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date: 06 June 2020

# Mantle Convection in Terrestrial Planets

## Summary and Keywords

All the rocky planets in our solar system, including the Earth, initially formed much hotter than their surroundings and have since been cooling to space for billions of years. The resulting heat released from planetary interiors powers convective flow in the mantle. The mantle is often the most voluminous and/or stiffest part of a planet and therefore acts as the bottleneck for heat transport, thus dictating the rate at which a planet cools. Mantle flow drives geological activity that modifies planetary surfaces through processes such as volcanism, orogenesis, and rifting. On Earth, the major convective currents in the mantle are identified as hot upwellings such as mantle plumes, cold sinking slabs, and the motion of tectonic plates at the surface. On other terrestrial planets in our solar system, mantle flow is mostly concealed beneath a rocky surface that remains stagnant for relatively long periods. Even though such planetary surfaces do not participate in convective circulation, they deform in response to the underlying mantle currents, forming geological features such as coronae, volcanic lava flows, and wrinkle ridges. Moreover, the exchange of material between the interior and surface, for example through melting and volcanism, is a consequence of mantle circulation and continuously modifies the composition of the mantle and the overlying crust. Mantle convection governs the geological activity and the thermal and chemical evolution of terrestrial planets and understanding the physical processes of convection helps us reconstruct histories of planets over billions of years after their formation.

# Mantle Convection

The interiors of terrestrial planets comprise three main layers: a metallic core at the center overlain by a rocky mantle, which is in turn enveloped by a rocky crust. The exact compositions and thicknesses of these layers, and their thermal and chemical evolution through time, vary from planet to planet depending on their size, distance from the sun, formation history, among other factors. However, common to all the terrestrial planets in our solar system, and even to some of its larger moons, is that their mantles undergo convective motions, wherein hot buoyant material rises from the deep interior, and the heavy cold material near the surface sinks.

Mantle convection is the dominant mechanism by which planets cool and undergo chemical segregation. The flow of the mantle induces motion in the overlying crust, which can lead to such phenomena as volcanoes, earthquakes, and (uniquely for Earth) plate tectonics. Ultimately, mantle convection governs the evolution of planetary surfaces and interiors.

The fundamental features of any convective system include cold and hot boundaries (e.g., the outer and inner boundaries of the mantle, respectively), and a fluid between the two boundaries on which gravity acts to move hot and cold material. Hot upwelling and cold downwelling vertical currents are connected along the horizontal boundaries by the hot and cold thermal boundary layers (TBLs): a hot TBL at the bottom, and a cold TBL at the top. The TBLs are where heat is conducted rapidly across the boundaries into or out of the convectively stirred mantle. The large thermal gradients across the TBLs, as opposed to a gradual increase in temperature from top to bottom, is what makes thermal convection such an efficient mechanism for heat transfer.

In planetary mantles, the convective currents can deform and chemically modify the top and bottom boundaries; their effect on the planetary surfaces is of particular interest, since that part can be most readily observed and used to interpret the workings of the underlying mantle. For example, hot upwelling mantle currents can generate surface uplift, seen as topographic highs, or induce volcanic activity, when hot material melts and erupts while approaching the surface. Extruded lavas on planetary surfaces record the presence and evolution of hot mantle regions and can be used to infer mantle temperature, chemistry, and flow velocity. Similarly, the downwelling currents can give rise to topographic lows, as the sinking mantle material pulls the surface down from below. In the possibly unique case of the Earth, the top cold thermal boundary layer is subdivided into tectonic plates, which are moving relative to each other and sink into the mantle at subduction zones. The rate at which a planet recycles cold material into the mantle largely determines its cooling rate.

Naturally, more observations are available for the Earth’s surface and mantle than for other planets. Thus, our understanding of planetary interiors, and their surface manifestations, is largely shaped by what is known about our home planet, as well as by our understanding of the fundamental processes that govern mantle convection, such as the physics of heat transport and rock deformation.

In what follows, the different components of convective mantle flow on Earth are described, tracking the material trajectory as it forms tectonic plates traversing the Earth’s surface, which then sink into the mantle as cold subducting slabs that eventually impinge on and flow laterally along the core-mantle boundary; some of this material ascends across the mantle again as mantle plumes, while most of it ascends broadly as part of the global tectonic circulation, thus closing the loop. The convective currents on other terrestrial planets are discussed as well, albeit our understanding of these is less certain due to fewer observational constraints. We will then survey the underlying physics of convection, which form the basis for understanding how mantle convection is both similar to and different from classical theories of convective flow and how this physics lets us infer mantle dynamics on Earth and other terrestrial planets.

# Mantle Top to Bottom

One of the greatest challenges in the studies of planetary mantles is their inaccessibility for direct observations. The structure and physical properties of planetary interiors have to be inferred from indirect measurements such as satellite observations of gravity, surface topography (Figure 2), and magnetic fields (Phillips & Ivins, 1979), see Sohl and Schubert (2015) for a more recent review. In addition, analysis of meteorites collected at the Earth’s surface constrains the chemistry of some other planets, as well as the building blocks of our own planet. Earth is special in this sense, because, in addition to the remote measurements, scientists have access to a wealth of geological samples and can perform seismological observations of the interior. Most of what we know about Earth’s interior is obtained indirectly from the analysis of seismic waves, which are triggered by powerful earthquakes and propagate through the mantle and core. Seismic waves travel faster through rocks that are stiffer. In the mantle, the rocks become denser, and therefore stiffer, when they are exposed to higher pressures at greater depths. The resulting increase with depth of the measured seismic velocities can thus be used to infer mantle’s density structure. When seismic waves pass through sharp changes in material properties (e.g., density), such as the boundaries between the felsic crust and the mafic mantle (or the silicate mantle and the metallic core), they get partially reflected, and these reflected signals allow us to determine the boundaries of the main layers comprising the Earth’s interior. Furthermore, hot rock is typically softer and more easily compressed, hence seismic waves are slower to pass through such material; the opposite is true for cold rocks, which are stiffer. The resulting seismic wave travel time variations can be used to infer pictures of the mantle showing “hot” (seismically slow) and “cold” (fast) regions, appearing much like an ultrasound of the mantle.

Figure 1. Cutaway views of the interiors of four terrestrial planets in the solar system. Reproduced from Solarviews.

While the metallic cores likely separated out of the mantles early in planetary histories (i.e., within the first few tens of millions of years of the life of the solar system) (Kleine, Münker, Mezger, & Palme, 2002), the segregation of the crust out of the mantle is still ongoing, as evident in recent volcanism, seen on all terrestrial planets except for Mercury, where global magmatic activity appears to have ceased about 3.5 Gyr ago (Namur & Charlier, 2017). Mantle melting at shallow depths (with the exact depth depending on temperature and composition) is induced by decompression and leads to magmatism that forms the mafic (or silica poor) crust (such as the oceanic crust on Earth). Specifically, as upwelling mantle material approaches the surface, toward lower pressure, its own temperature changes little (decreasing slightly by “adiabatic” decompression, further explained in the section “Basics of Thermal Convection”), but the temperature at which it melts decreases more rapidly (in essence, decreasing the confining pressure makes it easier for molecules to mobilize into a melt). At a certain depth (usually between a few 10s to 100 km, depending on temperature) the upwelling mantle’s temperature exceeds the melting temperature and undergoes melting. The mantle is made up of different chemical components and each have their own specific melting temperatures. The material that can melt at higher pressures (usually more silica-rich material with lower melting temperature) melts first, freezes last, and is typically chemically less dense and thus comes to the surface as lighter crust. The more refractory mantle material (i.e., harder to melt, silica-poor and heavier material) may melt little if at all, and much of it stays in the mantle. Such “pressure release” melting in hot vertical currents, such as mantle plumes arising from the deeper mantle, or by passive upwelling beneath mid-ocean-ridges (presently only known to occur on Earth), is vital for chemical segregation of the mantle and development of oceanic crust (and possibly the first kernels of proto-continental crust early in Earth’s history).

Figure 2. Global topography (top row), and the total gravitational anomaly (bottom row) of the four terrestrial planets in the solar system (modified from Wieczorek, 2015). The topography is referenced to the geoid, which is an equipotential surface on which the sum of the gravitational and centrifugal potential energies has the same value, and which on Earth would correspond to the sea level.

Melting at subduction zones (which is also only known to occur on Earth) is more complicated than melting at mid-ocean ridges or at hotspots, but is responsible for most of the production of continental crust (see also Stein & Ben-Avraham, 2015). For subduction zones, melting is facilitated by water. Tectonic plates entering a subduction zone have typically been submerged under water for hundreds of millions of years. When the first basalts are extruded at mid-ocean ridges they react with water and make hydrous minerals, such as amphibole and serpentine. Sediments washed off continents and islands into the ocean are also usually hydrated. When a plate reaches the subduction zone, many of its hydrated minerals are entrained with the slab into the mantle (though many sediments remain at the surface to form accretionary prisms). Once the entrained 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 mantle rock (hydrogen replacement weakens the mineral bonds), and so even at the “moderate” mantle temperatures next to a cold slab, the damp mantle material will partially melt, and the melt phase will percolate 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 re-melts silica-rich minerals, which are the easiest to melt, but not the more refractory silica-poor or “mafic” ones (e.g., dry basalt). The re-melted 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 mantle where melting takes place, most terrestrial mantles currently comprise solid rock, in spite of their fluidlike mechanical behavior over geological time scales. The large thicknesses of these mantles (with the exception of Mercury) means that their constituent materials experience a wide range of temperature and pressure conditions with depth. For example, the mantle’s pressure on Earth (likely similar to Venus) increases from top to bottom by about 140 GPa (about 1.4 million atmospheres of pressure) and temperature by 3,500 Kelvin (probably less by a few hundred K on Venus, due to its higher surface temperature); Martian pressure and temperature increase by about 23 GPa and 2,800 K, respectively, across the mantle (Schubert & Spohn, 1990; Harder, 1998); these extreme conditions strongly affect the physical properties of rocks, including their mineralogical structure, density, viscosity, among others.

Viscosity is the material’s resistance to deformation under an applied force or stress. The higher the viscosity, the higher the resistance to flow. For example, the viscosity of water is on the order of 10–3 Pa s and that of honey is about 1–10 Pa s, both at room temperature, while that of the mantle ranges between 1019 and 1023 Pa s. Mantle viscosity varies with pressure, temperature, and composition. While there remains uncertainty about the compositional variations in the mantle, the depth profiles of pressure and temperature, at least for the Earth, are relatively well constrained. The viscosity of mantle rocks increases with increasing pressure but decreases with increasing temperature. Generally, the strongest effect on viscosity is that of temperature, which allows for many orders of magnitude variations in viscosity. However, for most of the mantle depth (excluding the TBLs in the top and bottom few hundreds of kilometers), temperature varies only gradually along an adiabatic profile. Thus, the depth profile of viscosity is dominated by pressure variations (Steinberger & Calderwood, 2006; Steinberger, Werner, & Torsvik, 2010). For Earth, the combined effects of increasing pressure with depth with mineralogical phase transitions (discussed next) cause the viscosity to increase by up to three orders of magnitude across the mantle.

Mantle minerals may have different geometries of atomic arrangement (crystal structures) at different pressures and temperatures. Changing from one atomic arrangement to another is called a phase transition: or commonly for the mantle, a solid–solid phase transition, since the material remains in a solid state as it transforms to another phase. Thus, a material may have one crystal structure (or phase) at low pressures, but once the pressure reaches some critically high value, the material organizes into a more compact, higher-density state, which then has greater resistance to compression. The first major phase change in the Earth’s mantle occurs at 410 km depth, where olivine (which is the major component mineral of the upper mantle) transitions to the same material with a wadsleyite structure (Katsura et al., 2004), and that involves a moderate 5%–8% density increase (Dziewonski & Anderson, 1981). Wadsleyite changes to ringwoodite at 520 km depth (Ita & Stixrude, 1992), with an associated 1%–2% density increase (Dziewonski & Anderson, 1981). The largest phase change occurs from ringwoodite to perovskite/magnesiowüstite at 660 km depth (Katsura et al., 2003), with a density increase of 10%–11% (Dziewonski & Anderson, 1981) and involves a viscosity increase by about a factor of 30 (Hager, 1984; Ricard, Fleitout, & Froidevaux, 1984). The 410 km and 660 km phase changes are the two most remarkable, globally contiguous phase changes in the Earth’s mantle, and the region between them is called the Transition Zone, since it is where most of the mineralogical transitions occur, over a relatively narrow region (Ringwood, 1991). The mantle above the Transition Zone is typically identified as the Upper Mantle (although in some papers and books Upper Mantle includes the Transition Zone), and that below is the Lower Mantle. The temperature and pressure profiles, which together with the composition determine the depth at which the phase transitions occur, are more uncertain for the interiors of the other terrestrial planets. Nonetheless, it has been estimated that the olivine to wadsleyite transition occurs around 450–580 and 1,000–1,500 km depth on Venus and Mars, respectively, while the ringwoodite–perovskite transition occurs at about 710 and 1,910 km depth on Venus and Mars, respectively (Ito & Takahashi, 1989; Harder, 1998; Katsura et al., 2004). The mantle of Mercury appears to be too thin for it to sustain any phase transitions.

There is seismological evidence for other phase changes in the Earth’s mantle, although these are less well resolved and in some instances do not appear to be global: thus their effect on mantle convection will only be mentioned briefly.

# Mantle’s Heat Budget

The ultimate driver of mantle flow is that planets cool to space as they inexorably come to equilibrium with the rest of the much colder universe. A major source of heat within the mantle is the kinetic energy delivered to the planetary interiors by the impacts of planetesimals during accretion; another is the gravitational energy released upon the segregation of the metallic core from the silicate mantle. These are known collectively as primordial heat sources. Another source of heat arises from radioactive decay of unstable isotopes, mostly uranium (238U), thorium (232Th), and potassium (40K), which are collectively termed radiogenic heat sources. The total rate that heat is flowing out of the Earth is approximately 46 TW (Jaupart, Labrosse, Lucazeau, & Mareschal, 2015), as measured by heat-flow gauges in continents and oceans (see Turcotte & Schubert, 2014). About 20%–30% of the Earth’s total mantle heating is thought to come from the core (Jaupart et al., 2015). The relatively low endogenic heat flow emanating from within terrestrial planets, compared to radiative release of incident solar heating, makes surface heat-flows measurements challenging, and even so, such observations are available only for the Earth and the Moon.

Most radioactive elements in the mantle are incompatible, meaning that if their host rock undergoes partial melting, they tend to dissolve or “partition” into the liquid phase. Thus, in the process of crust formation through mantle melting, the incompatible radioactive elements partition toward and concentrate in the crust, which has two competing consequences for the mantle heat budget. On the one hand, forming a crust depletes the mantle of heat-producing elements. On the other hand, a radiogenically heated crust acts as a warm blanket that impedes 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 investigation (Rolf, Coltice, & Tackley, 2012).

Earth’s continental crust, which is inevitably extracted from the early mantle by melting and re-melting, acquired an especially high concentration of incompatible radioactive elements and thus produces a significant fraction of the net heat output through the surface. Subtracting the contribution to surface heat flow from the continental crust leaves approximately 38 TW emanating from the mantle and core (Jaupart et al., 2015).

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 6,371 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 5150 km. Reproduced from Lamb and Sington (1998).

It is not currently known exactly how much of the heat output from the mantle (and core) is due to primordial heat and how much is due to the heating by radioactive elements. The mantle’s abundance of radiogenic sources can potentially be constrained using the measured concentrations of U, Th, and K in chondritic meteorites, which are thought to represent the original building blocks of terrestrial planets. However, to what degree the chondritic concentrations (not to mention which families of chondrites) are representative of those for the bulk of Earth is still up for debate. Complicating the issue is the uncertainty about the efficiency of heat transport throughout Earth’s history, with different proposed models spanning more efficient and less efficient cooling rates on early Earth. There is a trade-off between what is assumed for the budget of radioactive elements and the efficiency of mantle heat transport through time. Chondritic concentrations of radioactive elements require the mantle to have released heat less efficiently in the past (Korenaga, 2008). Alternatively, if the present heat transport mechanism is representative of that on early Earth, then the mantle’s radiogenic sources must be super-chondritic and would also imply that the mantle holds a reservoir of heat-producing elements not sampled by plate tectonics (since we do not see these heat-producing elements in MORB) (Schubert, Stevenson, & Cassen, 1980; Jaupart et al., 2015).

The question about the efficiency of mantle convection through Earth’s history, as well as its characteristics on other planets, requires an understanding of how mantle dynamics change with varying temperature, planet size, etc.; this issue will be revisited later, after the basic physics of convection has been discussed.

# Mantle’s Cold Thermal Boundary Layer

The outer portion of a planet, its crust and lithosphere, makes up the cold thermal boundary layer (TBL), which is the layer across which heat escapes from the interior to space; the heat 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 (i.e., all except Earth), mantle convection occurs beneath the surface; while the surface may get deformed and have volcanic lavas emplaced on top of it, it remains in place for periods that are much longer than the characteristic timescale of mantle overturn. This mode of convective cooling is termed “stagnant lid convection,” with the lid being the portion of the TBL that does not participate in convective mantle flow, and planets cooling in this mode are termed “one-plate planets.” The lid can thicken over time due to cooling, compression in response to underlying mantle currents, or burial under the lavas emplaced on top of it (Moore, Simon, & Webb, 2017). Thickening of the basaltic crust may push its lowermost portion into depths where it transitions to eclogite. On Earth, Venus, Mars, and Mercury the basalt–eclogite transition occurs at about 45, 50, 65, and 100 km depth, respectively, with the exact depth being dependent on temperature (Arndt & Goldstein, 1989; Spohn, 1991; Babeyko & Zharkov, 2000). Eclogite is denser than the underlying mantle material and is therefore gravitationally unstable and prone to sink into the mantle, a process known as delamination. On one-plate planets, episodes of lithospheric delamination possibly act to thin the stagnant lid, or even remove it entirely and are often followed by extensive volcanic activity that effectively renews the surface (Turcotte, 1989; Spohn, 1991; Parmentier & Hess, 1992; Morschhauser, Grott, & Bruer, 2011; Ogawa & Yanagisawa, 2011). There is growing evidence for a mobile Venusian lithosphere (rather than a stagnant one, as was previously believed). Some of the observed topographic features on Venus, in particular in the vicinity of large coronae, resemble trenches, possibly indicative of subduction (Schubert & Sandwell, 1995; Davaille, Smrekar, & Tomlinson, 2017). Furthermore, some of the radar imagery of Venus has been interpreted as folds and faults, all indicative of lateral surface motion: Although this type of geological structures can be generated by the stresses of the underlying convective mantle, even if the lithosphere does not circulate into the mantle (Harris & Bédard, 2014).

The surface of planet Earth is unique in that most of it, namely the oceanic crust (which makes up about 60% of the surface area), is continuously renewed through the process of plate tectonics. Instead of a largely stagnant top TBL common for other terrestrials, the cold TBL of Earth is mobile, moving laterally along the planetary surface at a rate dictated by that of mantle overturn. The resulting high rate of surface rejuvenation, as reflected in the young age of the oceanic crust, typically less than 200 Myr (Condie, 1997), allows for efficient convective cooling of the planet. The theory and observation of plate tectonics on Earth, including its link to mantle flow, has revolutionized our understanding of planetary dynamics and evolution, and we discuss it in more detail in the following section.

## Plate Tectonics—The Unique Case of Planet Earth

The Earth’s surface, its crust and lithosphere, is subdivided into 12 major tectonic plates and a number of minor plates or microplates (Figure 4). Some plates consist entirely of the oceanic lithosphere, while others incorporate continents as well. The plates move relative to each other, and their movement away from, toward, or laterally past each other, characterizes their boundaries as divergent, convergent, or transform (or, alternatively, strike-slip), respectively. New tectonic plate material is formed at the mid-ocean ridges (MORs), which constitute the divergent plate boundaries; specifically, hot mantle material partially melts, and the resulting magma ascends to drive ridge volcanism and form new oceanic crust. The residual un-melted material remains in the mantle as the thin depleted portion of the lithosphere. As the plates move away from MORs they cool, and their lithosphere thickens as a thermal boundary layer, becomes heavier, and eventually sinks back into the mantle at subduction zones: this constitutes the convergent plate boundaries. The divergent and convergent motion of the plates is the surface manifestation of the upward and downward motion associated with convective currents in the underlying mantle, which is often also referred to as the poloidal component of mantle flow (Hager & O’Connell, 1981; Bercovici, Tackley, & Ricard, 2015). The plate motion that is not directly associated with spreading or subduction is associated with strike-slip shear or plate 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 important effect of non-linear rock rheology (i.e., the way a rock responds to stress through deformation, or strain rate) to indirectly couple it to convective motion (Kaula, 1980; Bercovici et al., 2015).

One of the first to recognize the mobility of the Earth’s surface was Alfred Wegener in his theory of continental drift, largely motivated by the striking correlation in the geometry of the margins of different continents (Wegener, 1924). Wegener’s theory, however, lacked a physically plausible mechanism that would provide a sufficient driving force for the continents to move through oceanic crust, which is why it was criticized and discredited. Decades later the accumulation of sea-floor sounding and magnetic data during and after World War II provided compelling evidence for sea-floor spreading (Hess, 1962; Vine & Matthews, 1963; Morley & Larochelle, 1964; and see Tivey, 2007), which marked the start of the plate tectonics revolution. The theory of plate tectonics, in which the plates comprise a mosaic of contiguous rafts blanketing the mantle—but all moving as solid blocks around their own rotation or Euler poles—was articulated by 1968 independently by McKenzie and Parker (1967) and Morgan (1968). Plate tectonics differs from continental drift in that the continents are passive riders on the backs of the plates, rather than plowing through oceanic lithosphere as Wegener assumed. Meanwhile, the theory that the mantle is convecting in order to get rid of its heat had become more physically sound, generating testable predictions of flow velocity and stress, which compared favorably to the Earth’s gravity, geoid, and topography measurements (Holmes, 1931; Pekeris, 1935; Hales, 1936; Runcorn, 1962a, 1962b; see Bercovici, 2015).

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 Pål Wessel, University of Hawaii at Manoa.)

Tectonic plates constitute the cold thermal boundary layer of the convective mantle system (i.e., the conductively cooled surface layer), made up of the differentiated mantle (crust and depleted lithosphere) in the uppermost part and the undifferentiated cold lithospheric mantle at the bottom. It is generally understood that plate tectonics is the surface manifestation of mantle convection. Complicating this picture is the fact that the mantle material behaves very differently when it is at depth (at higher pressures and temperatures) compared to when it is near the surface. Prior to becoming a plate, the mantle acts as a highly viscous fluid, with its deformation distributed over tens or hundreds of kilometers. In contrast, the cold tectonic plates appear to be strong (nearly rigid) in their interior, with most of their deformation confined to the weak and narrow plate boundaries. In fact, the strength of the plates appears to be high enough that they should not be able to bend and sink into the mantle, given the available convective forcing (Cloetingh, Wortel & Vlaar, 1989; Solomatov, 1995). The physical mechanism responsible for weakening of crustal and lithospheric rocks, which ultimately allows for the formation of tectonic plate boundaries, are still debated, with plastic yielding, percolation of fluids, and grain-size reduction being some of the leading theories. Nevertheless, understanding how the nearly discontinuous motion of plates self-consistently arises from the convective flow of the mantle and how the strong plates bend and sink into the mantle remain major goals in geodynamics (Bercovici, 1995; Bercovici et al., 2015; Foley & Becker, 2009; Tackley, 2000a, 2000b; van Heck & Tackley, 2008).

# Mantle’s Cold Downwelling Flow

Unless cold mantle downwellings entrain surface material, as in the case of plate tectonics on Earth, their presence is largely hidden from direct observation. However, the motion of cold dense material in the mantle generates topography and a measurable signal in the surface gravity field. For example, anomalously dense material in the mantle (such as from cold downwelling currents) induces a positive anomaly in the gravitational field (i.e., a gravity high). However, some (or all) of that positive signal may be offset by the flow-induced downward deflection of the surface, which effectively generates a negative mass anomaly. For the Earth, the seismic anomalies can be imaged independently using seismic tomography, which can then be combined with the topography and gravity measurements to constrain mantle structure (Hager, 1984; Ricard et al., 1984; Steinberger et al., 2010). Combining observations of topography, volcanism, and gravitational anomalies, and using Earth as a reference for mantle rock properties, it has been demonstrated that there exist large-scale density anomalies, likely induced by vertical convective currents, in the mantles of Earth, Mars, and Venus (Steinberger et al., 2010).

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

## Subduction on Earth

As the oceanic lithosphere migrates away from a spreading center (mid-ocean ridge), it becomes denser and heavier. The resulting thermally induced negative buoyancy causes the plate to eventually sink into the mantle. Oceanic plates bend and flow downward at subduction zones, forming trenches, which are the deepest parts of the Earth’s surface, such as the Marianas trench. While most subduction zones are located along continental margins where oceanic and continental plates meet, there exist examples of intra-oceanic subduction as well (e.g., the Izu-Bonin-Mariana arc system along the eastern margin of the Philippine plate). The ages of subducting plates vary from 0 (i.e., subducting ridges) to roughly 200 Myr. In all cases, the downwelling is asymmetric, with one plate sinking underneath the other, rather than two plates converging and sinking together (see Wada & King, 2015).

Convective mantle flow is extremely slow and laminar (i.e., there is no turbulent eddy transport of momentum) because of the high mantle viscosity. Therefore, the velocity of sinking slabs is well approximated by their terminal velocity, at which the gravitational force pulling the slabs downward is balanced by viscous resistance to their motion. The terminal slab velocity can be estimated from a slab’s thermally induced buoyancy and the viscosity of the mantle (see Davies & Richards, 1992). The result of this relatively simple approximation is in good agreement with the observations of tectonic plate velocities, especially for oceanic plates attached to appreciable slabs, which move at speeds on the order of 10 cm/yr (Forsyth & Uyeda, 1975).

Seismic tomography reveals that some slabs appear to stagnate and become deflected horizontally at around 660 km depth, which corresponds to the olivine–wadsleyite phase transition. Other slabs appear to traverse the entire depth of the mantle, with little deflection. The increasing mantle viscosity with depth causes the slabs to thicken as they descend, as indicated in seismic tomography models; in principle this occurs because the slab experiences more viscous resistance and slows down, causing it to effectively inflate or buckle, thus appearing thicker. An additional effect is that of thermal diffusion, where the deeper portions of the slab have had more time to cool the surrounding mantle. It is also worth noting that the resolution of tomography models is poor in the mid-mantle, such that at least some of the broadening may be an imaging artifact (see Wada & King, 2015, and references therein).

Although in total a subducting slab is cold and heavy, it is also compositionally stratified. Its top layer is basalt, which makes up the oceanic crust. This is underlain by harzburgite, which makes up the depleted portion of the lithosphere. And finally lherzolite is at the bottom, which is the undifferentiated part of the mantle (see Wada & King, 2015, and references therein). The intrinsic densities of basalt and harzburgite are lower than that of the upper mantle, which partially offsets the plate’s growing negative thermal buoyancy. However, once the plate sinks and becomes a slab, these chemical effects are counteracted by the transitions to intrinsically denser phases that occur at greater depths (most notably the transition from basalt to eclogite at about 60 km depth), rendering the net effect of lithospheric compositional stratification on subduction negligible (Bercovici et al., 2015). However, once the slab reaches the core-mantle boundary (CMB), which acts as an impenetrable boundary, the slab stalls, heats up, softens, and potentially segregates into different paths of the convective flow. Slab segregation is hypothesized to be one of the primary sources for compositional heterogeneity in the mantle (Hofmann & White, 1982; Coltice & Ricard, 1999; Mulyukova, Steinberger, Dabrowski, & Sobolev, 2015). Whether the resulting heterogeneity can form large-scale compositional anomalies, as detected by seismic tomography, or whether the different slab components get stirred by the convective flow and mechanically homogenized remains an active area of research.

When a slab sinking into the lower mantle impinges on the impermeable CMB, it is deflected horizontally and induces flow parallel to the CMB. The slab-induced flow can displace the material already residing at the CMB, and if that material happens to be compositionally anomalous, it may get swept up into large piles of seismically detectable anomalies, such as the large low shear velocity provinces (Tan, Leng, Zhong, & Gurnis, 2011; Bower, Gurnis, & Seton, 2013). Furthermore, as the slab pushes material along the CMB, it causes the hot thermal boundary layer to thicken ahead of the slab; this process has been hypothesized to trigger plume-formation (Weinstein & Olson, 1989; Steinberger & Torsvik, 2012; Dannberg & Gassmöller, 2018), discussed in the next section. If that is the case, then the flow along the CMB provides an important link between plate tectonics, which is mainly driven by the subducting slabs and the intraplate volcanism generated by plumes, which otherwise appears to be decoupled from surface plate motions.

# Core–Mantle Boundary and the Mantle’s Hot Thermal Boundary Layer

The bottom of the mantle is defined by the core–mantle boundary (CMB), which separates the silicate mantle material from the underlying molten metallic core. The efficiency of heat transport across the CMB is the determining factor for the generation of planetary dynamos: In order to sustain a dynamo, the electrically conductive core material needs to move at sufficiently high velocities, which in turn are dictated by the convective flow velocities and thus the rate of core cooling. In addition to thermal convection, an even more effective way to generate a dynamo is by chemical convection, whereby the core cools below the melting temperature and freezes; it then expels its light elements, such as sulfur and silicon, which then buoyantly rise up to the CMB, inducing flow (Stevenson, Spohn, & Schubert, 1983; Braginsky & Roberts, 1995). The rate of core freezing is, again, controlled by the rate of heat transport across the CMB, which in turn is limited by the convective heat transport across the mantle. Observations of intrinsic magnetic fields of terrestrial planets can thus provide important insight into their thermal histories and present states. For example, the apparent absence of magnetic field on Mars (Acuna et al., 1998) is linked to its relatively cold interior, possibly indicating that its mantle is too cold to efficiently convect heat out of the core. Venus does not seem to feature a measurable magnetic field either (Russell & Elphic, 1979), which has been linked to its relatively hot interior, with the mantle and the core being so hot that the core does not crystallize (Stevenson et al., 1983) (at least presently, although it may have undergone some freezing in the past). In contrast, Earth and Mercury possess substantial magnetic fields, indicating rapid heat transport across the mantle (Ness, Behannon, Lepping, Whang, & Schatten, 1974; Connerney & Ness, 1988; Anderson et al., 2011). Better constraints on the composition and interior structure of the Earth’s deep interior, thanks to seismic tomography and mineral physics data, provide a more detailed picture of the nature of the CMB.

## Earth’s Core–Mantle Boundary

The CMB is a natural place where dense heterogeneities accumulate: material that is heavier than the ambient mantle but lighter than the outer core can linger here. Moreover, since the core only exchanges heat with the mantle by conduction, leading to a 200–300-km-thick hot thermal boundary layer, across which the temperature increases with depth by about 1,000 K, from the ambient temperature profile of about 2,500 K in the lower mantle to about 4,000 K at the CMB (Calderwood, 1999; Kawai & Tsuchiya, 2009).

Seismic studies of the deep interior use the compressional and shear wave velocities and the bulk sound speed, which are related to the material’s bulk modulus (incompressibility), rigidity, and density (Masters, Laske, Bolton, & Dziewonski, 2000). For example, the correlation between anomalies in the shear wave velocity and the bulk sound speed can be used to infer the physical causes for an observed anomaly. If the anomaly is due to the variations in temperature, then the shear velocity and bulk sound speed should be correlated (i.e., both positive or both negative), while an anticorrelation (anomalies of opposite sign) is indicative of compositional variations. There is abundant evidence for the heterogeneous nature of the lowermost mantle from seismological observations, which indicate the presence of both thermal and compositional variations (Figure 5) (Ishii & Tromp, 1999; Garnero, 2004; Garnero & McNamara, 2008; Ritsema, Deuss, Van Heijst, & Woodhouse, 2011). The main observational features of the CMB region include the D” discontinuity, the large low shear velocity provinces (LLSVPs) and the ultralow velocity zones (ULVZs) (Lay, Williams, & Garnero, 1998; Thorne & Garnero, 2004). The D” discontinuity is seen as a sharp increase in shear-wave velocity with depth occurring several hundred kilometers above the CMB. The part of the mantle between the D” discontinuity and the CMB is commonly referred to as the D” layer. The D” varies in thickness and even appears to be absent in some regions, which suggests that it is not a global phase transition, unlike, for example, the 410 km and 660 km discontinuities bounding the transition zone (see also Hernlund & McNamara, 2015). A possible cause for the D” is the solid–solid phase transition from perovskite (Pv) to postperovskite (PPv) (Murakami, Hirose, Kawamura, Sata, & Ohishi, 2004), which would only occur at deep mantle pressures in sufficiently cold regions, such as in the vicinity of newly arrived slabs. Postperovskite is slightly denser (by 1%–2%) and less viscous (by up to an order of magnitude) than the perovskite phase, and thus can act to mildly destabilize the lowermost mantle material, making convection slightly more vigorous (Tackley, Nakagawa, & Hernlund, 2007; Nakagawa & Tackley, 2011).

Figure 5. A simplified sketch of a possible interpretation of the seismically observed structures in the Earth’s lower mantle. LLSVP stands for Large Low Shear Wave Velocity Province and ULVZ for Ultra-Low Velocity Zone. See the section “Earth’s Core-Mantle Boundary” for their possible formation scenarios and the proposed thermal and chemical properties. Adapted from Deschamps, Li, and Tackley (2015).

The two major LLSVPs appear as two large-scale heterogeneities in seismic tomography (Garnero & McNamara, 2008; Dziewonski, Lekic, & Romanowicz, 2010; Ritsema et al., 2011): one of them lies beneath Africa and the other beneath the Pacific Ocean. LLSVPs have irregular shapes and can measure up to 1,000 km in height and width; they cover nearly 20% of the CMB area and occupy about 2% of the mantles total volume (Burke, Steinberger, Torsvik, & Smethurst, 2008).The negative correlation between the bulk sound and shear velocity within the LLSVPs suggests that they are of chemical origin (Masters et al., 2000; Trampert, Deschamps, Resovsky, & Yuen, 2004; Steinberger & Holme, 2008). Moreover, the material that makes up the LLSVPs appears to be intrinsically denser than the ambient mantle (Ishii & Tromp, 2004). There is still no consensus on the origin of this compositional anomaly, with the proposed scenarios falling within two main categories: a primordial layer that formed early in the Earth’s history (e.g., Lee et al., 2010; Nomura et al., 2011), and accumulation of a dense eclogitic component from the subducted MORB that segregates at the CMB (Hofmann & White, 1982; Christensen & Hofmann, 1994; Tackley, 2011; Mulyukova et al., 2015) (see also review by Hernlund & McNamara, 2015).

The ULVZs are localized structures that are much smaller than the LLSVPs, extending around 1 to 10 km above the CMB and 50 to 100 km laterally (Thorne & Garnero, 2004; McNamara, Garnero, & Rost, 2010). However, ULVZs have a large seismic velocity reduction, 10% for P-waves and 10% to 30% for S-waves (Garnero & Helmberger, 1996) and a 10% density increase relative to the ambient mantle. Mechanisms for producing the ULVZs are still a matter of debate, with some of the candidates including partially molten and/or iron-enriched material, possibly formed early in Earth’s history when the mantle was much hotter and largely molten (Williams & Garnero, 1996; Labrosse, Hemlund, & Coltice, 2007), outer core material leaking into the lower mantle due to chemical disequilibrium or morphological instability (Otsuka & Karato, 2012), and subduction and gravitational settling of banded-iron formations (Dobson & Brodholt, 2005).

The compositionally anomalous nature of the deep mantle has important implications for mantle convection and hence Earth’s thermal evolution. In particular, the presence of compositionally dense material at the CMB reduces the amount of heat that flows from the core into the mantle, which is one of the energy sources for convective flow. This effective blanketing of the CMB has implications for the rate at which the mantle has been cooling since core formation. In addition, as discussed previously, the heat flow across the CMB controls the rate at which the Earth’s core cools and freezes: thus, the history of the geodynamo.

# Mantle’s Hot Upwelling Flow

As heat is conducted from the core into the mantle, it creates a hot thermal boundary layer (TBL) at the bottom of the mantle. The hot TBL material thermally expands and becomes buoyantly unstable. When the TBL is sufficiently thickened and buoyant to rise through the overlying viscous mantle, it can rise upward in the form of hot mantle currents, also called mantle plumes, and potentially reach the surface. Arrival of plume material at the surface can generate volcanic activity or a hotspot and deflect the surface upward, generating a high topography or a hotspot swell. Hot plume material will also undergo melting when it ascends to lower pressures and induce volcanism; the resulting lava flows may serve as another surface signature of the underlying convective mantle currents. For example, the large volcanic rises Themis, Eastern Eistla and Central Eistla on Venus (Smrekar & Stofan, 1999) and the Tharsis rise on Mars (Wenzel, Manga, & Jellinek, 2004) have been interpreted as manifestations of underlying plume activity (see Steinberger et al., 2010).

Plume geometry is hypothesized to be mushroomlike, with a plume head spanning a few hundred kilometers across, followed by a cylindrical plume tail that can be as long as the depth of the mantle, and a 100 km or less in diameter (Whitehead & Luther, 1975; White & McKenzie, 1989; Olson, 1990; Sleep, 2006]; see review in Ballmer, vanKeken, & Ito, 2015). The plume tails are relatively narrow, and in the case of the Earth, until recently these have been difficult to resolve seismologically (Montelli et al., 2004; French & Romanowicz, 2015). Moreover, planetary mantles are heated both from below (by the core) and from within (by primordial heat and radioactive elements); the strength of the plumes (i.e., their size and thermal anomaly) decreases with the decreasing contribution from bottom heating, since that is what controls the size and temperature of the TBL. Thus, plume detection, both through gravity measurements, seismology and volcanism, is challenging in planets that are predominantly heated from within, as seems to be the case for the terrestrial planets in our solar system.

## Plumes and Mid-Ocean Ridges on Earth

When a new starting plume-head first reaches the surface of the Earth, it is thought to initially generate extensive volcanic activity, often referred to as flood-basalt volcanism, leading to large igneous provinces (e.g., Ontong-Java Plateau, Columbia River Basalts, the Deccan Traps and the Siberian Traps). This initial eruption is associated with a massive flood basalt volcanism and is ostensibly followed by continuous hotspot activity, supplied by the narrow plume-tail (Richards, Duncan, & Courtillot, 1989; Ballmer et al., 2015). This ongoing hotspot volcanism can sometimes be seen as a chain of volcanic islands (typically on the sea floor where the plume material can readily penetrate the thinner lithosphere); in particular, the stationary plume conduit emplaces lava onto the surface of a tectonic plate that is moving relative to it, thus forming a chain of volcanoes with a characteristic age progression, the archetypical example of which is the Hawaiian–Emperor hotspot chain that extends across the North Pacific sea floor. In contrast to the more common forms of volcanism, which occur at mid-ocean ridges and subduction-related volcanic arcs, hotspots often occur in plate interiors and are not generally associated with plate boundary processes.

The classical view of mantle plumes as purely thermal upwelling currents has been challenged in recent years, due to the large kilometer scale topographic uplift that is predicted for a thermal plume impinging on the lithosphere (White & McKenzie, 1989), but that is not always observed (Czamanske, Gurevitch, Fedorenko, & Simonov, 1998; Korenaga, 2005; Sun et al., 2010). One of the proposed resolutions to this inconsistency are compositionally anomalous plumes (also known as thermochemical plumes), whose mantle material is enriched in heavier elements and is thus intrinsically dense relative to the “normal” mantle (but, of course, still positively buoyant due to their high temperature) (Dannberg & Sobolev, 2015). The thermochemical plumes are less buoyant than the classical purely thermal plumes and therefore rise more slowly and generate less dynamic topography, in agreement with the observations. Thermochemical plumes simultaneously explain another feature of plume volcanism, namely their geochemically distinct basaltic lavas, in terms of trace elements and isotopes, relative to basaltic lavas derived from mid-ocean ridges (Hofmann & White, 1982; Zindler & Hart, 1986; Kobayashi, Tanaka, Moriguti, Shimizu, & Nakamura, 2004; Jellinek & Manga, 2004; Sobolev, Hofmann, Sobolev, & Nikogosian, 2005; Jackson & Dasgupta, 2008; Sobolev et al., 2011). The distinct geochemistry of hotspot lavas is one of the arguments for why they are thought to be extracted from a mantle region that is deep seated and at least partly decoupled from the large tectonic scale mantle circulation. Furthermore, the spatial correlation of plume-derived lavas at the surface and their projection down to the LLSVPs and ULVZs at the CMB provides further supportive evidence for their deep origin (Torsvik, Smethurst, Burke, & Steinberger, 2006; Burke et al., 2008; Dziewonski et al., 2010; Steinberger & Torsvik, 2012).

The vertical flow of hot mantle upwellings induces lateral flow along the CMB, due to a dynamic low pressure that is created at the plumes base. As the ambient material gets sucked into the rising plume, it drags the underlying, possibly compositionally heterogeneous material along with it. This is the process by which plumes can potentially bring the chemically distinct material from the deep mantle all the way up to the surface, producing geochemically distinct lavas. As such, plume-derived lavas are a window into the chemical structure of the deep mantle.

Another component of the upwelling flow, which is associated with plate tectonics and is thus unique for the Earth, is the return flow of the mantle that compensates for (or gets displaced by) the downward motion of the slabs. The material that makes up the return flow eventually ends up becoming the bottom-most undifferentiated part of the tectonic plates, accounting for their thickening as they grow older. As opposed to the actively upwelling plumes, MOR volcanism is not associated with the excess buoyancy of hot material but rather with its passive rising in response to lithospheric spreading motion; this is, for example, evident in the East Pacific Rise, which is the fastest-spreading ridge on Earth and is devoid of a gravity anomaly or deep seismic structure (Forsyth et al., 1998), implying that it is isostatically supported and is not being lifted up by any deep upwelling current (Runcorn, 1963; Davies, 1988). MORs constitute the divergent plate boundaries where tectonic plates are first formed. Many ridges initiate as rift zones during continental breakup, eventually becoming sites of sea-floor spreading that separate the continents; these processes are an integral part of the classical Wilson cycle, involving repeated closing and opening of oceans (Wilson, 1968).

The mantle region that undergoes fractional melting beneath a ridge is several hundred kilometers wide (Forsyth, et al. 1998). However, as the melt migrates to the surface, it focuses within just a few kilometers of the spreading axis, creating narrow regions where the oceanic crust is emplaced and where the deformation is localized (Morgan, 1987; Spiegelman & McKenzie, 1987; Parmentier, 2015). The physical explanation for why MOR volcanism is focused into narrow ridge-structures is related to (and is as enigmatic as) the cause for strong plates and weak plate boundaries. The ridge orientation typically mirrors the subduction zones that they eventually feed, implying that they may initiate as a strain localization, such as a self-focusing necking instability (Ricard & Froidevaux, 1986). Such mechanisms are plausible if the stresses in the lithosphere due to the pull of slabs can be guided considerable distances. The cause for ridge formation and geometry remain an active area of research.

The lavas produced at MORs and hotspots are known as Mid-Ocean Ridge Basalts (MORB) and Ocean-Island Basalts (OIB), respectively. Being direct samples of the mantle, their petrological composition, and trace-element chemistry is of great interest for understanding mantle dynamics and structure (Hofmann, 1997, 2003; van Keken, Hauri, & Ballentine, 2002; Tackley, 2015). For example, the distinct features of MORB and OIB implies that they originate from different source regions in the mantle with limited material exchange between them. Geochemical measurements of trace elements, in particular incompatible elements (which dissolve more readily in a rock’s melt than its solid during partial melting), such as uranium, thorium, and helium, show that MORB and OIB are measurably distinct: MORBs appear to be significantly depleted in such trace elements relative to OIB, which implies that the MORB source region has undergone previous melting and depletion, compared to that of OIB (Hofmann & White, 1982; Zindler & Hart, 1986). The emerging model of upwelling mantle flow has the MORB source confined to an area in the upper mantle, which has been cycled repeatedly through the plate tectonic process of mid-ocean ridge melting and separation of oceanic crust and trace elements from the mantle. OIB, on the other hand, ostensibly come from a part of the mantle that has seen little if any of this melt processing and hence would be isolated presumably at depth from the upper mantle and the plate-tectonic cycling (Allégre, 1982; Tackley, 2015; and references therein).

Mantle layering is also implied by a putative heat-flow paradox. Specifically, if the mantle were composed entirely of MORB source material, which is depleted in U, Th, and K, then its radioactive heating would not be sufficient to account for the observed mantle heat outflow of 38 TW. This inconsistency can be resolved by assuming a higher concentration of radioactive elements in the lower mantle, which then also implies that the mantle is not well stirred, and there is at least some decoupling of convective flow between the upper and lower mantle. However, if the contribution from primordial heat to the net mantle heat output is equal to or larger than the radiogenic source, then the observed heat flow can be reconciled with the low concentration of radioactive elements, thus resolving this so-called heat-flow paradox (Christensen, 1985; Korenaga, 2003, 2008).

Another geochemical argument for limited exchange between lower and upper mantle comes from taking the “bulk silicate Earth” composition (i.e., with the mantle and crust combined) and assuming that the continental crust was removed from it uniformly. The mantle residue left behind from this thought experiment is too enriched in incompatible elements, compared to the MORB source. However, extracting the continental crust from only the top third to top half of the mantle causes sufficient depletion to reproduce MORB source composition (see van Keken et al., 2002). A stratified mantle, with a shallow portion of the mantle that has segregated to form the continental crust, leaving a complementary undepleted region in the deeper mantle, makes for a geochemically plausible mantle composition model. It is worth noting that the total volume of the two major LLSVPs or even the entire D” layer, is not enough to hold all of the unsegregated portion of the mantle, and thus cannot single-handedly account for all of the enriched mantle material. A 1,000-km-thick layer at the base of the mantle would potentially be big enough to serve as a storage of unsegregated material (Kellogg, Hager, & van der Hilst, 1999), however, such layer has never been seismologically observed.

There remains a contradiction between geochemical and geophysical inferences of layered versus whole mantle convection. There is compelling evidence from seismic tomography models for material exchange between the lower and upper mantle, with subducting slabs extending into the lower mantle (van der Hilst, Widiyantoro, & Engdahl, 1997; Grand, van der Hilst, & Widiyantoro, 1997), as well as mantle plumes traversing the transition zone (Montelli et al., 2004; Wolfe et al., 2009; French & Romanowicz, 2015), Yet the geochemical data appears to argue for a layered mantle with an isolated and undepleted mantle at depth. Some of the attempts to reconcile these observations circumvent the problem of layered convection (which is not observed) by instead invoking differential melting. For example, one model envisions the mantle as a plum pudding, where “plums” are scattered regions that are enriched in volatile elements, while the rest of the mantle is a depleted “pudding” (Morgan & Morgan, 1999; Becker, Kellogg, & O’Connell, 1999; Tackley, 2000c). The size of the plums and their degree of relative enrichment of incompatible and radiogenic elements depends on their assumed origin and the history of mantle stirring, both of which are highly uncertain. The enriched domains can melt at higher pressures, while the depleted ones require lower pressures to melt. One of the proposed scenarios envisions that a mantle plume impinging on the base of a 100-km-thick lithosphere would mostly melt the “plum” material (OIB source), while the part of the mantle that rises to lower pressures at ridges melts additional depleted “pudding” component (MORB source), resulting in MORB that appears depleted relative to OIB (Ito & Mahoney, 2005a, 2005b). Another model argues for whole-mantle convection but considers the different abilities of mantle minerals to absorb water: In particular transition zone materials absorb water more readily than the upper mantle. As mantle material passively upwells through the transition zone (as part of the slab-driven return flow) and enters the upper mantle at the 410 km boundary, it becomes closer to water saturation and more likely to melt. Melting at 410 km depth strips, or filters, the upwelling mantle from the incompatible elements, which forms the depleted MORB source. Mantle plumes, on the other hand, traverse the transition zone too fast to become hydrated, which limits the amount of melting and volatile filtering they can undergo as they cross the 410 km boundary. Thus, the lavas sourced by the plume material, the OIBs, would appear to come from an enriched mantle (Bercovici & Karato, 2003). The prediction of a melting site at 410 km depth inferred by this model, known as the Transition Zone Water Filter model, has been supported by some seismological studies (Revenaugh & Sipkin, 1994; Tauzin et al., 2010). However, there still exists significant uncertainty regarding the melting properties and the solubilities of incompatible elements, which require further constraints to test the models that invoke differential melting. In summary, the conflicting geochemical and geophysical inference of layered versus whole-mantle convection remains an unsolved problem.

# Basics of Thermal Convection

To understand the origin and mechanics of the important features of mantle convection surveyed above, it is necessary to review the basic physics of thermal convection. For example, tectonic plates, slabs, lithospheric drips, and mantle plumes are all forms of thermal boundary layers, which are common to convection in any fluid system. The simplest form of thermal convection is referred to as Rayleigh–Bénard convection, named after the French experimentalist Henri Bénard, who recognized the onset of convective motion in fluids from a static conductive state and the formation of regular flow patterns in a convecting layer (Bénard, 1900, 1901), and the British theoretical physicist and mathematician Lord Rayleigh (William John Strutt), who provided the theoretical framework to explain Bénard’s experimental results (Strutt, 1916).

The Rayleigh–Bénard system is an idealized model of a fluid layer that has a finite thickness but is infinite in all horizontal directions. The layer is heated uniformly from below and cooled from above by applying fixed high and low temperatures at the bottom and top boundaries, respectively. As the bottom part of the layer heats up, it thermally expands, which lowers its density and makes it buoyant relative to the overlying colder material (analogously, the material at the top cools, contracts, and becomes negatively buoyant). The resulting density stratification, with low-density material underlying high-density material, is gravitationally unstable and can lead to fluid flow that overturns the layer, bringing hot material up and cold material down. Of course, because the temperature at the boundaries remains fixed, the 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 downwelling currents.

Figure 6. Result of a numerical simulation of Rayleigh–Bénard 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).

Convective fluid flow is a form of heat transport that is activated when thermal conduction is not efficient enough to accommodate heat flow. For example, if the layer is thin enough, it can conduct heat diffusively through molecular vibrations, thus the fluid can remain static and obtain a conductive temperature profile across its depth. Convective motion emerges when thermally induced density anomalies induce flow that is sufficiently vigorous to withstand the stabilizing effects of thermal diffusion. In addition, while the thermal contrast across the layer supplies buoyancy to drive the flow, the viscous resistance of the fluid opposes it. The competition between forcing by thermal buoyancy and damping by viscosity and thermal diffusion is characterized by a dimensionless ratio called the Rayleigh number

$Display mathematics$
(1)

where $ρ$ is fluid density, $g$ is gravity, $α$ is thermal expansivity, $ΔT$ is the difference in temperature between the bottom and top boundaries, $d$ is the layer thickness, $μ$ is fluid viscosity and $κ$ is fluid thermal diffusivity. The higher the value of $Ra$, the higher the propensity for convective overturn. $Ra$ needs to exceed a certain value, called the critical Rayleigh number $Rac$, in order to excite convective flow. The value of $Rac$ is typically on the order of 1,000, with the exact value depending on the thermal and mechanical properties of the horizontal boundaries, (e.g., whether the boundary is rigid or open to the air or space, see Chandrasekhar, 1961).

The characteristic physical properties of the Earth’s mantle entering the Rayleigh number are $ρ≈4000kg/m3$, $g=10 m/s2$, $α=3×10–5K–1$, $ΔT≈3000K$, $d=2900km$, $μ=1022Pa$ s (dominated by the lower mantle), and $κ=10–6m2/s$ (see Schubert, Turcotte, & Olson, 2001). According to (1), these lead to a Rayleigh number of approximately 107, which is well beyond supercritical. Thus, in spite of the extremely high viscosity of the solid rock that makes up the Earth’s mantle, the mantle spans a large depth and is subject to a high thermal contrast and hence convects vigorously.

While the properties of other terrestrial planets are less well known than for Earth, there are reasonable constraints on their gravitational acceleration, mantle thickness, and surface temperature (Table 1). Assuming their material properties are similar to Earth’s, we can estimate the Rayleigh numbers for the mantles of other terrestrial planets: 104 for Mercury, 107 for Venus, and 106 for Mars. With the exception of Mercury, whose $Ra$ is at most an order of magnitude above critical, the mantle of the rocky planets in the solar system appear to be cooling predominantly by convection.

In a convecting system, heat that is being transported by the upwellings and downwellings first enters the fluid layer through the horizontal boundaries by conduction across thermal boundary layers (TBLs). TBLs are the portions of the fluid that once sufficiently heated or cooled become unstable and rise as upwellings or sink as downwellings, respectively. The longer it takes for thermal diffusion to induce enough buoyancy and destabilize the TBLs, the thicker they get prior to overturning and thus the vertical currents they form are broader. The lower the Rayleigh number, the longer it takes for TBLs to go unstable. In fact, another way to view a system at subcritical $Ra$ is that by the time the TBLs would be thick enough to overturn, they already span the entire layer depth, which is why the layer remains stable. On the opposite end, at $Ra$-values way above supercritical, only thin TBLs manage to develop before undergoing gravitational instability. As the hot bottom TBL starts to rise, the region it used to occupy gets replenished by the newly arriving cold material and analogous for the cold top TBL. Meanwhile, the material in between the laterally moving TBLs and the vertically moving upwellings and downwellings is simply moved around by the viscous drag from the ambient flow and eventually equilibrates to their average temperature. (In fact, if the layer is deep enough such that the pressures are comparable to fluid incompressibility, the fluid in-between the TBLs is not isothermal but adiabatic.) An adiabatic profile is caused by material moving up or down through large enough pressure changes to induce compression or decompression but fast enough so that the material has little time to exchange heat with its surroundings. Material that rises and expands from decompression must increase its mechanical or “reversible” internal energy (essentially pressure times volume change), and to do this it uses its own thermal internal energy, which results in the material “cooling” (although the only exchange of energy is with itself). Thus rising material has an adiabatic temperature decrease. Likewise, sinking, compressing material relinquishes its mechanical energy to thermal energy, causing it to apparently “heat up,” which leads to a temperature increase for sinking material. The average cooling and heating adiabatic temperature profiles appear as a mean adiabat. A typical temperature profile across the depth of a vigorously convecting layer has narrow regions (TBLs) at the top and bottom that accommodate most of the temperature jump across the layer, with most of the layer in the interior being isothermal or adiabatic (Figure 7).

The heat flow (power output per unit area) out of the convecting layer is essentially given by the heat that is conducted across the TBLs, given by $kΔT/δ$ where $k$ is thermal conductivity (units of $WK–1m–1$), $ΔT/2$ is the temperature drop from the isothermal (or adiabatic) interior to the surface and $δ/2$ is the thickness of the TBL. By comparison, the thermal conduction across a static non-convecting layer is $kΔT/d$ The ratio of heat flow in the convecting layer to the purely conductive layer is thus $d/δ$, which is called the Nusselt number $Nu$ (named after the German engineer, Wilhelm Nusselt, b. 1882–d. 1957). The relation between $Nu$ and convective vigor parameterized by $Ra$ is important for understanding the efficiency of convective cooling of planetary bodies. Convective heat transport is often written as $Nu(kΔT/d)$, and in considering this relation, Howard (1966) argued that heat transport across the depth of the vigorously convecting fluid layer is so fast that the layer thickness is not a rate limiting factor in releasing heat, and thus heat flow should be independent of fluid depth $d$; this implies that since $Ra~d3$ then $Nu~Ra1/3$, which yields a convective heat flow $Nu(kΔT/d)$ that is independent of $d$. In general, since the fluid is conductive for $Ra≤Rac$, one often writes that $Nu=(Ra/Rac)1/3$ (although $Nu=1$ for $Ra≤Rac$), which is a reasonably accurate relationship born out by simple experiments and computer modeling (Schubert et al., 2001; Ricard, 2015). This relationship also implies that the ratio of thermal boundary width to fluid layer depth is $δ/d~Ra–1/3$, which shows that the TBLs become increasingly thin as convection becomes more vigorous.

Table 1. Some Properties of Terrestrial Planets and the Moon Relevant to Mantle Convection Studies

Property

Mercury1

Venus2

Earth3

Mars4

Density [kg m–3]

3,500

4,000

4,000

3,500

Surface Temperature [K]

440

730

285

220

CMB Temperature [K]

3,000

3,500

3,500

3,000

Mantle Thickness [km]

400

2,900

2,900

2,000

Gravity [ms–2]

3.7

10

10

3.5

(1) Hauck et al. (2013); Tosi et al. (2013)

(2) Kaula (1990)

(3) Schubert et al. (2001)

(4) Schubert and Spohn (1990); Harder (1998)

While the average TBL thickness is well approximated by $δ~Ra–1/3$, it is worth noting that the TBL thickness varies laterally: for example, as the fluid in the top boundary layer moves from an upwelling to a downwelling, it cools and the boundary layer thickens as more material cools next to the cold surface. The thickening depends on the thermal diffusivity $κ$ and the residence time or time $t$ since leaving the upwelling. With regard to convection in the Earth’s mantle, the top cold thermal boundary layer is typically associated with the lithosphere, the layer of cold stiff mantle rock that is nominally divided into tectonic plates and reaches thickness of 100 km or so. Simple dimensional considerations show that the boundary layer thickness goes as $κt$; this corresponds to the well-known $age$ law for subsidence of ocean sea floor with age since formation at mid-ocean ridges, implying that sea-floor gets deeper because of the cooling and thickening of the lithosphere (e.g., Parsons & Sclater, 1977; Sclater, Jaupart, & Galson, 1980; Stein & Stein, 1992; Turcotte & Schubert, 2014); this emphasizes that the oceanic lithosphere is primarily a convective thermal boundary layer.

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.

A simple analysis of the heat transported by slabs demonstrates that slabs and plates are an integral part of mantle convection (Bercovici, 2003). The energy flux $Q$ associated with a slab sinking at velocity $vsink$ is given by

$Display mathematics$
(2)

where $ΔT≈700K$, $ρ≈3,500kgm–3$ and $cp=1,000JkgK–1$ are the slabs thermal anomaly, density, and heat capacity, respectively. $A≈2πRδ$ is the effective global cross-sectional area of all slabs crossing the depth at which the energy flux is being estimated, with $δ≈100km$ being a typical slab thickness, and using the Earth’s circumference with $R≈6,000km$ to approximate the net horizontal length of all slabs (since most slabs occur in a nearly large circle around the Pacific basin). Assuming that the sinking slabs account for about 80% of the mantles’ surface heat flow through the ocean floor (the other 20% coming from the plumes), such that $Q=0.8*38TW$, and solving (2) for $vsink$ yields a slab velocity $vsink≈10cmyear–1$. This is in good agreement with the observed velocity of tectonic plates, especially the ones with an appreciable slab attached to them, such that slab-pull is particularly significant. The agreement between the observed plate kinematics and the measured heat flow at the Earth’s surface is one of the major accomplishments of mantle dynamics theory. In fact, the matching convective fluid velocities and plate velocities have also been inferred using gravity and heat-flow measurements (Pekeris, 1935; Hales, 1936), as well as simple dynamical models of the force balance on sinking slabs (e.g., Davies & Richards, 1992).

Understanding the dynamics of mantle convection using the classical Rayleigh–Bénard model is complicated by the fact that the mantle rocks are far from a simple fluid, with the most notable distinction being that the viscosity of rocks is extremely sensitive to temperature. A drop in temperature by a few hundred degrees Kelvin—a plausible temperature difference across planetary TBLs—can raise the viscosity by several orders of magnitude, as will be described in detail in the following section. The dynamical consequence of such thermal stiffening is that as the rocks get colder and denser, and thus more prone to sink, they also become increasingly resistant to deformation and flow, making it harder for them to sink. Depending on the degree of thermal stiffening of the cold TBL, there are three possible modes of terrestrial mantle convection (Solomatov, 1995; Solomatov & Moresi, 1997). When the ratio of the maximum (coldest) to minimum (warmest) viscosity is moderate, for example less than about one order of magnitude, the cold TBL fully participates in convective circulation. This mode may be the most applicable to Earth, which features continuous downwelling of its surface at subduction zones. Thermal stiffening of the Earth’s lithosphere, however, is by significantly more than one order of magnitude, suggesting that there exists a weakening mechanism (unique to Earth, as discussed later) that offsets the thermal effect. At moderate viscosity ratios of about two to four orders of magnitude, the flow of the cold TBL is significantly impeded, meaning it flows much more sluggishly than the underlying mantle. Finally, at viscosity ratios more than four orders of magnitude, most of the cold TBL becomes immobile. The deeper softest portions of the TBL may participate in the convective mantle flow; however, the shallower coldest portions act as a rigid boundary condition to the underlying convective mantle layer. This so-called stagnant lid regime appears to take place on Mars and Mercury (if Mercury’s mantle at all convects). The failure to entrain the uppermost portion of the lithosphere effectively lowers the temperature difference that drives convection, $ΔT$ in (1), since the temperature drop across the lower, softer, mobile part of the cold TBL is smaller than for the drop across the entire TBL. The smaller effective TBL temperature contrast and the greater resistance of the rigid upper boundary act to lower the $Ra$ of the so-called single-plate planets, making them convect and cool less efficiently than the Earth does. While the cold TBL may not get recycled into the mantle, the surface of planets that are in the stagnant lid regime may still get renewed by volcanism, as has been proposed for planets exhibiting heat pipe behavior (Spohn, 1991; Moore et al., 2017), or as a consequence of lithospheric delamination, described in Section “Mantle’s Cold Thermal Boundary Layer.”

The dynamics of the hot TBL at the base of a planetary mantle is affected by the temperature dependence of viscosity as well. Specifically, for the onset of a new hot upwelling, since the hotter material is less viscous, it is less capable of displacing the colder and stiffer ambient mantle in order to rise through it. Fluid in the bottom TBL lingers at the CMB as it gathers enough buoyancy to overcome the viscous resistance of the overlying mantle. Once the fluid has accumulated enough thermal buoyancy, it starts rising rapidly through the mantle, first forming a diapiric plume (Whitehead & Luther, 1975), which efficiently drains the remaining low-viscosity hot TBL from the bottom (Bercovici & Kelly, 1997). The efficient supply of hot material from the bottom of the mantle further propels the plumes ascent. These two stages of plume formation are responsible for its mushroom shape—the initial gathering of hot material forms the large plume head, and the subsequent rapid draining of the hot TBL upon ascent forms the narrow plume tail (Campbell & Griffiths, 1990).

Another contrast between mantle convection and the idealized Rayleigh–Bénard model is that the planetary mantles are heated not just by the bottom boundary, referred to as “basal heating,” but also by the release of both radiogenic and primordial heat distributed through the volume of the fluid, termed “internal heating.” Adding the effect of internal heating to the model of a convecting layer raises the temperature of its interior, bringing it closer to the temperature of the bottom boundary (instead of the mean of the two boundary temperatures, as is the case in the classical symmetric Rayleigh–Bénard model). While this makes the temperature jump across the bottom TBL smaller, the jump across the top TBL becomes larger, since the top boundary now must conduct out heat injected through the bottom, plus heat generated from the interior (Figure 7). As a result, the top TBL in an internally heated system is more negatively buoyant and forms stronger downwellings, while the upwelling currents are smaller and weaker, compared to a system that is entirely basally heated. The strong temperature-dependence of viscosity of mantle rocks further adds to this asymmetry, with the thermally stiffened cold downwellings having to acquire more thermal buoyancy in order to overcome their own viscous resistance and sink. The convective currents on Earth do, indeed, feature large cold slabs with large thermal anomalies (of the order of 700 K) and smaller plumes with weaker thermal anomalies (on the order of 200 K).

Convective currents also self-organize in such a way that the horizontal spacing between the upwellings and the downwellings is optimized: not too small, so they do not exert too much viscous drag on each other and/or do not lose heat too rapidly to each other, and not too big, so they do not have to roll too much mass between them. In addition, the separation distance between the vertical currents is determined by the time it takes for the material that arrives to and moves laterally along the horizontal boundaries to conduct enough heat so as to become convectively unstable. The convective instability theory predicts that the horizontal spacing between the upwellings and the downwellings is approximately equal to the layer depth $d$ (a bit larger at the onset of convection, but identically $d$ as $Ra$ becomes very large). Applying this theoretical prediction to the mantle is complicated by the features of the mantle materials that tend to break the symmetry of flow observed in the idealized Rayleigh–Bénard model. In particular, the strongly temperature-dependent viscosity means that the cold TBL has to spend more time near the surface, and thus travel further laterally before it is heavy enough to sink against its own viscous resistance, resulting in convection cells that are wider than the depth of the mantle (Weinstein & Christensen, 1991). Notably, if the degree of thermal stiffening puts convection in a stagnant lid regime, then the aspect ratio of the convective part of the layer approaches unity. In addition, mantle viscosity increases with depth due to the effect of pressure (Sammis, Smith, Schubert, & Yuen, 1977), and the resulting impediment to vertical flow also acts to increase the width of the convective cells (Christensen & Harder, 1991; Bunge, Richards, & Baumgartener, 1996). For Earth, the characteristic length scale of mantle convection, with most downwellings occurring in a torus along the planet’s circumference, and upwelling flow focused in the two regions on the either side of the torus (one beneath Africa and the other beneath the Pacific, where perhaps not coincidentally the LLSVPs reside)—or what is known as spherical harmonic degree-2 convection pattern—is indeed larger than the depth of the mantle. Another example, albeit less well constrained, is the proposed degree-1 convection pattern on Mars, in which a single upwelling in the southern hemisphere, broadly beneath the Tharsis Bulge, has been invoked to explain the gravity anomaly and the observed topographic dichotomy (Zhong & Zuber, 2001; Roberts & Zhong, 2006; Keller & Tackley, 2009). For a Martian mantle thickness that is between 0.4–0.6 of the planetary radius (depending on the assumed core composition and density, see Harder, 1998), a degree-1 pattern implies a characteristic convective length scale that is much larger than the mantle depth. Thus, the temperature- and depth-dependent viscosity may serve to explain the large aspect ratio of convection cells of mantle convection, compared to that predicted by the Rayleigh–Bénard system. The three large volcanic rises on Venus, which are arguably produced by deep-rooted mantle plumes (Stofan, Bindschadler, Head, & Parmentier, 1991; Smrekar & Stofan, 1999), may also indicate a low-degree convective pattern, although the remote measurements of gravity and topography have not been able to confirm such planform of convection for the Venusian mantle (Steinberger et al., 2010). Whether the mantle of Mercury is presently convecting is unclear, since there are no indications of volcanism taking place since about 3.5 Gyr ago (Namur & Charlier, 2017), and its predicted Rayleigh number is only modestly supercritical.

The presence of phase transitions in planetary mantles affects the convective pattern as well. For example, the Earth’s endothermic wadsleyite-to-perovskite transition at 660 km depth impedes the vertical convective flow, with its effect being stronger for the smaller scale structures, as has been shown by analytical and numerical studies (Bercovici et al., 1993; Tackley, Stevenson, Glatzmaier, & Schubert, 1993, 1994; Tackley, 1996). Thus, the 660 km transition for Earth (or 710 km for Venus, see Ito & Takahashi, 1989) acts as a low-pass filter, effectively increasing the characteristic length scale of convective flow. This phase transition on Mars is thought to be much deeper, at about 1910 km depth (Harder, 1998), which puts it very close to the Martian CMB. Furthermore, the presence of a low viscosity asthenosphere on Earth lowers the horizontal drag on convective flow and acts to increase the size of the convection cells (Lenardic, Richards, & Busse, 2006). The absence of an asthenosphere on Venus precludes the same effect (Kaula, 1990), but has been speculated to occur on Mars and further support the large scale (degree-1) convection pattern of the Martian mantle (Harder & Christensen, 1996; Harder, 2000; Zhong & Zuber, 2001). The mantle thickness on Mercury is arguably too small to experience any solid-state phase transitions.

The 3D convection pattern in fluids with temperature-dependent viscosity has also been observed in experiments (White, 1988) and numerical models (Ratcliff, Tackley, Schubert, & Zebib, 1997; Schubert et al., 2001) to exhibit upwellings in the form of cylindrical plumes at the center of a canopy of sheetlike downwellings; this is crudely applicable to mantle convection on Earth, with the sheetlike slabs forming the downwelling flow and the cylindrical upwelling plumes forming the ocean islands, manifested as intraplate volcanism at the surface. At more modest viscosity ratios, for example due to a smaller temperature contrast across the mantle, as may be the case for Mars and Venus, the upwelling flow may organize into linear structures, possibly explaining the bands of volcanic highlands observed on Venus or the chain of volcanoes in the Tharsis region on Mars (Ratcliff et al., 1997; Schubert et al., 2001; Breuer & Moore, 2015). While Earth’s mid-ocean ridges or spreading centers are also linear, they primarily involve shallow upwelling, best explained as being pulled passively by a distant force (ostensibly slabs), rather than involving a deep convective upwelling that pries them open. The features of mantle convection that are not readily explained by the classical Rayleigh–Bénard model mainly arise because of the peculiar flow properties of the rock that makes up the mantle, which we discuss next.

# How Can Rock Flow?

Viscous flow of the solid rock that makes up the mantle (also called “solid-state creep”) is governed by a number of complex processes, or rock rheologies, a full survey of which is beyond the scope of this essay (see Ranalli, 1995; Karato, 2008). However, a brief outline of the dominant mechanisms that accommodate mantle flow, namely diffusion and dislocation creep, can help illustrate why the mantle is not a simple fluid and explain some of its main flow features.

Deformation by solid-state creep depends on the statistical-mechanical probability of an atom in a crystal lattice to leave the potential well of its lattice site. The potential well itself is defined by electrostatic or chemical bonds inhibiting escape and Pauli-exclusion pressure preventing molecules squeezing too closely to each other. The mobility of atoms is determined by a Boltzman distribution, which measures the probability of having sufficient energy to overcome the lattice potential well barrier, which is often called the “activation energy” (or allowing instead for pressure variations, the activation enthalpy). This probability depends on the Arrhenius factor $e−Ea/RT$ where $Ea$ is the activation energy ($J/mol$), $R$ is the gas constant ($J/K/mol$) and $T$ is temperature; $RT$ represents the thermal excitation energy of the molecule in the well. As $T$ goes to infinity, the probability of escaping the well goes to 1, while as $T$ goes to 0 the probability of escape goes to 0.

When there is stress acting on the material, the potential wells of the crystal change shape, with the walls on the side of the well under compression getting steeper (squeezing molecules closer makes Coulomb’s attraction in the chemical bonds stronger), while the walls on the side of the well under tension become shallower (separating molecules weakens the bonds). Thus, the probability of atoms escaping their wells is higher in the direction of tension, with the lower activation barrier and away from compression, causing the medium to deform in the tensile direction by solid-state diffusion of atoms.

The accommodation of deformation by diffusion of atoms is known as diffusion creep. For the deformation to occur, the atoms have to diffuse through mineral grains or along the grain boundaries. The smaller the grains, the smaller the distance that an atom has to migrate before encountering a grain boundary, where the more disordered atomic arrangement (compared to that of the bulk of the grain) makes it easier for the atom to move. Thus, the diffusion creep viscosity depends on grain size, wherein the smaller the grains the weaker the material.

When the material deforms by dislocation creep, the strain is accommodated by the propagation of dislocations through the grain. Dislocations are linear lattice defects, where a whole row of atoms can be out of order, displaced, or missing. It requires more energy to displace a dislocation, compared to a single atom as in diffusion creep, but once a dislocation is mobilized, it accommodates strain more efficiently than diffusion creep (unless the grains are sufficiently small). As the material creeps, new dislocations are nucleated, displaced, or annihilated, so that the dislocation density of the material evolves and eventually reaches a steady state that is determined predominantly by stress. Due to the relatively large size of the dislocations, they can interact with each other through the induced long-ranging stress fields, which makes their velocity depend on dislocation density, which is itself stress dependent. Thus, both the dislocation density and velocity depend on stress, and this makes for a nonlinear dislocation creep rheology (i.e., viscosity depends on stress to some power).

The viscosities for diffusion and dislocation creep mechanisms can be written as

$Display mathematics$
(3)

where $A$ and $B$ are proportionality constants, $a$ is grain size, $σ$ is stress (in fact, since stress is a tensor, $σ2$ is the scalar second invariant of the stress tensor), and $m$ and $n$ are exponents, typical values of which are $2 and $3. The activation energies are different for diffusion and dislocation creep, with, for example, typical values for olivine (most abundant mineral in the upper mantle) being $Ea=375kJmol–1$ and $E′a=530kJmol−1$, respectively (Hirth & Kohlstedt, 2003); however, these values may be different for other minerals. Diffusion and dislocation creep are thought to occur independently of each other depending on stress and grain size: for a given stress, dislocation creep dominates for large grains and diffusion creep for small grains; likewise, for a given grain size, dislocation creep dominates for large stress and diffusion creep for small stress (Figure 8).

Figure 8. Deformation map of stress-temperature space, including different creep mechanisms. Modified from Bercovici et al. (2015).

The temperature-dependence of rheology enables thermal variations to induce many orders of magnitude changes in viscosity. Its effect is most profound in the lithosphere. For example, a plausible temperature drop of 1,500 K across the Martian lithosphere (Harder, 1998; Plesa & Breuer, 2014), assuming 500 and 2,000 K at the top (about 100 km depth) and bottom (about 300 km depth) of the lithosphere, respectively, would increase the dislocation creep viscosity by a factor of 1041, or the diffusion creep viscosity by a factor of 1029 (using the activation energy values for olivine from the previous paragraph for the lack of better mineralogical constraints). It is unsurprising, then, that the thermally stiffened part of the Martian lithosphere does not participate in the convective mantle flow, rendering it in the stagnant lid regime. A more modest thermal contrast across the Venusian lithosphere, with about 1,200 and 1,500 K at the top and bottom, respectively (assuming, crudely, the same thermal conditions as on Earth, but with a 400 K hotter surface temperature), yields an increase in the dislocation creep viscosity by a factor of 104, or the diffusion creep viscosity by a factor of 103. A modest thermal stiffening of the lithosphere on Venus makes it more pliable to deformation by mantle flow, possibly explaining the episodic recycling of its surface, as witnessed by its relatively young 500 Myr old surface.

Cooling from the Earth’s upper mantle temperature of 1,500 K to 800 K at the top of its lithosphere (about 10 km depth) would increase the dislocation creep viscosity by a factor of 1016, or the diffusion creep viscosity by a factor of 1011 (using the activation energy values for olivine from the previous paragraph). In this case, the viscous resistance to deform and subduct a slab would require a force that far exceeds what is available from buoyancy, thus disallowing convective motion. However, Earth’s surface is clearly deforming, as is evidenced in plate tectonics, and so some other physical mechanism must exist that induces rheological weakening and allows for the lithosphere to deform. Dislocation creep allows for moderate softening as stress increases. However, for the above example for a typical lithospheric temperature drop, an unrealistic increase in stress by a factor of 108 would be required to offset thermal stiffening. Diffusion creep potentially allows for significant softening if the grain size is reduced, and for the above example a grain size reduction by a factor of 10–3 would suffice to mobilize a plate and/or allow a slab to sink. Geological examples of grain size reduction in the lithosphere by three and potentially more orders of magnitude in strongly deformed regions abound (more on this in section “Forming Tectonic Plates”). Understanding the physical mechanisms responsible for rheological weakening in the lithosphere that offsets therHmal stiffening and allows for platelike deformation is an active area of research.

# Forming Tectonic Plates

The plate-like character of the mantle’s cold thermal boundary layer, or the lithosphere, can be described as large areas of strong barely deforming plate interiors, separated by weak and narrow plate boundaries that undergo intense deformation (with a few exceptions, such as broad diffuse plate boundaries, for example in the Indian Ocean; see Gordon, DeMets, & Royer, 1998). Understanding the physical mechanisms responsible for such plate-like motion, which require some form of rheological weakening and strain localization in the lithosphere, is one of the biggest questions in the geodynamics (see Bercovici et al., 2015, for a recent review). The proposed solutions include complex deformational behavior, such as plastic, brittle, or grain-size dependent rheologies.

Brittle deformation is one of the most extreme cases of strain localization, where the material breaks along narrow faults that remain weak even after the deformation ceases. However, brittle rheology is not active for most of the depth of oceanic lithosphere, giving way to semiductile and eventually ductile behavior at depths greater than about 10 km (Kohlstedt, Evans, & Mackwell, 1995).

Another candidate for shear localization in the lithosphere is viscoplasticity, which dictates that the material acts as a strong viscous fluid at low stresses. But once the stress exceeds a yield stress, the viscosity drops; or in extreme cases, the resistance to flow remains small no matter the rate of deformation. Viscoplastic rheologies can be successful at generating plate-like motion (Moresi & Solomatov, 1998; Trompert & Hansen, 1998; Tackley, 2000b; van Heck & Tackley, 2008; Foley & Becker, 2009) but are difficult to reconcile with other important observations. For example, while plastic yielding is known to occur in rocks, laboratory experiments on rock deformation infer a much higher yield stress than what is used in geodynamic models. Moreover, weak zones formed as a result of plastic yielding are only active as long as the deformation is ongoing and vanish (or regain their strength) once deformation ceases. In contrast, tectonic plate boundaries are known to be enduring features, which remain weak for some time even without being deformed and can be transported with the material and get reactivated at a later time (Toth & Gurnis, 1998; Gurnis, Zhong, & Toth, 2000). In fact, dormant plate boundaries (e.g., sutures and inactive fracture zones) can retain their deformation memory in the form of intrinsic weak zones over timescales that are much longer than the typical convective mantle overturn time. In other words, the deformation-history dependent strength of the lithosphere cannot be explained with an instantaneous-type viscoplastic rheology.

For strain localization to occur, there needs to be a positive feedback mechanism in which deformation itself causes weakening, the weak zones subsequently concentrate deformation, which causes further weakening, and so on. One example of such dynamic self-weakening is the coupling of temperature-dependent viscosity and viscous heating: deformation causes frictional heating, which makes the material warmer and weaker and thus more readily deformed, causing the deformation to focus on the weak zone, leading to more heating and weakening, and so forth. Because thermal anomalies take time to dissipate away, the warm weak zones can be retained for some time and allow for some history dependence of the material strength. However, for lithospheric and mantle material, thermal diffusion is relatively fast, and the memory of induced weakness only lasts a few million years, which is less than what is needed to explain long-lived plate boundaries. There are other limitations for the thermal self-softening mechanism in explaining the localized lithospheric deformation. For example, the diffusive nature of thermal anomalies only allows for weak localization and toroidal motion. While not sufficient on its own, the thermal self-softening might still assist in strain localization (Kameyama, Yuen, & Fujimoto, 1997; Foley, 2018).

Fluids in the lithosphere, such as water, in the form of pores or hydrous mineral phases, can serve as long-lived weakening agents. In this case, weakening can occur due to the reduction of friction through pore pressure, or through lubrication of plate boundaries by introduction of sediments at subduction zones or serpentinization along faults. The longevity of the potential weak zones over geological time scales is ensured by the slow chemical diffusivity of hydrogen in minerals, as opposed to, for example, much faster thermal diffusion rates. One of the main difficulties with invoking water for lithospheric-scale weakening is that its effects are likely to be limited to shallow depths. Specifically, the frictional reduction by pore pressure aids brittle failure and frictional sliding, which are only relevant in the top roughly 10–20 km depth. Ingesting water to greater depths, say to the bottom of a plate boundary at about 100 km depth, would require pushing the fluid against a large lithospheric pressure gradient and then preventing it from escaping (e.g., by invoking negligible permeabilities). There are mechanisms, such as thermal cracking (Korenaga, 2007) or creating voids and microcracks through deformation damage (Bercovici, 1998; Bercovici & Ricard, 2003; Landuyt & Bercovici, 2009b) that can potentially allow for the water to penetrate and serpentinize the uppermost few tens of kilometers of the plate. However, there are no known mechanisms that would allow it to weaken the deepest, and potentially strongest, portion of the lithosphere.

An important clue to understanding the physics of lithospheric weakening, and thereby the formation of tectonic plate boundaries, comes from the observed microstructure of the deformed rocks, specifically the mineral grain size and the density of intragranular defects. The exposed plate boundaries at the Earth’s surface (i.e., in ophiolites and lithospheric shear zones), as well as samples from rock deformation experiments, show that parts of the rock that have undergone extreme deformation exhibit a substantial degree of recrystallization and grain-size reduction. Grain-size evolution, including the processes of grain growth by diffusion and grain shrinkage by dynamic recrystallization, is governed by atomic scale processes, the thermodynamics of which is described by grain damage theory (Bercovici & Ricard, 2005; Austin & Evans, 2007; Ricard & Bercovici, 2009; Rozel, Ricard, & Bercovici, 2011). Grain damage theory postulates that while most of the deformational work is dissipated as heat and irrecoverable viscous deformation, a small fraction of work goes toward recoverable energy, which is stored in the form of grain defects and new grain boundary area (i.e., by splitting the same volume of material into a larger number of grains). Grain damage can induce shear-localizing feedback through the interaction of grain-size sensitive rheology (such as diffusion creep or grain-boundary sliding (Hirth & Kohlstedt, 2003) and grain-size reduction via dynamic recrystallization (Karato, Toriumi, & Fuji, 1980; Derby & Ashby, 1987): smaller grain size makes the material weaker, which thus deforms more easily, increasing the amount of deformational work available to drive recrystallization and grain damage, reducing the grain size further, etc. (Braun et al., 1999; Kameyama et al., 1997; Bercovici & Ricard, 2005; Ricard & Bercovici, 2009; Rozel et al., 2011). In monomineralic materials, recrystallization takes place so long as the material deforms by dislocation creep, which dominates at high stresses and large grain sizes. Once the grains shrink to sizes at which the grain-size dependent rheologies set in, recrystallization process becomes limited, and so does the self-weakening localization feedback (De Bresser, ter Heege, & Spiers, 2001). However, lithospheric rocks are polymineralic (with olivine and pyroxene being the most abundant minerals, or phases), and the grain-size evolution of each phase is strongly affected by the presence of the other. First of all, the rate of grain coarsening, which occurs independently of whether the material is deforming or not and generally makes the material stronger, is significantly impeded by the secondary phase; this happens because grains grow by atomic diffusion, and it is difficult to exchange atoms between grains that are separated by another mineral. Thus, the grain growth becomes effectively blocked by the secondary phase, an effect known as “Zener pinning.” Second, as the grains of each phase deform to accommodate strain, be it in diffusion or dislocation creep, they are forced to move around the grains of the other phase, resulting in stronger distortion of the grain boundaries than if it was a single phase material; this increases the internal energy of the grain and lowers the amount of energy needed for it to recrystallize and split into smaller grains. Thus, the presence of the secondary phase facilitates grain damage and induces grain-size reduction even when the material deforms in the grain-size sensitive diffusion creep regime, thereby enabling self-weakening feedback by grain damage (Bercovici & Ricard, 2012). Indeed, the geological examples of peridotitic mylonites and ultramylonites, where large strains correlate with extreme grain-size reduction and have been observed at all types of plate boundaries, typically feature polymineralic rocks, often embedded in a matrix of coarse-grained single-phase material (Warren & Hirth, 2006; Herwegh, Linckens, Ebert, Berger, & Brodhag, 2011; Linckens, Herwegh, Müntener, & Mercolli, 2011; Linckens, Herwegh, & Müntener, 2015). Moreover, the slowing of the grain growth due to pinning in polymineralic materials promotes longevity of the damaged weak zones even after the deformation ceases, thus allowing for long-lived dormant plate boundaries (Bercovici & Ricard, 2014).

Geodynamic models featuring damage rheology have successfully reproduced some of the plate-like features of the lithospheric motion, including toroidal motion, strongly localized plate boundaries and observed microstructure (Bercovici & Ricard, 2005; Landuyt, Bercovici, & Ricard, 2008; Landuyt & Bercovici, 2009b; Foley, Bercovici, & Landyut, 2012; Bercovici & Ricard, 2013, 2014; Foley & Bercovici, 2014; Bercovici & Ricard, 2016; Bercovici & Mulyukova, 2018; Mulyukova & Bercovici, 2017, 2018) generated at stresses and temperatures typical for tectonic plates and is a promising venue for further testing in global mantle convection models. While grain damage and pinning is potentially an important plate generation mechanism (especially in the deepest cold and ductile portion of the lithosphere), it is likely that the effects of brittle deformation, lubrication by fluids, and potentially other processes play an important role at shallower depths (Lenardic & Kaula, 1994, 1996; Korenaga, 2007; Bercovici et al., 2015).

# Mantle Convection on Early Earth

Solid-state mantle convection likely started a few tens or hundreds of millions of years after the Earth experienced its last major impact, which happened about 4.5 Gyr ago and led to the formation of the moon (Canup & Asphaug, 2001). The energy released by the impact likely left the planet largely molten (although it could have been molten before the impact as well), a part of the Earth’s history referred to as magma ocean (Elkins-Tanton, 2008; Solomatov, 2015). It would take about 10 Myr or more (depending on the model) for nearly all of the magma ocean to crystallize, differentiate, and for solid-state mantle convection to set in (see Foley, Bercovici, & Elkins-Tanton, 2014, and references therein). Understanding the nature of this early convective flow (i.e., its heat transport efficiency and its ability to mobilize and deform the surface) are crucial for reconstructing the Earth’s dynamic history and evolution, as well as for interpreting its present state.

The geological record becomes increasingly sparse in the Earth’s deep past. However, a number of safe assumptions can be made about the early physical state of the planet based on some theoretical considerations. First of all, Earth’s size, or mass, has probably remained more or less the same after the last giant moon-forming impact. Second, the Earth’s interior has been getting colder for a significant portion of its history, although the rate of cooling of its different layers (core, mantle, and evolving crust) may vary, depending on their concentrations of heat-producing elements and on their ability to exchange heat with one another (e.g., thermal conduction across the CMB, or flow of cold downwellings and hot upwellings across the transition zone). The thermal history of the mantle is governed by the competition between internal heating by radioactive elements and surface heat loss by convection. The main uncertainty of the former is in the abundances of radiogenic elements in the mantle; while their half-lives are known, their initial concentration, and thus their net contribution, is unknown. By far the largest uncertainty about mantle thermal history, however, comes from the assumed rate of convective cooling through time and in particular the initiation and rate of subduction, which is the dominant mechanism by which the mantle cools (van Hunen & van den Berg, 2008; van Hunen & Moyen, 2012). Cooling of the mantle for at least the last 3 Gyr is constrained by the measured temperatures of the mantle source that formed lavas at midocean ridges, which appear to get progressively colder the younger they are: from 1500–1600 °C 2.5–3 Gyr ago to 1350 °C today (Herzberg, Condie, & Korenaga, 2010). In addition, the existence of the inner core, which is the product of a cooling and crystallizing liquid outer core, implies that the Earth’s deep interior is cooling through time.

The rate at which heat can escape from mantle to space depends on the temperature drop across the Earth’s top thermal boundary layer, and thus on surface temperature, which in turn is controlled by the thermally insulating effect of the atmosphere (the greenhouse effect), as well as the amount of incident solar energy. The greenhouse effect helps to keep the temperature of the atmosphere relatively stable, and thus one can assume that for most of the Earth’s history the temperature difference across the lithosphere has been controlled by the mantles internal temperature (Sleep & Zahnle, 2001; Lenardic, Jellinek, & Moresi, 2008).

Another important difference between the young and the modern Earth is the presence and volume of the continents. Continents have an insulating effect, which impedes surface heat flow due to their large thickness (compared to the oceanic plates) and a higher concentration of radiogenic elements. Heat-flow measurements on modern Earth support this notion: after correcting for the radioactive heating, the mantle heat flow is about one order of magnitude lower at the surface of the continents than for ocean seafloor (Stein & Stein, 1992; Jaupart et al., 2015, and references therein). The role of continents as thermal insulators, and the resulting anomalously hot and buoyant mantle beneath them, has been invoked as a mechanism for driving continental dispersal and the subsequent supercontinent reorganization—a key part of the Wilson cycle (Gurnis, 1988; Rolf et al., 2012). However, whether the thermal insulation effect is sufficient to move the continents around remains subject to debate (Lenardic, Moresi, Jellinek, & Manga, 2005, Lenardic et al., 2011; Heron & Lowman, 2011; Bercovici & Long, 2014]. The junction between the strong continental and the much weaker oceanic lithospheres helps to localize stresses there and may serve as a zone of heterogeneity and weakness where new plate boundaries can form (Kemp & Stevenson, 1996; Schubert & Zhang, 1997; Regenauer-Lieb, Yuen, & Branlund, 2001; Rolf & Tackley, 2011; Mulyukova & Bercovici, 2018).

Modeling mantle dynamics on early Earth entails understanding mantle convection at higher internal temperatures. Using the theoretical framework outlined, we can characterize mantle dynamics through time using the Rayleigh number, which describes the vigor of convection and the thermally induced viscosity difference across the lithosphere, which presents the biggest impediment to convective flow through stiffening of the cold thermal boundary layer.

It can be speculated that a hotter mantle in the past might have been convecting more vigorously (or at a higher Rayleigh number) due to the lower viscosity of mantle rocks, which are extremely sensitive to temperature. Some mathematical formulations of temperature-dependence of viscosity (e.g., the Frank–Kamenetskii parametrization) suggest that for a given temperature jump, the thermally induced viscosity difference is smaller at higher temperatures. Thus, a weaker mantle and lithosphere, compared to those on modern Earth, would make convection and plate tectonics more efficient in the past. Using some parameterization of this positive relationship between mantle temperature and convective heat flow (i.e., such as the canonical Nusselt number–Rayleigh number relationship presented in the section “Basics of Thermal Convection”), together with the rate of internal heating for some plausible abundances of radioactive elements, it is possible to extrapolate the internal temperature of the mantle back in time from present-day value. Depending on the details of this parametrization, such as the modern value assumed for the ratio of internal heating to convective heat flux, called Urey ratio (see Christensen, 1985), there is a range of possible thermal evolution models (Korenaga, 2006; Silver & Behn, 2008). The possible scenarios include the paradoxical thermal catastrophe case (Christensen, 1985), obtained for a low value of present-day Urey ratio (about 0.3), where the temperature of the mantle exceeds values that are well beyond uncertainty (mantle temperature quickly rises and diverges toward unrealistically high values before reaching 2 Ga). To avoid the thermal catastrophe, one could assume a higher value of modern Urey ratio, for example a value of 0.7 results in a reasonable thermal evolution model. However, such high Urey ratio implies a much higher concentration of radioactive elements in the mantle, which is difficult to reconcile with the range provided by the cosmogenic analysis. An alternative solution is to assume that the mantle heat flow is less sensitive to the temperature of the interior than what is predicted by the Rayleigh–Bénard model (i.e., $Nu~Rab$, where in simple Rayleigh–Bénard $b=1/3$, but $b<1/3$ for less temperature-dependent heat flow). In particular, factors other than temperature may play a role in the complex rheology of the lithosphere may need to be taken into account (Korenaga, 2006, 2007, 2013).

The mantle’s cold top thermal boundary layer differs from the rest of the mantle not just by its conductive thermal profile but also by its composition, since it undergoes melting-assisted differentiation (i.e., segregation by fractional melting and melt-migration, which separates the crust and the depleted lithosphere). Melting at higher temperatures leads to a more dehydrated lithosphere. It is even more difficult for a lithosphere that is drier, and thus stiffer, to founder under its own negative buoyancy (Conrad & Hager, 2001; Korenaga, 2006). Moreover, a higher degree of melting produces more of the chemically buoyant basaltic crust, which further reduces the ability of the lithosphere to sink (Davies, 2009). Thus, plate tectonics might have been less likely to occur on a hotter, younger Earth. If the lithosphere cannot subduct, mantle convection may proceed in a different regime, in which heat transport from the interior to the surface is restricted to conduction across a thick immobile layer (e.g., stagnant lid mode, Solomatov & Moresi, 1997) and volcanism (e.g., heat pipe mode, Spohn, 1991; Moore et al., 2017; Lourenço, Rozel, Gerya, & Tackley, 2018) and is thus relatively inefficient; this would mean that the rate of planetary cooling was slower in the past. How and when subduction, and more generally plate tectonics, started is a question of formidable importance in the Earth evolution models, but the answer is obscured by our currently limited understanding of the physical mechanisms responsible for the formation of plate boundaries, as well as the paucity of geological samples and data in the Earth’s deep history, which we discuss next.

There are no rock samples preserved from the first few hundred million years after the freezing of the magma ocean; the only geological data available to elucidate this early stage of the Earth’s history are mineral inclusions in zircons (Mojzsis, Harrison, & Pidgeon, 2001; Valley, Peck, King, & Wilde, 2002). Geochemical analysis of this sparse data set shows evidence of melting sediments and granite formation, which may imply that subduction may have already operated at this early stage (Hopkins, Harrison, & Manning, 2010). However, application of the extremely sparse zircons data set (in terms of their temporal and spatial distribution) to infer the global tectonic regime bears significant uncertainty with it (Korenaga, 2013).

One of the key features of plate tectonics is the continuous production and destruction of the oceanic lithosphere. Thus, the geological indicators of a mobilized lithosphere have to come from the more indirect markers, expected to be left behind on the fraction of the Earth’s surface that is less prone to destruction (Condie & Kröner, 2008). For example, when the sea floor is consumed by subduction, the continents on either side of it collide and form synchronous orogens, which can then be preserved even after the continents split up again. Earth’s surface appears to have gone through several episodes of continental assembly and dispersal, known as the Wilson cycle, in some cases forming supercontinents, where virtually all of the continents come together. The oldest supercontinent is thought to be Kenorland, which assembled about 2.7 Gyr ago. The need to close multiple oceans in order to form a supercontinent provides a compelling evidence that global-scale plate tectonics was already occurring at that time.

Furthermore, there exist examples of rocks that have arguably formed in geological settings characteristic of plate tectonics and that are older than 3 Gyr. Examples include 3-Gyr-old xenoliths from Kaapvaal craton, whose oxygen isotopic signature show that they may originate from subducted oceanic crust; a 3.6-Gyr-old suture zone and a 3.8-Gyr-old accretionary complex, both in Greenland, are some of the oldest geological structures indicative of convergent tectonics. However, it remains controversial as to whether the processes that formed these rocks are representative of the global state of the planetary surface; in addition, there exist other explanations for how to form them, which do not involve tectonic processes, adding to the uncertainty of interpreting these samples (Stern, 2004, 2005; Condie & Kröner, 2008; Palin & White, 2016; Condie, 2018).

The absence of rock samples that are expected to form if tectonics is widespread has been invoked as evidence for the absence of plate tectonics. For example, the lack of evidence for high-pressure and ultra-high pressure metamorphism earlier than about 1 Gyr, such as blueschists and eclogites, which are expected to form in subduction zone environments, has been suggested to indicate that subduction did not start until about 1 Gyr ago (Stern, 2005). However, other studies caution that the absence of preserved high-pressure rocks at the surface does not preclude the operation of subduction on earlier Earth, it may instead indicate that the processes required for the exhumation of previously subducted rocks were limited, or that the high-pressure phases formed upon subduction of the hotter, thicker, and more magnesium-rich oceanic lithosphere would be different than, for example, the blueschist-facies typically formed in modern-day subduction zones (Brown, 2006; Korenaga, 2013; Palin & White, 2016).

The initiation of subduction remains an extremely challenging issue in geodynamics today (Stern, 2004; Condie & Kröner, 2008; Wada & King, 2015). The physical mechanisms that allow for the lithosphere to overcome its thermal stiffening and spontaneously initiate subduction are hotly debated, with the proposed models including weakening by rifting (Kemp & Stevenson, 1996; Schubert & Zhang, 1997), sediment loading and water injection (Regenauer-Lieb et al., 2001], re-activation of preexisting fault zones (Toth & Gurnis, 1998; Hall, Gurnis, Sdrolias, Lavier, & Mueller, 2003), or the weak zones formed by accumulation of lithospheric damage from proto-subduction (Bercovici & Ricard, 2014), collapse of passive margins (e.g., Stern, 2004; Mulyukova & Bercovici, 2018) or at an active transform plate boundary (Casey & Dewey, 1984) and plume-induced subduction initiation (Gerya, Stern, Baes, Sobolev, & Whattam, 2015). A better understanding of the rock physics, as well as further interrogation of the geological, geochemical, and petrological record of the early Earth dynamics continue to be fruitful areas of research.

# Mantle Convection on Other Terrestrial Planets

The rocky planets of the solar system exhibit a large variation in their observed features, including size, gravity anomalies, topography, magnetic field, atmosphere, distance from the sun, all of which affect their interior dynamics. The heat sources available to drive mantle flow and convective cooling (with the possible exception of Mercury, whose mantle may cool by conduction), including the primordial as well as the radioactive heat sources, are finite and are not being replenished. This is why planetary activity driven by mantle convection, such as volcanism and crust production, becomes weaker and eventually dies out with time. The rate at which a planet cools is determined by its initial heat budget, as well as the efficiency at which it can release heat. For example, smaller planets have less primordial heat, as they have experienced fewer impacts upon accretion and the differentiation of their metallic cores had a smaller gravitational energy release associated with it. As for the heat transport out of the planetary interiors, plate tectonics is the most efficient mechanism (as on Earth), followed by the sluggish and stagnant lid convection regimes (for Venus and Mars), and finally by the conductive cooling (possibly for Mercury). In our solar system, Earth is the largest terrestrial body, with the largest amount of heat to dissipate away, and whose mantle is, at least at present, convectively transporting heat most efficiently. Importantly, none of the known terrestrial planets, besides Earth, appear to have surface rejuvenation by plate tectonics.

## Venus

Venus is arguably the most similar to our own planet, at least in terms of its size (which determines internal depth, or pressure, structure) and distance from the Sun (which determines the amount of surface heating by solar radiation). The Venusian surface appears to be young, dry, and wrapped in a thick, dense, and opaque atmosphere, which makes remote observations particularly challenging. At about 460 °C, the surface of Venus is hundreds of degrees hotter than Earth’s, which some studies have attributed to the runaway greenhouse effect and the eventual loss of water (Kasting, 1988): Liquid water is an important player in the geological carbon cycle, which on Earth drew down most of the carbon into carbonate rocks and allows for a temperate climate, while on Venus the dry conditions fail to allow the surface to extract the greenhouse gases from the atmosphere, thus keeping the surface hot (Driscoll & Bercovici, 2013). The Venusian mantle temperature is likely higher than that on Earth, because it appears to be in a less efficient convection regime (i.e., stagnant or mobile lid regime; see Solomatov & Moresi, 1997; Moresi & Solomatov, 1998); along with a hotter surface, this would make the heat flow out of the interior slower.

The relatively young age of the crust on Venus, inferred to be about 500 Myr old by crater counting (Strom, Schaber, & Dawson, 1994), points to global surface rejuvenation events, presumably by extensive volcanism or lithospheric foundering (Turcotte, 1993; Turcotte, Morein, Roberts, & Malamud, 1999). Depending on the chosen thermal evolution model, including the rate at which the cooled surface can be recycled into the mantle, the mantle temperature of Venus might be about 200 °C hotter than that of Earth (Lenardic et al., 2008; Landuyt & Bercovici, 2009a). A hotter surface and possibly interior makes Venus a popular analogue of the early Earth, and some of the reasoning of early Earth geodynamics can be applied to understand the dynamics of Venus and vice versa. For example, it has been speculated that the hotter conditions on Venus is the reason why it does not have plate tectonics. One of the arguments is that a hotter surface, but a similar mantle temperature on Venus compared to Earth, reduces the temperature contrast across the Venusian lithosphere, and thus the amount of negative buoyancy available to deform and potentially mobilize it (Lenardic et al., 2008). Another argument is that if grain damage is responsible for the formation of plate boundaries on Earth, which requires a high enough ratio between the rates of grain growth and grain size reduction, then the hotter surface temperature on Venus would make the grain growth faster, potentially inhibiting the formation of fine-grained localized shear zones, or zones of weakness where new plate boundaries can form (Landuyt & Bercovici, 2009a; Foley et al., 2012; Bercovici & Ricard, 2014). A potentially important difference between Earth and Venus is that, in spite of their similar size, Venus appears to not have a low-viscosity upper mantle, or asthenosphere; this has been inferred by numerical modeling studies of mantle convection on Venus, constrained by the observed surface topography, volcanism, and geoid (Huang et al., 2013). The convective stress acting on the Venusian lithosphere is thus presumably smaller, compared to that on Earth (Höink, Lenardic, & Richards, 2012). Furthermore, it has been argued that the Venusian lithosphere and mantle lack water, which is an important weakening agent, and are therefore stiffer than the Earth’s (Nimmo & McKenzie, 1998; Hirth & Kohlstedt, 1996), making the mobilization of the Venusian surface even more difficult. Strictly speaking, the observational evidence for dry conditions on Venus only exists for its atmosphere and not for its interior. However, water is an incompatible element and therefore gets preferentially extracted from the interior in the process of melting and volcanism, and there is no obvious mechanism on Venus by which water would be returned to the mantle (i.e., as is done by subduction on Earth). Thus, even if the mantles of Venus and Earth started off with similar compositions, the water may have been lost from the Venusian mantle, first to its surface, then to its atmosphere, and inevitably to space (Donahue & Hodges, 1992; Nimmo & McKenzie, 1998). These and other structural differences between Earth (or early Earth) and Venus prompt some caution in comparing the two planets.

## Mars

Mars is the next largest terrestrial body in the Solar System after Earth and Venus, although at its 3,390 km radius is still much smaller than the other two and is thus likely to cool much faster to space. In addition, the possible presence of water in the Martian mantle (within the range of 73 to 290 ppm $H2O$, which is comparable to that of Earth; see McCubbin, Hauri, Elardo, Vander Kaaden, Wang, & Shearer, 2012), as well as its high iron content (Martian olivines contain $FeO~18wt%$, compared to Earth’s $FeO~8wt%$; see Zhao, Zimmerman, & Kohlstedt, 2009), act to lower the mantle viscosity, facilitating convection and efficient heat transport. The rapid cooling of Mars constrains the time window for when its interior is hot enough to induce melting and to produce crust. Indeed, it appears that most of the Martian crust formed early in its history—in the first few hundred million years after accretion (Nimmo & Tanaka, 2005). At present, Mars is likely to have a colder and less active interior compared to Earth, possibly explaining the absence of an internal magnetic field on Mars (Acuna et al., 1998). The strongly magnetized Martian crust, however, suggests that the surface and interior of Mars may have undergone extensive activity in the past, in particular within the first billion years after solar system formation. Mars’s surface may have deformed similarly to plate tectonics on Earth, according to maps of Martian crustal remanent magnetization obtained from spacecraft missions: the quasi-parallel magnetic lines of alternating magnetic polarity (Connerney et al., 1999), as well as offsets in magnetic field contours that identify transform faults (Connerney et al., 2005), are similar to the magnetic features associated with sea-floor spreading on Earth. In addition, geological structures interpreted from the satellite data, such as rifting and strike-slip faulting, may also be indicative of plate tectonic–like surface deformation (Yin, 2012).

Another curious feature of the Mars’s surface is its crustal dichotomy, with a 20–30 km thick primordial crust in its northern hemisphere (Grott et al., 2013) and a much thicker, 30–80 km, and presumably younger crust in its southern hemisphere (Solomon et al., 2005), with the surface age difference of about one billion years between the two hemispheres. One of the proposed explanations for the Martian crustal dichotomy posits that it reflects the underlying mantle convection pattern. Numerical simulations of Martian interior dynamics obtain mantle flow pattern with a single hot upwelling on one hemisphere and thus predict enhanced crustal production in the region over mantle upwelling (Harder & Christensen, 1996; Harder, 2000; Keller & Tackley, 2009). The presence of extensive low-conducting crustal layer on Mars is thought to have thermally insulated the mantle so as to suppress its cooling rate and to prolong its history of volcanic activity (Plesa & Breuer, 2014). The high resolution images of the Martian surface reveal that it has been geologically active, albeit at a declining rate, for at least the last 3.8 billion years, with records of volcanism on the Tharsis edifices as young as two million years (Neukum et al., 2004). Such recent volcanic activity on Mars may suggest that its volcanoes may even erupt in the future and that its mantle is not yet geodynamically dead.

## Mercury

Mercury is the smallest rocky planet in our solar system (about 2,440 km in radius) and the one that is the closest to the Sun. The strikingly large mean density of Mercury implies that it is much more iron rich than the other terrestrial planets, or has the largest ratio of metallic core to silicate mantle, with the size of the core inferred to be over 2,000 km in radius (Harder & Schubert, 2001). The remaining few hundred kilometers thick (400 km typically used in modeling studies) mantle shell is likely convecting in the stagnant lid regime for seemingly all of its geologically recorded past, as indicated by the extremely well-preserved cratering history on its surface (Watters et al., 2016). A prolonged slow cooling of the planet’s interior appears to have left lobate scarps on Mercury’s surface (Watters, Robinson, & Cook, 1998), interpreted to be thrust faults that record the ancient pattern of mantle convection, in addition to global contraction (King, 2008). Most recent observations of the scarps cross-cutting the impact craters indicate that they are relatively young, less than 50 Myr, implying that Mercury is probably still tectonically active (Watters et al., 2016). The mineralogy of Mercury’s volcanic crust, inferred from the geochemical data from recent space missions, records the history of its cooling mantle: the fractional melting by which the crust was produced occurred at shallower depth and lower temperature with time, from about 1,900 K and 360 km 4.2 Gyr ago, to about 1,700 K and 160 km 3.5 Gyr ago, with the magmatic activity terminating about 3.5 Gyr ago as the mantle became too cold to melt (Spohn, 1991; Namur & Charlier, 2017). Although Mercury’s mantle is not generating any volcanic activity at present, its cooling must nonetheless be very efficient, since it is able to transport heat away from the core at a high enough rate to support the internally generated dynamo (Ness et al., 1974; Connerney & Ness, 1988). Numerical models of Mercury’s internal dynamics havse been able to reconcile its magnetic and thermochemical evolution, with the possible planforms of mantle convection ranging from numerous small-scale cells to a single upwelling and including scenarios where the Mercurian mantle convection ceases altogether after 3–4 Gyr (Heimpel, Aurnou, Al-Shamali, & Perez, 2005; Tosi, Grott, Plesa, & Breuer, 2013).

Comparing the observations made on different terrestrial planets is a powerful tool for teasing out the general physics that govern planetary evolution. Of course, the currently available data set is relatively sparse, but it is growing with the increased number of space missions. In addition, with the advent of extra-solar planet discovery, there is hope of finding other planets with plate-like mantle dynamics, which would elucidate the peculiar tectonic regime of our own planet (e.g., Valencia, O’Connell, & Sasselov, 2007; Sotin, Jackson, & Seager, 2010; Korenaga, 2010; van Heck & Tackley, 2011; Foley et al., 2012).

# Conclusion

Mantle convection governs the thermal and chemical evolution of the Earth and other terrestrial planets in our solar system, dictating the dynamics of planetary interiors and driving geological motions at the surface. The ultimate driver for convective mantle flow is that planets cool to space, releasing the heat acquired in the course of their accretion, as well as the radiogenic internal heating. Thermal convection theory itself is a well-established physical theory rooted in classical fluid dynamics and thermodynamics. The theoretical predictions of flow velocities, establishment of thermal boundary layers, and the convective pattern of slab-like downwellings and plume-like upwellings go far in describing circulation and structure in the Earth’s mantle. However, the solid rock that makes up the mantle flows and deforms in ways not easily captured by the properties of simple fluids on which classical convection theory is based. For instance, the manifestation of mantle convection as discrete tectonic plates at the surface, with strong and broad plate interiors separated by weak and narrow plate boundaries, remains one of the most puzzling phenomena in geoscience. Much of the progress in explaining how and why the Earth’s mantle convects in the form of plate tectonics, unlike any other known terrestrial planet, comes from the studies of the rheologies of rocks that make up planetary mantles, including their dependence on temperature, stress, chemistry, and mineral grain size. Understanding the physics that govern the geodynamics of modern Earth is essential to reconstructing the thermal and chemical history of our planet. For example, it remains problematic to explain how the Earth is stirred by deep subducting slabs but still appears unmixed when producing melts at mid-ocean ridges and ocean islands. To unravel the history of mantle stirring, a better understanding of melting, chemical segregation, and mixing in the mantle is needed.

The theory of mantle convection successfully explains many of the key features of planetary interior and surface dynamics, unifying the geoscientific observations with the fundamental physical and fluid mechanical theories. However, studies of mantle convection have also opened up many new questions and mysteries about the workings of the Earth and other rocky planets to be addressed by future generations of Earth and planetary scientists.

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