The composition and state of Earth's core, located deeper than 2,900 km from the surface, remain ... more The composition and state of Earth's core, located deeper than 2,900 km from the surface, remain largely uncertain. Recent static experiments on iron and alloys performed up to inner core pressure and temperature conditions have revealed phase relations and properties of core materials. These mineral physics constraints, combined with theoretical calculations, continue to improve our understanding of the core, in particular the crystal structure of the inner core and the chemical composition, thermal structure and evolution, and possible stratification of the outer core.
It has been proposed that the ultra low velocity zones at the base of the mantle are the remnants... more It has been proposed that the ultra low velocity zones at the base of the mantle are the remnants of the initially thick magma ocean (the basal magma ocean, BMO) that undergoes slow crystallization. The presence of a molten silicate layer between the solid mantle and the core can dramatically change the thermal coupling between them and affect the ability of the core to maintain a dynamo. Convection in the BMO can in particular change the way the lateral variation of heat flow at the bottom of the solid mantle are transmitted to ...
Although it is known that the geodynamo has been operating for at least 3.2 Ga, it remains diffic... more Although it is known that the geodynamo has been operating for at least 3.2 Ga, it remains difficult to infer the intensity, dipolarity and stability (occurrence of reversals) of the Precambrian magnetic field of the Earth. In order to assist the interpretation of palaeomagnetic data, we produce models for the long-term evolution of the geodynamo by combining core thermodynamics with a systematic scaling analysis of numerical dynamo simulations. We update earlier dynamo scaling results by exploring a parameter space, which has been extended in order to account for core aspect ratios and buoyancy source distributions relevant to Earth in the Precambrian. Our analysis highlights the central role of the convective power, which is an output of core thermodynamics and the main input of our updated scalings. As the thermal evolution of the Earth's core is not well known, two end-member models of heat flow evolution at the core–mantle boundary (CMB) are used, respectively, terminating at present heat flows of 11 TW (high-power scenario) and 3 TW (low power scenario). The resulting models predict that until the appearance of the inner core, a thermal dynamo driven only by secular cooling, and without any need for radioactive heating, can produce a dipole moment of strength comparable to that of the present field, thus precluding an interpretation of the oldest palaeomagnetic records as evidence of the inner core presence. The observed lack of strong long-term trends in palaeointensity data throughout the Earth's history can be rationalized by the weakness of palaeointensity variations predicted by our models relatively to the data scatter. Specifically, the most significant internal magnetic field increase which we predict is associated to the sudden power increase resulting from inner core nucleation, but the dynamo becomes deeper-seated in the core, thus largely cancelling the increase at the core and Earth surface, and diminishing the prospect of observing this event in palaeointensity data. Our models additionally suggest that the geodynamo has lied close to the transition to polarity reversals throughout its history. In the Precambrian, we predict a dynamo with similar dipolarity and less frequent reversals than at present times, due to conditions of generally lower convective forcing. Quantifying the typical CMB heat flow variation needed for the geodynamo to cross the transition from a reversing to a non-reversing state, we find that it is unlikely that such a variation may have caused superchrons in the last 0.5 Ga without shutting down dynamo action altogether.
Le manteau et le noyau de la Terre ont des échelles de temps caractéristiques très différentes et... more Le manteau et le noyau de la Terre ont des échelles de temps caractéristiques très différentes et l'évolution thermique du système couplé est contrôlée par l'échelle de temps de la convection dans le manteau. Un modèle de refroidissement de la Terre a été construit dans lequel la conservation de l'énergie est utilisée sous forme intégrale pour le noyau et le manteau et les deux ensembles sont couplés. Pour paramétriser la convection dans le manteau, un modèle numérique de convection avec chauffage par le bas et en volume a ...
The large temperature excess in young planets is probably evacuated as much by intense volcanic a... more The large temperature excess in young planets is probably evacuated as much by intense volcanic activity as by thermal diffusion across a lithosphere. However, most fluid dynamic codes in Earth Science are implementing a zero vertical velocity at the surface of their models. This condition forbids any direct transport of material and therefore any direct extraction of heat from depth. We propose a new set of boundary conditions on the top surface for the momentum and energy equations. The vertical velocity is not imposed to ...
Most terrestrial planets may have experienced a magma ocean period in their infancy where most of... more Most terrestrial planets may have experienced a magma ocean period in their infancy where most of their mantle was molten. Upon cooling to space, their surface must have crystallized, keeping a largely molten interior for some more time. The dynamics and evolution of planets at this stage is controlled by the surface heat flow, which is dominated by volcanism. This is in sharp contrast with the current situation on these planets (with the notable exception of Io) where heat is carried through the top surface of the mantle by ...
Core formation, crystal/melt separation, mingling of immiscible magmas, and diapirism are fundame... more Core formation, crystal/melt separation, mingling of immiscible magmas, and diapirism are fundamental geological processes that involve differential motions driven by gravity. Diffusion modifies the composition or/and temperature of the considered phases while they travel. Solid particles, liquid drops and viscous diapirs equilibrate while sinking/rising through their surroundings with a time scale that depends on the physics of the flow and the material properties. In particular, the internal circulation within a liquid drop or a diapir favors the diffusive exchange at the interface. To evaluate time scales of chemical/thermal equilibration between a material falling/rising through a deformable medium, we propose analytical laws that can be used at multiple scales. They depend mostly on the non‐dimensional Péclet and Reynolds numbers, and are consistent with numerical simulations. We show that equilibration between a particle, drop or diapir and its host needs to be considered in light of the flow structure complexity. It is of fundamental importance to identify the dynamic regime of the flow and take into account the role of the inner circulation within drops and diapirs, as well as inertia that reduces the thickness of boundary layers and enhances exchange through the interface. The scaling laws are applied to predict nickel equilibration between metals and silicates that occurs within 130 m of fall in about 4 minutes during the metal rain stage of the Earth’s core formation. For a mafic blob (10 cm diameter) sinking into a felsic melt, trace element equilibration would occur over 4500 m and in about 3 years.
The improvements of the knowledge of the seismic structure of the inner core and the complexities... more The improvements of the knowledge of the seismic structure of the inner core and the complexities thereby revealed ask for a dynamical origin. Sub-solidus convection was one of the early suggestions to explain the seismic anisotropy, but it requires an unstable density gradient either from thermal or compositional origin, or from both. Temperature and composition profiles in the inner core are computed using a unidimensional model of core evolution including diffusion in the inner core and fractional crystallisation at the inner core boundary (ICB). The thermal conductivity of the core has been recently revised upwardly and, moreover, found to increase with depth. Values of the heat flow across the core mantle boundary (CMB) sufficient to maintain convection in the whole outer core are not sufficient to make the temperature in the inner core super-isentropic and therefore prone to thermal instability. An unreasonably high CMB heat flow is necessary to this end. The compositional stratification results from a competition of the increase of the concentration of light elements in the outer core with inner core growth, which makes the inner core concentration also increase, and of the decrease of the liquidus, which makes the partition coefficient decrease as well as the concentration of light elements in the solid. While the latter (destabilizing) effect dominates at small inner core sizes, the former takes over for a large inner core. The turnover point is encountered for an inner core about half its current size in the case of S, but much larger for the case of O. The combined thermal and compositional buoyancy is stabilizing and solid-state convection in the inner core appears unlikely, unless an early double-diffusive instability can set in.
A typical heat flux density at the bottom of the solid mantle is 100mWm− 2, a value that has to b... more A typical heat flux density at the bottom of the solid mantle is 100mWm− 2, a value that has to be matched by the sum of the heat flux transported across the melt layer plus the latent heat released by crystallisation. The heat flow across the melt layer, carried by convection, scales with the super-isentropic temperature difference across it,∆ T, and the viscosity, µ, according to1, 2, q= Ck∆ T h (αρg∆ Th3 κµ
The problem of thermal evolution of the Earth is long standing and has sometimes been called “the... more The problem of thermal evolution of the Earth is long standing and has sometimes been called “the missing heat paradox”. This problem arises because most cooling models of the Earth, based on parameterized convection, are unable to get a present–time heat flow at Earth's surface that matches the observations, unless an unrealistically high value for the radiogenic heat production is used. In other words, the present Urey ratio of these models is higher than what is implied by geochemistry.
Results of current 1D models on planetesimal accretion yield an onion-like thermal structure with... more Results of current 1D models on planetesimal accretion yield an onion-like thermal structure with high internal temperatures due to powerful short-lived radiogenic heating in the planetesimals. These allow for silicate melting in the parent bodies [1] as suggested by meteorite samples. Yet, impact processes are not considered in these models and core formation is, if taken into account, assumed to be instantaneous with no feedback on the mantle evolution [1].
Abstract Of the terrestrial planets, Earth and Mercury have self-sustained fields while Mars and ... more Abstract Of the terrestrial planets, Earth and Mercury have self-sustained fields while Mars and Venus do not. Magnetic field data recorded at Ganymede have been interpreted as evidence of a self-generated magnetic field. The other icy Galilean satellites have magnetic fields induced in their subsurface oceans while Io and the Saturnian satellite Titan apparently are lacking magnetic fields of internal origin altogether. Parts of the lunar crust are remanently magnetized as are parts of the crust of Mars.
Abstract In our search for life on other planets over the past decades, we have come to understan... more Abstract In our search for life on other planets over the past decades, we have come to understand that the solid terrestrial planets provide much more than merely a substrate on which life may develop. Large-scale exchange of heat and volatile species between planetary interiors and hydrospheres/atmospheres, as well as the presence of a magnetic field, are important factors contributing to the habitability of a planet.
Ce cours a pour objectif d'utiliser la thermodynamique hors équilibre pour l'appliquera la Terre ... more Ce cours a pour objectif d'utiliser la thermodynamique hors équilibre pour l'appliquera la Terre interne, afin d'en étudier l'évolution. Avant d'entrer dans le vif du sujet, il convient de définir quelques concepts généraux de la thermodynamique hors équilibre telle qu'elle sera utilisée ici.
Abstract The distribution of seafloor ages determines fundamental characteristics of Earth such a... more Abstract 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.
Abstract Interpretation of the noble gas isotopic signature in hotspots is still controversial. I... more Abstract Interpretation of the noble gas isotopic signature in hotspots is still controversial. It suggests that relatively primitive material remains untapped in the deepest mantle, even while mantle convection and sub-surface melting efficiently erase primordial heterogeneities. A recent model suggests that significant differentiation and fractionation affects the deepest mantle following the formation of a dense basal magma ocean (BMO) right after core segregation (Labrosse et al., 2007).
The composition and state of Earth's core, located deeper than 2,900 km from the surface, remain ... more The composition and state of Earth's core, located deeper than 2,900 km from the surface, remain largely uncertain. Recent static experiments on iron and alloys performed up to inner core pressure and temperature conditions have revealed phase relations and properties of core materials. These mineral physics constraints, combined with theoretical calculations, continue to improve our understanding of the core, in particular the crystal structure of the inner core and the chemical composition, thermal structure and evolution, and possible stratification of the outer core.
It has been proposed that the ultra low velocity zones at the base of the mantle are the remnants... more It has been proposed that the ultra low velocity zones at the base of the mantle are the remnants of the initially thick magma ocean (the basal magma ocean, BMO) that undergoes slow crystallization. The presence of a molten silicate layer between the solid mantle and the core can dramatically change the thermal coupling between them and affect the ability of the core to maintain a dynamo. Convection in the BMO can in particular change the way the lateral variation of heat flow at the bottom of the solid mantle are transmitted to ...
Although it is known that the geodynamo has been operating for at least 3.2 Ga, it remains diffic... more Although it is known that the geodynamo has been operating for at least 3.2 Ga, it remains difficult to infer the intensity, dipolarity and stability (occurrence of reversals) of the Precambrian magnetic field of the Earth. In order to assist the interpretation of palaeomagnetic data, we produce models for the long-term evolution of the geodynamo by combining core thermodynamics with a systematic scaling analysis of numerical dynamo simulations. We update earlier dynamo scaling results by exploring a parameter space, which has been extended in order to account for core aspect ratios and buoyancy source distributions relevant to Earth in the Precambrian. Our analysis highlights the central role of the convective power, which is an output of core thermodynamics and the main input of our updated scalings. As the thermal evolution of the Earth's core is not well known, two end-member models of heat flow evolution at the core–mantle boundary (CMB) are used, respectively, terminating at present heat flows of 11 TW (high-power scenario) and 3 TW (low power scenario). The resulting models predict that until the appearance of the inner core, a thermal dynamo driven only by secular cooling, and without any need for radioactive heating, can produce a dipole moment of strength comparable to that of the present field, thus precluding an interpretation of the oldest palaeomagnetic records as evidence of the inner core presence. The observed lack of strong long-term trends in palaeointensity data throughout the Earth's history can be rationalized by the weakness of palaeointensity variations predicted by our models relatively to the data scatter. Specifically, the most significant internal magnetic field increase which we predict is associated to the sudden power increase resulting from inner core nucleation, but the dynamo becomes deeper-seated in the core, thus largely cancelling the increase at the core and Earth surface, and diminishing the prospect of observing this event in palaeointensity data. Our models additionally suggest that the geodynamo has lied close to the transition to polarity reversals throughout its history. In the Precambrian, we predict a dynamo with similar dipolarity and less frequent reversals than at present times, due to conditions of generally lower convective forcing. Quantifying the typical CMB heat flow variation needed for the geodynamo to cross the transition from a reversing to a non-reversing state, we find that it is unlikely that such a variation may have caused superchrons in the last 0.5 Ga without shutting down dynamo action altogether.
Le manteau et le noyau de la Terre ont des échelles de temps caractéristiques très différentes et... more Le manteau et le noyau de la Terre ont des échelles de temps caractéristiques très différentes et l'évolution thermique du système couplé est contrôlée par l'échelle de temps de la convection dans le manteau. Un modèle de refroidissement de la Terre a été construit dans lequel la conservation de l'énergie est utilisée sous forme intégrale pour le noyau et le manteau et les deux ensembles sont couplés. Pour paramétriser la convection dans le manteau, un modèle numérique de convection avec chauffage par le bas et en volume a ...
The large temperature excess in young planets is probably evacuated as much by intense volcanic a... more The large temperature excess in young planets is probably evacuated as much by intense volcanic activity as by thermal diffusion across a lithosphere. However, most fluid dynamic codes in Earth Science are implementing a zero vertical velocity at the surface of their models. This condition forbids any direct transport of material and therefore any direct extraction of heat from depth. We propose a new set of boundary conditions on the top surface for the momentum and energy equations. The vertical velocity is not imposed to ...
Most terrestrial planets may have experienced a magma ocean period in their infancy where most of... more Most terrestrial planets may have experienced a magma ocean period in their infancy where most of their mantle was molten. Upon cooling to space, their surface must have crystallized, keeping a largely molten interior for some more time. The dynamics and evolution of planets at this stage is controlled by the surface heat flow, which is dominated by volcanism. This is in sharp contrast with the current situation on these planets (with the notable exception of Io) where heat is carried through the top surface of the mantle by ...
Core formation, crystal/melt separation, mingling of immiscible magmas, and diapirism are fundame... more Core formation, crystal/melt separation, mingling of immiscible magmas, and diapirism are fundamental geological processes that involve differential motions driven by gravity. Diffusion modifies the composition or/and temperature of the considered phases while they travel. Solid particles, liquid drops and viscous diapirs equilibrate while sinking/rising through their surroundings with a time scale that depends on the physics of the flow and the material properties. In particular, the internal circulation within a liquid drop or a diapir favors the diffusive exchange at the interface. To evaluate time scales of chemical/thermal equilibration between a material falling/rising through a deformable medium, we propose analytical laws that can be used at multiple scales. They depend mostly on the non‐dimensional Péclet and Reynolds numbers, and are consistent with numerical simulations. We show that equilibration between a particle, drop or diapir and its host needs to be considered in light of the flow structure complexity. It is of fundamental importance to identify the dynamic regime of the flow and take into account the role of the inner circulation within drops and diapirs, as well as inertia that reduces the thickness of boundary layers and enhances exchange through the interface. The scaling laws are applied to predict nickel equilibration between metals and silicates that occurs within 130 m of fall in about 4 minutes during the metal rain stage of the Earth’s core formation. For a mafic blob (10 cm diameter) sinking into a felsic melt, trace element equilibration would occur over 4500 m and in about 3 years.
The improvements of the knowledge of the seismic structure of the inner core and the complexities... more The improvements of the knowledge of the seismic structure of the inner core and the complexities thereby revealed ask for a dynamical origin. Sub-solidus convection was one of the early suggestions to explain the seismic anisotropy, but it requires an unstable density gradient either from thermal or compositional origin, or from both. Temperature and composition profiles in the inner core are computed using a unidimensional model of core evolution including diffusion in the inner core and fractional crystallisation at the inner core boundary (ICB). The thermal conductivity of the core has been recently revised upwardly and, moreover, found to increase with depth. Values of the heat flow across the core mantle boundary (CMB) sufficient to maintain convection in the whole outer core are not sufficient to make the temperature in the inner core super-isentropic and therefore prone to thermal instability. An unreasonably high CMB heat flow is necessary to this end. The compositional stratification results from a competition of the increase of the concentration of light elements in the outer core with inner core growth, which makes the inner core concentration also increase, and of the decrease of the liquidus, which makes the partition coefficient decrease as well as the concentration of light elements in the solid. While the latter (destabilizing) effect dominates at small inner core sizes, the former takes over for a large inner core. The turnover point is encountered for an inner core about half its current size in the case of S, but much larger for the case of O. The combined thermal and compositional buoyancy is stabilizing and solid-state convection in the inner core appears unlikely, unless an early double-diffusive instability can set in.
A typical heat flux density at the bottom of the solid mantle is 100mWm− 2, a value that has to b... more A typical heat flux density at the bottom of the solid mantle is 100mWm− 2, a value that has to be matched by the sum of the heat flux transported across the melt layer plus the latent heat released by crystallisation. The heat flow across the melt layer, carried by convection, scales with the super-isentropic temperature difference across it,∆ T, and the viscosity, µ, according to1, 2, q= Ck∆ T h (αρg∆ Th3 κµ
The problem of thermal evolution of the Earth is long standing and has sometimes been called “the... more The problem of thermal evolution of the Earth is long standing and has sometimes been called “the missing heat paradox”. This problem arises because most cooling models of the Earth, based on parameterized convection, are unable to get a present–time heat flow at Earth's surface that matches the observations, unless an unrealistically high value for the radiogenic heat production is used. In other words, the present Urey ratio of these models is higher than what is implied by geochemistry.
Results of current 1D models on planetesimal accretion yield an onion-like thermal structure with... more Results of current 1D models on planetesimal accretion yield an onion-like thermal structure with high internal temperatures due to powerful short-lived radiogenic heating in the planetesimals. These allow for silicate melting in the parent bodies [1] as suggested by meteorite samples. Yet, impact processes are not considered in these models and core formation is, if taken into account, assumed to be instantaneous with no feedback on the mantle evolution [1].
Abstract Of the terrestrial planets, Earth and Mercury have self-sustained fields while Mars and ... more Abstract Of the terrestrial planets, Earth and Mercury have self-sustained fields while Mars and Venus do not. Magnetic field data recorded at Ganymede have been interpreted as evidence of a self-generated magnetic field. The other icy Galilean satellites have magnetic fields induced in their subsurface oceans while Io and the Saturnian satellite Titan apparently are lacking magnetic fields of internal origin altogether. Parts of the lunar crust are remanently magnetized as are parts of the crust of Mars.
Abstract In our search for life on other planets over the past decades, we have come to understan... more Abstract In our search for life on other planets over the past decades, we have come to understand that the solid terrestrial planets provide much more than merely a substrate on which life may develop. Large-scale exchange of heat and volatile species between planetary interiors and hydrospheres/atmospheres, as well as the presence of a magnetic field, are important factors contributing to the habitability of a planet.
Ce cours a pour objectif d'utiliser la thermodynamique hors équilibre pour l'appliquera la Terre ... more Ce cours a pour objectif d'utiliser la thermodynamique hors équilibre pour l'appliquera la Terre interne, afin d'en étudier l'évolution. Avant d'entrer dans le vif du sujet, il convient de définir quelques concepts généraux de la thermodynamique hors équilibre telle qu'elle sera utilisée ici.
Abstract The distribution of seafloor ages determines fundamental characteristics of Earth such a... more Abstract 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.
Abstract Interpretation of the noble gas isotopic signature in hotspots is still controversial. I... more Abstract Interpretation of the noble gas isotopic signature in hotspots is still controversial. It suggests that relatively primitive material remains untapped in the deepest mantle, even while mantle convection and sub-surface melting efficiently erase primordial heterogeneities. A recent model suggests that significant differentiation and fractionation affects the deepest mantle following the formation of a dense basal magma ocean (BMO) right after core segregation (Labrosse et al., 2007).
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