Planetary Mantles Research Articles

Recycling the lid: Effects of subduction and stirring on boundary layer dynamics in bottom-heated planetary mantle convection

[1] The subduction and stirring of cold oceanic lithosphere governs the thermal regime of the Earth's mantle. Whether upwelling mantle plumes are transient isoviscous thermals or long-lived low viscosity plumes depends on the magnitude of the resulting temperature variations in the thermal boundary layer at the base of the mantle. Previous laboratory experiments suggest that low viscosity “Earth-like” plumes occur where the hot thermal boundary layer (TBL) viscosity ratio, λh > O(10). Here, the results from two-dimensional numerical simulations, in which subduction is either forced from above or allowed to arise naturally show that: (1) a morphologic transition from upwellings in the form of isoviscous thermals to cavity plumes occurs where λh ≥ O(10) and is accompanied by a qualitative change in the temporal and spatial dynamics of the hot TBL; (2) this transition corresponds to a condition in which the velocity boundary layer (VBL) is concentrated within the basal part of the TBL for no- and free-slip boundaries; and (3) a regime in which λh ≥ O(10) can only occur if the total viscosity ratio across the convecting system, λT ≥ O(102). Our results support a recent conjecture that low viscosity mantle plumes in the Earth are a consequence of strong mantle cooling by plate tectonics. Moreover, Earth-like plume models may be inappropriate for explaining the origin of surface features on one plate planets such as Mars or Venus.

Temporal variations in the convective style of planetary mantles

Investigations of mantle convection with temperature- and strain-rate-dependent viscosity have shown the existence of fundamentally different convective styles: By varying e.g. the Rayleigh number, the viscosity contrast or the strain-rate dependency of viscosity, the planform of convection in the asymptotic stationary state changes from the so-called stagnant lid regime to an episodic behaviour and further to a state characterised by a permanently mobilised surface. Our studies suggest that this transition may not only be induced by a change of parameters but also occurs temporally for fixed parameters. We have in fact observed convective systems in the stagnant lid regime that show isolated events of surface mobilisation occurring out of a thermally equilibrated state. We use a 3D numerical mantle convection model to investigate mantle convection and surface dynamics as a coupled fluid dynamical system. Our studies focus on the existence of a transitional regime in which temporal variations between the stagnant lid and the episodic regime occur. We were able to deduce a mobilisation criterion that describes the stability of the stagnant surface, thus allowing for a quantitative analysis of the transition to a (temporarily) mobilised surface. This criterion is also suitable to predict the occurrence of surface mobilisation events.

An experimental study of the oxidation state of vanadium in spinel and basaltic melt with implications for the origin of planetary basalt

The distribution of V in magmatic rocks is controlled primarily by spinel stability. Extensive previous experimental work at oxidized conditions on doped (V-rich) compositions has led to the recognition of the importance of temperature, oxygen fugacity, and spinel composition, but also left ambiguity with respect to the relative importance of these variables in controlling DVspinel/melt. One major uncertainty has been the valence of V in the spinel and glass. Spinel-melt pairs were equilibrated at low and variable oxygen fugacities, with a range of V and Ti contents. XANES spectra were measured on the spinel and glass products, and pre-edge peaks measured and calibrated against valence with the use of glass and oxide standards. The valence of V is always greater in the glass than in the spinels. In spinel, V is dominantly 3+ at oxygen fugacities near the FMQ (fayalite magnetite quartz) buffer, but we find evidence for mixed 3+, 4+, and 5+ at oxidized conditions (FMQ to air), and 2+ and 3+ at very reduced conditions [FMQ to IW-1 (1 log fO₂ unit below the iron wüstite buffer)]. Increased V contents in spinels are correlated with increased DVspinel-melt, at constant temperature and oxygen fugacity. However, increased Ti content causes only a slight decrease in DVspinel-melt and a shift to more reduced V (smaller pre-edge peak), which may be related to Fe-V exchange equilibria. Using the new partition coefficients, together with published results and valence information, expressions have been derived to predict DVspinel/melt for basaltic systems. Application of these expressions to natural suites illustrate their utility and also the great range of DVspinel/melt values relevant to natural systems. Calculation of V depletions in planetary mantles from basalt suites must take silicate, oxide, and metal fractionation into account, as is demonstrated using terrestrial, lunar, martian, and eucritic samples.

Tungsten isotopes and oxidation in early planetary mantles

Tungsten isotopes and oxidation in early planetary mantles

Oscillating and stagnating plumes in the Earth's lower mantle

We investigate the coupled effects of mineralogy and pressure on the dynamics of axisymmetric thermochemical plumes in the lower mantle, using both high resolution numerical experiments and simple analytical theory. We focus on the effect of composition on the compressibility which has not been studied before. Our results show that the effect of mineralogy is considerable: For relatively low Si enrichment, the compressibility of the plume and of the surrounding mantle is similar therefore the compositional density excess of the plume is constant with depth. This leads to an oscillatory behavior in plume head vertical position with time, similar to previous work [A. Davaille. Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle. Nature, 402 (1999) 756–760.]. Si-enriched compositions instead induce a lower compressibility for the thermochemical plume with respect to the surrounding mantle, implying an increase of the compositional density excess with decreasing depth. Therefore, although thermochemical plumes can fully develop and rise toward the surface, their ascent may be impeded by the chemical density excess, leading to the stagnation of large plume heads at various depths in the lower mantle. As a consequence, Si-enriched thermochemical plumes may display broad (∼ 1200 km wide) negative seismic velocity anomalies at various lower mantle depths, which may not necessarily be associated with upwelling currents. In addition, the coupling between mineralogy and dynamics may provide an efficient mechanism for the long term survival of compositional heterogeneity in the lower mantle.

Big returns on small samples: Lessons learned from the analysis of small lunar samples and implications for the future scientific exploration of the Moon

Samples returned from the surface of planetary bodies are both complementary to orbital and in situ observations and provide a unique perspective for understanding the nature and evolution of that body. This unique perspective is based on the scale the sample is viewed (mm–Å), the ability to manipulate the sample, the capability to analyze the sample at high precision and accuracy, and the ability to significantly modify experiments as logic and technology dictates over an extended period of time (decades). Unlike the Apollo missions, robotic sample return missions in the next decade will result in the return of relatively small sample mass. Such robotically returned samples are scientifically more valuable if they can be placed within a planetary context through orbital observations and if information concerning planetary-scale processes and conditions can be extracted from them. Conversely, samples give remotely sensed data ground truth. That is, they act as a “calibration standard” for these data allowing a much enhanced global view to be constructed. The Moon is an example that illustrates how information can be extracted from small samples and then extended to planetary and solar system scales. Three examples from the Moon illustrate this point. First, multi-analytical and experimental studies of minute (10–500 μm) glass beads representing near-primary magmas provide constraints on the composition and condition of the lunar mantle, the style of early planetary differentiation, the history and character of early mantle dynamics and melting, and the isolation of the lunar mantle from late-stages of lunar accretion. Second, trace element analysis of individual mineral grains via ion microprobe and isotopic analysis of small rock fragments representing some of the oldest and youngest periods of lunar magmatism illustrate their usefulness for both fingerprinting distinct episodes of lunar magmatism and reconstructing the evolution of lunar magmatism. Third, mechanisms for primitive planetary mantles degassing and volatile transport on airless bodies can be understood by the analysis of volatile coatings on glass and mineral fragments in the lunar regolith. As many of our insights about the Moon are based on samples that primarily were collected within a limited lunar terrain, our understanding of the Moon is somewhat biased. Future scientifically strategic sampling targets are young mare basalts (Roris basalt in Oceanus Procellarum), far-side mare basalts (Mare Moscoviense), large pyroclastic deposits and potential mantle xenoliths (Aristarchus plateau, Rima Bode) major unsampled crustal lithologies outside the Procellarum KREEP terrane (central peak in Tsiolkovsky crater, South-pole Aitken basin), basin and crater melt sheets (South-pole Aitken basin, Giordano Bruno) and H deposits in permanently shaded areas (South-pole Aitken basin). Sampling these locations would further our understanding of processes at work during the early evolution of the terrestrial planets, provide a comprehensive history of endogenous (e.g., primary volcanic degassing) and exogenous (e.g., solar wind, galactic cosmic rays, volatiles from comets) volatile reservoirs and volatile transport and would provide unique historical information about events and processes that affected the entire inner solar system, a record obscured on the Earth and Mars.

Quantum-thermodynamic treatment of intrinsic anharmonicity; Wallace’s theorem revisited

Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg2SiO4). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate representation of thermodynamic properties and sound wave velocities of Mg2SiO4 in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly affected by the use of a different equation of state.

Significance of iron isotope mineral fractionation in pallasites and iron meteorites for the core–mantle differentiation of terrestrial planets

Seven bulk chondrites, with δ 57Fe/ 54Fe values between −0.1‰ and 0‰ relative to IRMM-14, tend to be slightly lighter than 11 bulk iron meteorites, which have δ 57Fe/ 54Fe values ranging from 0.04‰ to 0.2‰. At the mineral scale, taenite from two iron meteorites, Cranbourne and Toluca, shows δ 57Fe/ 54Fe values heavier by up to 0.3‰ than their kamacite counterpart, thus calling into question the significance of bulk iron meteorite data. On three pallasites (Esquel, Marjalahti and Springwater) we measured a heavier iron isotope composition for the metal fractions compared to the coexisting olivines as previously observed on two other pallasites (Eagle Station and Imilac), but the range of δ 57Fe/ 54Fe differences (from 0.32‰ to 0.07‰) is larger than that originally found. Troilite from two pallasites appears to be even heavier than the metal fraction, whereas schreibersite is lighter than its olivine counterpart. There is thus a general tendency for minerals within a given rock to show a heavier Fe isotope composition as the coordination number of Fe increases, although troilite is an exception to this rule. Iron meteorites are classically considered as remnants of asteroid cores and pallasites as core–mantle interfaces. The simultaneous finding that the metal fractions of pallasites have a higher δ 57Fe/ 54Fe signature than the coexisting olivines, and that the iron meteorites are slightly heavier than chondrites could be taken as an indication that planetary core–mantle differentiation is accompanied by sizeable iron isotope fractionation. In this hypothesis, mass balance constraints imply that resultant planetary mantles should be isotopically lighter than the chondritic starting material. That is not observed, however, since all planetary mantles analyzed so far have δ 57Fe/ 54Fe values equivalent to or heavier than those of chondrites. It thus appears that the moderate temperature and pressure metal–silicate fractionation that occurred in pallasite and iron parent bodies is not readily transposable to planets as far as Fe isotopes are concerned. Instead, these mantle signatures could reflect equilibrium fractionation at a higher temperature, or the lack of a global core–mantle equilibration at the planetary scale. Overall, these new results show that the mass-dependent isotopic scatter observed among inner solar system bodies from the bulk-rock to the planetary scale (∼0.3‰ δ 57Fe/ 54Fe) is more restricted than previously thought. This likely confirms a homogenization process that occurred in the protoplanetary accretion disk, between refractory inclusion condensation and chondrule formation.

Interior structure of terrestrial planets: Modeling Mars' mantle and its electromagnetic, geodetic, and seismic properties

We present a new procedure to describe the one‐dimensional thermodynamical state and mineralogy of any Earth‐like planetary mantle, with Mars as an example. The model parameters are directly related to expected results from a geophysical network mission, in this case electromagnetic, geodetic, and seismological processed observations supplemented with laboratory measurements. We describe the internal structure of the planet in terms of a one‐dimensional model depending on a set of eight parameters: for the crust, the thickness and the mean density, for the mantle, the bulk volume fraction of iron, the olivine volume fraction, the pressure gradient, and the temperature profile, and for the core, its mass and radius. Currently, available geophysical and geochemical knowledge constrains the range of the parameter values. In the present paper, we develop the forward problem and present the governing equations from which synthetic data are computed using a set of parameter values. Among all Martian models fitting the currently available knowledge, we select eight candidate models for which we compute synthetic network science data sets. The synergy between the three geophysical experiments of electromagnetic sounding, geodesy, and seismology is emphasized. The stochastic inversion of the synthetic data sets will be presented in a companion paper.

Numerical investigation of layered convection in a three‐dimensional shell with application to planetary mantles

Stratified stable layered mantle convection in a three‐dimensional (3‐D) spherical shell is investigated for a range of depth of layer, intrinsic density contrast between the layers (Δρ), and heating mode. Three heating modes are studied: internal heating, bottom heating across core‐mantle boundary, and both combined. For each heating mode, layers were investigated centered at depths from 500 km to 2500 km in 500 km steps and with Δρ from 1 to 5% in 1% steps. We did not find stable layering for Δρ of 1%. Cases with no bottom heating were stable with Δρ of 2%, but Δρ of at least 3% were required by cases with a component of bottom heating. All cases with Δρ of 4% or more were stable. We found that the stability of the layer is strongly dependent on the buoyancy ratio B (B = Δρ ÷ ραΔT, where Δρ is the chemical density increase across the boundary, ρ is the density in the upper layer, α is the thermal expansivity and ΔT is the radial temperature difference across the whole system) with a dense layer becoming unstable B ≈ 0.5. We characterize the height and length scale of the undulations and the area of the interface. Deformations of the interface are largest for cases in which interface is in the midmantle and for cases with small density contrasts. We find that the heating mode does not affect the thermal structure of the layered system, which can be explained with energy balance considerations. The amplitude of the interfacial deformation is found to be unaffected by the heating mode and can be predicted using B. Our results suggest the interfacial thermal boundary layers require large temperature contrasts; therefore the lack of evidence for thermal boundary layers in global seismology studies between 500 and 2500 km depth suggests interfaces at these depths are unlikely.

Motion of a Planet with a Complex Structure

The motion of a planet consisting of a mantle and a core (solid bodies) connected by a viscoelastic layer and interacting with each other and an external point mass by the law of gravitation is considered. The mutual motions of the core and mantle are investigated assuming that the centers of mass of the planet and external point mass moves along undisturbed Keplerian orbits around the common center of mass of the system. The planetary core and mantle have an axial symmetry and different principal moments of inertia, which leads to a displacement of the center of mantle relative to the center of core and to their mutual rotations. The results obtained on the basis of averaged equations are illustrated by the example of the Earth–Moon system.

Convective cooling of an initially stably stratified fluid with temperature‐dependent viscosity: Implications for the role of solid‐state convection in planetary evolution

The possible role of solid‐state convective cooling is important in understanding planetary thermal evolution. A stable compositional stratification in planetary mantles, which can arise from partial melting due to adiabatic decompression or from early magmatic differentiation, may suppress or delay convective instability, restrict the depth scale of convective motions, and reduce the convective heat flux out of the mantle. Two‐dimensional numerical experiments on convection in a stably stratified viscous fluid with a strongly temperature‐dependent viscosity cooled from above are carried out to understand how convecting, well‐mixed layers form and thicken in time because of cooling at the planetary surface. Simple scaling laws and parameterizations are developed that allow the results of our numerical experiments to be extrapolated to viscosity variations as large as would be expected for thermally activated creep in planetary mantles. Strongly temperature‐dependent viscosity reduces the available thermal buoyancy in the cold top boundary layer and therefore increases the impact of compositional stratification. Scaling laws for the mixed layer thickening rate indicate that thickening occurs mainly by buoyant, rather than viscous, entrainment of the underlying still stratified fluid. Compositional stratification may be important in the thermal evolution of the oceanic upper mantle, formation of cratonic continental lithosphere, and in planetary evolution, more generally. In several geologically realistic settings, a restricted depth of stratification or mantle viscosities on the order of 1018 Pa s or less are required for convective instability.

Whole layer convection in a heterogeneous planetary mantle

Geochemical observations demonstrate that Earth's mantle is heterogeneous, but the sizes, forms, and characteristics of its reservoirs are not constrained. Using laboratory experiments, we have systematically studied a simple nonhomogeneous system, where two layers of miscible fluids with different densities, depths, and viscosities are subjected to a destabilizing temperature contrast. When the buoyancy number B (i.e., the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly) is lower than 0.3–0.5, the whole layer regime develops, with a deformed interface and convective patterns over the whole tank depth. The system systematically evolves toward one‐fluid Rayleigh‐Bénard convection because of stirring. However, the two isolated fluids can persist for very long time compared to the characteristic timescale of thermal convection and give rise to numerous transient behaviors. Of particular interest for planetary mantles are the pulsatory dynamics, where the interface between the two layers deforms in large domes moving up and down quasiperiodically: According to the scaling laws derived from the experiments, such a mechanism could indeed provide a simple and single physical explanation for the superswells observed at present on Earth and more generally for the long‐term episodicity in planetary interiors observed in geological records.

Magmatic fractionation of Hf and W: constraints on the timing of core formation and differentiation in the Moon and Mars

Excesses of 182W have previously been measured in samples from the Moon and Mars, and can be derived from high Hf/W regions in their interiors during their early histories. Although planetary mantles will have superchondritic Hf/W after core formation, the extent to which high Hf/W regions could be generated by magmatic fractionation has not been evaluated. In order to address the latter possibility, we have carried out experiments from 100 MPa to 10.0 GPa, 1150 to 1850°C, at oxygen fugacities near the IW (iron-wüstite) buffer, and measured partition coefficients for W and Hf for plagioclase-liquid, olivine-liquid, orthopyroxene-liquid, clinopyroxene-liquid, garnet-liquid, and metal-liquid pairs. Clinopyroxene and garnet are both capable of fractionating Hf from W during magmatic crystallization or mantle melting, and minor variations in the measured D’s can be attributed to crystal chemical effects. Excesses of 182W and 142Nd in lunar samples can be explained by fractionation of Hf from W, and Sm from Nd (by ilmenite and clinopyroxene) during crystallization of the latest stages of a lunar magma ocean. Correlations of ε W with ε Nd in martian samples could be a result of early silicate fractionation in the martian mantle (clinopyroxene and/or garnet).

Anatomy of black veins in Zagami: clues to the formation of high-pressure phases

Abstract Black melt veins in the Martian basaltic meteorite Zagami were investigated using analytical transmission electron microscopy, with the goal to constrain the mechanisms and PTt conditions that result in the formation of high-pressure phases therein. Our study reveals the existence of a number of high-pressure minerals: stishovite, K- and Na,Ca-rich hollandites, akimotoite (silicate ilmenite), as well as amorphous grains of silicate perovskite composition. Crystals of a ferro-magnesian silicate titanite with a low Ca content have been identified for the first time. The veins formed by rapid shear melting and solidified in extremely short times. As a consequence, the vein melt could not homogeneously mix and it partially preserves the chemical heterogeneity of precursor minerals, accounting for the large diversity of high-pressure minerals. Most of the tiny phases directly crystallized from the melt under high pressure at very high temperatures. Silicate perovskite probably amorphized upon decompression and evolved, at its grain boundaries, by solid-state diffusion toward the lower pressure assemblage wustite+stishovite. Not only do these observations help to understand the formation of high-pressure phases in shock events, but they also provide clues to the mineralogical complexity that can be expected in planetary mantles.

A matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection

We apply a two-dimensional Cartesian finite element treatment to investigate infinite Prandtl number thermal convection with temperature, strain rate and yield stress dependent rheology using parameters in the range estimated for the mantles of the terrestrial planets. To handle the strong viscosity variations that arise from such nonlinear rheology in solving the momentum equation, we exploit a multigrid method based on matrix-dependent intergrid transfer and the Galerkin coarse grid approximation. We observe that the matrix-dependent transfer algorithm provides an exceptionally robust and efficient means for solving convection problems with extreme viscosity gradients. Our algorithm displays a convergence rate per multigrid cycle about five times better than what other published methods (e.g., CITCOM of Moresi and Solomatov, 1995) offer for cases with similar extreme viscosity variation. The algorithm is explained in detail in this paper. When this method is applied to problems with temperature and strain rate dependent rheologies, we obtain strongly time dependent solutions characterized by episodic avalanching of cold material from the upper boundary layer to the bottom of the convecting domain for a significantly broad range of parameter values. In particular, we observe this behavior for the relatively simple case of temperature dependent Newtonian rheology with a plastic yield stress. The intensity and temporal character of the episodic behavior depends sensitively on the yield stress value. The regions most strongly affected by the yield stress are thickened portions of the cold upper boundary layer which can suddenly become unstable and form downgoing diapirs. These computational results suggest that the finite yield properties of silicate rocks must play a vitally important role in planetary mantle dynamics. Although our example calculations were selected mainly to illustrate the power of our multigrid method, they suggest that many possible exotic behaviors in planetary mantles have yet to be discovered.

Inversion of two-dimensional numerical convection experiments for a fluid with a strongly temperature-dependent viscosity

2-D thermal convection numerical experiments are conducted for a fluid with an infinite Prandtl number, a strongly temperature-dependent viscosity, and isothermal horizontal boundaries. The core Rayleigh number (Raθ¯), determined with the temperature of the well-mixed interior, is in the range 5 × 105 < Raθ¯ < 2 × 107, and the ratio of the top to the bottom viscosity (Δµ) can be as large as Δµ = 106. Different convective regimes are possible, depending on the values of Raθ¯ and Δµ. This paper focuses on the conductive-lid regime, in which convection is confined to a sublayer. First, a least-squares fit of more than 40 numerical experiments suggests that the temperature difference across the lower thermal boundary layer (ΔT1) depends mostly on the viscous temperature scale (ΔTv) defined by Davaille & Jaupart (1993), and slightly on the temperature difference across the fluid layer (ΔT): ΔT1 = 1.43ΔTv − 0.03ΔT. Second, a generalized non-linear inversion of the data does not support the assumptions that the temperature difference across the upper boundary layer is proportional to ΔTv, and that isoviscous scaling laws can be used for describing heat flux through the convective sublayer. Third, a generalized non-linear inversion of the data is carried out in order to avoid any assumptions on the parameters. This leads to the following heat flux scaling law: Nu=3.8(ΔTv/ΔT)1.63Raθ¯0.258, where the Nusselt number (Nu) is the non-dimensional heat flux. This scaling law is different from that proposed by previous studies. It reproduces the data at better than 1 per cent and fits the results of previous numerical experiments very well (e.g. Christensen 1984). Finally, a thermal boundary layer analysis is performed. For a fluid heated from below, the upper and lower thermal boundary layers interact with one another, inducing a thermal erosion of the conductive lid. This study suggests that the dynamics of convection is driven by the instability of the lower thermal boundary layer. Therefore, an alternative way to determine the heat flux is to use the value of the lower thermal boundary layer Rayleigh number (Ra). This value is not independent of Raθ¯, unlike the case for an isoviscous fluid. A least-squares fit of the data leads to Raδ=0.28Raθ¯0.21. This law provides a very convenient way to model the thermal evolution of planetary mantles.

CO/CO2 Molecular Number Ratio Produced by ion Irradiation of Ices

We have quantitatively studied, by infrared absorption spectroscopy, the CO/CO2 molecular number ratio after ion irradiation of ices and mixtures containing astrophysically relevant species such as CO, CO2, H2O, CH4, CH3OH, NH3, O2, and N2 at 12–15 K. The ratios have also been measured after warm up to temperatures between 12 and 200 K. As a general result we find that the CO/CO2 ratio decreases with the irradiation dose (amount of energy deposited on the sample). In all of the studied mixtures, as expected, it decreases with increasing temperature because of CO sublimation. However the temperature where CO sublimes strongly depends on the initial mixture, remaining at a temperature over 100 K in some cases. Our results might be relevant to interpret the observed CO/CO2 ratio in several astrophysical scenarios such as planetary icy surfaces and ice mantles on grains in the interstellar medium.

Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle

Mounting evidence indicates that the Earth's mantle is chemically heterogeneous. To understand the forms that convection might take in such a mantle, I have conducted laboratory experiments on thermochemical convection in a fluid with stratified density and viscosity. For intermediate density contrasts, a ‘doming’ regime of convection is observed, in which hot domes oscillate vertically through the whole layer while thin tubular plumes rise from their upper surfaces. These plumes could be responsible for the ‘hot spots’ and the domes themselves for the ‘superwells’ observed at the Earth's surface. In the Earth's mantle, the doming regime should occur for density contrasts less than about 1%. Moreover, quantitative scaling laws derived from the experiments show that the mantle might have evolved from strictly stratified convection 4 Gyr ago to doming today. Thermochemical convection can thus reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.

Stagnant lid convection in a spherical shell

A compelling explanation for the observed lack of mobile surface plates on the terrestrial planets is that the strong temperature dependence of silicate rheology leads to a quasi-rigid stagnant lid at the cool surface of the convecting planetary mantle. We investigate such stagnant lid convection in an internally heated spherical shell. For the parameter range we study, convection beneath the lid is steady in time and characterized by cylindrical upwellings surrounded by cold sheet-like downwellings that exhibit dodecahedronal ( l=6, m={0,5}) symmetry. The scaling relationship we obtain for the heat flux is very similar to results from two-dimensional numerical experiments and asymptotic boundary layer analyses. It seems that the predictions of two-dimensional models, in particular, low heat transport efficiency and extensive melting, also apply in fully three-dimensional spherical geometry.