Stéphane Labrosse

A crystallizing dense magma ocean at the base of the Earth’s mantle

The distribution of geochemical species in the Earth’s interior is largely controlled by fractional melting and crystallization processes that are intimately linked to the thermal state and evolution of the mantle. The existence of patches of dense partial melt at the base of the Earth’s mantle, together with estimates of melting temperatures for deep mantle phases and the amount of cooling of the underlying core required to maintain a geodynamo throughout much of the Earth’s history, suggest that more extensive deep melting occurred in the past. Here we show that a stable layer of dense melt formed at the base of the mantle early in the Earth’s history would have undergone slow fractional crystallization, and would be an ideal candidate for an unsampled geochemical reservoir hosting a variety of incompatible species (most notably the missing budget of heat-producing elements) for an initial basal magma ocean thickness of about 1,000 km. Differences in 142Nd/144Nd ratios between chondrites and terrestrial rocks can be explained by fractional crystallization with a decay timescale of the order of 1 Gyr. These combined constraints yield thermal evolution models in which radiogenic heat production and latent heat exchange prevent early cooling of the core and possibly delay the onset of the geodynamo to 3.4–4 Gyr ago.

The age of the inner core

Abstract The energy conservation law, when applied to the Earth’s core and integrated between the onset of the crystallization of the inner core and the present time, gives an equation for the age of the inner core. In this equation, all the terms can be expressed theoretically and, given values and uncertainties of all relevant physical parameters, the age of the inner core can be obtained as a function of the heat flux at the core–mantle boundary and the concentrations in radioactive elements. It is found that in absence of radioactive elements in the core, the age of the inner core cannot exceed 2.5 Ga and is most likely around 1 Ga. In addition, to have an inner core as old as the Earth, concentrations in radioactive elements needed in the core are too high to be acceptable on geochemical grounds.

On cooling of the Earth's core

Abstract We have constructed a self-consistent model for cooling of the Earths core in which the thermal history of the core is computed as a function of the time evolution of the heat flux delivered to the mantle across the core-mantle boundary. The temperature profile in the convecting core is first assumed to be adiabatic, and its evolution in time is calculated with the only constraint that energy be globally conserved. When the temperature at the centre drops below the freezing point of the core alloy, the inner core starts growing and cools by conduction; it is found that it cannot have reached its present size in more than 1.7 billion years. If the heat flux delivered to the mantle becomes less than that conducted down the adiabat, the temperature profile becomes subadiabatic in a shell at the top of the core, through which heat is evacuated by conduction. Although it is stable against thermal convection, this shell is not necessarily stagnant and may be the seat of motions owing to compositional convection.

Three-dimensional thermal convection in an iso-viscous, infinite Prandtl number fluid heated from within and from below: applications to the transfer of heat through planetary mantles

Numerical experiments have been carried out to explore the efficiency of heat transfer through a three-dimensional layer heated from both within and below as it is the case for the mantle of earth-like planets. A systematic study for Rayleigh numbers (Ra) between 105 and 107 and non-dimensional internal heating rate (Hs) between 0 and 40 allows us to investigate the pattern of convection and the thermal characteristics of the layer in a range of parameters relevant to mantle convection in earth-like planets. Inversion of the results for the mean temperature and non-dimensional heat flux at the top and the bottom boundaries yields simple parameterization of the heat transfer. It is shown that the mean temperature of the convective fluid (θ) is the sum of the temperature that would exist with no internal heating and a contribution of the non-dimensional internal heating rate (Hs). As predicted by thermal boundary layer analysis, the non-dimensional heat flux at the upper boundary layer can be described by Q=[(Ra)/(Raδ)]1/3θ4/3 with θ=0.5+1.236[(Hs)3/4/(Ra)1/4], and Raδ being the thermal boundary layer Rayleigh number equal to 24.4. In agreement with laboratory experiments, this value slightly increases with the value of the Rayleigh number. This value is identical to that obtained for fluids heated from within only. In most cases, the hot plumes that form at the lower thermal boundary layer do not reach the upper boundary layer. No simple law has been found to describe the heat transfer through the lower thermal boundary layer, but the bottom heat flux can be determined using the global energy balance. The thermal boundary layer analysis performed in this study allows us to extrapolate our results to 3D spherical geometry and our predictions are in good agreement with numerical experiments described in the literature. A simple case of spherical 3D convection has been performed and provides the same thermal history of planetary mantles than that obtained from 3D numerical runs. Compared to previous parameterized analysis, this study shows that the behaviour of the thermal boundary layers is much different than that predicted by experiments for a fluid heated only from below: at similar Rayleigh numbers, the mean temperature is larger and the surface heat flux is much larger. It seems therefore necessary to reconsider previous models of the thermal evolution of planetary mantles.

Hotspots, Mantle Plumes and Core Heat Loss

Abstract The heat flux at the core–mantle boundary (CMB) is a key parameter for core dynamics since it controls its cooling. However, it is poorly known and estimates range from 2 TW to 10 TW. The lowest bound comes from estimates of buoyancy fluxes of hotspots under two assumptions: that they are surface expression of mantle plumes originating from the base of the mantle, and that they are responsible for the totality of the heat flux at the CMB. Using a new procedure to detect plumes in a numerical model of Rayleigh–Benard convection (convection between isothermal horizontal planes) with internal heating, it is shown that many hot plumes that start from the bottom boundary do not reach the top surface and that the bottom heat flux is primarily controlled by the arrival of cold plumes. Hot plumes easily form at the bottom boundary but they are mostly due to the spreading of cold plume heads that allow the concentration of hot matter. These plumes are generally not buoyant enough to cross the whole system and the hot plumes that reach the top surface result from an interaction between several hot plumes. According to this simple dynamical behavior, the heat flux at the bottom boundary is shown to be strongly correlated with the advection due to cold plumes and not with advection by hot plumes that arrive at the surface. It is then inferred that the heat flux out of hotspots can only give a lower bound to the heat flow at the CMB and that knowing the advection by subducted plates would give a better estimate.

Convective heat transfer as a function of wavelength: Implications for the cooling of the Earth

[1] Attempting to reconstruct the thermal history of the Earth from a geophysical point of view has for a long time been in disagreement with geochemical data. The geophysical approach uses parameterized models of mantle cooling. The rate of cooling of the Earth at the beginning of its history obtained in these models is generally too rapid to allow a sufficient present-day secular cooling rate. Geochemical estimates of radioactive element concentrations in the mantle then appear too low to explain the observed present mantle heat loss. Cooling models use scaling laws for the mean heat flux out of the mantle as a function of its Rayleigh number of the form Q / Ra b . Recent studies have introduced very low values of the exponent b, which can help reduce the cooling rate of the mantle. The present study instead focuses on the coefficient C in the relation Q = CR a b and, in particular, on its variation with the wavelength of convection. The heat transfer strongly depends on the wavelength of convection. The length scale of convection in Earth’s mantle is that of plate tectonics, implying convective cells of wide aspect ratio. Taking into account the long wavelength of convection in Earth’s mantle can significantly reduce the efficiency of heat transfer. The likely variations of this wavelength with the Wilson cycle thus imply important variations of the heat flow out of the Earth on a intermediate timescale of 100 Ma, which renders parameterized models of thermal evolution inaccurate for quantitative predictions.

Effects of continents on Earth cooling: Thermal blanketing and depletion in radioactive elements

Estimate of mantle heat flow under continental shields are very low, indicating a strong insulating effect of continents on mantle heat loss. This effect is investigated with a simple approach: continents are introduced in an Earth cooling model as perfect thermal insulators. Continental growth rate has then a strong influence on mantle cooling. Various continental growth models are tested and are used to compute the mantle depletion in radioactive elements as a function of continental crust extraction. Results show that the thermal blanketing effect of continents strongly affects mantle cooling, and that mantle depletion must be taken into account in order not to overestimate mantle heat loss. In order to obtain correct oceanic heat flow for present time, continental growth must begin at least 3 Gy ago and steady-state for continental area must be reached for at least 1.5 Gy in our cooling model.

Dynamic Causes of the Relation Between Area and Age of the Ocean Floor

Old Plates and the Sea Estimates for the area and age of the ocean floor are at odds with assumptions for mantle convection, which imply that an older sea floor—rather than a new one—would be preferentially subducted over time. Previous efforts to explain these relationships have been based on geologic evidence and simple models. Coltice et al. (p. 335) created numerical three-dimensional convection models representing more realistic physical boundaries, including a spherical Earth, the existence of continents and supercontinents over time, and realistic rheologies. A combination of continents and plate-like behavior of the ocean floor sufficed to produce the observed relationship between plate area and plate age, which explains why some old oceanic crust still remains. Numerical simulations show that the presence of continents influences the area of old sea floor. The distribution of seafloor ages determines fundamental characteristics of Earth such as sea level, ocean chemistry, tectonic forces, and heat loss from the mantle. The present-day distribution suggests that subduction affects lithosphere of all ages, but this is at odds with the theory of thermal convection that predicts that subduction should happen once a critical age has been reached. We used spherical models of mantle convection to show that plate-like behavior and continents cause the seafloor area-age distribution to be representative of present-day Earth. The distribution varies in time with the creation and destruction of new plate boundaries. Our simulations suggest that the ocean floor production rate previously reached peaks that were twice the present-day value.

Geophysically consistent values of the perovskite to post‐perovskite transition Clapeyron slope

The double‐crossing hypothesis posits that post‐perovskite bearing rock in Earths D″ layer exists as a layer above the core‐mantle boundary bounded above and below by intersections between a curved thermal boundary layer geotherm and a relatively steep phase boundary. Increasing seismic evidence for the existence of pairs of discontinuities predicted to occur at the top and bottom of this layer motivates an examination of the consistency of this model with mineral physics constraints for the Clapeyron slope of this phase transition. Using independent constraints for a lower bound on temperature in Earths deep mantle and the temperature of Earths inner core boundary, we show that a post‐perovskite double‐crossing is inconsistent with plausible core temperatures for a Clapeyron slope less than about 7 MPa/K, with the higher range of experimental values yielding better agreement with recent estimates of the melting temperature of Earths core.

Crystallization of silicon dioxide and compositional evolution of the Earth’s core

The Earth’s core is about ten per cent less dense than pure iron (Fe), suggesting that it contains light elements as well as iron. Modelling of core formation at high pressure (around 40–60 gigapascals) and high temperature (about 3,500 kelvin) in a deep magma ocean predicts that both silicon (Si) and oxygen (O) are among the impurities in the liquid outer core. However, only the binary systems Fe–Si and Fe–O have been studied in detail at high pressures, and little is known about the compositional evolution of the Fe–Si–O ternary alloy under core conditions. Here we performed melting experiments on liquid Fe–Si–O alloy at core pressures in a laser-heated diamond-anvil cell. Our results demonstrate that the liquidus field of silicon dioxide (SiO2) is unexpectedly wide at the iron-rich portion of the Fe–Si–O ternary, such that an initial Fe–Si–O core crystallizes SiO2 as it cools. If crystallization proceeds on top of the core, the buoyancy released should have been more than sufficient to power core convection and a dynamo, in spite of high thermal conductivity, from as early on as the Hadean eon. SiO2 saturation also sets limits on silicon and oxygen concentrations in the present-day outer core.