Flow instabilities occur at all scales in planetary systems. In this thesis we examine three cases of such instabilities, on three very different length scales. In the first part, we test the idea that Archean granite-greenstone belts (GGBs) form by crustal diapirism, or Rayleigh-Taylor instabilities. GGBs are characterized by large granitic domes (50-100 km in diameter) embedded in narrow keel-shaped greenstones. They are ubiquitous in Archean (> 2.5 Ga) terrains, but rare thereafter. We performed finite element calculations for a visco-elastic, temperature-dependent, non-Newtonian crust under conditions appropriate for the Archean, which show that dense low-viscosity volcanics overlying a felsic basement will overturn diapirically in as little as 10 Ma, displacing as much as 60 % of the volcanics to the lower crust. This surprisingly fast overturn rate suggests that diapiric overturn dominated crustal tectonics in the hot conditions of the Early Earth, becoming less important as the Earth cooled. Moreover, the deposition of large volumes of wet basaltic volcanics to the lower crust may provide the source for the formation of the distinctly Archean granitic rocks which dominate Earth's oldest continents. The second part examines the origin of Venusian coronae, circular volcanic features unique to Venus. Coronae are thought to result from small instabilities (diapirs) from the core-mantle boundary, which are typical of stagnant-lid convection. However, most young coronae are located in a region surrounded by long-lived hotspots, typical of a more active style of mantle convection. Using analogue experiments in corn syrup heated from below, we show that the co-existence of diapirs and long-lived mantle plumes are a direct consequence of the catastrophic overturn of the cold Venusian lithosphere thought to have occurred ~ 700 Ma ago. In the last part we analyze the thermal effect of fluid flow through a full-scale experiment testing clay and concrete tunnel seals in a Deep Geological Repository for nuclear was finite element software, we were able to show that the formation of fissures in the heated chamber between the two seals effectively limited heat flow, and could explain the discrepancy between the predicted and measured temperatures.

Plane-layer geometry convection models remain useful for modelling planetary mantle dynamics however they yield significantly warmer mean temperatures than spherical shell models. For example, in a uniform property spherical shell with the same radius ratio, f, as the Earth's mantle; a bottom heating Rayleigh number, Ra, of 10^7 and a nondimensional internal heating rate, H, of 23 (arguably Earth-like values) are insufficient to heat the mean temperature, θ, above the mean of the non-dimensional boundary value temperatures (0.5), the temperature in a plane-layer model with no internal heating. This study investigates the impact of this geometrical effect in convection models featuring uniform and stratified viscosity. To address the effect of geometry, heat sinks are implemented to lower the mean temperature in 3D plane-layer isoviscous convection models. Over 100 models are analyzed, and their mean temperatures are used to derive a single equation for predicting θ, as a function of Ra, H and f in spherical and plane-layer systems featuring free-slip surfaces. The inclusion of first-order terrestrial characteristics is introduced to quantitatively assess the influence of system geometry on planetary scale simulations. Again, over 100 models are analyzed featuring a uniform upper mantle viscosity and a lower mantle viscosity that increases by a factor of 30 or 100. An effective Rayleigh number, Raη, is defined based on the average viscosity of the mantle. Equations for the relationship between θ, Raη, and H are derived for convection in a spherical shell with f = 0.547 and plane-layer geometries. These equations can be used to determine the appropriate heating rate for a plane-layer convection model to emulate spherical shell convection mean temperatures for effective Rayleigh numbers comparable to the Earth’s value and greater. Comparing cases with the same H and Raη, the increased lower mantle viscosity amplifies the mismatch in mean temperatures between spherical shell and plane-layer models. These findings emphasize the importance of adjusting heating rates in plane-layer geometry models and have important implications for studying convection with temperature-dependent parameters in plane-layer systems. The findings are particularly relevant to the study of convection in super-Earths where full spherical shell calculations remain intractable.

Flow instabilities occur at all scales in planetary systems. In this thesis we examine three cases of such instabilities, on three very different length scales. In the first part, we test the idea that Archean granite-greenstone belts (GGBs) form by crustal diapirism, or Rayleigh-Taylor instabilities. GGBs are characterized by large granitic domes (50-100 km in diameter) embedded in narrow keel-shaped greenstones. They are ubiquitous in Archean (> 2.5 Ga) terrains, but rare thereafter. We performed finite element calculations for a visco-elastic, temperature-dependent, non-Newtonian crust under conditions appropriate for the Archean, which show that dense low-viscosity volcanics overlying a felsic basement will overturn diapirically in as little as 10 Ma, displacing as much as 60 % of the volcanics to the lower crust. This surprisingly fast overturn rate suggests that diapiric overturn dominated crustal tectonics in the hot conditions of the Early Earth, becoming less important as the Earth cooled. Moreover, the deposition of large volumes of wet basaltic volcanics to the lower crust may provide the source for the formation of the distinctly Archean granitic rocks which dominate Earth's oldest continents. The second part examines the origin of Venusian coronae, circular volcanic features unique to Venus. Coronae are thought to result from small instabilities (diapirs) from the core-mantle boundary, which are typical of stagnant-lid convection. However, most young coronae are located in a region surrounded by long-lived hotspots, typical of a more active style of mantle convection. Using analogue experiments in corn syrup heated from below, we show that the co-existence of diapirs and long-lived mantle plumes are a direct consequence of the catastrophic overturn of the cold Venusian lithosphere thought to have occurred ~ 700 Ma ago. In the last part we analyze the thermal effect of fluid flow through a full-scale experiment testing clay and concrete tunnel seals in a Deep Geological Repository for nuclear was finite element software, we were able to show that the formation of fissures in the heated chamber between the two seals effectively limited heat flow, and could explain the discrepancy between the predicted and measured temperatures.

In this thesis, we present results of a numerical modelling study focused on the thermal evolution of the Earth and terrestrial planets. We focus particularly on two problems: I) constraining the internal structure of Venus and Mercury using their geoid and surface topography data and II) evaluating the effects of a rhe- ologically distinct post-perovskite on the secular cooling of the Earth. In part I, we performed simulations in a broad group of models of the Venusian man- tle, characterised by different rheological descriptions, and we compared spectra of their geoid and their surface topography with the observed quantities. Our analysis suggested that the geoid and the surface topography of Venus are con- sistent with a radially symmetric viscosity model with a strong 200 km thick lithosphere, without an asthenosphere and with a gradual viscosity increase in the underlying mantle. In the case of Mercury, none of our models was able to predict observed data, thus suggesting other than a dynamic origin of observed geoid and topography. In part II, we investigated style of Earth's mantle con- vection and its long-term evolution in the models that take into account a weak post-perovskite. We conclude that the presence of the weak post-perovskite en- hances the core cooling. This effect is comparable in...

Cette thèse vise à proposer de nouvelles méthodes permettant de reconstruire la circulation dans le manteau terrestre et l'évolution de la tectonique de surface pour les deux cents derniers millions d'années. Nous utilisons des modèles numériques de convection mantellique dans lesquels la dynamique de surface est comparable à la tectonique terrestre. En combinant ces modèles avec des reconstructions de la tectonique des plaques il est possible d'estimerla structure et l'évolution du champ de température dans le manteau. Jusqu'à présent, l'inclusion des reconstructions de la tectonique des plaques se faisait en imposant des conditions aux limites du modèle (équilibre des forces, vitesses imposées...). Ces techniques, bien que permettant de tester la validité de différents scénarios tectoniques alternatifs, n'autorisent pas de rétroaction dynamique de la convection mantellique sur la tectonique de surface.Dans ce travail, nous avons développé des techniques d'assimilation de données permettant d'intégrer les reconstructions de la tectonique des plaques dans un modèle numérique tout en laissant se développer de manière auto-cohérente cette rétroaction. Les techniques développées permettent également de prendre en compte les incertitudes associées aux reconstructions de la tectonique des plaques et de calculer les erreurs sur l'estimation finale de la circulationmantellique.Dans un premier temps, nous avons développé un filtre de Kalman suboptimal qui permet d'estimer la structure et l'évolution de la circulation mantellique la plus probable à partir d'un modèle numérique de convection et d'une sérietemporelle d'observations de surface, ainsi que de leurs incertitudes respectives.Ce filtre a été testé sur des expériences synthétiques. Celles-ci consistent à tenter de retrouver une évolution témoin à partir d'une série temporelle de données issues de cette évolution. Ces expériences ont montré qu'il était possible, enprincipe, de reconstruire la structure et l'évolution de l'ensemble du manteau à partir d'observations de vitesses et de flux de chaleur à la surface.Dans un second temps, nous avons développé un filtre de Kalman d'ensemble. Ce filtre permet non seulement d'estimer de manière plus précise la géométrie des structures mantelliques, mais aussi les incertitudes sur cette estimation. / This dissertation focuses on the developpement of data assimilation methods to reconstruct the circulation of the Earth's mantle and the evolution of its surface tectonics for the last 200~Myrs. We use numerical models of mantle convection in which the surface dynamics is similar to the Earth's. By combining these models with plate tectonics reconstructions, it is possible to estimate the structure and evolution of the temperature field of the mantle. So far, the assimilation of plate tectonics reconstructions was done by imposing specific boundary conditions in the model (force balance, imposed velocities...). These techniques, although insightful to test the likeliness of alternative tectonic scenarios, do not allow the full expression of the dynamical feedback between mantle convection and surface tectonics. We develop sequential data assimilation techniques able to assimilate plate tectonics reconstructions in a numerical model while simultaneously letting this dynamicalfeedback develop self-consistently. Moreover, these techniques take into account errors in plate tectonics reconstructions, and compute the error on the final estimation of mantle circulation.First, we develop a suboptimal Kalman filter. This filter estimates the most likely structure and evolution of mantle circulation from a numerical model of mantle convection, a time series of surface observations and the uncertainty on both. This filter was tested on synthetic experiments. The principle of a synthetic experiment is to apply the data assimilation algorithm to a set of synthetic observations obtained from a reference run, and to then compare the obtained estimation of the evolution with the reference evolution. The synthetic experiments we conducted showed that it was possible, in principle, to reconstruct the structure and evolution of the whole mantle from surface velocities and heat flux observations.Second, we develop an Ensemble Kalman Filter. Instead of estimating the most likely evolution, an ensemble of possible evolutions are computed. This technique leads to a better estimation of the geometry of mantle structures and a more complete estimation of the uncertainties associated.

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