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Convection in the primitive mantle in interaction with global magma oceans
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A common scenario considered during the formation of Earth-like bodies is that of magma oceans. Indeed, the accretion energy as well as the heat produced by the radioactive decay of short-period elements is more than enough to melt entirely the primitive mantle, thereby forming a global magma ocean. The pressure-dependence of the solidification temperature as well as the steep isentropic temperature profile at the base of the mantle could lead to a crystallization of that global magma ocean from the middle. The primitive solid mantle could therefore be bounded by two global magma oceans: one above and one below.This PhD thesis focuses on two aspects of such a system. First, the solid part of the mantle and the magma oceans being of similar composition, convecting matter in the solid is not necessarily stopped by the solid/liquid interface but could instead go through it by melting/freezing provided that the phase change timescale is short enough compared to the viscous timescale needed to build a solid topography in the liquid oceans. A linear stability analysis and direct numerical simulations show the phase change at the boundary greatly affects convection in the solid part of the mantle. The critical Rayleigh number decreases, convective patterns have a larger wavelength, and the heat flux carried through the solid increases of up to several orders of magnitude compared to cases with classical boundary conditions.The second aspect explored in this thesis is the long-term evolution of the primitive mantle. Coupling convection in the solid with simple evolution models for the magma oceans allowed us to build a global evolution model of the primitive mantle monitoring the thermo-compositional evolution of the solid mantle and magma oceans. A linear stability analysis shows convection sets in the solid before the surface magma ocean crystallizes entirely. A preliminary direct numerical simulation shows the fractional crystallization of the basal magma ocean may lead to the formation of large thermo-chemical piles at the base of the solid mantle. These piles are similar to the large low-shear velocity provinces (LLSVP) observed today.The presence of global magma oceans could therefore have important consequences on the long-term evolution of the Earth: first, fractional crystallization of the magma oceans and convection in the solid part affect the resulting thermal and compositional structures; and second, the global heat budget could be tremendously affected by the high heat flux carried out by the solid part owing to the phase change boundary conditions.
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... L'océan est alors divisé en deux couches distinctes séparées par un solide. La dynamique de ce nouveau système peut s'avérer complexe, le solide développant éventuellement des modes de convection de translation (Morison et al., 2019) dès lors qu'il est autorisé à changer de phase à chaque interface (Agrusta et al., 2020;Labrosse et al., 2018;Morison, 2020). ...
... In the long term, nevertheless, it could be beneficial to take into account the behavior of these interactions with the solidified mantle. Previous studies (see for example Agrusta et al. (2020); Morison (2020)) have shown that convection in a mantle bounded above and below by magma oceans could produce translation modes, with melting-freezing at their interfaces. This mechanism would authorize indirect exchanges between a basal and a surface magma oceans. ...
This thesis manuscript main focus is the thermo-compositional convection in a terrestrial magma ocean. This latter is a spherical shell of liquid silicates, similar to a rocky planets' melt mantle. Earth may have undergone such a phasis during the end of its accretion period because of, for example, moon forming impact.Up to now, most of physical models for terrestrial magma ocean remained quite simple, postulating a well-mixed ocean by vigorous thermal convection. This hypothesis could be mitigated by a basal incongruent crystallization. This work's objective is to provide a more detail model via hydrodynamical approach helped by numerical tool.First, we study thermal convection in a rotating spherical shell submitted to a Robin boundary condition. This one is intermediate between Neumann and Dirichlet ones. It enables to model radiative equilibrium between atmosphere and surface of a terrestrial magma ocean. We show, in that pure thermal setup, that the Robin boundary condition plays little role in a rotation dominant context (except regarding convective structures). More generally, we give the range of parameters in which Robin boundary condition can be safely replaced by more usual ones.Thereafter, we focus on the thermo-compositional convection inside a non-rotating terrestrial magma ocean crystallizing from the bottom upward. We list the different transport regimes developped by the system as a function of the input parameters, particularly we discuss the sustainability of a basal stably straified chemical layer. We show that a terrestrial magma ocean under thick H2O atmosphere may not be able to erode such a pre-existant basal layer.
... Considering that ± values are low when TMO and BMO (or just TMO) crystallisation starts Morison, 2019), mantle convection would first assume a degree-1 pattern (Fig. 5), possibly with implications for the origin of crustal dichotomy on the Moon (e.g. Ishihara et al., 2009) and Mars (e.g. ...
After accretion and formation, terrestrial planets go through at least one magma ocean episode. As the magma ocean crystallises, it creates the first layer of solid rocky mantle. Two different scenarios of magma ocean crystallisation involve that the solid mantle either (1) first appears at the core–mantle boundary and grows upwards or (2) appears at mid-mantle depth and grows in both directions. Regardless of the magma ocean freezing scenario, the composition of the solid mantle and liquid reservoirs continuously change due to fractional crystallisation. This chemical fractionation has important implications for the long-term thermo-chemical evolution of the mantle as well as its present-day dynamics and composition. In this work, we use numerical models to study convection in a solid mantle bounded at one or both boundaries by magma ocean(s) and, in particular, the related consequences for large-scale chemical fractionation. We use a parameterisation of fractional crystallisation of the magma ocean(s) and (re)melting of solid material at the interface between these reservoirs. When these crystallisation and remelting processes are taken into account, convection in the solid mantle occurs readily and is dominated by large wavelengths. Related material transfer across the mantle–magma ocean boundaries promotes chemical equilibrium and prevents extreme enrichment of the last-stage magma ocean (as would otherwise occur due to pure fractional crystallisation). The timescale of equilibration depends on the convective vigour of mantle convection and on the efficiency of material transfer between the solid mantle and magma ocean(s). For Earth, this timescale is comparable to that of magma ocean crystallisation suggested in previous studies , which may explain why the Earth's mantle is rather homogeneous in composition, as supported by geophysical constraints.
... The specific value of Φ is difficult to constrain (because τ φ is non-trivial to determine), and also is expected to vary with 140 time (i.e., because τ η depends on the thickness of the solid mantle) (Deguen, 2013;Deguen et al., 2013). However, for a purely thermal case, Morison et al. (2019) and Morison (2019) estimate Φ + ∼ 10 −5 and Φ − ∼ 10 −3 for the Earth. Therefore, significant transfer of material across the solid-mantle magma-ocean boundaries is expected. ...
Abstract. After accretion and formation, terrestrial planets go through at least one magma ocean episode. As the magma ocean crystallises, it creates the first layer of solid rocky mantle. Two different scenarios of magma ocean crystallisation involve that the solid mantle either (1) first appears at the core-mantle boundary and grows upwards, or (2) appears at mid-mantle depth and grows in both directions. Regardless of the magma ocean freezing scenario, the composition of the solid mantle and liquid reservoirs continuously change due to fractional crystallisation. This chemical fractionation has important implications for the long-term thermo-chemical evolution of the mantle, as well as its present-day dynamics and composition. In this work we use numerical models to study convection in a solid mantle bounded at either or both boundaries by magma ocean(s), and in particular, the related consequences for large-scale chemical fractionation. We use a parameterisation of fractional crystallisation of the magma ocean(s) and (re-)melting of solid material at the interface between these reservoirs. When these crystallisation/re-melting processes are taken into account, convection in the solid mantle occurs readily and is dominated by large wavelengths. Related material transfer across the mantle magma-ocean boundaries promotes chemical equilibrium, and prevents extreme enrichment of the last-stage magma ocean (as would otherwise occur due to pure fractional crystallisation). The timescale of equilibration depends on the convective vigour of mantle convection and on the efficiency of material transfer between the solid mantle and magma ocean(s). For Earth, this timescale is comparable to that of magma ocean crystallisation suggested in previous studies (Lebrun et al., 2013), which may explain why the Earth's mantle is rather homogeneous in composition, as supported by geophysical constraints.
The number of heat flow measurements at the Earth surface has significantly increased since the last global analysis (Pollack et al., 1993, https://doi.org/10.1029/93RG01249), and the most recent of them provide insights into key locations. This paper presents a new compilation, which includes approximately 70,000 measurements. Continental heat flow (67 mWm⁻²) does not change significantly, but the differences are more important for oceanic heat flow. The divergence with conductive cooling models is reduced significantly for young ages of the seafloor, since the most recent measurements (92 mWm⁻²) are significantly higher on average than the older ones (79 mWm⁻²). This is related to a better quality and a better sampling of measurements in regions affected by hydrothermal circulation. The total Earth heat loss derived from these most recent measurements is estimated to ∼40–42 TW and represents only 3–5 TW less than with a conductive cooling model (∼45–47 TW). Hydrothermal heat loss in the oceanic domain is estimated with a new method based on the ruggedness of the seafloor and represents ∼1.5 TW more than previous estimates. The heat flow variability on continents is so large that defining a trend with stratigraphic or tectono‐thermal age is difficult and makes extrapolation from age a poor predictor. On the other hand, additional geological and geophysical information can be combined with age for better predictions. A generalized similarity method was used here to predict heat flow on a global 0.5° × 0.5° grid. The agreement with local measurements is generally good and increases with the number and quality of proxies.
The crystallization of a magma ocean (MO) early in Earth's history shaped the entire evolution of our planet. The buoyancy relations between the forming crystals and the residual melt is the most important but also the most unknown parameter affecting the large-scale structure and evolution of the MO. The accumulation of crystals, near the depth of neutral buoyancy between crystals and the coexisting melt, if happening at mid-depths, can separate convecting regions within the MO. Here we use jointly first-principles molecular-dynamics calculations and diamond-anvil cell experiments to obtain the density relations between the molten bulk silicate Earth and the bridgmanite crystals during the crystallization of the MO. The chemical evolutions of the liquid and the coexisting solid during progressive crystallization were constrained by experiments, and the relevant densities were calculated by molecular dynamics. We find that the first crystal of bridgmanite that is formed in a fully molten mantle is Fe-poor, and becomes neutrally buoyant at 110–120 GPa. Since the cooling of the deep MO is fast, and related convection is vigorous, however, first crystals remain entrained. As crystallization advances, the relative Fe content increases in the melt, and the pressure of neutral buoyancy decreases. At 50% solidification, close to the rheological transition, the pressure of the density crossover moves to ∼50 GPa. At this pressure, crystals form an interconnected network and block global convection currents, which in turn leads to the separation of the partly crystallized MO into a surficial MO and a basal MO through melt-solid segregation. Such a shallow segregation of a crystal mush at mid-mantle depth has important implications for the dynamics and timescales of early mantle differentiation. Moreover, the shallow segregation should have promoted the formation of a voluminous basal MO that evolves into a large geochemically enriched reservoir. Accordingly, the seismically observed residues of basal MO crystallization in the present-day mantle may host an unmixed reservoir for the missing budget of highly incompatible elements.
The formation and differentiation of planetary bodies are thought to involve magma oceans stages. We study the case of a planetary mantle crystallizing upwards from a global magma ocean. In this scenario, it is often considered that the magma ocean crystallizes more rapidly than the time required for convection to develop in the solid cumulate. This assumption is appealing since the temperature and composition profiles resulting from the crystallization of the magma ocean can be used as an initial condition for convection in the solid part. We test here this assumption with a linear stability analysis of the density profile in the solid cumulate as crystallization proceeds. The interface between the magma ocean and the solid is a phase change interface. Convecting matter arriving near the interface can therefore cross this boundary via melting or freezing. We use a semi-permeable condition at the boundary between the magma ocean and the solid to account for that phenomenon. The timescale with which convection develops in the solid is found to be several orders of magnitude smaller than the time needed to crystallize the magma ocean as soon as a few hundreds kilometers of cumulate are formed on a Mars-to Earth-size planet. The phase change boundary condition is found to decrease this timescale by several orders of magnitude. For a Moon-size object, the possibility of melting and freezing at the top of the cumulate allows the overturn to happen before complete crystallization. The convective patterns are also affected by melting and freezing at the boundary: the linearly most-unstable mode is a degree-1 translation mode instead of the approximately aspect-ratio-one convection rolls found with classical non-penetrative boundary conditions. The first overturn of the crystallizing cumulate on Mars and the Moon could therefore be at the origin of their observed degree-1 features.
The Earth is in a plate tectonics regime with high surface heat flow concentrated at constructive plate boundaries. Other terrestrial bodies that lack plate tectonics are thought to lose their internal heat by conduction through their lids and volcanism: hotter planets (Io and Venus) show widespread volcanism whereas colder ones (modern Mars and Mercury) are less volcanically active. However, studies of terrestrial magmatic processes show that less than 20% of melt volcanically erupts, with most melt intruding into the crust. Signatures of large magmatic intrusions are also found on other planets. Yet, the influence of intrusive magmatism on planetary cooling remains unclear. Here we use numerical magmatic-thermo-mechanical models to simulate global mantle convection in a planetary interior. In our simulations, warm intrusive magmatism acts to thin the lithosphere, leading to sustained recycling of overlying crustal material and cooling of the mantle. In contrast, volcanic eruptions lead to a thick lithosphere that insulates the upper mantle and prevents efficient cooling. We find that heat loss due to intrusive magmatism can be particularly efficient compared to volcanic eruptions if the partitioning of heat-producing radioactive elements into the melt phase is weak. We conclude that the mode of magmatism experienced by rocky bodies determines the thermal and compositional evolution of their interior. Rocky planets dominated by intrusive magmatism can cool more efficiently than those dominated by extrusive volcanism, according to numerical simulations of mantle convection.
Matrices coming from elliptic Partial Differential Equations have been shown to have a low-rank property that can be efficiently exploited in multifrontal solvers to provide a substantial reduction of their complexity. Among the possible low-rank formats, the Block Low-Rank format (BLR) is easy to use in a general purpose multifrontal solver and its potential compared to standard (full-rank) solvers has been demonstrated. Recently, new variants have been introduced and it was proved that they can further reduce the complexity but their performance has never been analyzed. In this article, we present a multithreaded BLR factorization and analyze its efficiency and scalability in shared-memory multicore environments. We identify the challenges posed by the use of BLR approximations in multifrontal solvers and put forward several algorithmic variants of the BLR factorization that overcome these challenges by improving its efficiency and scalability. We illustrate the performance analysis of the BLR multifrontal factorization with numerical experiments on a large set of problems coming from a variety of real-life applications.
The hemispherical asymmetry of the inner core has been interpreted as resulting from a high-viscosity mode of inner core convection, consisting in a translation of the inner core. A thermally driven translation, as originally proposed, is unlikely if the currently favoured high values of the thermal conductivity of iron at core conditions are correct. We consider here the possibility that inner core translation results from an unstable compositional gradient, which would develop either because the light elements present in the core become increasingly incompatible as the inner core grows, or because of a possibly positive feedback of the development of the F-layer on inner core convection. Though themagnitude of the destabilizing effect of the compositional field is predicted to be similar to or smaller than the stabilizing effect of the thermal field, the huge difference between thermal and chemical diffusivities implies that double-diffusive instabilities can still arise even if the net buoyancy increases upward. Using linear stability analysis and numerical simulations, we demonstrate that a translation mode can indeed exist if the compositional field is destabilizing, even if the temperature profile is subadiabatic, and irrespectively of the relative magnitudes of the composition and potential temperature gradients. The existence of this double diffusive mode of translation requires that the following conditions are met: (i) the compositional profile within the inner core is destabilizing, and remains so for a duration longer than the destabilization timescale (on the order of 200 Myr, but strongly dependent on the magnitude of the initial perturbation); and (ii) the inner core viscosity is sufficiently large, the required value being a strongly increasing function of the inner core size (e.g. 10¹⁷ Pa s when the inner core was 200 km in radius, and ≃3 × 10²¹ Pa s at the current inner core size). If these conditions are met, the predicted inner core translation rate is found to be similar to the inner core growth rate, which is more consistent with inferences from the geomagnetic field morphology and secular variation than the higher translation rate predicted for a thermally driven translation. © The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.
Solidification of magma oceans (MOs) formed early in the evolution of planetary bodies sets the initial condition for their evolution on much longer time scales. Ideal fractional crystallization would generate an unstable chemical stratification that subsequently overturns to form a stably stratified mantle. The simplest model of overturn assumes that cumulates remain immobile until the end of MO solidification. However, overturning of cumulates and thermal convection during solidification may act to reduce this stratification and introduce chemical heterogeneity on scales smaller than the MO thickness. We explore overturning of cumulates before the end of MO crystallization and the possible consequences for mantle structure and composition. In this model, increasingly dense iron-rich layers, crystallized from the overlying residual liquid MO, are deposited on a thickening cumulate layer. Overturn during solidification occurs if the dimensionless parameter, Rc, measuring the ratio of the MO time of crystallization τMO to the timescale associated with compositional overturn τov=μ/ΔρgH exceeds a threshold value. If overturn did not occur until after solidification, this implies that the viscosity of the solidified mantle must have been sufficiently high (possibly requiring efficient melt extraction from the cumulate) for a given rate of solidification. For the lunar MO, possible implications for the generation of the Mg-suites and mare basalt are suggested.
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Crystallization and chemical differentiation of the early Earth were governed by a combination of various processes. Within the uncertainties of physical parameters, the two end-member models, equilibrium crystallization and fractional crystallization, are both possible. In terms of crystal size, the boundary between these models is ~1mm. Analysis of nucleation and crystal growth in the convecting magma ocean suggests that the crystals in the magma ocean are approximately this size. The equilibrium model is preferred because it seems to satisfy better the geochemical constraints. According to this model, at the early stages, crystallization proceeds from bottom up without any substantial crystal-melt segregation. In a vigorously convecting magma ocean, the thermal profile is approximately adiabatic and the crystal fraction decreases gradually with depth. The basic physical reason for equilibrium crystallization is a fast convective cooling during which the solid and the liquid phases had a very limited time window for crystal-melt segregation, about 1000 years. Chemical differentiation due to crystal-melt segregation is more significant at low pressures corresponding - with large uncertainties - to the upper mantle. It is caused by several factors. When the temperature drops below liquidus everywhere, the nucleation-growth-dissolution cycle of crystals changes to continuous crystal growth. This increases the crystal size to ~1cm indicating the beginning of crystal-melt segregation. When the crystal fraction increases to about 60% near the surface, the convective heat transport is controlled by solid-state creep, which is many orders of magnitude slower. Crystal-melt segregation occurs via melt percolation, which is consistent with the geochemical constraints. Crystallization of the remaining partially molten layers takes about 10⁷-10⁹ years. This stage merges with the subsequent planetary evolution controlled by mantle convection and radiogenic heating. The long lifetime of the shallow magma ocean suggests that this might be the place where liquid iron equilibrates with the mantle before it sinks down to the core.
This chapter presents the fundamental physics necessary to understand the complex fluid dynamics of mantle convection. The first section derives the equations of conservation for mass, momentum, and energy and the boundary and interface conditions for the various physical quantities. The thermodynamic and rheological properties of solids are discussed in the second section. The mechanism of thermal convection and the classical Boussinesq and anelastic approximations are presented in the third section. As the subject is not often included in geophysical textbooks, an introduction to the physics of multicomponent and multiphase flows is given in the fourth section. At last, the specific applications to mantle convection are reviewed in the fifth section.