MANTLE CONVECTION IN TERRESTRIAL PLANETS

Elvira Mulyukova & David Bercovici Department of Geology & Geophysics Yale University New Haven, Connecticut 06520-8109, USA E-mail: [email protected]

May 15, 2019

Summary surfaces do not participate in convective circu- lation, they deform in response to the underly- All the rocky planets in our Solar System, in- ing mantle currents, forming geological features cluding the Earth, initially formed much hot- such as coronae, volcanic lava flows and wrin- ter than their surroundings and have since been kle ridges. Moreover, the exchange of mate- cooling to space for billions of years. The result- rial between the interior and surface, for exam- ing heat released from planetary interiors pow- ple through melting and volcanism, is a conse- ers convective flow in the mantle. The man- quence of mantle circulation, and continuously tle is often the most voluminous and/or stiffest modifies the composition of the mantle and the part of a planet, and therefore acts as the bottle- overlying crust. Mantle convection governs the neck for heat transport, thus dictating the rate at geological activity and the thermal and chemical which a planet cools. Mantle flow drives geo- evolution of terrestrial planets, and understand- logical activity that modifies planetary surfaces ing the physical processes of convection helps through processes such as volcanism, orogene- us reconstruct histories of planets over billions sis, and rifting. On Earth, the major convective of years after their formation. currents in the mantle are identified as hot up- wellings like mantle plumes, cold sinking slabs and the motion of tectonic plates at the surface. On other terrestrial planets in our Solar System, Keywords mantle flow is mostly concealed beneath a rocky surface that remains stagnant for relatively long Mantle convection, terrestrial planets, planetary periods of time. Even though such planetary evolution, plate tectonics, volcanism

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Mantle Convection In planetary mantles, the convective currents can deform and chemically modify the top and The interiors of terrestrial planets are comprised bottom boundaries; their effect on the planetary of three main layers: a metallic core at the surfaces is of particular interest, since that center, overlain by a rocky mantle, which part can be most readily observed and used is in turn enveloped by a rocky crust. The to interpret the workings of the underlying exact compositions and thicknesses of these mantle. For example, hot upwelling mantle layers, and their thermal and chemical evolu- currents can generate surface uplift, seen as tion through time, vary from planet to planet, topographic highs, or induce volcanic activity, depending on their size, distance from the sun, when hot material melts and erupts while formation history, etc. However, common to all approaching the surface. Extruded lavas on the terrestrial planets in our Solar System, and planetary surfaces record the presence and even to some of its larger moons, is that their evolution of hot mantle regions, and can be mantles undergo convective motions, wherein used to infer mantle temperature, chemistry hot buoyant material rises from the deep interior and flow velocity. Similarly, the downwelling and the heavy cold material near the surface currents can give rise to topographic lows, as sinks. the sinking mantle material pulls the surface down from below. In the possibly unique case Mantle convection is the dominant mech- of the Earth, the top cold thermal boundary anism by which planets cool and undergo layer is subdivided into tectonic plates, which chemical segregation. The flow of the mantle are moving relative to each other and sink into induces motion in the overlying crust, which the mantle at subduction zones. The rate at can lead to such phenomena as volcanoes, which a planet recycles cold material into the earthquakes and, uniquely for Earth, plate tec- mantle largely determines its cooling rate. tonics. Ultimately, mantle convection governs the evolution of planetary surfaces and interiors. Naturally, more observations are available for the Earth’s surface and mantle than for other The fundamental features of any convective planets. Thus, our understanding of planetary system include cold and hot boundaries (such interiors, and their surface manifestations, is as the outer and inner boundaries of the mantle, largely shaped by what is known about our respectively), and a fluid between the two home planet, as well as by our understanding of boundaries on which gravity acts to move hot the fundamental processes that govern mantle and cold material. Hot upwelling and cold convection, such as the physics of heat transport downwelling vertical currents are connected and rock deformation. along the horizontal boundaries by the hot and cold thermal boundary layers (TBLs): a In what follows, the different components of hot TBL at the bottom, and a cold TBL at the convective mantle flow on Earth are described, top. The TBLs are where heat is conducted tracking the material trajectory as it forms tec- rapidly across the boundaries into or out of the tonic plates traversing the Earth’s surface, which convectively stirred mantle. The large thermal then sink into the mantle as cold subducting gradients across the TBLs, compared to if the slabs, that eventually impinge on and flow lat- temperature increased gradually from top to erally along the core-mantle boundary; some of bottom, is what makes thermal convection such this material ascends across the mantle again as an efficient mechanism for heat transfer. mantle plumes, while most of it ascends broadly as part of the global tectonic circulation, thus

2 Oxford Research Encyclopedia of Planetary Science Mantle Convection closing the loop. The convective currents on they get partially reflected, and these reflected other terrestrial planets are discussed as well, signals allow to determine the boundaries of the albeit our understanding of these is less certain main layers that make up the Earth’s interior. due to fewer observational constraints. We will Furthermore, hot rock is typically softer and then survey the underlying physics of convec- more easily compressed, hence seismic waves tion, which forms the basis for understanding are slower passing through such material; how mantle convection is both similar to and the opposite is true for cold rocks which are different from classical theories of convective stiffer. The resulting seismic wave travel time flow, and how this physics lets us infer mantle variations can be used to infer pictures of the dynamics on Earth and other terrestrial planets. mantle showing “hot” (seismically slow) and “cold” (fast) regions, appearing much like an ultrasound of the mantle. Mantle Top to Bottom The distance to the center of the Earth is One of the greatest challenges in the studies approximately 6400 km, of which the mantle of planetary mantles is their inaccessibility comprises about 2900 km, sandwiched between for direct observations. The structure and the thin crust (average thickness of about 20 physical properties of planetary interiors have km: 7 km in the ocean and 40 km in continents) to be inferred from indirect measurements such and iron core (about 3500 km radius). Although as satellite observations of gravity, surface the core is thicker, the mantle envelops it and topography and magnetic fields [Phillips and thus the mantle constitutes about 80% of our Ivins, 1979], see Sohl and Schubert [2015] planet’s volume (Figure 3). The similar size for a recent review. In addition, analysis of and density of Earth and Venus, which has meteorites collected at the Earth’s surface a total radius of about 6100 km, makes it constrain the chemistry of some other planets, likely that the thicknesses of the venusian core as well as the building blocks of our own and mantle are similar to those of Earth. At planet. Earth is special in this sense, because, in abour 3400 km total radius, Mars is the third addition to the remote measurements, scientists largest terrestrial body in the Solar system. The have access to a wealth of geological samples combined measurements of the martian mass, and can perform seismological observations moment of inertia (i.e., inertial resistance to of the interior. Most of what we know about being spun), and chemical analysis of martian Earth’s interior is obtained indirectly from the meteorites, constrain the radius of the martian analysis of seismic waves, which are triggered core to be about 1400 km, leaving about 1900 by powerful earthquakes and propagate through km to be taken up by the mantle, and 100 km the mantle and core. Seismic waves travel faster by the crust [Harder, 1998]. The radial mass through rocks that are stiffer. In the mantle, the distribution of Mercury is unusual, compared rocks become denser, and therefore stiffer, when to other terrestrial bodies, in that most of it is they are exposed to higher pressures at greater occupied by a dense metallic core, which is depths. The resulting increase with depth of the about 2020 km in in radius, overlain by a 400 measured seismic velocities can thus be used to km thick mantle [Hauck et al., 2013] and a 50 infer mantle’s density structure. When seismic km thick crust [Smith et al., 2012]. waves pass through sharp changes in material properties (e.g., density), such as the boundaries While the metallic cores likely separated between the felsic crust and the mafic mantle, out of the mantles early in planetary histories, or the silicate mantle and the metallic core, i.e., within the first few tens of Myr of the life

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Venus Earth

Mars Mercury

Figure 1: Cutaway views of the interiors of four terrestrial planets in the Solar System. Reproduced from http://solarviews.com/cap/index/cutawaymodels1.html of the Solar System [Kleine et al., 2002], the crust. The more refractory mantle material segregation of the crust out of the mantle is still (i.e., harder to melt, silica poor and heavier ongoing, as evident in recent volcanism, seen material) may melt little if at all and much of on all terrestrial planets except for Mercury, it stays in the mantle. Such ‘pressure release’ where global magmatic activity appears to have melting in hot vertical currents, such as mantle ceased about 3.5 Gyr ago [Namur and Charlier, plumes arising from the deeper mantle, or by 2017]. Mantle melting at shallow depths (with passive upwelling beneath mid-ocean-ridges the exact depth depending on temperature and (presently only known to occur on Earth), is composition) is induced by decompression, vital for chemical segregation of the mantle and and leads to magmatism that forms the mafic development of oceanic crust (and possibly the (or silica poor) crust (such as the oceanic crust first kernels of proto-continental crust early in on Earth). Specifically, as upwelling mantle Earth’s history). material approaches the surface, towards lower pressure, its own temperature changes little Melting at subduction zones (which is (decreasing slightly by “adiabatic” decompres- also only known to occur on Earth) is more sion, further explained in the Section “Basics complicated than melting at mid-ocean ridges of Thermal Convection”), but the temperature or at hotspots, but is responsible for most of at which it melts decreases more rapidly (in the production of continental crust [see also essence, decreasing the confining pressure Stein and Ben-Avraham, 2015]. For subduction makes it easier for molecules to mobilize into zones, melting is facilitated by water. Tectonic a melt). At a certain depth (usually between a plates entering a subduction zone have typically few 10s to 100 km, depending on temperature) been submerged under water for hundreds of the upwelling mantle’s temperature exceeds the millions of years. When the first basalts are melting temperature and undergoes melting. extruded at mid-ocean ridges they react with The mantle is made up of different chemical water and make hydrous minerals, such as components and each have their own specific amphibole and serpentine. Sediments washed melting temperatures. The material that can off continents and islands into the ocean are melt at higher pressures (usually more silica rich also usually hydrated. When a plate reaches material with lower melting temperature) melts subduction zone, many of its hydrated minerals first, freezes last and is typically chemically less are entrained with the slab into the mantle dense, and thus comes to the surface as lighter (though many sediments remain at the surface

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to form accretionary prisms). Once the en- trained minerals reach about 100 km or more, they are unstable at the higher temperature and pressure conditions, and they release their water into the mantle wedge above the slab, which in turn gets modestly hydrated. The hydrated mantle rock melts more readily than dry man- tle rock (hydrogen replacement weakens the mineral bonds), and so even at the ‘moderate’ mantle temperatures next to a cold slab, the Mars damp mantle material will partially melt, and the melt phase percolates to the surface. This original melt phase is basaltic (as typical of mantle melts), but cooler than plume-derived basalts. Thus, when this cool/damp melt comes into contact with crustal rocks (which formed by prior melting events), it remelts silica rich minerals, which are the easiest to melt, but not the more refractory silica-poor or ‘mafic’ Earth ones (e.g. dry basalt). The remelted silica rich rocks are separated and ascend to produce, for example, granitic magmas. Indeed, granite tends to be the final product of such repeated melting, and it is the primary component of continental crust.

Except for the very small portions of the

Venus mantle where melting takes place, most terres- trial mantles are currently comprised of solid rock, in spite of their fluid-like mechanical behavior over geological time scales. The large thicknesses of these mantles (with the exception of Mercury) means that their con- stituent materials experience a large range of temperature and pressure conditions with depth. For example, the mantles pressure on Earth

Mercury (and likely similar on Venus) increases from top to bottom by about 140 GPa (about 1.4 million atmospheres of pressure), and temperature 3500

, 2015]. The topography is referencedby to the geoid, which is an equipotential surface on which the sumK of the gravitational and (probably less by a few hundred Kelvin on Venus, due to its higher surface

Global topography (top row), and the total gravitational anomaly (bottom row) of the four terrestrialtemperature); planets in the Solar System [modified martian pressure and temperature increase by about 23 GPa and 2800 K across Wieczorek the mantle [Schubert and Spohn, 1990; Harder,

Figure 2: from centrifugal potential energies has1998]; the same value, and which on Earth would correspond to the sea level. these extreme conditions strongly affect

5 Oxford Research Encyclopedia of Planetary Science Mantle Convection the physical properties of rocks, including their state, which then has greater resistance to mineralogical structure, density, viscosity, etc. compression. The first major phase change in the Earth’s mantle occurs at 410 km depth, Viscosity is the material’s resistance to de- where olivine (which is the major component formation under an applied force or stress. The mineral of the upper mantle) transitions to higher the viscosity, the higher the resistance to the same material with a wadsleyite structure flow. For example, the viscosity of water is on [Katsura et al., 2004], and which involves a the order of 10−3 Pa s and that of honey is about moderate 5 − 8% density increase [Dziewonski 1 − 10 Pa s, both at room temperature, while and Anderson, 1981]. Wadsleyite changes to that of the mantle ranges between 1019 − 1023 ringwoodite at 520km depth [Ita and Stixrude, Pa s. Mantle viscosity varies with pressure, 1992], with an associated 1 − 2% density temperature and composition. While there increase [Dziewonski and Anderson, 1981]. The remains uncertainty about the compositional largest phase change occurs from ringwoodite variations in the mantle, the depth-profiles of to perovskite/magnesiowustite¨ at 660km depth pressure and temperature, at least for the Earth, [Katsura et al., 2003], with a density increase of are relatively well constrained. The viscosity of 10−11% [Dziewonski and Anderson, 1981] and mantle rocks increases with increasing pressure, involves a viscosity increase by about a factor but decreases with increasing temperature. Gen- of 30 [Hager, 1984; Ricard et al., 1984]. The erally, the strongest effect on viscosity is that of 410km and 660km phase changes are the two temperature, which allows for many orders of most remarkable, globally contiguous phase magnitude variations in viscosity. However, for changes in the Earth’s mantle, and the region most of the mantle depth (excluding the TBLs between them is called the Transition Zone, in the top and bottom few hundreds of kilome- since it is where most of the mineralological ters), temperature varies only gradually along transitions occur, over a relatively narrow an adiabatic profile. Thus, the depth-profile of region [Ringwood, 1991]. The mantle above viscosity is dominated by pressure-variations the Transition Zone is typically identified as the [Steinberger and Calderwood, 2006; Stein- Upper Mantle (although in some papers and berger et al., 2010]. For Earth, the combined books Upper Mantle includes the Transition effects of increasing pressure with depth with Zone), and that below is the Lower Mantle. mineralogical phase transitions (discussed next) The temperature and pressure profiles, which, cause the viscosity to increase by up to three together with the composition, determine orders of magnitude across the mantle. the depth at which the phase transitions oc- cur, are more uncertain for the interiors of Mantle minerals may have different geome- the other terrestrial planets. Nonetheless, it tries of atomic arrangement (crystal structures) has been estimated that the olivine to wads- at different pressures and temperatures. Chang- leyite transition occurs around 450-580 and ing from one atomic arrangement to another 1000-1500 km depth on Venus and Mars, is called a phase transition, or, commonly respectively, while the ringwoodite-perovskite for the mantle, a solid-solid phase transition, transition occurs at about 710 and 1910 km since the material remains in a solid state depth on Venus and Mars, respectively [Ito as it transforms to another phase. Thus, a and Takahashi, 1989; Harder, 1998; Katsura material may have one crystal structure (or et al., 2004]. The mantle of Mercury appears to phase) at low pressures, but once the pressure be too thin for it to sustain any phase transitions. reaches some critically high value, the material organizes into a more compact, higher density There is seismological evidence for other

6 Oxford Research Encyclopedia of Planetary Science Mantle Convection phase changes in the Earth’s mantle, although mantle heat budget. On the one hand, forming these are less well resolved, and in some in- a crust depletes the mantle of heat producing stances do not appear to be global, thus their elements. On the other hand, a radiogenically effect on mantle convection will only be men- heated crust acts as a warm blanket that impedes tioned briefly. heat flow out of the mantle. Whether the net effect of crustal production is to help or impede mantle cooling remains a matter for further Mantle’s Heat Budget investigation [Rolf et al., 2012].

The ultimate driver of mantle flow is that Earth’s continental crust, which is inevitably planets cool to space as they inexorably come extracted from the early mantle by melting and to equilibrium with the rest of the much colder remelting, acquired an especially high concen- universe. A major source of heat within the tration of incompatible radioactive elements, mantle is the kinetic energy delivered to the and thus produces a significant fraction of the planetary interiors by the impacts of planetes- net heat output through the surface. Subtracting imals during accretion, and the gravitational the contribution to surface heat flow from the energy released upon the segregation of the continental crust leaves approximately 38 TW metallic core from the silicate mantle, known emanating from the mantle and core [Jaupart collectively as primordial heat sources. Another et al., 2015]. source of heat arises from radioactive decay of unstable isotopes, mostly uranium ( 238U), It is not currently known exactly how much thorium ( 232Th) and potassium ( 40K), which of the heat output from the mantle (and core) is are collectively termed radiogenic heat sources. due to primordial heat, and how much of it is The total rate that heat is flowing out of the due to the heating by radioactive elements. The Earth is approximately 46 TW [Jaupart et al., mantle’s abundance of radiogenic sources can 2015], as measured by heat-flow gauges in potentially be constrained using the measured continents and oceans [see Turcotte and Schu- concentrations of U, Th and K in chondritic bert, 2014]. About 20-30% of the Earth’s total meteorites, which are thought to represent the mantle heating is thought to come from the original building blocks of terrestrial planets. core [Jaupart et al., 2015]. The relatively low However, to what degree the chondritic con- endogenic heat flow emanating from within centrations (not to mention which families of terrestrial planets, compared to radiative release chondrites) are representative of those for the of incident solar heating, makes surface heat bulk Earth is still an active area of debate. flows measurements challenging, and even so, Complicating the issue is the large uncertainty such observations are available only for the in the efficiency of heat transport throughout Earth and the Moon. Earth’s history, with different proposed mod- els spanning more efficient and less efficient Most radioactive elements in the mantle are cooling rates on early Earth. There is a trade incompatible, meaning that if their host rock off between what is assumed for the budget undergoes partial melting, they tend to dissolve of radioactive elements, and the efficiency of or “partition” into the liquid phase. Thus, in mantle heat transport through time. Chondritic the process of crust formation through mantle concentrations of radioactive elements require melting, the incompatible radioactive elements the mantle to have released heat less efficiently partition towards and concentrate in the crust, in the past [Korenaga, 2008]. Alternatively, which has two competing consequences for the if the present heat transport mechanism is

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Figure 3: Graphic rendition of cutaway view of Earth’s structure showing crust, convecting mantle and core. The relevant dimensions are that the Earth’s average radius is 6371 km; the depth of the base of the oceanic crust is about 7 km and continental crust about 35 km; the base of the lithosphere varies from 0 at mid-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. Reproduced from Lamb and Sington [1998]. representative of that on early Earth, then Mantle’s Cold Thermal the mantle’s radiogenic sources must be super- chondritic, and would also imply that the mantle Boundary Layer holds a reservoir of heat-producing elements The outer portion of a planet, its crust and litho- that are not sampled by plate tectonics (since sphere, makes up the cold thermal boundary we don’t see these heat-producing elements in layer (TBL), which is the layer across which MORB) [Schubert et al., 1980; Jaupart et al., heat escapes from the interior to space; the heat 2015]. transfer across the cold TBL happens mainly by conduction, but is also helped by the volcanic transport of hot material to the surface. On most terrestrial planets (that is, all except Earth), mantle convection occurs beneath the surface; while the surface may get deformed and have The question about the efficiency of mantle volcanic lavas emplaced on top of it, it remains convection through Earth’s history, as well as in place for periods of time that are much longer its characteristics on other planets, requires un- than the characteristic timescale of mantle over- derstanding how mantle dynamics changes with turn. This mode of convective cooling is termed varying temperature, planet size, etc.; this issue stagnant lid convection, with the lid being the will be revisited later, after the basic physics of portion of the TBL that does not participate convection has been discussed. in convective mantle flow, and planets cooling

8 Oxford Research Encyclopedia of Planetary Science Mantle Convection in this mode are termed one-plate planets. Earth is mobile, moving laterally along the plan- The lid can thicken over time due to cooling, etary surface at a rate dictated by that of man- compression in response to underlying mantle tle overturn. The resulting high rate of surface currents, or burial under the lavas emplaced on rejuvenation, as reflected in the young ages of top of it [Moore et al., 2017]. Thickening of the the oceanic crust, typically less than 200 Myr basaltic crust may push its lowermost portion [Condie, 1997], allows for efficient convective into depths where it transitions to eclogite. On cooling of the planet. The theory and observa- Earth, Venus, Mars and Mercury the basalt- tion of plate tectonics on Earth, including its link eclogite transition occurs at about 45, 50, 65 to mantle flow, has revolutionized our under- and 100 km depth, respectively, with the exact standing of planetary dynamics and evolution, depth being dependent on temperature [Arndt and we discuss it in more detail in the follow- and Goldstein, 1989; Spohn, 1991; Babeyko ing. and Zharkov, 2000]. Eclogite is denser than the underlying mantle material, and is therefore gravitationally unstable and prone to sink into Plate Tectonics - The Unique Case of the mantle, a process known as delamination. Planet Earth On one-plate planets, episodes of lithospheric delamination possibly act to thin the stagnant The Earth’s surface, its crust and lithosphere, is lid, or even remove it entirely, and are often subdivided into 12 major tectonic plates and a followed by extensive volcanic activity that number of minor plates or microplates (Figure effectively renew the surface [Turcotte, 1989; 4). Some plates consist entirely of the oceanic Spohn, 1991; Parmentier and Hess, 1992; lithosphere, while others incorporate continents Morschhauser et al., 2011; Ogawa and Yanag- as well. The plates move relative to each other, isawa, 2011]. There is a growing evidence and their movement away from, towards or for a mobile Venusian lithosphere (rather than laterally past each other, characterizes their a stagnant one, as was previously believed). boundaries as divergent, convergent or trans- Some of the observed topographic features form (or, alternatively, strike-slip), respectively. on Venus, in particular in the vicinity of large New tectonic plate material is formed at the coronae, resemble trenches, possibly indicative mid-ocean ridges (MORs), which constitute of subduction [Schubert and Sandwell, 1995; the divergent plate boundaries; specifically, hot Davaille et al., 2017]. Furthermore, some of mantle material partially melts and the resulting the radar imagery of Venus has been interpreted magma ascends to drive ridge volcanism and as folds and faults, all indicative of lateral form new oceanic crust. The residual unmelted surface motion, although this type of geological material remains in the mantle as the thin structures can be generated by the stresses of depleted portion of the lithosphere. As the the underlying convective mantle, even if the plates move away from MORs they cool, and lithosphere does not circulate into the mantle the lithosphere of which they are comprised [Harris and Bedard´ , 2014]. thickens as a thermal boundary layer, becomes heavier and eventually sinks back into the man- The surface of planet Earth is unique in that tle at subduction zones, which constitute the most of it, namely the oceanic crust (which convergent plate boundaries. The divergent and makes up about 60% of the surface area), is con- convergent motion of the plates is the surface tinuously renewed through the process of plate manifestation of the upwards and downwards tectonics. Instead of a largely stagnant top TBL motion associated with convective currents common for other terrestrials, the cold TBL of in the underlying mantle, which is often also

9 Oxford Research Encyclopedia of Planetary Science Mantle Convection referred to as the poloidal component of mantle velocity and stress, which compared favorably flow [Hager and O’Connell, 1981; Bercovici to the Earth’s gravity, geoid, and topography et al., 2015]. The plate-motion that is not measurements [Holmes, 1931; Pekeris, 1935; directly associated with spreading or subduction Hales, 1936; Runcorn, 1962a,b], see Bercovici is associated with strike-slip shear or plate [2015]. spin, and is also referred to as the toroidal component of flow. Such motion has no direct energy source (such as gravitational energy release for poloidal flow), which points to the Tectonic plates constitute the cold thermal important effect of non-linear rock rheology boundary layer of the convective mantle system, (i.e., the way a rock responds to stress through i.e., the conductively cooled surface layer, made deformation, or strain rate) to indirectly couple up of the differentiated mantle (crust and de- it to convective motion [Kaula, 1980; Bercovici pleted lithosphere) in the uppermost part, and et al., 2015]. the undifferentiated cold lithospheric mantle at the bottom. It is generally understood that plate One of the first to recognize the mobility tectonics is the surface manifestation of man- of the Earth’s surface was Alfred Wegener tle convection. Complicating this picture is the in his theory of Continental Drift, largely fact that the mantle material behaves very dif- motivated by the striking correlation in the ferently when it is at depth (at higher pressures geometry of the margins of different continents and temperatures) compared to when it is near [Wegener, 1924]. Wegener’s theory, however, the surface. Prior to becoming a plate, the man- lacked a physically plausible mechanism that tle acts as a highly viscous fluid, with its de- would provide a sufficient driving force for formation distributed over tens or hundreds of the continents to move through oceanic crust, kilometers. In contrast, the cold tectonic plates which is why it was criticized and discredited. appear to be strong, nearly rigid, in their inte- Decades later the accumulation of sea-floor rior, with most of their deformation confined to sounding and magnetic data during and after the weak and narrow plate boundaries. In fact, War World II provided compelling evidence the strength of the plates appears to be so high for sea-floor spreading [Hess, 1962; Vine and that they shouldn’t be able to bend and sink into Matthews, 1963; Morley and Larochelle, 1964], the mantle, given the available convective forc- see Tivey [2007], which marked the start of the ing [Cloetingh et al., 1989; Solomatov, 1995]. Plate Tectonics revolution. The theory of plate The physical mechanism responsible for weak- tectonics, in which the plates comprise a mosaic ening of crustal and lithospheric rocks, which of contiguous rafts blanketing the mantle, but ultimately allows for the formation of tectonic all moving as solid blocks around their own plate boundaries, are still debated, with plastic rotation or Euler poles, was articulated by 1968 yielding, percolation of fluids and grain size re- independently by McKenzie and Parker [1967] duction being some of the leading theories. Nev- and Morgan [1968]. Plate tectonics differs ertheless, understanding how the nearly discon- from Continental drift in that the continents tinuous motion of plates self-consistently arises are passive riders on the backs of the plates, from the convective flow of the mantle, and rather than plowing through oceanic lithosphere how the strong plates bend and sink into the as Wegener assumed. Meanwhile, the theory mantle, remains a major goal in geodynamics that the mantle is convecting in order to get [Bercovici, 1995; Tackley, 2000a,b; van Heck rid of its heat had become more physically and Tackley, 2008; Foley and Becker, 2009; sound, generating testable predictions of flow Bercovici et al., 2015].

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60˚N 60˚N

Juan de Fuca Eurasia N. America

Arabia Africa Philippine Caribbean Cocos Indian 0˚ 0˚ Pacific S. America

Nazca Australia

60˚S Scotia 60˚S

Antarctic

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

Mantle’s Cold Downwelling gravitational anomalies, and using Earth as a reference for mantle rock properties, it has been Flow demonstrated that there exist large-scale density anomalies, likely induced by vertical convective Unless cold mantle downwellings entrain currents, in the mantles of Earth, Mars and surface material, as in the case of plate tectonics Venus [Steinberger et al., 2010]. on Earth, their presence is largely hidden from direct observation. However, the motion of The cold downwelling mantle flow on Earth cold dense material in the mantle generates is linked to the subduction zones at the surface, topography and a measurable signal in the which we discuss next. surface gravity field. For example, anomalously dense material in the mantle (such as from Subduction on Earth cold downwelling currents) induces a positive anomaly in the gravitational field (i.e., a gravity As oceanic lithosphere migrates away from a high), albeit some, or all, of that positive signal spreading center (mid-ocean ridge), it becomes may be offset by the flow-induced downward denser and heavier. The resulting thermally deflection of the surface, which effectively induced negative buoyancy causes the plate to generates a negative mass anomaly. For the eventually sink into the mantle. Oceanic plates Earth, the seismic anomalies can be imaged bend and flow downwards at subduction zones, independently using seismic tomography, forming trenches, which are the deepest parts which can then be combined with the topog- of the Earth’s surface, like the Marianas trench. raphy and gravity measurements to constrain While most subduction zones are located mantle structure [Hager, 1984; Ricard et al., along continental margins where oceanic and 1984; Steinberger et al., 2010]. Combining continental plates meet, there exist examples observations of topography, volcanism and of intraoceanic subduction as well (e.g., the

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Izu-Bonin-Mariana arc system along the eastern the broadening may be an imaging artifact [see margin of the Philippine plate). The ages of Wada and King, 2015, and references therein]. subducting plates vary from 0 (i.e., subducting ridges) to roughly 200 Myr. In all cases, the Although in total a subducting slab is cold downwelling is asymmetric, with one plate and heavy, it is also compositionally strati- sinking underneath the other, rather than two fied: its top layer is basalt, which makes up plates converging and sinking together [see the oceanic crust, underlain by harzburgite, Wada and King, 2015]. which makes up the depleted portion of the lithosphere, and finally lherzolite at the bottom, Convective mantle flow is extremely slow and which is the undifferentiated part of the mantle laminar (i.e., there is no turbulent eddy transport [see review by Wada and King, 2015, and of momentum), because of the high mantle vis- references therein]. The intrinsic densities of cosity. Therefore, the velocity of sinking slabs basalt and harzburgite are lower than that of the is well approximated by their terminal velocity, upper mantle, which partially offsets the plate’s at which the gravitational force pulling the slabs growing negative thermal buoyancy. However, downward is balanced by viscous resistance to once the plate sinks and becomes a slab, these their motion. The terminal slab velocity can chemical effects are counter-acted by the tran- be estimated from a slab’s thermally induced sitions to intrinsically denser phases that occur buoyancy, and the viscosity of the mantle [see at greater depths (most notably the transition Davies and Richards, 1992].The result of this from basalt to eclogite at about 60 km depth), relatively simple approximation is in good rendering the net effect of lithospheric compo- agreement with the observations of tectonic sitional stratification on subduction negligible plate velocities, especially for oceanic plates [Bercovici et al., 2015]. However, once the attached to appreciable slabs, which move at slab reaches the core-mantle boundary (CMB), speeds on the order of 10 cm/yr [Forsyth and which acts as an impenetrable boundary, the Uyeda, 1975]. slab stalls, heats up, softens, and potentially segregates into different paths of the convective Seismic tomography reveals that some flow. Slab segregation is hypothesized to be one slabs appear to stagnate and become deflected of the primary sources for compositional het- horizontally at around 660 km depth, which erogeneity in the mantle [Hofmann and White, corresponds to the olivine-wadsleyite phase 1982; Coltice and Ricard, 1999; Mulyukova transition. Other slabs appear to traverse the et al., 2015]. Whether the resulting hetero- entire depth of the mantle, with little deflection. geneity can form large scale compositional The increasing mantle viscosity with depth anomalies, as detected by seismic tomography, causes the slabs to thicken as they descend, as or whether the different slab components get indicated in seismic tomography models; in stirred by the convective flow and mechanically principle this occurs because the slab experi- homogenized remains an active area of research. ences more viscous resistance and slows down, causing it to effectively inflate or buckle, thus When a slab sinking into the lower mantle im- appearing thicker. An additional effect is that pinges on the impermeable CMB, it is deflected of thermal diffusion, where the deeper portions horizontally and induces flow parallel to the of the slab have had more time to cool the CMB. The slab-induced flow can displace the surrounding mantle. It is also worth noting that material already residing at the CMB, and if that the resolution of tomography models is poor material happens to be compositionally anoma- in the mid mantle, such that at least some of lous, it may get swept up into large piles of seis-

12 Oxford Research Encyclopedia of Planetary Science Mantle Convection mically detectable anomalies, such as the large terrestrial planets can thus provide important low shear velocity provinces [Tan et al., 2011; insight into their thermal histories and present Bower et al., 2013]. Furthermore, as the slab states. For example, the apparent absence of pushes material along the CMB, it causes the magnetic field on Mars [Acuna et al., 1998] is hot thermal boundary layer to thicken ahead of linked to its relatively cold interior, possibly in- the slab; this process has been hypothesized to dicating that its mantle is too cold to efficiently trigger plume-formation [Weinstein and Olson, convect heat out of the core. Venus does not 1989; Steinberger and Torsvik, 2012; Dannberg seem to feature a measurable magnetic field and Gassmoller¨ , 2018], discussed in the next either [Russell and Elphic, 1979], which has Section. If that is the case, then the flow along been linked to its relatively hot interior, with the the CMB provides an important link between mantle and the core being so hot that the core plate tectonics, which is mainly driven by the is not crystallizing [Stevenson et al., 1983] (at subducting slabs, and the intraplate volcanism least presently, albeit it may have undergone generated by plumes, which otherwise appears some freezing in the past). In contrast, Earth to be decoupled from surface plate motions. and Mercury possess substantial magnetic fields, indicating rapid heat transport across the mantle [Ness et al., 1974; Connerney and Ness, Core-Mantle Boundary and the 1988; Anderson et al., 2011]. Better constraints on the composition and interior structure of Mantle’s Hot Thermal Bound- the Earth’s deep interior, thanks to seismic ary Layer tomography and mineral physics data, provide a more detailed picture of the nature of the CMB. The bottom of the mantle is defined by the core-mantle boundary (CMB), which separates the silicate mantle material from the underlying Earth’s Core-Mantle Boundary molten metallic core. The efficiency of heat transport across the CMB is the determining The CMB is a natural place where dense factor for the generation of planetary dynamos: heterogeneities accumulate: material that is in order to sustain a dynamo, the electrically heavier than the ambient mantle but lighter than conductive core material needs to move at the outer core can linger here. Moreover, since sufficiently high velocities, which in turn are the core only exchanges heat with the mantle dictated by the convective flow velocities and by conduction, leading to a 200 − 300 km thick thus the rate of core cooling. In addition to hot thermal boundary layer, across which the thermal convection, an even more effective temperature increases with depth by about 1000 way to generate a dynamo is by chemical K, from the ambient temperature profile of convection, whereby as the core cools below the about 2500 K in the lower mantle to about 4000 melting temperature and freezes, it expels its K at the CMB [Calderwood, 1999; Kawai and light elements, such as sulfur and silicon, which Tsuchiya, 2009]. then buoyantly rise up to the CMB, inducing flow [Stevenson et al., 1983; Braginsky and Seismic studies of the deep interior use the Roberts, 1995]. The rate of core freezing is, compressional and shear wave velocities and again, controlled by the rate of heat transport the bulk sound speed, which are related to the across the CMB, which in turn is limited by material’s bulk modulus (incompressibility), the convective heat transport across the mantle. rigidity and density [Masters et al., 2000]. For Observations of intrinsic magnetic fields of example, the correlation between anomalies

13 Oxford Research Encyclopedia of Planetary Science Mantle Convection in the shear wave velocity and the bulk sound scale heterogeneities in seismic tomography speed can be used to infer the physical causes [Garnero and McNamara, 2008; Dziewonski for an observed anomaly. If the anomaly is et al., 2010; Ritsema et al., 2011]: one of them due to the variations in temperature, then the lies beneath Africa and the other beneath the shear velocity and bulk sound speed should be Pacific Ocean. LLSVPs have irregular shapes correlated (i.e., both positive or both negative), and can measure up to 1000 km in height and while an anti-correlation (anomalies of opposite width; they cover nearly 20% of the CMB and sign) is indicative of compositional variations. occupy about 2% of the mantles total volume There is abundant evidence for the heteroge- [Burke et al., 2008].The negative correlation neous nature of the lowermost mantle from between the bulk sound and shear velocity seismological observations, which indicate the within the LLSVPs suggests that they are of presence of both thermal and compositional chemical origin [Masters et al., 2000; Trampert variations (Figure 5) [Ishii and Tromp, 1999; et al., 2004; Steinberger and Holme, 2008]. Garnero, 2004; Garnero and McNamara, 2008; Moreover, the material that makes up the Ritsema et al., 2011]. The main observational LLSVPs appears to be intrinsically denser than features of the CMB region include the D” the ambient mantle [Ishii and Tromp, 2004]. discontinuity, the large low shear velocity There is yet no consensus on the origin of provinces (LLSVPs) and the ultralow velocity this compositional anomaly, with the proposed zones (ULVZs) [Lay et al., 1998; Thorne and scenarios falling within two main categories: a Garnero, 2004]. The D” discontinuity is seen primordial layer that formed early in the Earth’s as a sharp increase in shear-wave velocity with history [e.g. Lee et al., 2010; Nomura et al., depth occurring several hundred kilometers 2011], and accumulation of a dense eclogitic above the CMB. The part of the mantle between component from the subducted MORB that the D” discontinuity and the CMB is commonly segregates at the CMB [Hofmann and White, referred to as the D” layer. The D” varies in 1982; Christensen and Hofmann, 1994; Tackley, thickness and even appears to to be absent in 2011; Mulyukova et al., 2015]; [see also review some regions, which suggests that it is not a by Hernlund and McNamara, 2015]. global phase transition, unlike, for example, the 410km and 660km discontinuities bounding The ULVZs are localized structures that the transition zone; [see also Hernlund and are much smaller in size than the LLSVPs, McNamara, 2015]. A possible cause for the extending around 1-10 km above the CMB D” is the solid-solid phase transition from and 50-100 km laterally [Thorne and Garnero, perovskite (Pv) to postperovskite (PPv) [Mu- 2004; McNamara et al., 2010]. However, rakami et al., 2004], which would only occur ULVZ’s have a large seismic velocity reduction, at deep mantle pressures in sufficiently cold 10% for P-waves and 10-30% for S-waves regions, such as in the vicinity of newly arrived [Garnero and Helmberger, 1996], and a 10% slabs. Postperovskite is slightly denser (by density increase relative to the ambient mantle. 1 − 2%) and less viscous (by up to an order Mechanisms for producing the ULVZs are still of magnitude) than the perovskite phase, and a matter of debate, with some of the candidates thus can act to mildly destabilize the lowermost including partially molten and/or iron-enriched mantle material, making convection slightly material, possibly formed early in Earth’s more vigorous [Tackley et al., 2007; Nakagawa history when the mantle was much hotter and and Tackley, 2011]. largely molten [Williams and Garnero, 1996; Labrosse et al., 2007], outer core material The two major LLSVPs appear as two large leaking into the lower mantle due to chemical

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Figure 5: A simplified sketch of a possible interpretation of the seismically observed structures in the Earth’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 formation scenarios and the proposed thermal and chemical properties. Adapted from Deschamps et al. [2015]. disequilibrium or morphological instability becomes buoyantly unstable. When the TBL [Otsuka and Karato, 2012], and subduction and is sufficiently thickened and buoyant to rise gravitational settling of banded-iron formations through the overlying viscous mantle, it can rise [Dobson and Brodholt, 2005]. upwards in the form of hot mantle currents, also called mantle plumes, and potentially reach the The compositionally anomalous nature of the surface. Arrival of plume material at the surface deep mantle has important implications for man- can generate volcanic activity or a hotspot and tle convection and hence Earth’s thermal evo- deflect the surface upwards, generating a high lution. In particular, the presence of composi- topography or a hotspot swell. Hot plume tionally dense material at the CMB reduces the material will also undergo melting when it as- amount of heat that flows from the core into the cends to lower pressures and induce volcanism; mantle, which is one of the energy sources for the resulting lava flows may serve as another convective flow. This effective blanketing of the surface signature of the underlying convective CMB has implications for the rate at which the mantle currents. For example, the large volcanic mantle has been cooling since core formation. rises Themis, Eastern Eistla and Central Eistla In addition, as discussed previously, the heat on Venus [Smrekar and Stofan, 1999] and the flow across the CMB controls the rate at which Tharsis rise on Mars [Wenzel et al., 2004] have the Earth’s core cools and freezes, and thus the been interpreted as manifestations of underly- history of the geodynamo. ing plume activity [see Steinberger et al., 2010].

Plume geometry is hypothesized to be Mantle’s Hot Upwelling Flow mushroom-like, with a plume-head spanning a few hundred kilometers across, followed by a As heat is conducted from the core into the cylindrical plume-tail that can be as long as the mantle, it creates a hot thermal boundary depth of the mantle, and a 100 km or less in layer (TBL) at the bottom of the mantle. diameter [Whitehead and Luther, 1975; White The hot TBL material thermally expands and and McKenzie, 1989; Olson, 1990; Sleep, 2006];

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[see review by Ballmer et al., 2015]. The forms of volcanism, which occur at mid-ocean plume-tails are relatively narrow and, in the ridges and subduction-related volcanic arcs, case of the Earth, until recently have been dif- hotspots often occur in plate interiors and are ficult to resolve seismologically [Montelli et al., not generally associated with plate boundary 2004; French and Romanowicz, 2015]. More- processes. over, planetary mantles are heated both from below (by the core) and from within (by pri- The classical view of mantle plumes as purely mordial heat and radioactive elements); the thermal upwelling currents has been challenged strength of the plumes (i.e., their size and ther- in recent years, due to the large kilometer mal anomaly) decreases with the decreasing scale topographic uplift that is predicted for a contribution from bottom heating, since that’s thermal plume impinging on the lithosphere what controls the size and temperature of the [White and McKenzie, 1989], but that is not TBL. Thus, plume detection, both through grav- always observed [Czamanske et al., 1998; ity measurements, seismology and volcanism, Korenaga, 2005; Sun et al., 2010]. One of is challenging in planets that are predominantly the proposed resolutions to this inconsistency heated from within, as seems to be the case for are compositionally anomalous plumes (also the terrestrial planets in our Solar System. called thermochemical plumes), whose mantle- material is enriched in heavier elements and is thus intrinsically dense relative to the ‘normal’ Plumes and Mid-Ocean Ridges on mantle (but, of course, still positively buoyant Earth due to their high temperature) [Dannberg and Sobolev, 2015]. The thermochemical plumes When a new starting plume head first reaches are less buoyant than the classical purely ther- the surface of the Earth, it is thought to initially mal plumes, and therefore rise more slowly and generate extensive volcanic activity, often generate less dynamic topography, in agreement referred to as flood-basalt volcanism, leading with the observations. Thermochemical plumes to large igneous provinces (e.g., Ontong-Java simultaneously explain another feature of Plateau, Columbia River Basalts, the Deccan plume-volcanism, namely their geochemically Traps and the Siberian Trapps). This initial distinct basaltic lavas, in terms of trace elements eruption is associated with a massive flood and isotopes, relative to basaltic lavas derived basalt volcanism and is ostensibly followed from mid-ocean ridges [Hofmann and White, by continuous hotspot activity, supplied by 1982; Zindler and Hart, 1986; Kobayashi et al., the narrow plume-tail [Richards et al., 1989; 2004; Jellinek and Manga, 2004; Sobolev et al., Ballmer et al., 2015]. This ongoing hotspot 2005; Jackson and Dasgupta, 2008; Sobolev volcanism can sometimes be seen as a chain et al., 2011]. The distinct geochemistry of of volcanic islands (typically on the sea floor hotspot-lavas is one of the arguments for why where the plume material can readily penetrate they are thought to be extracted from a mantle- the thinner lithosphere); in particular, the region that is deep-seated and that is at least stationary plume conduit emplaces lava onto the partly decoupled from the large tectonic scale surface of a tectonic plate that is moving relative mantle circulation. Furthermore, the spatial to it, thus forming a chain of volcanoes with a correlation of plume-derived lavas at the surface characteristic age progression, the archetypical and their projection down to the LLSVPs and example of which is the Hawaiian-Emperor ULVZs at the CMB provides further supportive hotspot chain that extends across the North Pa- evidence for their deep origin [Torsvik et al., cific sea-floor. In contrast to the more common 2006; Burke et al., 2008; Dziewonski et al.,

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2010; Steinberger and Torsvik, 2012]. melting beneath a ridge is several hundred kilometers wide [Forsyth, 1998]. However, The vertical flow of hot mantle upwellings as the melt migrates to the surface, it focuses induces lateral flow along the CMB, due to a dy- within just a few kilometers of the spreading namic low-pressure that is created at the plumes axis, creating narrow regions where the oceanic base. As the ambient material gets sucked into crust is emplaced and where the deformation the rising plume, it drags the underlying, pos- is localized [Morgan, 1987; Spiegelman and sibly compositionally heterogeneous material McKenzie, 1987; Parmentier, 2015]. The phys- along with it. This is the process by which ical explanation for why MOR-volcanism is plumes can potentially bring the chemically focused into narrow ridges-structures is related distinct material from the deep mantle all the to, and is as enigmatic as, the cause for strong way up to the surface, producing geochemically plates and weak plate boundaries. The ridge distinct lavas. As such, plume-derived lavas orientation typically mirrors the subduction are a window into the chemical structure of the zones that they eventually feed, implying that deep mantle. they may initiate as a strain localization, such as a self-focusing necking instability [Ricard Another component of the upwelling flow, and Froidevaux, 1986]. Such mechanisms are which is associated with plate tectonics and is plausible if the stresses in the lithosphere due thus unique for the Earth, is the return flow of to the pull of slabs can be guided considerable the mantle that compensates for, or gets dis- distances. The cause for ridge formation and placed by, the downward motion of the slabs. geometry remain an active area of research. The material that makes up the return flow even- tually ends up becoming the bottom-most un- The lavas produced at MORs and hotspots are differentiated part of the tectonic plates, ac- known as Mid-Ocean Ridge Basalts (MORB) counting for their thickening as they grow older. and Ocean-Island Basalts (OIB), respectively. As opposed to the actively upwelling plumes, Being direct samples of the mantle, their MOR volcanism is not associated with the ex- petrological composition, and trace-element cess buoyancy of hot material, but rather with its chemistry is of great interest for understanding passive rising in response to lithospheric spread- mantle dynamics and structure [Hofmann, 1997, ing motion; this is for example evident in the 2003; van Keken et al., 2002; Tackley, 2015]. East Pacific Rise, which is the fastest spreading For example, the distinct features of MORB and ridge on Earth, and which is devoid of a grav- OIB implies that they originate from different ity anomaly or deep seismic structure [Forsyth source regions in the mantle with limited et al., 1998], implying that it is isostatically sup- material exchange between them. Geochemical ported and is not being lifted up by any deep up- measurements of trace elements, in particular welling current [Runcorn, 1963; Davies, 1988]. incompatible elements (which dissolve more MORs constitute the divergent plate boundaries readily in a rock’s melt than its solid during where tectonic plates are first formed. Many partial melting), such as uranium, thorium and ridges initiate as rift zones during continental helium, show that MORB and OIB are measur- break up, eventually becoming sites of sea floor ably distinct: MORBs appear to be significantly spreading that separate the continents; these pro- depleted in such trace elements relative to cesses are an integral part of the classical Wilson OIB, which implies that the MORB source cycle, involving repeated closing and opening of region has undergone previous melting and oceans [Wilson, 1968]. depletion, compared to that of OIB [Hofmann The mantle region that undergoes fractional and White, 1982; Zindler and Hart, 1986]. The

17 Oxford Research Encyclopedia of Planetary Science Mantle Convection emerging model of upwelling mantle flow has composition [see van Keken et al., 2002]. A the MORB source confined to an area in the stratified mantle, with a shallow portion of upper mantle, which has been cycled repeatedly the mantle that has segregated to form the through the plate tectonic process of mid-ocean continental crust, leaving a complementary un- ridge melting and separation of oceanic crust depleted region in the deeper mantle, makes for and trace elements from the mantle. OIB, on a geochemically plausible mantle composition the other hand, ostensibly come from a part model. It is worth noting that the total volume of the mantle that has seen little if any of this of the two major LLSVPs or even the entire D” melt processing, and hence would be isolated layer, is not enough to hold all of the unseg- presumably at depth from the upper mantle regated portion of the mantle, and thus cannot and the plate-tectonic cycling [Allegre´ , 1982; single-handedly account for all of the enriched Tackley, 2015, and references therein]. mantle material. A 1000 km thick layer at the base of the mantle would potentially be big Mantle layering is also implied by a putative enough to serve as a storage of unsegregated heat flow paradox. Specifically, if the mantle material [Kellogg et al., 1999], however, such were composed entirely of MORB-source layer has never been seismologically observed. material, which is depleted in U, Th and K, then its radioactive heating would not be sufficient to There remains a contradiction between geo- account for the observed mantle heat outflow of chemical and geophysical inferences of layered 38 TW. This inconsistency can be resolved by vs whole mantle convection: while there is com- assuming a higher concentration of radioactive pelling evidence from seismic tomography mod- elements in the lower mantle, which then also els for material exchange between the lower and implies that the mantle is not well-stirred and upper mantle, with subducting slabs extending there is at least some decoupling of convective into the lower mantle [van der Hilst et al., 1997; flow between the upper and lower mantle. Grand et al., 1997], as well as mantle plumes However, if the contribution from primordial traversing the transition zone [Montelli et al., heat to the net mantle heat output is equal to 2004; Wolfe et al., 2009; French and Romanow- or larger than the radiogenic source, then the icz, 2015], the geochemical data appears to ar- observed heat flow can be reconciled with gue for a layered mantle with an isolated and un- the low concentration of radioactive elements, depleted mantle at depth. Some of the attempts thus resolving this so-called heat-flow para- to reconcile these observations circumvent the dox [Christensen, 1985; Korenaga, 2003, 2008]. problem of layered convection, which is not ob- served, by instead invoking differential melting. Another geochemical argument for limited For example, one model envisions the mantle exchange between lower and upper mantle as a plum-pudding, where ‘plums’ are scattered comes from taking the “bulk silicate earth” regions that are enriched in volatile elements, composition (i.e., with the mantle and crust while the rest of the mantle is a depleted ‘pud- combined) and assuming that the continental ding’ [Morgan and Morgan, 1999; Becker et al., crust was removed from it uniformly. The 1999; Tackley, 2000c]. The size of the plums mantle residue left behind from this thought and their degree of relative enrichment of in- experiment is too enriched in incompatible compatible and radiogenic elements depends on elements, compared to the MORB-source. their assumed origin and the history of mantle However, extracting the continental crust from stirring, both of which are highly uncertain. The only the top 1/3 to 1/2 of the mantle causes enriched domains can melt at higher pressures, sufficient depletion to reproduce MORB-source while the depleted ones require lower pressures

18 Oxford Research Encyclopedia of Planetary Science Mantle Convection to melt. One of the proposed scenarios envisions Basics of Thermal Convection that a mantle plume impinging on the base of a 100 km thick lithosphere would mostly melt the To understand the origin and mechanics of ‘plum’ material (OIB-source), while the part of the important features of mantle convection the mantle that rises to lower pressures at ridges surveyed above, it is necessary to review the melts additional depleted ‘pudding’-component basic physics of thermal convection. For (MORB-source), resulting in MORB that ap- example, tectonic plates, slabs, lithospheric pears depleted relative to OIB [Ito and Ma- drips and mantle plumes are all forms of honey, 2005a,b]. Another model argues for thermal boundary layers, which are common to whole-mantle convection, but takes into account convection in any fluid system. The simplest the different abilities of mantle minerals to ab- form of thermal convection is referred to as sorb water, in particular transition zone mate- Rayleigh-Benard´ convection, named after the rials absorb water more readily than the up- French experimentalist Henri Benard,´ who per mantle. As mantle material passively up- recognized the onset of convective motion in wells through the transition zone (as part of fluids from a static conductive state and the the slab-driven return flow) and enters the up- formation of regular flow patterns in a convect- per mantle at the 410 km boundary, it becomes ing layer [Benard´ , 1900, 1901], and the British closer to water-saturation and more likely to theoretical physicist and mathematician Lord melt. Melting at 410 km depth strips, or filters, Rayleigh (William John Strutt), who provided the upwelling mantle from the incompatible ele- the theoretical framework to explain Benard’s´ ments, which forms the depleted MORB-source. experimental results [Strutt, 1916]. Mantle plumes, on the other hand, traverse the transition zone too fast to become hydrated, The Rayleigh-Benard´ system is an idealized which limits the amount of melting and volatile- model of a fluid layer that has a finite thickness, filtering they can undergo as they cross the 410 but is infinite in all horizontal directions. The km boundary. Thus, the lavas sourced by the layer is heated uniformly from below and plume material, the OIBs, would appear to come cooled from above by applying fixed high from an enriched mantle [Bercovici and Karato, and low temperatures at the bottom and top 2003]. The prediction of a melting site at 410 boundaries, respectively. As the bottom part of km depth inferred by this model, known as the the layer heats up, it thermally expands, which Transition Zone Water Filter model, has been lowers its density and makes it buoyant relative supported by some seismological studies [Reve- to the overlying colder material (analogously, naugh and Sipkin, 1994; Tauzin et al., 2010]. the material at the top cools, contracts and However, there still exists relatively large uncer- becomes negatively buoyant). The resulting tainty regarding the melting properties and the density stratification, with low density material solubilities of incompatible elements, which re- underlying high density material, is gravita- quire further constraints to test the models that tionally unstable and can lead to fluid flow that invoke differential melting. In summary, the overturns the layer, bringing hot material up conflicting geochemical and geophysical infer- and cold material down. Of course, because the ence of layered vs whole mantle convection re- temperature at the boundaries remains fixed, the mains an unsolved problem. cycle continues with the newly arriving material at the bottom heating up and rising, while the material at the top cools and sinks. Eventually, the system reaches a dynamic equilibrium with laterally alternating regions of upwelling and

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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 Bercovici et al. [2015].

downwelling currents. der to excite convective flow. The value of Rac is typically on the order of 1000, with the exact Convective fluid flow is a form of heat trans- value depending on the thermal and mechanical port that is activated when thermal conduction is properties of the horizontal boundaries, (e.g., not efficient enough to accommodate heat flow. whether the boundary is rigid or open to the air For example, if the layer is thin enough, it can or space, see Chandrasekhar [1961]). conduct heat diffusively through molecular vi- brations, thus the fluid can remain static and ob- The characteristic physical properties of the tain a conductive temperature profile across its Earth’s mantle entering the Rayleigh num- depth. Convective motion emerges when ther- ber are ρ ≈ 4000 kg/m3, g = 10 m/s2, mally induced density anomalies induce flow α = 3 × 10−5 K−1, ∆T ≈ 3000 K, that is sufficiently vigorous to withstand the sta- d = 2900 km, µ = 1022 Pa s (dominated bilizing effects of thermal diffusion. In addition, by the lower mantle), and κ = 10−6 m2/s [see while the thermal contrast across the layer sup- Schubert et al., 2001]. According to (1), these plies buoyancy to drive the flow, the viscous re- lead to a Rayleigh number of approximately sistance of the fluid opposes it. The competi- 107, which is well beyond supercritical. Thus, in tion between forcing by thermal buoyancy, and spite of the extremely high viscosity of the solid damping by viscosity and thermal diffusion, is rock that makes up the Earth’s mantle, the man- characterized by a dimensionless ratio called the tle spans a large depth and is subject to a high Rayleigh number thermal contrast, and hence convects vigorously. ρgα∆T d3 Ra = (1) While the properties of other terrestrial plan- µκ ets are less well known than for Earth, there are where ρ is fluid density, g is gravity, α is thermal reasonable constraints on their gravitational ac- expansivity, ∆T is the difference in temperature celeration, mantle thickness and surface temper- between the bottom and top boundaries, d is ature (Table 1). Assuming their material prop- the layer thickness, µ is fluid viscosity and κ is erties are similar to Earth’s, we can estimate the fluid thermal diffusivity. The higher the value Rayleigh numbers for the mantles of other ter- of Ra, the higher the propensity for convective restrial planets: 104 for Mercury, 107 for Venus, overturn. Ra needs to exceed a certain value, and 106 for Mars. With the exception of Mer- called the critical Rayleigh number Rac, in or- cury, whose Ra is at most an order of magnitude

20 Oxford Research Encyclopedia of Planetary Science Mantle Convection above critical, the mantle of the rocky planets in pressure times volume change), and to do this the Solar System appear to be cooling predomi- it uses its own thermal internal energy, which nantly by convection. results in the material ”cooling” (although the In a convecting system, heat that is being only exchange of energy is with itself). Thus transported by the upwellings and downwellings rising material has an adiabatic temperature de- first enters the fluid layer through the horizon- crease. Likewise, sinking, compressing material tal boundaries by conduction across thermal relinquishes its mechanical energy to thermal boundary layers (TBLs). TBLs are the portions energy, causing it to apparently ”heat up”, of the fluid that, once sufficiently heated or which leads to a temperature increase for sink- cooled, become unstable and rise as upwellings ing material. The average cooling and heating or sink as downwellings, respectively. The adiabatic temperature profiles appear as a mean longer time it takes for thermal diffusion to adiabat. A typical temperature-profile across induce enough buoyancy and destabilize the the depth of a vigorously convecting layer has TBLs, the thicker they get prior to overturning, narrow regions (TBLs) at the top and bottom and thus the broader the vertical currents that that accommodate most of the temperature jump they form. The lower the Rayleigh number, across the layer, with most of the layer in the the longer the time that it takes for TBLs to interior being isothermal or adiabatic (Figure 7). go unstable. In fact, another way to view a system at subcritical Ra is that by the time the The heat flow (power output per unit area) TBLs would be thick enough to overturn, they out of the convecting layer is essentially already span the entire layer depth, which is given by the heat that is conducted across the why the layer remains stable. On the opposite TBLs, given by k∆T/δ where k is thermal end, at Ra-values way above supercritical, conductivity (units of WK−1m−1), ∆T/2 is only thin TBLs manage to develop before the temperature drop from the isothermal (or undergoing gravitational instability. As the hot adiabatic) interior to the surface and δ/2 is the bottom TBL starts to rise, the region it used to thickness of the TBL. By comparison, the ther- occupy gets replenished by the newly arriving mal conduction across a static non-convecting cold material, and analogous for the cold top layer is k∆T/d. The ratio of heat flow in TBL. Meanwhile, the material in between the convecting layer to the purely conductive the laterally moving TBLs and the vertically layer is thus d/δ, which is called the Nusselt moving upwellings and downwellings is simply number Nu (named after the German engineer, moved around by the viscous drag from the Wilhelm Nusselt 1882-1957). The relation ambient flow, and eventually equilibrates to between Nu and convective vigor parameter- their average temperature. (In fact, if the ized by Ra is important for understanding the layer is deep enough such that the pressures efficiency of convective cooling of planetary are comparable to fluid incompressibility, the bodies. Convective heat transport is often fluid in-between the TBLs is not isothermal written as Nu(k∆T/d), and in considering but adiabatic). An adiabatic profile is caused this relation, Howard [1966] argued that heat by material moving up or down through large transport across the depth of the vigorously enough pressure changes to induce compression convecting fluid layer is so fast that the layer or decompression, but fast enough so that the thickness is not a rate limiting factor in re- material has little time to exchange heat with its leasing heat, and thus heat flow should be surroundings. Material that rises and expands independent of fluid depth d; this implies that from decompression must increase its mechan- since Ra ∼ d3 then Nu ∼ Ra1/3, which yields ical or ”reversible” internal energy (essentially a convective heat flow Nu(k∆T/d) that is

21 Oxford Research Encyclopedia of Planetary Science Mantle Convection

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 Mantle Convection Studies 1 [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 fluid material cools next to the cold surface. The is conductive for Ra ≤ Rac, one often writes thickening depends on the thermal diffusivity κ 1/3 that Nu = (Ra/Rac) (although Nu = 1 and the residence time or time t since leaving for Ra ≤ Rac), which is a reasonably accurate the upwelling. With regard to convection relationship born out by simple experiments in the Earth’s mantle, the top cold thermal and computer modeling [Schubert et al., 2001; boundary layer is typically associated with Ricard, 2015]. This relationship also implies the lithosphere, the layer of cold stiff mantle that the ratio of thermal boundary width to fluid rock that is nominally divided into tectonic layer depth is δ/d ∼ Ra−1/3, which shows plates and reaches thickness of 100km or so. that the TBLs become increasingly thin as Simple dimensional considerations show√ that convection becomes more vigorous. the boundary layer thickness goes as κt; this √ corresponds to the well known age law for While the average TBL thickness is well subsidence of ocean sea floor with age since approximated by δ ∼ Ra−1/3, it is worth noting formation at mid-ocean ridges, implying that that the TBL thickness varies laterally: for sea-floor gets deeper because of the cooling example, as the fluid in the top boundary layer and thickening of the lithosphere [e.g., Parsons moves from an upwelling to a downwelling, it and Sclater, 1977; Sclater et al., 1980; Stein cools and the boundary layer thickens as more and Stein, 1992; Turcotte and Schubert, 2014];

22 Oxford Research Encyclopedia of Planetary Science Mantle Convection

convection

conduction height

temperature all bottom heated

add internal heating height

temperature temperature

Figure 7: Sketch of temperature profiles, showing how convective mixing homongenizes the conductive mean temperature into a nearly isothermal state (if the fuid is incompressible) with thermal boundary layers connecting it to the cold surface and hot base (top frame). With no internal heating the interior mean temperature is the average of the top and bottom temperatures; the effect of adding internal heating (bottom frames) is to increase the interior mean temperature and thus change the relative size and temperature drop across the top and bottom thermal boundary layers. this emphasizes that the oceanic lithosphere is anomaly, density and heat capacity, respectively. primarily a convective thermal boundary layer. A ≈ 2πRδ is the effective global cross-sectional area of all slabs crossing the depth at which the A simple analysis of the heat transported by energy flux is being estimated, with δ ≈ 100 slabs demonstrates that slabs and plates are an km being a typical slab thickness, and using integral part of mantle convection [Bercovici, the Earth’s circumference with R ≈ 6000 km 2003]. The energy flux Q associated with a slab to approximate the net horizontal length of all sinking at velocity vsink is given by slabs (since most slabs occur in a nearly large circle around the Pacific basin). Assuming that Q = vsinkAρcp∆T (2) the sinking slabs account for about 80% of the mantles surface heat flow through the ocean where ∆T ≈ 700 K, ρ ≈ 3500 kg m−3 floor (the other 20% coming from the plumes), −1 and cp = 1000 J kg K are the slabs thermal

23 Oxford Research Encyclopedia of Planetary Science Mantle Convection such that Q = 0.8 ∗ 38 TW, and solving (2) for lithosphere, however, is by significantly more −1 vsink yields a slab velocity vsink ≈ 10 cm year . than one order of magnitude, suggesting that This is in good agreement with the observed there exists a weakening mechanism (unique to velocity of tectonic plates, especially the ones Earth, as discussed later) that offsets the thermal with an appreciable slab attached to them, such effect. At moderate viscosity ratios of about that slab-pull is particularly significant. The two to four orders of magnitude, the flow of the agreement between the observed plate kinemat- cold TBL is significantly impeded, meaning it ics and the measured heat flow at the Earth’s flows much more sluggishly than the underlying surface is one of the major accomplishments of mantle. Finally, at viscosity ratios more than mantle dynamics theory. In fact, the matching four orders of magnitude, most of the cold TBL convective fluid velocities and plate velocities becomes immobile. The deeper softest portions have also been inferred using gravity and of the TBL may participate in the convective heat-flow measurements [Pekeris, 1935; Hales, mantle flow; however, the shallower coldest 1936], as well as simple dynamical models of portions act as a rigid boundary condition to the the force balance on sinking slabs [e.g., Davies underlying convective mantle layer. This so- and Richards, 1992]. called stagnant lid regime appears to take place on Mars and Mercury (if Mercury’s mantle at all Understanding the dynamics of mantle convects). The failure to entrain the uppermost convection using the classical Rayleigh- portion of the lithosphere effectively lowers the Benard´ model is complicated by the fact that temperature difference that drives convection, the mantle rocks are far from a simple fluid, ∆T in (1), since the temperature drop across with the most notable distinction being that the lower, softer, mobile part of the cold TBL is the viscosity of rocks is extremely sensitive smaller than for the drop across the entire TBL. to temperature. A drop in temperature by The smaller effective TBL temperature contrast a few hundred degrees Kelvin - a plausible and the greater resistance of the rigid upper temperature difference across planetary TBLs boundary act to lower the Ra of the so-called - can raise the viscosity by several orders of single-plate planets, making them convect and magnitude, as will be described in detail in the cool less efficiently than the Earth does. While following section. The dynamical consequence the cold TBL may not get recycled into the of such thermal stiffening is that as the rocks mantle, the surface of planets that are in the get colder and denser, and thus more prone to stagnant lid regime may still get renewed by sink, they also become increasingly resistant volcanism, as has been proposed for planets to deformation and flow, making it harder exhibiting heat pipe behavior [Spohn, 1991; for them to sink. Depending on the degree Moore et al., 2017], or as a consequence of of thermal stiffening of the cold TBL, there lithospheric delamination, described in Section are three possible modes of terrestrial mantle “Mantle’s Cold Thermal Boundary Layer”. convection [Solomatov, 1995; Solomatov and Moresi, 1997]. When the ratio of the maximum The dynamics of the hot TBL at the base of a (coldest) to minimum (warmest) viscosity is planetary mantle is affected by the temperature- moderate, say less than about one order of dependence of viscosity as well. Specifically, magnitude, the cold TBL fully participates for the onset of a new hot upwelling, since the in convective circulation. This mode may be hotter material is less viscous, it is less capa- the most applicable to Earth, which features ble of displacing the colder and stiffer ambi- continuous downwelling of its surface at sub- ent mantle in order to rise through it. Fluid duction zones. Thermal stiffening of the Earth’s in the bottom TBL lingers at the CMB as it

24 Oxford Research Encyclopedia of Planetary Science Mantle Convection gathers enough buoyancy to overcome the vis- currents on Earth do, indeed, feature large cold cous resistance of the overlying mantle. Once slabs with large thermal anomalies (of the order the fluid has accumulated enough thermal buoy- of 700 K) and smaller plumes with weaker ancy, it starts rising rapidly through the mantle, thermal anomalies (on the order of 200 K). first forming a diapiric plume [Whitehead and Luther, 1975], which efficiently drains the re- Convective currents also self-organize in such maining low-viscosity hot TBL from the bot- a way that the horizontal spacing between the tom [Bercovici and Kelly, 1997]. The efficient upwellings and the downwellings is optimized: supply of hot material from the bottom of the not too small, so that they don’t exert too much mantle further propels the plumes ascent. These viscous drag on each other and/or don’t lose two stages of plume formation are responsible heat too rapidly to each other, and not too big, for its mushroom shape - the initial gathering of so that they don’t have to roll too much mass be- hot material forms the large plume head, and the tween them. In addition, the separation distance subsequent rapid draining of the hot TBL upon between the vertical currents is determined by ascent forms the narrow plume tail [Campbell the time it takes for the material that arrives to and Griffiths, 1990]. and moves laterally along the boundary to con- Another contrast between mantle convection duct enough heat so as to become convectively and the idealized Rayleigh-Benard´ model is that unstable. The convective instability theory the planetary mantles are heated not just by the predicts that the horizontal spacing between the bottom boundary, referred to as ‘basal heating’, upwellings and the downwellings is approxi- but also by the release of both radiogenic and mately equal to the layer depth d (a bit larger at primordial heat distributed through the volume the onset of convection, but identically d as Ra of the fluid, termed ‘internal heating’. Adding becomes very large). Applying this theoretical the effect of internal heating to the model of a prediction to the mantle is complicated by the convecting layer raises the temperature of its features of the mantle materials that tend to interior, bringing it closer to the temperature of break the symmetry of flow observed in the the bottom boundary (instead of the mean of the idealized Rayleigh-Benard´ model. In particular, two boundary temperatures, as is the case in the the strongly temperature-dependent viscosity classical symmetric Rayleigh-Benard´ model). means that the cold TBL has to spend longer While this makes the temperature jump across time near the surface, and thus travel further the bottom TBL smaller, the jump across the laterally, before it is heavy enough to sink top TBL becomes larger, since the top boundary against its own viscous resistance, resulting in now must conduct out heat injected through the convection cells that are wider than the depth of bottom, plus heat generated from the interior the mantle [Weinstein and Christensen, 1991]. (Figure 7). As a result, the top TBL in an inter- Notably, if the degree of thermal stiffening puts nally heated system is more negatively buoyant convection in a stagnant lid regime, then the and forms stronger downwellings, while the aspect ratio of the convective part of the layer upwelling currents are smaller and weaker, approaches unity. In addition, mantle viscosity compared to a system that is entirely basally increases with depth due to the effect of pres- heated. The strong temperature-dependence of sure [Sammis et al., 1977], and the resulting viscosity of mantle rocks further adds to this impediment to vertical flow also acts to increase asymmetry, with the thermally stiffened cold the width of the convective cells [Christensen downwellings having to acquire more thermal and Harder, 1991; Bunge et al., 1996]. For buoyancy in order to overcome their own Earth, the characteristic length scale of mantle viscous resistance and sink. The convective convection, with most downwellings occurring

25 Oxford Research Encyclopedia of Planetary Science Mantle Convection in a torus along the planet’s circumference, its effect being stronger for the smaller scale and upwelling flow focused in the two regions structures, as has been shown by analytical on the either side of the torus (one beneath and numerical studies [Bercovici et al., 1993; Africa and the other beneath the Pacific, where Tackley et al., 1993, 1994; Tackley, 1996]. perhaps not coincidentally the LLSVPs reside), Thus, the 660-km transition for Earth [or the or what is know as spherical harmonic degree-2 710-km for Venus, Ito and Takahashi, 1989] convection pattern, is indeed larger than the acts as a low-pass filter, effectively increasing depth of the mantle. Another example, albeit the characteristic length scale of convective less well constrained, is the proposed degree-1 flow. This phase transition on Mars is thought convection pattern on Mars, in which a single to be much deeper, at about 1910 km depth upwelling in the southern hemisphere, broadly [Harder, 1998], which puts it very close to the beneath the Tharsis Bulge, has been invoked to martian CMB. Furthermore, the presence of a explain the gravity anomaly and the observed low viscosity asthenosphere on Earth lowers topographic dichotomy [Zhong and Zuber, the horizontal drag on convective flow and 2001; Roberts and Zhong, 2006; Keller and acts to increase the size of the convection cells Tackley, 2009]. For a martian mantle thickness [Lenardic et al., 2006]. The absence of an as- that is between 0.4-0.6 of the planetary radius thenosphere on Venus precludes the same effect [depending on the assumed core-composition [Kaula, 1990], but has been speculated to occur and density, see Harder, 1998], a degree-1 pat- on Mars and further support the large scale tern implies a characteristic convective length (degree-1) convection pattern of the martian scale that is much larger than the mantle depth. mantle [Harder and Christensen, 1996; Harder, Thus, the temperature- and depth-dependent 2000; Zhong and Zuber, 2001]. The mantle viscosity may serve to explain the large aspect thickness on Mercury is arguably too small to ratio of convection cells of mantle convection, experience any solid-state phase transitions. compared to that predicted by the Rayleigh- Benard´ system. The three large volcanic rises The 3-D convection pattern in fluids with on Venus, which are arguably produced by temperature-dependent viscosity has also been deep-rooted mantle plumes [Stofan et al., 1991; observed in experiments [White, 1988] and nu- Smrekar and Stofan, 1999], may also indicate a merical models [Ratcliff et al., 1997; Schubert low-degree convective pattern, although the re- et al., 2001] to exhibit upwellings in the form of mote measurements of gravity and topography cylindrical plumes at the center of a canopy of have not been able to confirm such planform of sheet-like downwellings; this is crudely applica- convection for the venusian mantle [Steinberger ble to mantle convection on Earth, with the sheet et al., 2010]. Whether the mantle of Mercury like slabs forming the downwelling flow and the is presently convecting is unclear, since there cylindrical upwelling plumes forming the ocean are no indications of volcanism taking place islands, manifested as intraplate volcanism at since about 3.5 Gyr ago [Namur and Charlier, the surface. At more modest viscosity ratios, for 2017], and its predicted Rayleigh number is example due to a smaller temperature contrast only modestly supercritical. across the mantle, as may be the case for Mars and Venus, the upwelling flow may organize The presence of phase transitions in plane- into linear structures, possibly explaining the tary mantles affects the convective pattern as bands of volcanic highlands observed on Venus well. For example, the Earth’s endothermic or the chain of volcanoes in the Tharsis region wadsleyite-to-perovskite transition at 660 km on Mars [Ratcliff et al., 1997; Schubert et al., depth impedes the vertical convective flow, with 2001; Breuer and Moore, 2015]. While Earth’s

26 Oxford Research Encyclopedia of Planetary Science Mantle Convection mid-ocean ridges or spreading centers are also of escaping the well goes to 1, while as T goes linear, they primarily involve shallow upwelling, to 0 the probability of escape goes to 0. best explained as being pulled passively by a distant force (ostensibly slabs), rather than in- When there is stress acting on the mate- volving a deep convective upwelling that pries rial, the potential wells of the crystal change them open. The features of mantle convection shape, with the walls on the side of the well that are not readily explained by the classical under compression getting steeper (squeezing Rayleigh-Benard´ model mainly arise because molecules closer makes Coulomb’s attraction in of the peculiar flow properties of the rock that the chemical bonds stronger), while the walls makes up the mantle, which we discuss next. on the side of the well under tension become shallower (separating molecules weakens the bonds). Thus, the probability of atoms to escape How Can Rock Flow? their wells is higher in the direction of tension, with the lower activation barrier and away from Viscous flow of the solid rock that makes up compression, causing the medium to deform in the mantle (also called solid-state creep) is the tensile direction by solid-state diffusion of governed by a number of complex processes, atoms. or rock rheologies, a full survey of which is beyond the scope of this essay [see Ranalli, The accommodation of deformation by 1995; Karato, 2008]. However, a brief outline diffusion of atoms is known as diffusion creep. of the dominant mechanisms that accommodate For the deformation to occur, the atoms have to mantle flow, namely diffusion and dislocation diffuse through mineral grains or along the grain creep, can help illustrate why the mantle is not a boundaries. The smaller the grains, the smaller simple fluid, and explain some of its main flow the distance that an atom has to migrate before features. encountering a grain boundary, where the more disordered atomic arrangement (compared to Deformation by solid-state creep depends that of the bulk of the grain) makes it easier for on the statistical-mechanical probability of an the atom to move. Thus, the diffusion creep atom in a crystal lattice to leave the potential viscosity depends on grain size, wherein the well of its lattice site. The potential-well itself smaller the grains the weaker the material. is defined by electrostatic or chemical bonds inhibiting escape, and Pauli-exclusion pressure When the material deforms by disloca- preventing molecules squeezing too closely to tion creep, the strain is accommodated by each other. The mobility of atoms is determined the propagation of dislocations through the by a Boltzman distribution, which measures grain. Dislocations are linear lattice defects, the probability of having sufficient energy to where a whole row of atoms can be out of overcome the lattice potential well barrier, order, displaced or missing. It requires more which is often called the activation energy (or energy to displace a dislocation, compared to allowing instead for pressure variations, the a single atom as in diffusion creep, but once activation enthalpy). This probability depends a dislocation is mobilized, it accommodates −Ea/RT on the Arrhenius factor e where Ea is the strain more efficiently than diffusion creep activation energy (J/mol), R is the gas constant (unless the grains are sufficiently small). As the (J/K/mol) and T is temperature; RT represents material creeps, new dislocations are nucleated, the thermal excitation energy of the molecule in displaced or annihilated, so that the dislocation the well. As T goes to infinity, the probability density of the material evolves and eventually

27 Oxford Research Encyclopedia of Planetary Science Mantle Convection reaches a steady state that is determined pre- 2000 K at the top (about 100 km depth) and dominantly by stress. Due to the relatively large bottom (about 300 km depth) of the lithosphere, size of the dislocations, they can interact with respectively, would increase the dislocation each other through the induced long-ranging creep viscosity by a factor of 1041, or the diffu- stress fields, which makes their velocity depend sion creep viscosity by a factor of 1029 (using on dislocation density, which is itself stress- the activation energy values for olivine from dependent. Thus both the dislocation density the previous paragraph for the lack of better and velocity depend on stress, and this makes mineralogical constraints). It is unsurprising, for a non-linear dislocation creep rheology, i.e., then, that the thermally stiffened part of the viscosity depends on stress to some power. martian lithosphere does not participate in the convective mantle flow, rendering it in the The viscosities for diffusion and dislocation stagnant lid regime. A more modest thermal creep mechanisms can be written as contrast across the venusian lithosphere, with about 1200 and 1500 K at the top and bottom, ( m Ea Ba e RT for diffusion creep respectively (assuming, crudely, the same µ = E0 (3) 1−n a Aσ e RT for dislocation creep thermal conditions as on Earth, but with a 400 K hotter surface temperature), yields an where A and B are proportionality constants, increase in the dislocation creep viscosity by a a is grain size, σ is stress (in fact, since stress factor of 104, or the diffusion creep viscosity is a tensor, σ2 is the scalar second invariant of by a factor of 103. A modest thermal stiffening the stress tensor), and m and n are exponents, of the lithosphere on Venus makes it more typical values of which are 2 < m < 3 and pliable to deformation by mantle flow, possibly 3 < n < 5. The activation energies are different explaining the episodic recycling of its surface, for diffusion and dislocation creep, with, for ex- as witnessed by its relatively young 500 Myr ample, typical values for olivine (most abundant old surface. mineral in the upper mantle) being Ea = 375 −1 0 −1 kJ mol and Ea = 530 kJ mol , respectively Cooling from the the Earth’s upper mantle [Hirth and Kohlstedt, 2003]; however, these temperature of 1500 K to 800 K at the top of values may be different for other minerals. its lithosphere (about 10 km depth) would in- Diffusion and dislocation creep are thought to crease the dislocation creep viscosity by a fac- occur independently of each other depending tor of 1016, or the diffusion creep viscosity by a on stress and grain size: for a given stress, factor of 1011 (using the activation energy val- dislocation creep dominates for large grains and ues for olivine from the previous paragraph). In diffusion creep for small grains; likewise, for this case, the viscous resistance to deform and a given grain-size, dislocation creep dominates subduct a slab would require a force that is much for large stress and diffusion creep for small in excess of what is available from buoyancy, stress (Figure 8). thus disallowing convective motion. However, Earth’s surface is clearly deforming, as is ev- The temperature-dependence of rheology idenced in plate tectonics, and so some other enables thermal variations to induce many physical mechanism must exist that induces rhe- orders of magnitude changes in viscosity. Its ological weakening and allows for the litho- effect is most profound in the lithosphere. For sphere to deform. Dislocation creep allows for example, a plausible temperature drop of 1500 moderate softening as stress increases. How- K across the martian lithosphere [Harder, 1998; ever, for the above example for a typical litho- Plesa and Breuer, 2014], assuming 500 and spheric temperature drop, an unrealistic increase

28 Oxford Research Encyclopedia of Planetary Science Mantle Convection

Figure 8: Deformation map of stress-temperature space, including different creep mechanisms. Modified from Bercovici et al. [2015]. in stress by a factor of 108 would be required be described as large areas of strong barely to offset thermal stiffening. Diffusion creep po- deforming plate interiors, separated by weak tentially allows for significant softening if the and narrow plate boundaries that undergo grain size is reduced, and for the above exam- intense deformation [with a few exceptions, ple a grain size reduction by a factor of 10−3 such as broad diffuse plate boundaries, for would suffice to mobilize a plate and/or or al- example in the Indian Ocean Gordon et al., low a slab to sink. Geological examples of grain 1998]. Understanding the physical mechanisms size reduction in the lithosphere by three and po- responsible for such plate-like motion, which tentially more orders of magnitude in strongly require some form of rheological weakening deformed regions abound (more on this in Sec- and strain localization in the lithosphere, is one tion “Forming Tectonic Plates”). Understanding of the biggest questions in the geodynamics the physical mechanisms responsible for rheo- [see Bercovici et al., 2015, for a recent review]. logical weakening in the lithosphere that offsets The proposed solutions include complex defor- thermal stiffening and allows for plate-like de- mational behavior, such as plastic, brittle, or formation is an active area of research. grain size dependent rheologies.

Forming Tectonic Plates Brittle deformation is one of the most extreme cases of strain localization, where the material The plate-like character of the mantle’s cold breaks along narrow faults that remain weak thermal boundary layer, or the lithosphere, can even after the deformation ceases. However,

29 Oxford Research Encyclopedia of Planetary Science Mantle Convection brittle rheology is not active for most of the zones subsequently concentrate deformation, depth of oceanic lithosphere, giving way to which causes further weakening, and so on. semiductile and eventually ductile behavior at One example of such dynamic self-weakening depths greater than about 10 km [Kohlstedt is the coupling of temperature-dependent vis- et al., 1995]. cosity and viscous heating: deformation causes frictional heating, which makes the material Another candidate for shear localization in warmer and weaker, and thus more readily the lithosphere is viscoplasticity, which dictates deformed, causing the deformation to focus that the material acts as a strong viscous fluid on the weak zone, leading to more heating at low stresses, but once the stress exceeds a and weakening, and so forth. Because thermal yield stress, the viscosity drops or in an extreme anomalies take time to dissipate away, the warm case the resistance to flow remains small no weak zones can be retained for some time matter the rate of deformation. Viscoplastic and allow for some history dependence of the rheologies can be successful at generating material strength. However, for lithospheric and plate-like motion [Moresi and Solomatov, 1998; mantle material, thermal diffusion is relatively Trompert and Hansen, 1998; Tackley, 2000b; fast and the memory of induced weakness van Heck and Tackley, 2008; Foley and Becker, only lasts a few million years, which is less 2009], but are difficult to reconcile with other than what is needed to explain long-lived plate important observations. For example, while boundaries. There are other limitations for the plastic yielding is known to occur in rocks, thermal self-softening mechanism in explaining laboratory experiments on rock deformation the localized lithospheric deformation. For ex- infer a much higher yield stress than what is ample, the diffusive nature of thermal anomalies used in geodynamic models. Moreover, weak only allows for weak localization and toroidal zones formed as a result of plastic yielding motion. While not sufficient on its own, the are only active as long as the deformation is thermal self-softening might still assist in strain ongoing, and vanish, or regain their strength, localization [Kameyama et al., 1997; Foley, once deformation ceases. In contrast, tectonic 2018]. plate boundaries are known to be long-lived features, which remain weak for some time Fluids in the lithosphere, such as water, in even without being deformed, and can be the form of pores or hydrous mineral phases, transported with the material and get reactivated can serve as a long-lived weakening agents. at a later time [Toth and Gurnis, 1998; Gurnis In this case, weakening can occur due to the et al., 2000]. In fact, dormant plate boundaries reduction of friction through pore pressure, (e.g., sutures and inactive fracture zones) can or through lubrication of plate boundaries by retain their deformation memory in the form of introduction of sediments at subduction zones intrinsic weak zones over timescales that are or serpentinization along faults. The longevity much longer than the typical convective mantle of the potential weak zones over geological overturn time. In other words, the deformation- time scales is ensured by the slow chemical history dependent strength of the lithosphere diffusivity of hydrogen in minerals, as opposed cannot be explained with an instanteneous-type to, for example, much faster thermal diffusion viscoplastic rheology. rates. One of the main difficulties with invoking water for lithospheric-scale weakening is that its For strain localization to occur, there needs effects are likely to be limited to shallow depths. to be a positive feedback mechanism in which Specifically, the frictional reduction by pore deformation itself causes weakening, the weak pressure aids brittle failure and frictional slid-

30 Oxford Research Encyclopedia of Planetary Science Mantle Convection ing, which are only relevant in the top roughly splitting the same volume of material into a 10-20 km depth. Ingesting water to greater larger number of grains). Grain damage can depths, say to the bottom of a plate boundary at induce shear-localizing feedback through the about 100 km depth, would require pushing the interaction of grain-size sensitive rheology fluid against a very large lithospheric pressure (such as diffusion creep or grain-boundary gradient and then preventing it from escaping sliding [Hirth and Kohlstedt, 2003]) and grain (e.g., by invoking negligible permeabilities). size reduction via dynamic recrystallization While there are mechanisms, such as thermal [Karato et al., 1980; Derby and Ashby, 1987]: cracking [Korenaga, 2007] or creating voids smaller grain size makes the material weaker, and microcracks through deformation dam- which thus deforms more readily, increasing the age [Bercovici, 1998; Bercovici and Ricard, amount of deformational work available to drive 2003; Landuyt and Bercovici, 2009b], that can recrystallization and grain damage, reducing potentially allow for the water to penetrate the grain size further, etc [Braun et al., 1999; and serpentinize the uppermost few tens of Kameyama et al., 1997; Bercovici and Ricard, kilometers of the plate, there are no known 2005; Ricard and Bercovici, 2009; Rozel et al., mechanisms that would allow it to weaken the 2011]. In monomineralic materials, recrys- deepest, and potentially strongest, portion of the tallization takes place so long as the material lithosphere. deforms by dislocation creep, which dominates at high stresses and large grain sizes. Once the An important clue to understanding the grains shrink to sizes at which the grain size physics of lithospheric weakening, and thereby dependent rheologies set in, recrystallization the formation of tectonic plate boundaries, process becomes limited, and so does the self- comes from the observed microstructure of the weakening localization feedback [De Bresser deformed rocks, specifically the mineral grain et al., 2001]. However, lithospheric rocks size and the density of intragranular defects. are polymineralic (with olivine and pyroxene The exposed plate boundaries at the Earth’s being the most abundant minerals, or phases), surface (i.e., in ophiolites and lithospheric and the grain size evolution of each phase is shear zones), as well as samples from rock strongly affected by the presence of the other. deformation experiments, show that parts of the First of all, the rate of grain coarsening, which rock that have undergone extreme deformation occurs independent of whether the material is exhibit a substantial degree of recrystallization deforming or not, and which generally makes and grain size reduction. Grain size evolution, the material stronger, is significantly impeded including the processes of grain growth by by the secondary phase; this happens because diffusion and grain shrinkage by dynamic grains grow by atomic diffusion, and it is dif- recrystallization, is governed by atomic scale ficult to exchange atoms between grains which processes, the thermodynamics of which is are separated by another mineral. Thus, the described by grain damage theory [Bercovici grain growth becomes effectively blocked by and Ricard, 2005; Austin and Evans, 2007; the secondary phase, an effect known as Zener Ricard and Bercovici, 2009; Rozel et al., 2011]. pinning. Second, as the grains of each phase Grain damage theory postulates that while deform to accommodate strain, be it in diffusion most of the deformational work is dissipated as or dislocation creep, they are forced to move heat and irrecoverable viscous deformation, a around the grains of the other phase, resulting small fraction of work goes towards recoverable in stronger distortion of the grain boundaries energy, which is stored in the form of grain than if it was a single phase material; this defects and new grain boundary area (i.e., by increases the internal energy of the grain and

31 Oxford Research Encyclopedia of Planetary Science Mantle Convection lowers the amount of energy needed for it to Mantle Convection on Early recrystallize and split into smaller grains. Thus, the presence of the secondary phase facilitates Earth grain damage and induces grain size reduction even when the material deforms in the grain Solid state mantle convection likely started a size sensitive diffusion creep regime, thereby few tens or hundreds of millions of years after enabling self-weakening feedback by grain the Earth experienced its last major impact, damage [Bercovici and Ricard, 2012]. Indeed, which happened about 4.5 Gyr ago and led to the geological examples of peridotitic mylonites the formation of the moon [Canup and Asphaug, and ultramylonites, where large strains correlate 2001]. The energy released by the impact likely with extreme grain size reduction, and which left the planet largely molten (although it could have been observed at all types of plate bound- very well have been molten before the impact aries, typically feature polymineralic rocks, also), a part of the Earth’s history referred to as often embedded in a matrix of coarse-grained magma ocean [Elkins-Tanton, 2008; Solomatov, single-phase material [Warren and Hirth, 2015]. It would take about 10 Myr or more 2006; Herwegh et al., 2011; Linckens et al., (depending on the model) for nearly all of the 2011, 2015]. Moreover, the slowing of the magma ocean to crystallize, differentiate, and grain growth due to pinning in polymineralic for solid state mantle convection to set in [see materials promotes longevity of the damaged Foley et al., 2014, and references therein]. Un- weak zones even after the deformation ceases, derstanding the nature of this early convective thus allowing for long-lived dormant plate flow, i.e., its heat transport efficiency and its boundaries [Bercovici and Ricard, 2014]. ability to mobilize and deform the surface, are crucial for reconstructing the Earth’s dynamic Geodynamic models featuring damage rhe- history and evolution, as well as for interpreting ology have successfully reproduced some of its present state. the plate-like features of the lithospheric mo- tion, including toroidal motion, strongly local- The geological record becomes increasingly ized plate boundaries and observed microstruc- sparse in the Earth’s deep past. However, a ture [Bercovici and Ricard, 2005; Landuyt et al., number of safe assumptions can be made about 2008; Landuyt and Bercovici, 2009b; Foley the early physical state of the planet based on et al., 2012; Bercovici and Ricard, 2013, 2014; some theoretical considerations. First of all, Foley and Bercovici, 2014; Bercovici and Ri- Earth’s size, or mass, has probably remained card, 2016; Bercovici and Mulyukova, 2018; more or less the same after the last giant moon- Mulyukova and Bercovici, 2017, 2018] gener- forming impact. Second, the Earth’s interior ated at stresses and temperatures typical for tec- has been getting colder for a significant portion tonic plates, and is a promising venue for fur- of its history, although the rate of cooling of ther testing in global mantle convection models. its different layers (core, mantle and evolving While grain damage and pinning is potentially crust) may vary, depending on their concen- an important plate generation mechanism, es- trations of heat-producing elements, and their pecially in the deepest cold and ductile portion ability to exchange heat with one another (e.g., of the lithosphere, it is likely that the effects of thermal conduction across the CMB, or flow of brittle deformation, lubrication by fluids and po- cold downwellings and hot upwellings across tentially other processes play an important role the transition zone). The thermal history of the at shallower depths [Lenardic and Kaula, 1994, mantle is governed by the competition between 1996; Korenaga, 2007; Bercovici et al., 2015]. internal heating by radioactive elements and

32 Oxford Research Encyclopedia of Planetary Science Mantle Convection surface heat loss by convection. The main on modern Earth support this notion: after cor- uncertainty of the former is in the abundances recting for the radioactive heating, the mantle of radiogenic elements in the mantle; while their heat flow is about one order of magnitude lower half-lives are known, their initial concentration at the surface of the continents than for ocean and thus their net contribution is unknown. By seafloor [Stein and Stein, 1992; Jaupart et al., far the largest uncertainty about mantle thermal 2015, and references therein]. The role of con- history, however, comes from the assumed tinents as thermal insulators, and the resulting rate of convective cooling through time, and in anomalously hot and buoyant mantle beneath particular the initiation and rate of subduction, them, has been invoked as a mechanism for which is the dominant mechanism by which the driving continental dispersal and the subsequent mantle cools [van Hunen and van den Berg, supercontinent reorganization - a key part of the 2008; van Hunen and Moyen, 2012]. Cooling Wilson cycle [Gurnis, 1988; Rolf et al., 2012]. of the mantle for at least the last 3 Gyr is However, whether the thermal insulation effect constrained by the measured temperatures of is sufficient to move the continents around the mantle source that formed lavas at mid- remains subject to debate [Lenardic et al., 2005, ocean ridges, which appear to get progressively 2011; Heron and Lowman, 2011; Bercovici colder the younger they are: from 1500-1600 and Long, 2014]. The junction between the ◦C 2.5-3 Gyr ago to 1350 ◦C today [Herzberg strong continental and the much weaker oceanic et al., 2010]. In addition, the existence of the lithospheres helps to localize stresses there inner core, which is the product of a cooling and may serve as zones of heterogeneity and and crystallizing liquid outer core, implies that weakness where new plate boundaries can form the Earth’s deep interior is cooling through time. [Kemp and Stevenson, 1996; Schubert and Zhang, 1997; Regenauer-Lieb et al., 2001; Rolf The rate at which heat can escape from man- and Tackley, 2011; Mulyukova and Bercovici, tle to space depends on the temperature drop 2018]. across the Earth’s top thermal boundary layer, and thus on surface temperature, which in turn Modelling mantle dynamics on early Earth is controlled by the thermally insulating effect entails understanding mantle convection at of the atmosphere (the greenhouse effect), as higher internal temperatures. Using the theoret- well as the amount of incident solar energy. The ical framework outlined in, we can characterize greenhouse effect helps to keep the temperature mantle dynamics through time using the of the atmosphere relatively stable, and thus Rayleigh number, which describes the vigor one can assume that for most of the Earth’s of convection, and the thermally induced vis- history the temperature difference across the cosity difference across the lithosphere, which lithosphere has been controlled by the mantles presents the biggest impediment to convective internal temperature [Sleep and Zahnle, 2001; flow through stiffening of the cold thermal Lenardic et al., 2008]. boundary layer.

Another important difference between the It can be speculated that a hotter mantle young and the modern Earth is the presence and in the past might have been convecting more volume of the continents. Continents have an vigorously, or at a higher Rayleigh number, insulating effect, which impedes surface heat due to the lower viscosity of mantle rocks, flow due to their large thickness (compared to which is extremely sensitive to tempera- the oceanic plates) and a higher concentration of ture. Some mathematical formulations of radiogenic elements. Heat flow measurements temperature-dependence of viscosity (e.g., the

33 Oxford Research Encyclopedia of Planetary Science Mantle Convection

Frank-Kamenetskii parametrization) suggest temperature may play a role in the complex that, for a given temperature jump, the thermally rheology of the lithosphere may need to be induced viscosity difference is smaller at higher taken into account [Korenaga, 2006, 2007, temperatures. Thus, a weaker mantle and litho- 2013]. sphere, compared to those on modern Earth, would make convection and plate tectonics The mantle’s cold top thermal boundary layer more efficient in the past. Using some parame- differs from the rest of the mantle not just by its terization of this positive relationship between conductive thermal profile, but also by its com- mantle temperature and convective heat flow position, since it undergoes melting-assisted (i.e., such as the canonical canonical Nusselt differentiation (i.e., segregation by fractional number Rayleigh number relationship presented melting and melt-migration, which separates in Section “Basics of Thermal Convection”), the crust and the depleted lithosphere). Melting together with the rate of internal heating for at higher temperatures leads to a more dehy- some plausible abundances of radioactive ele- drated lithosphere. It is even more difficult ments, it is possible to extrapolate the internal for a lithosphere that is drier, and thus stiffer, temperature of the mantle back in time from to founder under its own negative buoyancy present day value. Depending on the details [Conrad and Hager, 2001; Korenaga, 2006]. of this parametrization, such as the modern Moreover, a higher degree of melting produces value assumed for the ratio of internal heating more of the chemically buoyant basaltic crust, to convective heat flux, called Urey ratio [see which further reduces the ability of the litho- Christensen, 1985], there is a range of possible sphere to sink [Davies, 2009]. Thus, plate thermal evolution models [Korenaga, 2006; tectonics might have been less likely to occur Silver and Behn, 2008]. The possible scenarios on a hotter younger Earth. If the lithosphere include the paradoxical thermal catastrophe cannot subduct, mantle convection may proceed case [Christensen, 1985], obtained for a low in a different regime, in which heat transport value of present day Urey ratio (about 0.3), from the interior to the surface is restricted to where the temperature of the mantle exceeds conduction across a thick immobile layer [e.g., values that are well beyond uncertainty (mantle stagnant lid mode, Solomatov and Moresi, temperature quickly rises and diverges toward 1997] and volcanism [e.g., heat pipe mode, unrealistically high values before reaching 2 Spohn, 1991; Moore et al., 2017; Lourenc¸o Ga). To avoid the thermal catastrophe, one et al., 2018], and is thus relatively inefficient; could assume a higher value of modern Urey this would mean that the rate of planetary ratio, for example a value of 0.7 results in a cooling was slower in the past. How and when reasonable thermal evolution model. However, subduction, and more generally plate tectonics, such high Urey ratio implies a much higher started is a question of formidable importance concentration of radioactive elements in the in the Earth evolution models, but the answer is mantle, which is difficult to reconcile with the obscured by our currently limited understanding range provided by the cosmogenic analysis. An of the physical mechanisms responsible for the alternative solution is to assume that the mantle formation of plate boundaries, as well as the heat flow is less sensitive to the temperature paucity of geological samples and data in the of the interior than what is predicted by the Earth’s deep history, which we discuss next. Rayleigh-Benard´ model (i.e., Nu ∼ Rab, where in simple Rayleigh-Benard´ b = 1/3, There are no rock samples preserved from the but b < 1/3 for less temperature-dependent first few hundred million years after the freezing heat flow). In particular, factors other than of the magma ocean; the only geological data

34 Oxford Research Encyclopedia of Planetary Science Mantle Convection available to elucidate this early stage of the plex, both in Greenland, are some of the oldest Earth’s history are mineral inclusions in zircons geological structures indicative of convergent [Mojzsis et al., 2001; Valley et al., 2002]. tectonics. However, it remains controversial Geochemical analysis of this sparse dataset as to whether the processes that formed these shows evidence for melting of sediments and rocks are representative of the global state of formation of granites, which may imply that the planetary surface; in addition, there exist subduction may have operated already at this other explanations for how to form them, which early stage [Hopkins et al., 2010]. However, ap- don’t involve tectonic processes, adding to the plication of the extremely sparse zircons-dataset uncertainty of interpreting these samples [Stern, (in terms of their temporal and spatial distribu- 2004, 2005; Condie and Kroner¨ , 2008; Palin tion) to infer the global tectonic regime bears and White, 2016; Condie, 2018]. significant uncertainty with it [Korenaga, 2013]. The absence of rock samples that are ex- One of the key features of plate tectonics is pected to form if tectonics is widespread has the continuous production and destruction of been invoked as evidence for the absence of the oceanic lithosphere. Thus, the geological plate tectonics. For example, the lack of evi- indicators of a mobilized lithosphere have to dence for high-pressure and ultra-high pressure come from the more indirect markers, expected metamorphism earlier than about 1Gyr, such as to be left behind on the fraction of the Earth’s blueschists and eclogites, which are expected surface that is less prone to destruction [Condie to form in subduction zone environments, has and Kroner¨ , 2008]. For example, when the sea been suggested to indicate that subduction floor is consumed by subduction, the continents didn’t start until about 1 Gyr ago [Stern, 2005]. on either side of it collide and form synchronous However, other studies caution that the absence orogens, which can then be preserved even after of preserved high-pressure rocks at the surface the continents split up again. Earth’s surface doesn’t preclude the operation of subduction on appears to have gone through several episodes earlier Earth, it may instead indicate that the of continental assembly and dispersal, known processes required for the exhumation of previ- as the Wilson cycle, in some cases forming ously subducted rocks were limited, or that the supercontinents, where virtually all of the conti- high-pressure phases formed upon subduction nents come together. The oldest supercontinent of the hotter, thicker and more magnesium-rich is thought to be Kenorland, which assembled oceanic lithosphere would be different than, for about 2.7 Gyr ago. The need to close multiple example, the blueschist-facies typically formed oceans in order to form a supercontinent pro- in modern-day subduction zones [Brown, 2006; vides a compelling evidence that global scale Korenaga, 2013; Palin and White, 2016]. plate tectonics was occurring already at that time. The initiation of subduction remains an ex- tremely challenging issue in geodynamics to- Furthermore, there exist examples of rocks day [Stern, 2004; Condie and Kroner¨ , 2008; that have arguably formed in geological settings Wada and King, 2015]. The physical mech- characteristic of plate tectonics and that are anisms that allow for the lithosphere to over- older than 3 Gyr. Examples include 3 Gyr old come its thermal stiffening and spontaneously xenoliths from Kaapvaal craton, whose oxygen initiate subduction are hotly debated, with the isotopic signature show that they may originate proposed models including weakening by rift- from subducted oceanic crust; a 3.6 Gyr old ing [Kemp and Stevenson, 1996; Schubert and suture zone and a 3.8 Gyr old accretionary com- Zhang, 1997], sediment loading and water injec-

35 Oxford Research Encyclopedia of Planetary Science Mantle Convection tion [Regenauer-Lieb et al., 2001], re-activation and Mars), and finally by the conductive cool- of pre-existing fault-zones [Toth and Gurnis, ing (possibly for Mercury). In our Solar Sys- 1998; Hall et al., 2003], or the weak zones tem, Earth is the largest terrestrial body, with formed by accumulation of lithospheric dam- the largest amount of heat to dissipate away, and age from proto-subduction [Bercovici and Ri- whose mantle is, at least at present, convectively card, 2014], collapse of passive margins [e.g., transporting heat most efficiently. Importantly, Stern, 2004; Mulyukova and Bercovici, 2018] none of the known terrestrial planets, besides or at an active transform plate boundary [Casey Earth, appear to have surface rejuvenation by and Dewey, 1984] and plume-induced subduc- plate tectonics. tion initiation [Gerya et al., 2015]. A better un- derstanding of the rock physics, as well as fur- Venus ther interrogation of the geological, geochemi- cal and petrological record of the early Earth dy- Venus is arguably the most similar to our own namics continue to be fruitful areas of research. planet, at least in terms of its size (which deter- mines internal depth, or pressure, structure) and distance from the Sun (which determines the Mantle Convection on Other amount of surface heating by solar radiation). The Venusian surface appears to be young, Terrestrial Planets dry and wrapped in a thick, dense and opaque atmosphere, which makes remote observations The rocky planets of the solar system exhibit a particularly challenging. At about 460 ◦C, large variation in their observed features, includ- the surface of Venus is hundreds of degrees ing size, gravity anomalies, topography, mag- hotter than that of Earth, which some studies netic field, atmosphere, distance from the sun, have attributed to the runaway greenhouse etc, all of which affect their interior dynamics. effect and the eventual loss of water [Kasting, The heat sources available to drive mantle flow 1988]: liquid water is an important player in and convective cooling (with the possible excep- the geological carbon cycle, which on Earth tion of Mercury, whose mantle may cool by con- drew down most of the carbon into carbonate duction), including the primordial as well as the rocks and allows for a temperate climate, while radioactive heat sources, are finite and are not on Venus the dry conditions fail to allow the being replenished, which is why planetary activ- surface to extract the greenhouse gases from ity driven by mantle convection, such as volcan- the atmosphere, thus keeping the surface hot ism and crust production, become weaker and [Driscoll and Bercovici, 2013]. The Venusian eventually die out with time. The rate at which mantle temperature is likely higher than that on a planet cools is determined by its initial heat Earth, because it appears to be in a less efficient budget, as well as the efficiency at which it can convection regime [i.e., stagnant or mobile lid release heat. For example, smaller planets have regime, Solomatov and Moresi, 1997; Moresi less primordial heat, as they have experienced and Solomatov, 1998] which, along with a fewer impacts upon accretion and the differenti- hotter surface, would make the heat flow out of ation of their metallic cores had a smaller grav- the interior slower. itational energy release associated with it. As for the heat transport out of the planetary inte- The relatively young age of the crust on riors, plate tectonics is the most efficient mech- Venus, inferred to be about 500 Myr old by anism (as on Earth), followed by the sluggish crater counting [Strom et al., 1994], points to and stagnant lid convection regimes (for Venus global surface rejuvenation events, presumably

36 Oxford Research Encyclopedia of Planetary Science Mantle Convection by extensive volcanism or lithospheric founder- than the Earth’s [Nimmo and McKenzie, 1998; ing [Turcotte, 1993; Turcotte et al., 1999]. De- Hirth and Kohlstedt, 1996], making the mobi- pending on the chosen thermal evolution model, lization of the Venusian surface even more dif- including the rate at which the cooled surface ficult. Strictly speaking, the observational ev- can be recycled into the mantle, the mantle tem- idence for dry conditions on Venus only ex- perature of Venus might be about 200 ◦C hotter ists for its atmosphere, and not for its interior. than that of Earth [Lenardic et al., 2008; Lan- However, water is an incompatible element, and duyt and Bercovici, 2009a]. A hotter surface and therefore gets preferentially extracted from the possibly interior makes Venus a popular ana- interior in the process of melting and volcanism, logue of the early Earth, and some of the reason- and there is no obvious mechanism on Venus ing of early Earth geodynamics can be applied by which water would be returned to the mantle to understand the dynamics of Venus and vice (i.e., as is done by subduction on Earth). Thus, versa. For example, it has been speculated that even if the mantles of Venus and Earth started the hotter conditions on Venus is the reason why off with similar compositions, the water may it doesn’t have plate tectonics. One of the argu- have been lost from the Venusian mantle, first to ments is that a hotter surface, but a similar man- its surface, then to its atmosphere, and inevitably tle temperature on Venus compared to Earth, re- to space [Donahue and Hodges, 1992; Nimmo duces the temperature contrast across the Venu- and McKenzie, 1998]. These and other struc- sian lithosphere, and thus the amount of negative tural differences between Earth (or early Earth) buoyancy available to deform and potentially and Venus prompt some caution in comparing mobilize it [Lenardic et al., 2008]. Another ar- the two planets. gument is that if grain damage is responsible for the formation of plate boundaries on Earth, Mars which requires a high enough ratio between the rates of grain growth and grain size reduction, Mars is the next largest terrestrial body in the then the hotter surface temperature on Venus solar system after Earth and Venus, although at would make the grain growth faster, potentially its 3390 km radius is still much smaller than the inhibiting the formation of fine-grained local- other two, and is thus likely to cool much faster ized shear zones, or zones of weakness where to space. In addition, the possible presence of new plate boundaries can form [Landuyt and water in the Martian mantle [within the range of Bercovici, 2009a; Foley et al., 2012; Bercovici 73-290 ppm H2O, which is comparable to that and Ricard, 2014]. A potentially important dif- of Earth, McCubbin et al., 2012], as well as its ference between Earth and Venus is that, in spite high iron content [Martian olivines contain FeO of their similar size, Venus appears to not have ∼ 18 wt%, compared to Earth’s FeO ∼ 8 wt% a low-viscosity upper mantle, or asthenosphere; Zhao et al., 2009], act to lower the mantle vis- this has been inferred by numerical modeling cosity, facilitating convection and efficient heat studies of mantle convection on Venus, con- transport. The rapid cooling of Mars constrains strained by the observed surface topography, the time-window for when its interior is hot volcanism and geoid [Huang et al., 2013]. The enough to induce melting and to produce crust. convective stress acting on the Venusian litho- Indeed, it appears that most of the Martian crust sphere is thus presumably smaller, compared formed early in its history - in the first few to that on Earth [Hoink¨ et al., 2012]. Further- hundred million years after accretion [Nimmo more, it has been argued that the Venusian litho- and Tanaka, 2005]. At present, Mars is likely to sphere and mantle lack water, which is an impor- have a colder and less active interior, compared tant weakening agent, and are therefore stiffer to Earth, possibly explaining the absence of an

37 Oxford Research Encyclopedia of Planetary Science Mantle Convection internal magnetic field on Mars [Acuna et al., at least the last 3.8 billion years, with records 1998]. The strongly magnetized martian crust, of volcanism on the Tharsis edifices as young as however, suggests that the surface and interior two million years [Neukum et al., 2004]. Such of Mars may have undergone extensive activity recent volcanic activity on Mars may suggest in the past, in particular within the first billion that its volcanoes may even erupt in the future, years after solar system formation. Mars’s and that its mantle is not yet geodynamically surface may have deformed similarly to plate dead. tectonics on Earth, according to maps of mar- tian crustal remanent magnetization obtained Mercury from spacecraft missions: the quasi-parallel magnetic lines of alternating magnetic polarity Mercury is the smallest rocky planet in our [Connerney et al., 1999], as well as offsets in solar system (about 2440 km in radius) and the magnetic field contours that identify transform one that is the closest to the Sun. The strikingly faults [Connerney et al., 2005], are similar to large mean density of Mercury implies that it is the magnetic features associated with sea floor much more iron-rich than the other terrestrial spreading on Earth. In addition, geological planets, or has the largest ratio of metallic core structures interpreted from the satellite data, to silicate mantle, with the size of the core in- such as rifting and strike-slip faulting, may ferred to be over 2000 km in radius [Harder and also be indicative of plate-tectonic like surface Schubert, 2001]. The remaining few hundred deformation [Yin, 2012]. kilometers thick (400 km typically used in mod- eling studies) mantle shell is likely convecting Another curious feature of the Mars’s sur- in the stagnant lid regime for seemingly all of its face is its crustal dichotomy, with a 20-30 km geologically recorded past, as indicated by the thick primordial crust in its northern hemisphere extremely well preserved cratering history on [Grott et al., 2013] and a much thicker, 30-80 its surface [Watters et al., 2016]. A prolonged km, and presumably younger crust in its south- slow cooling of the planet’s interior appears to ern hemisphere [Solomon et al., 2005], with the have left lobate scarps on Mercury’s surface surface age difference of about one billion years [Watters et al., 1998], interpreted to be thrust between the two hemispheres. One of the pro- faults that record the ancient pattern of mantle posed explanations for the martian crustal di- convection, in addition to global contraction chotomy posits that it reflects the underlying [King, 2008]. Most recent observations of the mantle convection pattern. Numerical simula- scarps crosscuting the impact craters indicate tions of Martian interior dynamics obtain mantle that they are relatively young, less than 50 flow pattern with a single hot upwelling on one Myr, implying that Mercury is probably still hemisphere, and thus predict enhanced crustal tectonically active at present day [Watters et al., production in the region over mantle upwelling 2016]. The mineralogy of Mercury’s volcanic [Harder and Christensen, 1996; Harder, 2000; crust, inferred from the geochemical data from Keller and Tackley, 2009]. The presence of ex- recent space missions, records the history of its tensive low-conducting crustal layer on Mars is cooling mantle: the fractional melting by which thought to have thermally insulated the mantle the crust was produced occurred at shallower so as to suppress its cooling rate and to pro- depth and lower temperature with time, from long its history of volcanic activity [Plesa and about 1900 K and 360 km 4.2 Gyr ago, to Breuer, 2014]. The high resolution images of about 1700 K and 160 km 3.5 Gyr ago, with the martian surface reveal that its has been ge- the magmatic activity terminating about 3.5 ologically active, albeit at a declining rate, for Gyr ago as the mantle became too cold to melt

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[Spohn, 1991; Namur and Charlier, 2017]. thermodynamics. The theoretical predictions of Although Mercury’s mantle is not generating flow velocities, establishment of thermal bound- any volcanic activity at present, its cooling must ary layers and the convective pattern of slab-like nonetheless be very efficient, since it is able downwellings and plume-like upwellings go far to transport heat away from the core at high in describing circulation and structure in the enough rate to support the internally generated Earth’s mantle. However, the solid rock that dynamo [Ness et al., 1974; Connerney and makes up the mantle flows and deforms in ways Ness, 1988]. Numerical models of Mercury’s that are not easily captured by the properties internal dynamics have been able to reconcile its of simple fluids on which classical convection magnetic and thermochemical evolution, with theory is based. For instance, the manifestation the possible planforms of mantle convection of mantle convection as discrete tectonic plates ranging from numerous small-scale cells to at the surface, with strong and broad plate a single upwelling, and including scenarios interiors separated by weak and narrow plate where the mercurian mantle convection ceases boundaries, remains one of the most puzzling altogether after 3-4 Gyr [Heimpel et al., 2005; phenomenons in geoscience. Much of the Tosi et al., 2013]. progress in explaining how and why the Earth’s mantle convects in the form of plate tectonics, Comparing the observations made on differ- unlike any other known terrestrial planet, comes ent terrestrial planets is a powerful tool for teas- from the studies of the rheologies of rocks that ing out the general physics that govern plane- make up planetary mantles, including their de- tary evolution. Of course, the currently available pendence on temperature, stress, chemistry and dataset is relatively sparse, but it is growing with mineral grain size. Understanding the physics the increased number of space missions. In ad- that govern the geodynamics of modern Earth dition, with the advent of extra-solar planet dis- is essential to reconstructing the thermal and covery, there is hope to find other planets with chemical history of our planet. For example, it plate-like mantle dynamics, which would elu- remains problematic to explain how the Earth cidate the peculiar tectonic regime of our own is stirred by deep subducting slabs, but still planet [e.g., Valencia et al., 2007; Sotin et al., appears unmixed when producing melts at mid- 2010; Korenaga, 2010; van Heck and Tackley, ocean ridges and ocean-islands. To unravel the 2011; Foley et al., 2012]. history mantle stirring, a better understanding of melting, chemical segregation and mixing in the mantle are needed. Conclusion

Mantle convection governs the thermal and The theory of mantle convection successfully chemical evolution of the Earth and other explains many of the key features of planetary terrestrial planets in our solar system, dictating interior and surface dynamics, unifying the the dynamics of planetary interiors and driving geoscientific observations with the fundamental geological motions at the surface. The ultimate physical and fluid mechanical theories. How- driver for convective mantle flow is that planets ever, studies of mantle convection have also cool to space, releasing the heat acquired in opened up many new questions and mysteries the course of their accretion, as well as the about the workings of the Earth and other rocky radiogenic internal heating. Thermal convection planets to be addressed by future generations of theory itself is a well established physical Earth and planetary scientists. theory rooted in classical fluid dynamics and

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Suggested Further Reading Becker, T., J. Kellogg, and R. O’Connell, Thermal con- straints on the survival of primitive blobs in the lower • Schubert, G., D. Turcotte, and P. Olson, mantle, Earth and planetary science letters, 171(3), Mantle Convection in the Earth and Plan- 351–365, 1999. ets, Cambridge Univ. Press, 2001 Benard,´ H., Les tourbillons cellulaires dans une nappe liq- uide, Revue gen´ erale´ des Sciences pures et appliquees´ , • Bercovici, D., Mantle Dynamics, Treatise 11, 1261–1271 and 1309–1328, 1900. on Geophysics (Second Edition), edited by Benard,´ H., Les tourbillons cellulaires dans une nappe G. Schubert, second edition ed., Volume 7, liquide transportant de la chaleur par convection en Elsevier, Oxford, 2015 regime´ permanent, Annales de Chimie et de Physique, 23, 62–144, 1901. • Davies, G. F., Mantle Convection for Geol- Bercovici, D., A source-sink model of the generation ogists, Cambridge Univ. Press, 2011 of plate tectonics from non-newtonian mantle flow, J. Geophys. Res., 100, 2013–2030, 1995. • Ribe, N., Theoretical Mantle Dynamics, Cambridge Univ. Press, 2018 Bercovici, D., Generation of plate tectonics from lithosphere-mantle flow and void-volatile self- lubrication, Earth Planet. Sci. Lett., 154, 139–151, References 1998. Bercovici, D., The generation of plate tectonics from Acuna, M., et al., Magnetic field and plasma observations mantle convection, Earth and Planetary Science Let- at mars: Initial results of the mars global surveyor mis- ters, 205(3), 107–121, 2003. sion, Science, 279(5357), 1676–1680, 1998. Bercovici, D., 7.01 - mantle dynamics: An introduction Allegre,´ C. J., Chemical geodynamics, Tectonophysics, and overview, in Treatise on Geophysics (Second Edi- 81(3–4), 109 – 132, doi:http://dx.doi.org/10.1016/ tion), edited by G. Schubert, second edition ed., pp. 0040-1951(82)90125-1, 1982. 1 – 22, Elsevier, Oxford, doi:https://doi.org/10.1016/ B978-0-444-53802-4.00125-1, 2015. Anderson, B. J., et al., The global magnetic field of mercury from messenger orbital observations, Science, Bercovici, D., and S. Karato, Whole mantle convection 333(6051), 1859–1862, 2011. and the transition-zone water filter, Nature, 425, 39– 44, 2003. Arndt, N. T., and S. L. Goldstein, An open boundary be- tween lower continental crust and mantle: its role in Bercovici, D., and A. Kelly, Nonlinear initiation of diapirs crust formation and crustal recycling, Tectonophysics, and plume heads, Phys. Earth Planet. Int., 101, 119– 161(3-4), 201–212, 1989. 130, 1997. Bercovici, D., and M. D. Long, Slab rollback instability Austin, N. J., and B. Evans, Paleowattmeters: A scaling and supercontinent dispersal, Geophysical Research relation for dynamically recrystallized grain size, Ge- Letters, 41, 6659–6666, doi:10.1002/2014GL061251, ology, 35(4), 343–346, 2007. 2014.

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