fundamentalphysical and fluid mechanical theories. How-ever, studies of mantle convection have alsoopened up many new questions and mysteriesabout the workings of the Earth and other rockyplanets to be addressed by future generations ofEarth and planetary scientists.

39


Suggested Further Reading• Schubert, G., D. Turcotte, and P. Olson,

Mantle Convection in the Earth and Plan-ets, Cambridge Univ. Press, 2001

• Bercovici, D., Mantle Dynamics, Treatiseon Geophysics (Second Edition), edited byG. Schubert, second edition ed., Volume 7,Elsevier, Oxford, 2015

• Davies, G. F., Mantle Convection for Geol-ogists, Cambridge Univ. Press, 2011

• Ribe, N., Theoretical Mantle Dynamics,Cambridge Univ. Press, 2018

ReferencesAcuna, M., et al., Magnetic field and plasma observations

at mars: Initial results of the mars global surveyor mis-sion, Science, 279(5357), 1676–1680, 1998.

Allegre, C. J., Chemical geodynamics, Tectonophysics,81(3–4), 109 – 132, doi:http://dx.doi.org/10.1016/0040-1951(82)90125-1, 1982.

Anderson, B. J., et al., The global magnetic field ofmercury from messenger orbital observations, Science,333(6051), 1859–1862, 2011.

Arndt, N. T., and S. L. Goldstein, An open boundary be-tween lower continental crust and mantle: its role incrust formation and crustal recycling, Tectonophysics,161(3-4), 201–212, 1989.

Austin, N. J., and B. Evans, Paleowattmeters: A scalingrelation for dynamically recrystallized grain size, Ge-ology, 35(4), 343–346, 2007.

Babeyko, A. Y., and V. Zharkov, Martian crust: a model-ing approach, Physics of the Earth and planetary inte-riors, 117(1-4), 421–435, 2000.

Ballmer, M., P. van Keken, and G. Ito, 7.10 -hotspots, large igneous provinces, and melting anoma-lies, in Treatise on Geophysics (Second Edition),edited by G. Schubert, second edition ed., pp. 393– 459, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00133-0, 2015.

Becker, T., J. Kellogg, and R. O’Connell, Thermal con-straints on the survival of primitive blobs in the lowermantle, Earth and planetary science letters, 171(3),351–365, 1999.

Benard, H., Les tourbillons cellulaires dans une nappe liq-uide, Revue generale des Sciences pures et appliquees,11, 1261–1271 and 1309–1328, 1900.

Benard, H., Les tourbillons cellulaires dans une nappeliquide transportant de la chaleur par convection enregime permanent, Annales de Chimie et de Physique,23, 62–144, 1901.

Bercovici, D., A source-sink model of the generationof plate tectonics from non-newtonian mantle flow, J.Geophys. Res., 100, 2013–2030, 1995.

Bercovici, D., Generation of plate tectonics fromlithosphere-mantle flow and void-volatile self-lubrication, Earth Planet. Sci. Lett., 154, 139–151,1998.

Bercovici, D., The generation of plate tectonics frommantle convection, Earth and Planetary Science Let-ters, 205(3), 107–121, 2003.

Bercovici, D., 7.01 - mantle dynamics: An introductionand overview, in Treatise on Geophysics (Second Edi-tion), edited by G. Schubert, second edition ed., pp.1 – 22, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00125-1, 2015.

Bercovici, D., and S. Karato, Whole mantle convectionand the transition-zone water filter, Nature, 425, 39–44, 2003.

Bercovici, D., and A. Kelly, Nonlinear initiation of diapirsand plume heads, Phys. Earth Planet. Int., 101, 119–130, 1997.

Bercovici, D., and M. D. Long, Slab rollback instabilityand supercontinent dispersal, Geophysical ResearchLetters, 41, 6659–6666, doi:10.1002/2014GL061251,2014.

Bercovici, D., and E. Mulyukova, A continuum theoryfor phase mixing and grain-damage relevant to tec-tonic plate boundary evolution, Physics of the Earthand Planetary Interiors, 2018.

Bercovici, D., and Y. Ricard, Energetics of a two-phasemodel of lithospheric damage, shear localization andplate-boundary formation, Geophysical Journal Inter-national, 152(3), 581–596, doi:10.1046/j.1365-246X.2003.01854.x, 2003.

40


Bercovici, D., and Y. Ricard, Tectonic plate gener-ation and two-phase damage: void growth versusgrainsize reduction, J. Geophys. Res., 110, B03,401,doi:10.1029/2004JB003,181, 2005.

Bercovici, D., and Y. Ricard, Mechanisms for the genera-tion of plate tectonics by two-phase grain-damage andpinning, Phys. Earth Planet. Int., 202-203, 27–55, doi:10.1016/j.pepi.2012.05.003, 2012.

Bercovici, D., and Y. Ricard, Generation of plate tecton-ics with two-phase grain-damage and pinning: Source–sink model and toroidal flow, Earth and Planetary Sci-ence Letters, 365(0), 275 – 288, doi:10.1016/j.epsl.2013.02.002, 2013.

Bercovici, D., and Y. Ricard, Plate tectonics, damage andinheritance, Nature, 508, 513–516, doi:doi:10.1038/nature13072, 2014.

Bercovici, D., and Y. Ricard, Grain-damage hysteresisand plate-tectonic states, Phys. Earth Planet. Int., 253,31–47, doi:10.1016/j.pepi.2016.01.005., 2016.

Bercovici, D., G. Schubert, and P. J. Tackley, On the pen-etration of the 660 km phase change by mantle down-flows, Geophysical research letters, 20(23), 2599–2602, 1993.

Bercovici, D., P. J. Tackley, and Y. Ricard, The Genera-tion of Plate Tectonics from Mantle Dynamics, in Trea-tise on Geophysics, vol. 7 Mantle Dynamics, edited byDavid Bercovici (Gerald Schubert editor-in-chief), 2nded., chap. 7, pp. 271 – 318, Elsevier, doi:http://dx.doi.org/10.1016/B978-0-444-53802-4.00135-4, 2015.

Bower, D. J., M. Gurnis, and M. Seton, Lower man-tle structure from paleogeographically constraineddynamic earth models, Geochemistry, Geophysics,Geosystems, 14(1), 44–63, 2013.

Braginsky, S. I., and P. H. Roberts, Equations governingconvection in earth’s core and the geodynamo, Geo-physical & Astrophysical Fluid Dynamics, 79(1-4), 1–97, 1995.

Braun, J., J. Chery, A. Poliakov, D. Mainprice,A. Vauchez, A. Tomassi, and M. Daignieres, A sim-ple parameterization of strain localization in the duc-tile regime due to grain size reduction: A casestudy for olivine, Journal of Geophysical Research:Solid Earth, 104(B11), 25,167–25,181, doi:10.1029/1999JB900214, 1999.

Breuer, D., and W. Moore, 10.08 - dynamics andthermal history of the terrestrial planets, the moon,and io, in Treatise on Geophysics (Second Edition),edited by G. Schubert, second edition ed., pp. 255– 305, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00173-1, 2015.

Brown, M., Duality of thermal regimes is the distinctivecharacteristic of plate tectonics since the neoarchean,Geology, 34(11), 961–964, 2006.

Bunge, H., M. Richards, and J. Baumgardner, Effect ofdepth-dependent viscosity on the planform of mantle-convection, Nature, 379, 436–438, 1996.

Burke, K., B. Steinberger, T. H. Torsvik, and M. A.Smethurst, Plume generation zones at the marginsof large low shear velocity provinces on the core–mantle boundary, Earth and Planetary Science Letters,265(1), 49–60, 2008.

Calderwood, A., Mineral physics constraints on the tem-perature and composition of the earth’s mantle, Ph.D.thesis, Ph. D. thesis, Univ. of Br. Columbia, Vancouver,BC, Canada, 1999.

Campbell, I. H., and R. W. Griffiths, Implications of man-tle plume structure for the evolution of flood basalts,Earth and Planetary Science Letters, 99(1-2), 79–93,1990.

Canup, R. M., and E. Asphaug, Origin of the moon ina giant impact near the end of the earth’s formation,Nature, 412, 708 EP –, 2001.

Casey, J., and J. Dewey, Initiation of subduction zonesalong transform and accreting plate boundaries, triple-junction evolution, and forearc spreading centres—implications for ophiolitic geology and obduction, Ge-ological Society, London, Special Publications, 13(1),269–290, 1984.

Chandrasekhar, S., Hydrodynamic and HydromagneticStability, Oxford University Press, New York, 1961.

Christensen, U., and H. Harder, Three-dimensional con-vection with variable viscosity, Geophys. J. Int., 104,213–226, 1991.

Christensen, U., and A. Hofmann, Segregation of sub-ducted oceanic crust in the convecting mantle, Journalof Geophysical Research, 99(B10), 19,867–19, 1994.

Christensen, U. R., Thermal evolution models for theearth, Journal of Geophysical Research: Solid Earth,90(B4), 2995–3007, 1985.

41


Cloetingh, S., R. Wortel, and N. Vlaar, On the initiationof subduction zones, Pure and Applied Geophysics PA-GEOPH, 129(1-2), 7–25, 1989.

Coltice, N., and Y. Ricard, Geochemical observations andone layer mantle convection, Earth Planet. Sci. Lett.,174, 125–137, 1999.

Condie, K., and A. Kroner, When did plate tectonicsbegin? Evidence from the geologic record, in WhenDid Plate Tectonics Begin on Planet Earth?, edited byK. Condie and V. Pease, pp. 281–294, Geological So-ciety of America, special Paper 440, 2008.

Condie, K. C., Contrasting sources for upper and lowercontinental crust: the greenstone connection, The Jour-nal of Geology, 105(6), 729–736, 1997.

Condie, K. C., A planet in transition: The onset of platetectonics on earth between 3 and 2 ga?, GeoscienceFrontiers, 9(1), 51–60, 2018.

Connerney, J., and N. Ness, Mercury’s magnetic field andinterior, Mercury, pp. 494–513, 1988.

Connerney, J. E. P., M. H. Acuna, N. F. Ness,G. Kletetschka, D. L. Mitchell, R. P. Lin, and H. Reme,Tectonic implications of mars crustal magnetism, Pro-ceedings of the National Academy of Sciences of theUnited States of America, 102(42), 14,970–14,975,doi:10.1073/pnas.0507469102, 2005.

Connerney, J. E. P., et al., Magnetic lineations in the an-cient crust of mars, Science, 284(5415), 794–798, doi:10.1126/science.284.5415.794, 1999.

Conrad, C. P., and B. H. Hager, Mantle convection withstrong subduction zones, Geophysical Journal Interna-tional, 144(2), 271–288, 2001.

Czamanske, G. K., A. B. Gurevitch, V. Fedorenko, andO. Simonov, Demise of the siberian plume: Paleo-geographic and paleotectonic reconstruction from theprevolcanic and volcanic record, north-central siberia,International Geology Review, 40(2), 95–115, doi:10.1080/00206819809465200, 1998.

Dannberg, J., and R. Gassmoller, Chemical trends inocean islands explained by plume–slab interaction,Proceedings of the National Academy of Sciences,115(17), 4351–4356, 2018.

Dannberg, J., and S. V. Sobolev, Low-buoyancy thermo-chemical plumes resolve controversy of classical man-tle plume concept, Nature communications, 6, 6960,2015.

Davaille, A., S. Smrekar, and S. Tomlinson, Experimentaland observational evidence for plume-induced subduc-tion on venus, Nature Geoscience, 10(5), 349, 2017.

Davies, G., The role of the lithosphere in mantle convec-tion, J. Geophys. Res., 93, 10451–10466, 1988.

Davies, G., and M. Richards, Mantle convection, J. Geol-ogy, 100, 151–206, 1992.

Davies, G. F., Effect of plate bending on the urey ratioand the thermal evolution of the mantle, Earth andPlanetary Science Letters, 287(3–4), 513 – 518, doi:http://dx.doi.org/10.1016/j.epsl.2009.08.038, 2009.

De Bresser, J., J. ter Heege, and C. Spiers, Grain size re-duction by dynamic recrystallization: can it result inmajor rheological weakening?, Intl. J. Earth Sci., 90,28–45, 2001.

Derby, B., and M. Ashby, On dynamic recrystallization,Scripta Metallurgica, 21, 879–884, 1987.

Deschamps, F., Y. Li, and P. J. Tackley, Large-scalethermo-chemical structure of the deep mantle: ob-servations and models, in The Earth’s HeterogeneousMantle, pp. 479–515, Springer, 2015.

Dobson, D. P., and J. P. Brodholt, Subducted banded ironformations as a source of ultralow-velocity zones at thecore–mantle boundary, Nature, 434(7031), 371, 2005.

Donahue, T., and R. Hodges, Past and present water bud-get of venus, Journal of Geophysical Research: Plan-ets, 97(E4), 6083–6091, 1992.

Driscoll, P., and D. Bercovici, Divergent evolution ofearth and venus: Influence of degassing, tectonics,and magnetic fields, Icarus, 226, 1447–1464, doi:http://dx.doi.org/10.1016/j.icarus.2013.07.025, 2013.

Dziewonski, A., and D. Anderson, Preliminary referenceearth model, Phys Earth Planet. Int., 25, 297–356,1981.

Dziewonski, A., V. Lekic, and B. Romanowicz, MantleAnchor Structure: An argument for bottom up tecton-ics, Earth and Planetary Science Letters, 299, 69–79,2010.

Elkins-Tanton, L., Linked magma ocean solidification andatmospheric growth for earth and mars, Earth andPlanetary Science Letters, 271(1–4), 181 – 191, doi:10.1016/j.epsl.2008.03.062, 2008.

42


Foley, B., and T. Becker, Generation of plate-like behavior and mantle heterogeneityfrom a spherical, visco-plastic convectionmodel, Geochem., Geophys., Geosys., 10(8),Q08,001, doi:10.1029/2009GC002,378, doi:10.1029/2009GC002378, 2009.

Foley, B. J., On the dynamics of coupled grain size evo-lution and shear heating in lithospheric shear zones,Physics of the Earth and Planetary Interiors, 283,7 – 25, doi:https://doi.org/10.1016/j.pepi.2018.07.008,2018.

Foley, B. J., and D. Bercovici, Scaling laws for convec-tion with temperature-dependent viscosity and grain-damage, Geophysical Journal International, 199(1),580–603, doi:10.1093/gji/ggu275, 2014.

Foley, B. J., D. Bercovici, and W. Landuyt, The condi-tions for plate tectonics on super-earths: Inferencesfrom convection models with damage, Earth and Plan-etary Science Letters, 331-332, 281–290, 2012.

Foley, B. J., D. Bercovici, and L. T. Elkins-Tanton, Initi-ation of plate tectonics from post-magma ocean ther-mochemical convection, Journal of Geophysical Re-search: Solid Earth, 119(11), 8538–8561, doi:10.1002/2014JB011121, 2014.

Forsyth, D., the melt seismic team, imaging the deepstructure beneath a mid-ocean ridge: overview of theseismological component of the melt experiment, Sci-ence, 1998.

Forsyth, D., and S. Uyeda, On the relative importance ofthe driving forces of plate motion, Geophys. J. R. Astr.Soc., 43, 163–200, 1975.

Forsyth, D., et al., Imaging the deep seismic structure be-neath a mid-ocean ridge: The melt experiment, Sci-ence, 280, 1215–1218, 1998.

French, S. W., and B. Romanowicz, Broad plumesrooted at the base of the earth’s mantle beneath majorhotspots, Nature, 525(7567), 95, 2015.

Garnero, E., and A. McNamara, Structure and dynam-ics of Earth’s lower mantle, Science, 320(5876), 626,2008.

Garnero, E. J., A new paradigm for earth’s core-mantleboundary, Science, 304(5672), 834–836, 2004.

Garnero, E. J., and D. V. Helmberger, Seismic detectionof a thin laterally varying boundary layer at the baseof the mantle beneath the central-pacific, GeophysicalResearch Letters, 23(9), 977–980, 1996.

Gerya, T. V., R. J. Stern, M. Baes, S. V. Sobolev, andS. A. Whattam, Plate tectonics on the earth trig-gered by plume-induced subduction initiation, Nature,527(7577), 221–225, 2015.

Gordon, R., C. DeMets, and J. Royer, Evidence for long-term diffuse deformation of the lithosphere of the equa-torial indian ocean, Nature, 395, 370–374, 1998.

Grand, S., R. van der Hilst, and S. Widiyantoro, Globalseismic tomography: A snapshot of convection in theearth, GSA Today, 7, 1–7, 1997.

Grott, M., et al., Long-term evolution of the martian crust-mantle system, Space Science Reviews, 174(1-4), 49–111, 2013.

Gurnis, M., Large-scale mantle convection and the ag-gregation and dispersal of supercontinents, Nature,332(6166), 695–699, doi:{10.1038/332695a0}, 1988.

Gurnis, M., S. Zhong, and J. Toth, On the competing rolesof fault reactivation and brittle failure in generatingplate tectonics from mantle convection, in History andDynamics of Global Plate Motions, Geophys. Monogr.Ser., vol. 121, edited by M. A. Richards, R. Gordon,and R. van der Hilst, pp. 73–94, Am. Geophys. Union,Washington, DC, 2000.

Hager, B., Subducted slabs and the geoid: constraints onmantle rheology and flow, Journal of Geophysical Re-search, 89(B7), 6003–6015, 1984.

Hager, B., and R. O’Connell, A simple global model ofplate dynamics and mantle convection, J. Geophys.Res., 86, 4843–4867, 1981.

Hales, A., Convection currents in the Earth, Monthly No-tices Roy. Astron. Soc., Geophys. Suppl., 3, 372–379,1936.

Hall, C. E., M. Gurnis, M. Sdrolias, L. L. Lavier, and R. D.Mueller, Catastrophic initiation of subduction follow-ing forced convergence across fracture zones, EarthPlanet. Sci. Lett, 212, 15–30, 2003.

Harder, H., Phase transitions and the three-dimensionalplanform of thermal convection in the martian mantle,Journal of Geophysical Research: Planets, 103(E7),16,775–16,797, 1998.

Harder, H., Mantle convection and the dynamic geoid ofmars, Geophysical Research Letters, 27(3), 301–304,doi:10.1029/1999GL008418, 2000.

43


Harder, H., and U. R. Christensen, A one-plume modelof martian mantle convection, Nature, 380, 507 EP –,1996.

Harder, H., and G. Schubert, Sulfur in mercury’s core?,Icarus, 151(1), 118–122, 2001.

Harris, L. B., and J. H. Bedard, Crustal evolution and de-formation in a non-plate-tectonic archaean earth: Com-parisons with venus, in Evolution of archean crust andearly life, pp. 215–291, Springer, 2014.

Hauck, S. A., et al., The curious case of mercury’s internalstructure, Journal of Geophysical Research: Planets,118(6), 1204–1220, 2013.

Heimpel, M., J. Aurnou, F. Al-Shamali, and N. G. Perez,A numerical study of dynamo action as a function ofspherical shell geometry, Earth and Planetary ScienceLetters, 236(1-2), 542–557, 2005.

Hernlund, J., and A. McNamara, 7.11 - the core–mantleboundary region, in Treatise on Geophysics (SecondEdition), edited by G. Schubert, second edition ed.,pp. 461 – 519, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00136-6, 2015.

Heron, P. J., and J. P. Lowman, The effects of supercon-tinent size and thermal insulation on the formation ofmantle plumes, Tectonophysics, 510(1-2), 28–38, doi:{10.1016/j.tecto.2011.07.002}, 2011.

Herwegh, M., J. Linckens, A. Ebert, A. Berger, andS. Brodhag, The role of second phases for controllingmicrostructural evolution in polymineralic rocks: A re-view, Journal of Structural Geology, 33(12), 1728 –1750, doi:10.1016/j.jsg.2011.08.011, 2011.

Herzberg, C., K. Condie, and J. Korenaga, Thermal his-tory of the earth and its petrological expression, Earthand Planetary Science Letters, 292(1-2), 79–88, 2010.

Hess, H., History of ocean basins, in Petrologic Studies - AVolume in Honor of A.F. Buddington, edited by A. En-geln, H. James, and B. Leonard, pp. 599–620, Geol.Soc. America, New York, 1962.

Hirth, G., and D. Kohlstedt, Water in the oceanic up-per mantle: implications for rheology, melt extractionand the evolution of the lithosphere, Earth Planet. Sci.Lett., 144, 93–108, 1996.

Hirth, G., and D. Kohlstedt, Rheology of the upper mantleand the mantle wedge: a view from the experimental-ists, in Subduction Factor Mongraph, vol. 138, editedby J. Eiler, pp. 83–105, Am. Geophys. Union, Wash-ington, DC, 2003.

Hofmann, A., Mantle geochemistry: the message fromoceanic volcanism, Nature, 385, 219–228, 1997.

Hofmann, A., Sampling mantle heterogeneity throughoceanic basalts: Isotopes and trace elements, in Trea-tise on Geochemistry: The Mantle and Core, edited byR. C. H. Holland and c. e. K.K. Turekian, pp. 61–101,Elsevier, 2003.

Hofmann, A. W., and W. M. White, Mantle plumes fromancient oceanic crust, Earth and Planetary ScienceLetters, 57(2), 421–436, 1982.

Hoink, T., A. Lenardic, and M. Richards, Depth-dependent viscosity and mantle stress amplification:implications for the role of the asthenosphere in main-taining plate tectonics, Geophysical Journal Interna-tional, 191(1), 30–41, doi:10.1111/j.1365-246X.2012.05621.x, 2012.

Holmes, A., Radioactivity and earth movements, Geol.Soc. Glasgow Trans., 18, 559–606, 1931.

Hopkins, M. D., T. M. Harrison, and C. E. Manning, Con-straints on hadean geodynamics from mineral inclu-sions in >4Ga zircons, Earth and Planetary ScienceLetters, 298(3–4), 367 – 376, doi:10.1016/j.epsl.2010.08.010, 2010.

Howard, L. N., Convection at high Rayleigh number, inProceedings of the Eleventh International Congress ofApplied Mechanics, edited by H. Gortler, pp. 1109–1115, Springer-Verlag, New York, 1966.

Huang, J., A. Yang, and S. Zhong, Constraints of the to-pography, gravity and volcanism on venusian mantledynamics and generation of plate tectonics, Earth andPlanetary Science Letters, 362(Supplement C), 207– 214, doi:https://doi.org/10.1016/j.epsl.2012.11.051,2013.

Ishii, M., and J. Tromp, Normal-mode and free-air grav-ity constraints on lateral variations in velocity and den-sity of earth’s mantle, Science, 285(5431), 1231–1236,1999.

Ishii, M., and J. Tromp, Constraining large-scale man-tle heterogeneity using mantle and inner-core sensitivenormal modes, Physics of the Earth and Planetary In-teriors, 146(1-2), 113–124, 2004.

Ita, J., and L. Stixrude, Petrology, elasticity, and compo-sition of the mantle transition zone, Journal of Geo-physical Research: Solid Earth, 97(B5), 6849–6866,doi:10.1029/92JB00068, 1992.

44


Ito, E., and E. Takahashi, Postspinel transformation in thesystem mg2sio4 − fe2sio4 and some geophysical im-plications, J. Geophys. Res., 94, 10637–10646, 1989.

Ito, G., and J. Mahoney, Flow and melting of a heteroge-neous mantle: 1. method and importance to the geo-chemistry of ocean island and mid-ocean ridge basalts,Earth Planet. Sci. Lett., 230, 29–46, 2005a.

Ito, G., and J. Mahoney, Flow and melting of a hetero-geneous mantle: 2. implications for a chemically non-layered mantle, Earth Planet. Sci. Lett., 230, 47–63,2005b.

Jackson, M. G., and R. Dasgupta, Compositions of himu,em1, and em2 from global trends between radiogenicisotopes and major elements in ocean island basalts,Earth and Planetary Science Letters, 276(1-2), 175–186, 2008.

Jaupart, C., S. Labrosse, F. Lucazeau, and J.-C.Mareschal, Temperatures, heat and energy in the man-tle of the earth, in Treatise on Geophysics, vol. 7,Mantle Dynamics, edited by D. Bercovici (G. Schu-bert, chief editor), 2nd ed., pp. 223–270, Elsevier, NewYork, 2015.

Jellinek, A., and M. Manga, Links between long-livedhotspots, mantle plumes, D” and plate tectonics, Rev.Geophys., 42(3), doi:10.1029/2003RG000,144, 2004.

Kameyama, M., D. Yuen, and H. Fujimoto, The interac-tion of viscous heating with grain-size dependent rhe-ology in the formation of localized slip zones, Geo-phys. Res. Lett., 24, 2523–2526, 1997.

Karato, S., Deformation of Earth Materials: An Introduc-tion to the Rheology of Solid Earth, Cambridge Univ.Press, 2008.

Karato, S.-i., M. Toriumi, and T. Fujii, Dynamic re-crystallization of olivine single crystals during high-temperature creep, Geophysical Research Letters, 7(9),649–652, 1980.

Kasting, J., Runaway and moist greenhouse atmospheresand the evolution of earth and venus, Icarus, 74, 472–494, 1988.

Katsura, T., et al., Post-spinel transition in mg2sio4 de-termined by high p–t in situ x-ray diffractometry,Physics of the Earth and Planetary Interiors, 136(1),11 – 24, doi:https://doi.org/10.1016/S0031-9201(03)00019-0, phase transitions and mantle discontinuities,2003.

Katsura, T., et al., Olivine-wadsleyite transition in the sys-tem (mg,fe)2sio4, Journal of Geophysical Research:Solid Earth, 109(B2), doi:10.1029/2003JB002438,2004.

Kaula, W. M., Material properties for mantle convec-tion consistent with observed surface fields, Journal ofGeophysical Research: Solid Earth, 85(B12), 7031–7044, 1980.

Kaula, W. M., Venus: A contrast in evolution to earth,Science, 247(4947), 1191–1196, 1990.

Kawai, K., and T. Tsuchiya, Temperature profile inthe lowermost mantle from seismological and mineralphysics joint modeling, Proceedings of the NationalAcademy of Sciences, 106(52), 22,119–22,123, 2009.

Keller, T., and P. J. Tackley, Towards self-consistent mod-eling of the martian dichotomy: The influence ofone-ridge convection on crustal thickness distribution,Icarus, 202(2), 429–443, 2009.

Kellogg, L., B. Hager, and R. van der Hilst, Composi-tional stratification in the deep mantle, Science, 283,1881–1884, 1999.

Kemp, D. V., and D. J. Stevenson, A tensile, flexuralmodel for the initiation of subduction, GeophysicalJournal International, 125(1), 73–93, 1996.

King, S. D., Pattern of lobate scarps on mercury’s surfacereproduced by a model of mantle convection, NatureGeoscience, 1(4), 229, 2008.

Kleine, T., C. Munker, K. Mezger, and H. Palme, Rapidaccretion and early core formation on asteroids andthe terrestrial planets from hf–w chronometry, Nature,418(6901), 952–955, doi:10.1038/nature00982, 2002.

Kobayashi, K., R. Tanaka, T. Moriguti, K. Shimizu, andE. Nakamura, Lithium, boron, and lead isotope sys-tematics of glass inclusions in olivines from hawaiianlavas: evidence for recycled components in the hawai-ian plume, Chemical Geology, 212(1), 143–161, 2004.

Kohlstedt, D., B. Evans, and S. Mackwell, Strength of thelithosphere: Constraints imposed by laboratory exper-iments, J. Geophys. Res., 100, 17,587–17,602, 1995.

Korenaga, J., Energetics of mantle convection and the fateof fossil heat, Geophysical Research Letters, 30(8),n/a–n/a, doi:10.1029/2003GL016982, 2003.

45


Korenaga, J., Why did not the ontong java plateau formsubaerially?, Earth and Planetary Science Letters,234(3), 385 – 399, doi:https://doi.org/10.1016/j.epsl.2005.03.011, 2005.

Korenaga, J., Archean geodynamics and the thermal evo-lution of earth, in Archean Geodynamics and Environ-ments, vol. 164, edited by K. Benn, J.-C. Mareschal,and K. Condie, pp. 7–32, AGU Geophysical Mono-graph Series, 2006.

Korenaga, J., Thermal cracking and the deep hydration ofoceanic lithosphere: a key to the generation of platetectonics?, Journal of Geophysical Research: SolidEarth, 112(B5), 2007.

Korenaga, J., Urey ratio and the structure and evolu-tion of earth’s mantle, Rev. Geophys., 46, RG2007,doi:10.1029/2007RG000,241, 2008.

Korenaga, J., On the likelihood of plate tectonics onsuper-earths: Does size matter?, Astrophys. J. Lett.,725(1), L43–L46, 2010.

Korenaga, J., Initiation and evolution of plate tec-tonics on earth: Theories and observations, Ann.Rev. Earth Planet. Sci., 41, 117–151, doi:10.1146/annurev-earth-050212-124208, 2013.

Labrosse, S., J. Hernlund, and N. Coltice, A crystallizingdense magma ocean at the base of the earth’s mantle,Nature, 450(7171), 866–869, 2007.

Lamb, S., and D. Sington, Earth Story, Princeton Univ.Press, Princeton, New Jersey, 1998.

Landuyt, W., and D. Bercovici, Variations in planetaryconvection via the effect of climate on damage, EarthPlanet. Sci. Lett., 277, 29–37, 2009a.

Landuyt, W., and D. Bercovici, Formation and structureof lithospheric shear zones with damage, Phys. EarthPlanet. Int., 175, 115–126, doi:10.1016/j.pepi.2009.03.005, 2009b.

Landuyt, W., D. Bercovici, and Y. Ricard, Plate genera-tion and two-phase damage theory in a model of mantleconvection, Geophys. J. Int., 174, 1065–1080, 2008.

Lay, T., Q. Williams, and E. J. Garnero, The core–mantle boundary layer and deep earth dynamics, Na-ture, 392(6675), 461, 1998.

Lee, C., P. Luffi, T. Hoink, J. Li, R. Dasgupta, and J. Hern-lund, Upside-down differentiation and generation ofa ‘primordial’lower mantle, Nature, 463(7283), 930–933, 2010.

Lenardic, A., and W. Kaula, Self-lubricated mantle con-vection: Two-dimensional models, Geophys. Res.Lett., 21, 1707–1710, 1994.

Lenardic, A., and W. Kaula, Near surface ther-mal/chemical boundary layer convection at infiniteprandtl number: Two-dimensional numerical experi-ments, Geophys. J. Int., 126, 689–711, 1996.

Lenardic, A., L. N. Moresi, A. M. Jellinek, and M. Manga,Continental insulation, mantle cooling, and the sur-face area of oceans and continents, Earth and Plan-etary Science Letters, 234(3–4), 317–333, doi:http://dx.doi.org/10.1016/j.epsl.2005.01.038, 2005.

Lenardic, A., M. A. Richards, and F. H. Busse, Depth-dependent rheology and the horizontal length scaleof mantle convection, J. Geophys. Res., 111(B07404),doi:10.1029/2005JB003,639, 2006.

Lenardic, A., M. Jellinek, and L.-N. Moresi, A climatechange induced transition in the tectonic style of a ter-restrial planet, Earth Planet. Sci. Lett., 271, 34–42,2008.

Lenardic, A., L. Moresi, A. M. Jellinek, C. J. O’Neill,C. M. Cooper, and C. T. Lee, Continents, super-continents, mantle thermal mixing, and mantle ther-mal isolation: Theory, numerical simulations, andlaboratory experiments, Geochem. Geophys. Geosys.,12, doi: 10.1029/2011GC003,663, doi:{10.1029/2011GC003663}, 2011.

Linckens, J., M. Herwegh, O. Muntener, and I. Mercolli,Evolution of a polymineralic mantle shear zone andthe role of second phases in the localization of defor-mation, J. Geophys. Res., 116, B06,210, 21 pp, doi:10.1029/2010JB008119, 2011.

Linckens, J., M. Herwegh, and O. Muntener, Small quan-tity but large effect —how minor phases control strainlocalization in upper mantle shear zones, Tectono-physics, 643(0), 26–43, doi:http://dx.doi.org/10.1016/j.tecto.2014.12.008, 2015.

Lourenco, D. L., A. B. Rozel, T. Gerya, and P. J. Tackley,Efficient cooling of rocky planets by intrusive magma-tism, Nature Geoscience, 11(5), 322, 2018.

Masters, G., G. Laske, H. Bolton, and A. Dziewonski, Therelative behavior of shear velocity, bulk sound speed,and compressional velocity in the mantle: implicationsfor chemical and thermal structure, Earth’s deep inte-rior: mineral physics and tomography from the atomicto the global scale, pp. 63–87, 2000.

46


McCubbin, F. M., E. H. Hauri, S. M. Elardo, K. E. Van-der Kaaden, J. Wang, and C. K. Shearer Jr, Hydrousmelting of the martian mantle produced both depletedand enriched shergottites, Geology, 40(8), 683–686,2012.

McKenzie, D., and R. Parker, The north pacific: an exam-ple of tectonics on a sphere, Nature, 216, 1276–1280,1967.

McNamara, A. K., E. J. Garnero, and S. Rost, Trackingdeep mantle reservoirs with ultra-low velocity zones,Earth and Planetary Science Letters, 299(1-2), 1–9,2010.

Mojzsis, S. J., T. M. Harrison, and R. T. Pidgeon, Oxygen-isotope evidence from ancient zircons for liquid wa-ter at the Earth’s surface 4,300 Myr ago, Nature,409(6817), 178–181, 2001.

Montelli, R., G. Nolet, F. A. Dahlen, G. Masters, E. R.Engdahl, and S.-H. Hung, Finite-frequency tomogra-phy reveals a variety of plumes in the mantle, Science,303, 338–343, 2004.

Moore, W. B., J. I. Simon, and A. A. G. Webb, Heat-pipeplanets, Earth and Planetary Science Letters, 474, 13–19, 2017.

Moresi, L., and V. Solomatov, Mantle convection witha brittle lithosphere: Thoughts on the global tectonicstyle of the earth and venus, Geophys. J. Int., 133, 669–682, 1998.

Morgan, J. P., Melt migration beneath mid-ocean spread-ing centers, Geophysical Research Letters, 14(12),1238–1241, 1987.

Morgan, J. P., and W. J. Morgan, Two-stage melting andthe geochemical evolution of the mantle: a recipe formantle plum-pudding, Earth and Planetary ScienceLetters, 170(3), 215–239, 1999.

Morgan, W., Rises, trenches, great faults and crustalblocks, J. Geophys. Res., 73, 1959–1982, 1968.

Morley, L., and A. Larochelle, Paleomagnetism as ameans of dating geological events, Geochronology inCanada, 8, 39–51, 1964.

Morschhauser, A., M. Grott, and D. Breuer, Crustal recy-cling, mantle dehydration, and the thermal evolution ofmars, Icarus, 212(2), 541–558, 2011.

Mulyukova, E., and D. Bercovici, Formation of litho-spheric shear zones: Effect of temperature on two-phase grain damage, Physics of the Earth and Plane-tary Interiors, 270, 195 – 212, doi:http://dx.doi.org/10.1016/j.pepi.2017.07.011, 2017.

Mulyukova, E., and D. Bercovici, Collapse of passivemargins by lithospheric damage and plunging grainsize, Earth and Planetary Science Letters, 484, 341–352, 2018.

Mulyukova, E., B. Steinberger, M. Dabrowski, and S. V.Sobolev, Survival of llsvps for billions of years in avigorously convecting mantle: Replenishment and de-struction of chemical anomaly, Journal of Geophysi-cal Research: Solid Earth, 120(5), 3824–3847, doi:10.1002/2014JB011688, 2014JB011688, 2015.

Murakami, M., K. Hirose, K. Kawamura, N. Sata, andY. Ohishi, Post-perovskite phase transition in MgSiO3,Science, 304, 855–858, 2004.

Nakagawa, T., and P. J. Tackley, Effects of low-viscositypost-perovskite on thermo-chemical mantle convectionin a 3-d spherical shell, Geophysical Research Letters,38(4), 2011.

Namur, O., and B. Charlier, Silicate mineralogy at the sur-face of mercury, Nature Geoscience, 10(1), 9, 2017.

Ness, N., K. Behannon, R. Lepping, Y. Whang, andK. Schatten, Magnetic field observations near mer-cury: Preliminary results from mariner 10, Science,185(4146), 151–160, 1974.

Neukum, G., et al., Recent and episodic volcanic andglacial activity on mars revealed by the high resolutionstereo camera, Nature, 432(7020), 971, 2004.

Nimmo, F., and D. McKenzie, Volcanism and tectonicson venus, Annual Review of Earth and Planetary Sci-ences, 26(1), 23–51, 1998.

Nimmo, F., and K. Tanaka, Early crustal evolution ofmars, Annu. Rev. Earth Planet. Sci., 33, 133–161,2005.

Nomura, R., H. Ozawa, S. Tateno, K. Hirose, J. Hernlund,S. Muto, H. Ishii, and N. Hiraoka, Spin crossover andiron-rich silicate melt in the earth’s deep mantle, Na-ture, 473(7346), 199, 2011.

Ogawa, M., and T. Yanagisawa, Numerical models ofmartian mantle evolution induced by magmatism andsolid-state convection beneath stagnant lithosphere,Journal of Geophysical Research: Planets, 116(E8),2011.

47


Olson, P., Hot spots, swells and mantle plumes, Magmatransport and storage, pp. 33–51, 1990.

Otsuka, K., and S. Karato, Deep penetration of molteniron into the mantle caused by a morphological insta-bility, Nature, 492(7428), 243–246, 2012.

Palin, R. M., and R. W. White, Emergence of blueschistson earth linked to secular changes in oceanic crustcomposition, Nature Geoscience, 9(1), 60, 2016.

Parmentier, E., 7.08 - the dynamics and convective evo-lution of the upper mantle, in Treatise on Geophysics(Second Edition), edited by G. Schubert, second edi-tion ed., pp. 319 – 337, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00131-7, 2015.

Parmentier, E., and P. Hess, Chemical dieferentiation of aconvecting planetary interior: Consequences for a oneplate planet such as venus, Geophysical Research Let-ters, 19(20), 2015–2018, 1992.

Parsons, B., and J. Sclater, An analysis of the variation ofocean floor bathymetry with age, J. Geophys. Res., 82,803–827, 1977.

Pekeris, C., Thermal convection in the interior of theearth, Monthly Notices Roy. Astron. Soc., Geophys.Suppl., 3, 343–367, 1935.

Phillips, R., and E. Ivins, Geophysical observations per-taining to solid-state convection in the terrestrial plan-ets, Physics of the Earth and Planetary Interiors,19(2), 107–148, 1979.

Plesa, A.-C., and D. Breuer, Partial melting in one-plateplanets: Implications for thermo-chemical and atmo-spheric evolution, Planetary and Space Science, 98,50–65, 2014.

Ranalli, G., Rheology of the Earth, Chapman and HallPublishers, London, 1995.

Ratcliff, J. T., P. J. Tackley, G. Schubert, and A. Zebib,Transitions in thermal convection with strongly vari-able viscosity, Physics of the earth and planetary inte-riors, 102(3), 201–212, 1997.

Regenauer-Lieb, K., D. A. Yuen, and J. Branlund, The ini-tiation of subduction: criticality by addition of water?,Science, 294(5542), 578–580, 2001.

Revenaugh, J., and S. Sipkin, Seismic evidence for sil-icate melt atop the 410-km mantle discontinuity, Na-ture, 369, 474–476, 1994.

Ricard, Y., 7.02 - physics of mantle convection, inTreatise on Geophysics (Second Edition), editedby G. Schubert, second edition ed., pp. 23 –71, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00127-5, 2015.

Ricard, Y., and D. Bercovici, A continuum theory ofgrain size evolution and damage, J. Geophys. Res., 114,B01,204, doi:10.1029/2007JB005,491, 2009.

Ricard, Y., and C. Froidevaux, Stretching instabilities andlithospheric boudinage, J. Geophys. Res., 91, 8314–8324, 1986.

Ricard, Y., L. Fleitout, and C. Froidevaux, Geoid heightsand lithospheric stresses for a dynamic earth, AnnalesGeophysicae, 2, 267–286, 1984.

Richards, M. A., R. A. Duncan, and V. E. Courtillot, Floodbasalts and hot-spot tracks: plume heads and tails, Sci-ence, 246, 103–105, 1989.

Ringwood, A., Phase transformations and their bearingson the consitution and dynamics of the mantle, Geo-chemica et Cosmochemica Acta, 55, 2083–2110, 1991.

Ritsema, J., A. Deuss, H. Van Heijst, and J. Woodhouse,S40rts: a degree-40 shear-velocity model for the man-tle from new rayleigh wave dispersion, teleseismictraveltime and normal-mode splitting function mea-surements, Geophysical Journal International, 184(3),1223–1236, 2011.

Roberts, J. H., and S. Zhong, Degree-1 convection in themartian mantle and the origin of the hemispheric di-chotomy, Journal of Geophysical Research: Planets,111(E6), 2006.

Rolf, T., and P. J. Tackley, Focussing of stress bycontinents in 3d spherical mantle convection withself-consistent plate tectonics, Geophysical ResearchLetters, 38(18), n/a–n/a, doi:10.1029/2011GL048677,l18301, 2011.

Rolf, T., N. Coltice, and P. J. Tackley, Linking continen-tal drift, plate tectonics and the thermal state of theEarth’s mantle, Earth Planet. Sci. Lett., 351, 134–146,doi:{10.1016/j.epsl.2012.07.011}, 2012.

Rozel, A., Y. Ricard, and D. Bercovici, A thermodynam-ically self-consistent damage equation for grain sizeevolution during dynamic recrystallization, Geophys.J. Int., 184(2), 719–728, doi:10.1111/j.1365-246X.2010.04875.x, 2011.

48


Runcorn, S., Towards a theory of continental drift, Nature,193, 311–314, 1962a.

Runcorn, S., Convection currents in the earth’s mantle,Nature, 195, 1248–1249, 1962b.

Runcorn, S., Satellite gravity measreuments and convec-tion in the mantle, Nature, 200, 628–630, 1963.

Russell, C. T., and R. Elphic, Observation of magneticflux ropes in the venus ionosphere, Nature, 279(5714),616, 1979.

Sammis, C. G., J. C. Smith, G. Schubert, and D. A. Yuen,Viscosity-depth profile of the earth’s mantle: Effects ofpolymorphic phase transitions, Journal of GeophysicalResearch, 82(26), 3747–3761, 1977.

Schubert, G., and D. Sandwell, A global survey of pos-sible subduction sites on Venus, Icarus, 117(1), 173 –196, doi:10.1006/icar.1995.1150, 1995.

Schubert, G., and T. Spohn, Thermal history of mars andthe sulfur content of its core, Journal of GeophysicalResearch: Solid Earth, 95(B9), 14,095–14,104, 1990.

Schubert, G., and K. Zhang, Foundering of the lithosphereat the onset of subduction, Geophys. Res. Lett., 24,1527–1529, 1997.

Schubert, G., D. Stevenson, and P. Cassen, Whole planetcooling and the radiogenic heat source contents of theearth and moon, J. Geophys. Res., 85, 2531–2538,1980.

Schubert, G., D. Turcotte, and P. Olson, Mantle Convec-tion in the Earth and Planets, Cambridge Univ. Press,2001.

Sclater, J., C. Jaupart, and D. Galson, The heat flowthrough the oceanic and continental crust and the heatloss of the earth, Rev. Geophys. and Space Phys., 18,269–311, 1980.

Silver, P. G., and M. D. Behn, Intermittent plate tecton-ics?, science, 319(5859), 85–88, 2008.

Sleep, N., Mantle plumes from top to bottom, Earth-Science Reviews, 77(4), 231–271, 2006.

Sleep, N., and K. Zahnle, Carbon dioxide cycling andimplications for climate on ancient earth, J. Geophys.Res., 106, 1373–1399, 2001.

Smith, D. E., et al., Gravity field and internal structureof mercury from messenger, science, 336(6078), 214–217, 2012.

Smrekar, S. E., and E. R. Stofan, Origin of corona-dominated topographic rises on venus, Icarus, 139(1),100 – 115, doi:https://doi.org/10.1006/icar.1999.6090,1999.

Sobolev, A. V., A. W. Hofmann, S. V. Sobolev, and I. K.Nikogosian, An olivine-free mantle source of hawaiianshield basalts, Nature, 434(7033), 590–597, 2005.

Sobolev, S., A. Sobolev, D. Kuzmin, N. Krivolutskaya,A. Petrunin, N. Arndt, V. Radko, and Y. Vasiliev, Link-ing mantle plumes, large igneous provinces and envi-ronmental catastrophes, Nature, 477(7364), 312–316,2011.

Sohl, F., and G. Schubert, 10.02 - interior structure,composition, and mineralogy of the terrestrial plan-ets, in Treatise on Geophysics (Second Edition),edited by G. Schubert, second edition ed., pp. 23– 64, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00166-4, 2015.

Solomatov, V., Scaling of temperature-and stress-dependent viscosity convection, Physics of Fluids(1994-present), 7(2), 266–274, 1995.

Solomatov, V., 9.04 - magma oceans and primordial man-tle differentiation, in Treatise on Geophysics (SecondEdition), edited by G. Schubert, second edition ed.,pp. 81 – 104, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00155-X, 2015.

Solomatov, V., and L.-N. Moresi, Three regimes of mantleconvection with non-newtonian viscosity and stagnantlid convection on the terrestrial planets, GeophysicalResearch Letters, 24(15), 1907–1910, 1997.

Solomon, S. C., et al., New perspectives on ancient mars,science, 307(5713), 1214–1220, 2005.

Sotin, C., J. Jackson, and S. Seager, Terrestrial planet in-teriors, Exoplanets, pp. 375–395, 2010.

Spiegelman, M., and D. McKenzie, Simple 2-d modelsfor melt extraction at mid-ocean ridges and island arcs,Earth Planet. Sci. Lett., 83, 137–152, 1987.

Spohn, T., Mantle differentiation and thermal evolutionof mars, mercury, and venus, Icarus, 90(2), 222–236,1991.

Stein, C., and S. Stein, A model for the global variationin oceanic depth and heat flow with lithospheric age,Nature, 359, 123–129, 1992.

49


Stein, M., and Z. Ben-Avraham, 9.07 - mechanism of con-tinental crustal growth, in Treatise on Geophysics (Sec-ond Edition), edited by G. Schubert, second edition ed.,pp. 173 – 199, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00159-7, 2015.

Steinberger, B., and A. Calderwood, Models of large-scale viscous flow in the earth’s mantle with constraintsfrom mineral physics and surface observations, Geo-physical Journal International, 167(3), 1461–1481,2006.

Steinberger, B., and R. Holme, Mantle flow models withcore-mantle boundary constraints and chemical hetero-geneities in the lowermost mantle, J. geophys. Res,113, 05,403, 2008.

Steinberger, B., and T. H. Torsvik, A geodynamic modelof plumes from the margins of large low shear veloc-ity provinces, Geochemistry, Geophysics, Geosystems,13(1), 2012.

Steinberger, B., S. C. Werner, and T. H. Torsvik, Deepversus shallow origin of gravity anomalies, topogra-phy and volcanism on earth, venus and mars, Icarus,207(2), 564–577, 2010.

Stern, R. J., Subduction initiation: spontaneous and in-duced, Earth and Planetary Science Letters, 226, 275–292, 2004.

Stern, R. J., Evidence from ophiolites, blueschists, andultrahigh-pressure metamorphic terranes that the mod-ern episode of subduction tectonics began in neopro-terozoic time, Geology, 33(7), 557–560, 2005.

Stevenson, D. J., T. Spohn, and G. Schubert, Magnetismand thermal evolution of the terrestrial planets, Icarus,54(3), 466–489, 1983.

Stofan, E. R., D. L. Bindschadler, J. W. Head, and E. M.Parmentier, Corona structures on venus: Models oforigin, Journal of Geophysical Research: Planets,96(E4), 20,933–20,946, 1991.

Strom, R. G., G. G. Schaber, and D. D. Dawson, Theglobal resurfacing of venus, Journal of GeophysicalResearch: Planets, 99(E5), 10,899–10,926, 1994.

Strutt, J., On convective currents in a horizontal layer offluid when the higher temperature is on the under side,Phil. Mag., 32, 529–546, 1916.

Sun, Y., et al., Dating the onset and nature of the middlepermian emeishan large igneous province eruptions in

sw china using conodont biostratigraphy and its bear-ing on mantle plume uplift models, Lithos, 119(1), 20– 33, doi:https://doi.org/10.1016/j.lithos.2010.05.012,the Emeishan large igneous province: Advances in thestratigraphic correlations and petrogenetic and metal-logenic models, 2010.

Tackley, P., On the ability of phase transitions and vis-cosity layering to induce long-wavelength heterogene-ity in the mantle, Geophys. Res. Lett., 23, 1985–1988,1996.

Tackley, P., The quest for self-consistent generation ofplate tectonics in mantle convection models, in His-tory and Dynamics of Global Plate Motions, Geo-phys. Monogr. Ser., vol. 121, edited by M. A. Richards,R. Gordon, and R. van der Hilst, pp. 47–72, Am. Geo-phys. Union, Washington, DC, 2000a.

Tackley, P., Self-consistent generation of tectonic plates intime-dependent, three-dimensional mantle convectionsimulations, 1. pseudoplastic yielding, Geochem. Geo-phys. Geosystems (G3), 1, 2000GC000,036, 2000b.

Tackley, P., Mantle convection and plate tectonics: towardan integrated physical and chemical theory, Science,288(5473), 2002–2007, 2000c.

Tackley, P., Living dead slabs in 3-d: The dynamics ofcompositionally-stratified slabs entering a “slab grave-yard”above the core-mantle boundary, Physics of theEarth and Planetary Interiors, 188(3-4), 150–162,2011.

Tackley, P., D. Stevenson, G. Glatzmaier, and G. Schubert,Effects of an endothermic phase transition at 670 kmdepth in a spherical model of convection in the earth’smantle, Nature, 361(6414), 699–704, 1993.

Tackley, P., D. Stevenson, G. A. Glatzmaier, and G. Schu-bert, Effects of a multiple phase transitions in a 3-dimensional spherical model of convection in earth’smantle, J. Geophys. Res., 99, 15,877–15,901, 1994.

Tackley, P. J., Mantle geochemical geodynamics, in Trea-tise on Geophysics, vol. 7 Mantle Dynamics, edited byDavid Bercovici (Gerald Schubert editor-in-chief), 2nded., chap. 12, pp. 521–585, Elsevier, 2015.

Tackley, P. J., T. Nakagawa, and J. W. Hernlund,Influence of the post-perovskite transition on ther-mal and thermo-chemical mantle convection, GEO-PHYSICAL MONOGRAPH-AMERICAN GEOPHYSI-CAL UNION, 174, 229, 2007.

50


Tan, E., W. Leng, S. Zhong, and M. Gurnis, On the loca-tion of plumes and lateral movement of thermochemi-cal structures with high bulk modulus in the 3-d com-pressible mantle, Geochemistry, Geophysics, Geosys-tems, 12(7), 2011.

Tauzin, B., E. Debayle, and G. Wittlinger, Seismicevidence for a global low-velocity layer within theearth’s upper mantle, Nature Geoscience, 3, 718–721,doi:10.1038/ngeo969, 2010.

Thorne, M. S., and E. J. Garnero, Inferences on ultralow-velocity zone structure from a global analysis of spdkswaves, Journal of Geophysical Research: Solid Earth,109(B8), 2004.

Tivey, M. A., Vine-matthews-morley hypothesis, in En-cyclopedia of Geomagnetism and Paleomagnetism, pp.980–984, Springer, 2007.

Torsvik, T., M. Smethurst, K. Burke, and B. Steinberger,Large igneous provinces generated from the marginsof the large low-velocity provinces in the deep man-tle, Geophysical Journal International, 167(3), 1447–1460, 2006.

Tosi, N., M. Grott, A.-C. Plesa, and D. Breuer, Thermo-chemical evolution of mercury’s interior, Journal ofGeophysical Research: Planets, 118(12), 2474–2487,2013.

Toth, G., and M. Gurnis, Dynamics of subduction initia-tion at preexisting fault zones, J. Geophys. Res., 103,18,053–18,067, 1998.

Trampert, J., F. Deschamps, J. Resovsky, and D. Yuen,Probabilistic tomography maps chemical hetero-geneities throughout the lower mantle, Science,306(5697), 853–856, 2004.

Trompert, R., and U. Hansen, Mantle convection simula-tions with rheologies that generate plate-like behavior,Nature, 395, 686–689, 1998.

Turcotte, D., and G. Schubert, Geodynamics, CambridgeUniversity Press, Cambridge, UK, 2014.

Turcotte, D., G. Morein, D. Roberts, and B. Malamud,Catastrophic resurfacing and episodic subduction onvenus, Icarus, 139(1), 49 – 54, doi:http://dx.doi.org/10.1006/icar.1999.6084, 1999.

Turcotte, D. L., A heat pipe mechanism for volcanism andtectonics on venus, Journal of Geophysical Research:Solid Earth, 94(B3), 2779–2785, 1989.

Turcotte, D. L., An episodic hypothesis for venusiantectonics, Journal of Geophysical Research: Plan-ets, 98(E9), 17,061–17,068, doi:10.1029/93JE01775,1993.

Valencia, D., R. O’Connell, and D. Sasselov, Inevitabilityof plate tectonics on super-earths, Astrophys. J., 670,L45–L48, 2007.

Valley, J. W., W. H. Peck, E. M. King, and S. A.Wilde, A cool early earth, Geology, 30(4), 351–354, doi:10.1130/0091-7613(2002)030〈0351:ACEE〉2.0.CO;2, 2002.

van der Hilst, R., S. Widiyantoro, and E. Engdahl, Evi-dence for deep mantle circulation from global tomog-raphy, Nature, 386, 578–584, 1997.

van Heck, H., and P. Tackley, Planforms of self-consistently generated plates in 3D sphericalgeometry, Geophys. Res. Lett., 35, L19,312,doi:10.1029/2008GL035,190, 2008.

van Heck, H., and P. Tackley, Plate tectonics on super-earths: Equally or more likely than on earth, Earth andPlanetary Science Letters, 310(3–4), 252–261, doi:10.1016/j.epsl.2011.07.029, 2011.

van Hunen, J., and J.-F. Moyen, Archean subduc-tion: Fact or fiction?, Annual Review of Earth andPlanetary Sciences, 40(1), 195–219, doi:10.1146/annurev-earth-042711-105255, 2012.

van Hunen, J., and A. P. van den Berg, Plate tectonics onthe early earth: Limitations imposed by strength andbuoyancy of subducted lithosphere, Lithos, 103(1-2),217–235, 2008.

van Keken, P., E. Hauri, and C. Ballentine, Mantle mix-ing: The generation, preservation, and destruction ofchemical heterogeneity, Annu. Rev. Earth Planet. Sci.,30, 493–525, 2002.

Vine, F., and D. Matthews, Magnetic anomalies overoceanic ridges, Nature, 199, 947–949, 1963.

Wada, I., and S. D. King, Dyamics of subductingslabs: numerical modeling and constraints fromseismology, geoid, topography, geochemistry andpetrology, in Treatise on Geophysics, vol. 7 Man-tle Dynamics, edited by David Bercovici (Ger-ald Schubert editor-in-chief), 2nd ed., chap. 9,pp. 339–392, Elsevier, doi:http://dx.doi.org/10.1016/B978-0-444-53802-4.00135-4, 2015.

51


Warren, J. M., and G. Hirth, Grain size sensitive defor-mation mechanisms in naturally deformed peridotites,Earth Planet. Sci. Lett., 248(1-2), 438–450, doi:DOI:10.1016/j.epsl.2006.06.006, 2006.

Watters, T. R., M. S. Robinson, and A. C. Cook, Topog-raphy of lobate scarps on mercury: New constraintson the planet’s contraction, Geology, 26(11), 991–994,1998.

Watters, T. R., K. Daud, M. E. Banks, M. M. Selvans,C. R. Chapman, and C. M. Ernst, Recent tectonic ac-tivity on mercury revealed by small thrust fault scarps,Nature Geoscience, 9(10), 743, 2016.

Wegener, A., The Origin of Continents and Oceans,Methuen and Co., Ltd., 1924.

Weinstein, S., and U. Christensen, Convection planformsin a fluid with a temperature-dependent viscosity be-neath a stress-free upper boundary, Geophys. Res. Lett.,18, 2035–2038, 1991.

Weinstein, S., and P. Olson, The proximity of hotspots toconvergent and divergent plate boundaries, Geophys.Res. Lett., 16, 433–436, 1989.

Wenzel, M. J., M. Manga, and A. M. Jellinek, Tharsis asa consequence of mars’ dichotomy and layered mantle,Geophysical research letters, 31(4), 2004.

White, D., The planforms and onset of convection withtemperature-dependent viscosity, J. Fluid Mech., 191,247–286, 1988.

White, R., and D. McKenzie, Magmatism at rift zones:the generation of volcanic continental margins andflood basalts, Journal of Geophysical Research: SolidEarth, 94(B6), 7685–7729, 1989.

Whitehead, J., and D. Luther, Dynamics of laboratory di-apir and plume models, Journal of Geophysical Re-search, 80(5), 705–717, 1975.

Wieczorek, M., Gravity and topography of the ter-restrial planets, in Treatise on Geophysics (SecondEdition), vol. 10, edited by Tilman Spohn (GeraldSchubert, ed. in chief), second edition ed., pp. 153– 193, Elsevier, Oxford, doi:https://doi.org/10.1016/B978-0-444-53802-4.00169-X, 2015.

Williams, Q., and E. J. Garnero, Seismic evidence forpartial melt at the base of earth’s mantle, Science,273(5281), 1528–1530, 1996.

Wilson, J. T., Static or mobile earth: the current scientificrevolution, Proceedings of the American PhilosophicalSociety, 112(5), 309–320, 1968.

Wolfe, C., S. Solomon, G. Laske, J. Collins, R. Detrick,J. Orcutt, D. Bercovici, and E. Hauri, Mantle shear-wave velocity structure beneath the hawaiian hotspot,Science, 326, 1388–1390, 2009.

Yin, A., Structural analysis of the valles marineris faultzone: Possible evidence for large-scale strike-slipfaulting on mars, Lithosphere, 4(4), 286–330, 2012.

Zhao, Y.-H., M. E. Zimmerman, and D. L. Kohlstedt, Ef-fect of iron content on the creep behavior of olivine:1. anhydrous conditions, Earth and Planetary ScienceLetters, 287(1-2), 229–240, 2009.

Zhong, S., and M. T. Zuber, Degree-1 mantle convectionand the crustal dichotomy on mars, Earth and Plane-tary Science Letters, 189(1-2), 75–84, 2001.

Zindler, A., and S. Hart, Chemical geodynamics, Annualreview of earth and planetary sciences, 14, 493–571,1986.

52

Date post:	24-Aug-2020
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

MANTLE CONVECTION IN TERRESTRIAL PLANETS …...Mantle convection is the dominant mech-anism by which...

Documents