An analytic boundary layer model for thermal convection with a finite-strength plate and depth-dependent viscosity is developed. The model includes a specific energy balance for the lithosphere and accounts for coupling between the plate and underlying mantle. Multiple solutions are possible with three solution branches representing three distinct modes of thermal convection. One branch corresponds to the classic boundary layer solution for active lid plate tectonics while two new branches represent solutions for sluggish lid convection. The model is compared to numerical simulations with highly temperature dependent viscosity and is able to predict both the type of convection (active, sluggish, or stagnant lid) as well as the presence of single and multiple solution regimes. The existence of multiple solutions suggests that the mode of planetary convection may be history dependent. The dependence of mantle viscosity on temperature and water concentration is found to introduce a strong dynamic feedback with plate tectonics. A dimensionless parameter is defined to quantitatively evaluate the relative strength of this feedback and demonstrates that water and heat transport may be equally important in controlling present-day platemantle dynamics for the Earth. A simple parameterized evolution model illustrates the feedback and agrees well with our analytic results. This suggests that a simple relationship may exist between the rate of change of water concentration and the rate of change of temperature in the mantle. This study concludes by investigating the possibility of a magnetic field dynamo in early solar system planetesimals. The thermal evolution of planetesimals is modeled by considering melting, core formation, and the onset of mantle convection and then employing thermal boundary layer theory for stagnant lid convection (if possible) to determine the cooling rate of the body. We assess the presence, strength and duration of a dynamo for a range of planetesimal sizes and other parameters. We find that a minimum radius of O(500) km is required for a thermally driven dynamo of duration O(10) My. The dependence of the results on model parameters is made explicit through the derivation of an analytic solution. / Earth and Planetary Sciences

Over the last fifty years, our knowledge of the Solar System has increased exponentially. Many planetary surfaces were seen for the first time through spacecraft observations. Yet the interiors of most planetary bodies remain poorly studied. This dissertation focuses on two main topics: the formation of central pit craters and what this reveals about the subsurface volatile content of the target material, and the mantle dynamics of Io and how they relate to the extensive volcanism on its surface. Central pit craters are seen on icy satellites, Mars, the Moon, and Mercury. They have terraced rims, flat floors, and a pit at or near their center. Several formation mechanisms have been suggested. This dissertation assesses the feasibility of central pit crater formation via drainage of impact melt through impact-generated fractures. For impacts on Ganymede, the expected volume of melt and volume of fracture space generated during the impact and the volume of melt able to drain before fractures freeze shut all exceed the observed central pit volumes on Ganymede. This suggests that drainage of impact melt could contribute to central pit crater formation on Ganymede. Molten rock draining through solid rock fractures will freeze shut more rapidly, so this work suggests that impact melt drainage is unlikely to be a significant factor in the formation of central pit craters on rocky bodies unless a significant amount of volatiles are present in the target. Io is the most volcanically active body in the Solar System. While volcanoes are most often associated with plate tectonics on Earth, Io shows no signs of plate tectonics. Previous work has suggested that Io could lose a significant fraction of its internal heat through volcanic eruptions. In this dissertation, I investigate the relationship between mantle convection and magma generation, migration by porous flow, and eruptions on Io. I couple convective scaling laws to a model solving the two-phase flow equations applied to a rising column of mantle. I show that Io has a partially molten upper mantle and loses the majority of its internal heat through volcanic eruption. Next, I present two-dimensional numerical simulations that self-consistently solve the two-phase flow equations including mantle convection and magma generation, migration by porous flow, and eruption. These simulations produce a high heat flux due to volcanic eruption, a thick lithosphere, a partially molten upper mantle, and a high eruption rate—all consistent with observations of Io. This model also reveals the eruption rate oscillates around the statistical steady state average eruption rate suggesting that the eruption rate and total heat flux measurements from the past 35 years may not be representative of Io's long term behavior.

abstract: The origin of the solar system and formation of planets such as Earth are among the most fascinating, outstanding scientific problems. From theoretical models to natural observations, it is possible to infer a general way of how the solar system evolved from the gravitational collapse of the molecular cloud to accretion and differentiation of planetary-sized bodies. This dissertation attempts to place additional constraints on the source, distribution, and evolution of chemical variability in the early solar system, Mars, and Earth. A new method was developed for the measurement of titanium isotopes in calcium-aluminum-rich inclusions (CAIs) by laser ablation multi-collector inductively coupled plasma mass spectrometry. The isotopic compositions of 17 Allende CAIs define a narrow range with clearly resolved excesses in 46Ti and 50Ti and suggests that "normal" CAIs formed from a relatively uniform reservoir. Petrologic and isotopic analysis of a new FUN (Fractionated and Unknown Nuclear effects) CAI suggests that normal and FUN CAIs condensed in similar environments, but subsequently evolved under vastly different conditions. Volatiles may have influenced the formation and evolution of basaltic magmas on Mars. Light lithophile element (LLE) and fluorine (F) concentrations and isotopic compositions of pyroxene determined in situ in several Martian meteorites suggests that the primary magmatic signature of LLE and F zonation in Shergottite pyroxene has been disturbed by post-crystallization diffusive equilibration. Using relevant crystal-melt partition coefficients the F contents for Martian meteorite parental melts are ~910 and ~220 ppm. Estimates of the F content in the Shergottite and Nakhlite source regions are similar to that of mid-ocean ridge basalts (MORB) and ocean island basalts (OIB), respectively, here on Earth. Noble gas systematics of OIBs relative to MORBs, suggests OIBs preferentially sample a primordial reservoir located within Earth's mantle. Geodynamic calculations were performed to investigate the time-dependent rate of material entrained into plumes from these primordial reservoirs. These models predict melts rising to the surface will contain variable proportions of primordial material. The results demonstrate that although high 3He/4He ratios may mandate a mantle plume that samples a primordial reservoir, more MORB-like 3He/4He ratios in OIBs do not preclude a deep plume source. / Dissertation/Thesis / Doctoral Dissertation Geological Sciences 2014

Depuis sa formation, la Terre subit un refroidissement lent. La chaleur provenant du noyau et de la désintégration des éléments radioactifs présents dans le manteau est évacuée vers la surface par convection. L’évolution des structures thermiques ainsi créées contrôle de nombreux phénomènes de surface tels que le mouvement des continents et le niveau marin. L’étude présentée ici s’attache à déterminer quelles structures convectives terrestres peuvent être reconstruites, sur quelle période de temps et avec quelle précision. La chaoticité de la convection implique que les incertitudes initialement présentes sur le champ de température croissent exponentiellement au cours du temps et peuvent créer des structures convectives artificielles dans les modèles. A l’aide de la méthode des expériences jumelles initialement développée par Lorenz [1965] en météorologie, le temps de Lyapunov et l’horizon de prédiction sont calculés pour la première fois en géodynamique mantellique. Différentes rhéologies sont étudiées. La valeur du temps de Lyapunov pour notre modèle le plus proche de la Terre suggère qu’une erreur de 5% sur les conditions initiales limite l’horizon de prédiction à 95 millions d’années. D’autre part, la qualité de la prédiction des structures thermiques dépend de notre capacité à décrire de façon réaliste les propriétés rhéologiques du manteau. L’utilisation d’une rhéologie pseudo-plastique dans les modélisations de convection en 3D sphérique, permet aujourd’hui de générer une tectonique de plaques compatible au premier ordre avec les caractéristiques cinématiques de la surface terrestre. Une stratégie cohérente de reconstruction peut alors être élaborée. L’état thermique actuel du manteau est reconstruit en imposant les vitesses de surface de ces 200 derniers millions d’années [Seton et al., 2012; Shephard et al., 2013] sur un modèle de convection généré par le code StagYY [Tackley, 2008]. La morphologie et la position des slabs reconstruits varient considérablement avec le contraste de viscosité et la pseudo-plasticité. L’erreur introduite par l’utilisation de rhéologies différentes lors des reconstructions est ainsi plus importante que les erreurs liées aux incertitudes sur les conditions initiales et les vitesses de surface. Ces résultats montrent l’importance du choix la rhéologie sur la qualité des prédictions réalisées. Ils mettent également en évidence rôle clé du contraste de viscosité et de la pseudo-plasticité pour reconstruire des slabs cohérents et des subductions plates, structures propres à la convection terrestre. / Since its formation, the Earth is slowly cooling. The heat produced by the core and the radioactive decay in the mantle is evacuated toward the surface by convection. The evolving convective structures thereby created control a diversity of surface phenomena such as vertical motion of continents or sea level variation. The study presented here attempts to determine which convective structures can be predicted, to what extent and over what timescale. Because of the chaotic nature of convection in the Earth’s mantle, uncertainties in initial conditions grow exponentially with time and limit forecasting and hindcasting abilities. Following the twin experiments method initially developed by Lorenz [1965] in weather forecast, we estimate for the first time the Lyapunov time and the limit of predictability of Earth’s mantle convection. Our numerical solutions for 3D spherical convection in the fully chaotic regime, with diverse rheologies, suggest that a 5% error on initial conditions limits the prediction of Earth’s mantle convection to 95 million years. The quality of the forecast of convective structures also depends on our ability to describe the mantle properties in a realistic way. In 3D numerical convection experiments, pseudo plastic rheology can generate self-consistent plate tectonics compatible at first order with Earth surface behavior [Tackley, 2008]. We assessed the role of the temperature dependence of viscosity and the pseudo plasticity on reconstructing slab evolution, studying a variety of mantle thermal states obtained by imposing 200 million years of surface velocities extracted form tectonic reconstructions [Seton et al., 2012; Shephard et al., 2013]. The morphology and position of the reconstructed slabs largely vary when the viscosity contrast increases and when pseudo plasticity is introduced. The errors introduced by the choices in the rheological description of the mantle are even larger than the errors created by the uncertainties in initial conditions and surface velocities. This work shows the significant role of initial conditions and rheology on the quality of predicted convective structures, and identifies pseudo plasticity and large viscosity contrast as key ingredients to produce coherent and flat slabs, notable features of Earth’s mantle convection.

La subduction est une des principales expressions superficielles de la convection mantellique et représente un ingrédient crucial de la géodynamique globale. Cela affecte différents processus de la Terre comme la génération des méga-tremblements de terre et des volcans explosifs sur la surface ou le recyclage des espèces volatiles dans l’intérieur profond. Malgré son importance, plusieurs aspects de la subduction restent à clarifier.Dans ce travail, nous avons étudié la mécanique et l’énergétique du phénomène en adoptant un modèle numérique 2-D de “subduction libre”, basé sur la méthode des éléments frontière. En interprétant systématiquement nos solutions numériques utilisant la théorie des couches minces visqueuses, nous avons déterminé diverses lois d’échelle décrivant les mécanismes physiques sous-jacents aux différents aspects du phénomène. Deux paramètres adimensionnels se distinguent par leur récurrence dans ces lois d’échelle: i) la résistance (adimensionelle) de l’interface de subduction, qui contrôle la contrainte de cisaillement agissant à l’interface entre les deux plaques et ii) la rigidité de la plaque en subduction, qui décrit la résistance mécanique opposée par cette plaque à la flexion. Ce dernier paramètre est particulièrement important, car il met en évidence l’échelle de longueur qui décrit correctement la déformation en flexion de la plaque en subduction (bending length).En ce qui concerne les aspects énergétiques de la subduction, nous avons également étudié l’effet de la dissipation de l’énergie produite dans les zones de subduction sur la convection du manteau à grande échelle. Nos résultats semblent suggérer que la loi d’échelle classique trouvée dans l’étude de la convection de Rayleigh-Bénard en régime permanent d’une couche de fluide isovisqueux reste généralement valable aussi pour la convection du manteau terrestre.Pour conclure, nous avons mis en place une expérience de convection basée sur le séchage d’une suspension colloidale de nanoparticules de silice. Comme les résultats préliminaires ont montré, grâce à sa rhéologie particulière, ce matériau semble être un candidat prometteur pour la modélisation de la convection mantellique en laboratoire. / Subduction is one of the principal surface expressions of mantle convection and it represents a key ingredient of global geodynamics. It affects Earth processes ranging from the generation of mega-earthquakes and explosive volcanoes at thesurface to the recycling of volatile species back into the deep interior. Yet despite its obvious importance, several aspects of subduction remain to be clarified.In this work we endeavored to shed light on the mechanics and the energetics of the phenomenon adopting of a 2-D numerical model of “free subduction” based on the Boundary-Element Method. Systematically interpreting our numerical solutions in the light of thin viscous-sheet theory, we determined various scaling laws describing the physical mechanisms underlying different aspects of the phenomenon. Two dimensionless parameters stand out for their recurrence in suchscaling laws: i) the (dimensionless) strength of the subduction interface, which controls the shear stress acting at the interface between the two plates and ii) the flexural stiffnes of the subducting plate, which describes the mechanical resistance opposed by such plate to bending. This latter parameter is particularly important as it highlights the length scale that properly describes the bending deformation of the subducting plate (bending length).For what concerns the energetics of subduction, we also investigated the effect of the dissipation of energy occurring at subduction zones on large-scale mantleconvection. Our results seem to suggest that the classical scaling law found in the study of the steady-state Rayleigh-Bénard convection of an isoviscous fluid layer remains generally valid also for Earth’s mantle convection.To conclude, we ran a convection experiment based on the drying of a colloidal suspension of silica nanoparticles. As preliminary results have shown, thanksto its particular rheology, this material seems to be a promising candidate for effective laboratory modeling of mantle convection.

This dissertation presents a numerical model constructed to investigate the dynamics and structures of the Earth’s mantle. Deformation of the Earth’s mantle, which is composed of solid silicate minerals, is strongly governed by the constitutive relation-ship among multiple length-scale structures and properties. To explain the realistic consti-tutive behavior of the silicate mantle, an Internal State Variable (ISV) theory that is an advanced and novel constitutive approach for history-dependent elastoviscoplasticity was applied. The ISV constitutive model was, in turn, implemented into a three-dimensional geodynamic code, TERRA3D, which uses the Finite Element method developed for the mantle convection problem. The sequential studies performed in this dissertation are presented in the follow-ing order: i) a comprehensive summary of the mantle material structures (compositions and microstructural features) and its mechanical properties (elasticity and rheology), ii) a development of a recrystallization and grain size dependent ISV constitutive model for the polycrystalline materials such as minerals and metals, which explains comprehensive mineral physics occurring under the conditions of pressure, temperature, and strain rate within the mantle and their history dependence, and iii) an application of the recrystalli-zation and grain size dependent ISV model to the Earth’s mantle convection problem us-ing the TERRA3D for an investigation of the grain size and dynamic recrystallization efect on the mantle dynamics. The applied ISV constitutive model within the TERRA3D Finite Element frame-work captures the subscale dynamics (dislocation density evolution, dynamic and static recrystallization, grain growth, and grain refinement) and their effect on the large-scale rheology and dynamics of the Earth’s mantle. The numerical investigations reveal that the potential for the mechanical instability and weakening within the mantle arises from the kinetics of grain size and recrystallization and their rheological effect. This mechanical instability leads to the mantle convection entering the episodic overturn regime. The TERRA3D-ISV mantle convection model herein also provides some insightful discover-ies regarding the dynamics and structures within the mantle, explaining its complex rhe-ology caused by the kinetics of recrystallization, grain size, hardening, dislocation recov-ery, and diffusion in the geological settings.

Modern geodynamic modeling is more complex than ever, and has been used to answer questions about Earth pertaining to the dynamics of the convecting mantle and core, layers humans have never directly interacted with. While the insights gleaned from these models cannot be argued, it is important to ensure calculations are understood and behaving correctly according to known math and physics. Here I perform several thermal 3-D spherical shell tests using the geodynamic code ASPECT, and compare the results against the legacy code CitcomS. I find that these two codes match to within 1.0% using a number of parameters. The application of geodynamic modeling is also traditionally to expand our understanding of Earth; however, even with a scarcity of data modern methods can provide insight into other planetary bodies. I use machine learning to show that coronae, circular features on the surface of the planet Venus, are not randomly distributed. I suggest the idea of coronae being fed by secondary mantle plumes in connected clusters. The entirety of the Venusian surface is poorly understood as well, with a large percentage being topographically smooth and much younger than the planet's hypothesized age. I use modeling to test the hypothesis of a large impact being responsible for a major resurfacing event in Venus's history, and find three distinct scenarios following impact: relatively little change, some localized change evolving into resurfacing through geologic time, or large-scale overturn and injection of heat deep into the Venusian mantle. / Doctor of Philosophy / Modern geodynamic modeling has been used to answer questions about Earth in wide-ranging fields. Despite technological improvements, it is important to ensure the calculations are understood and behaving correctly. Here I perform several tests using a code called ASPECT and compare the results against another code, CitcomS. I find that the two codes are in good agreement. Application of these techniques is also traditionally done for Earth, but modern methods can provide insight into other planets or moons as well. Coronae are circular features on the surface of Venus that are poorly understood. I use machine learning to show that these are not randomly distributed, and suggest a mechanism for the formation of clusters of coronae. The surface of Venus is also strange: it is both too flat and too young based on current ideas in planetary science. I use modeling to test whether a large impact could cause the details of Venus's surface we see today.

Constituant la couche limite supérieure de la convection mantellique, la lithosphère terrestre est à l'interface entre les enveloppes externes et internes de notre Planète. Les interactions multiples entre celle-ci et le manteau sont à l'origine de déformations latérales (tectonique des plaques) et verticales (topographie dynamique) de la surface terrestre. Comprendre comment la formation et l'évolution d'instabilités convectives mantelliques renouvellent sans-cesse la surface est donc primordial pour améliorer nos interprétations d'un grand nombre d'observations de surface, telles que la formation de bassins sédimentaires, le mouvement des continents, la localisation des points chauds, la formation d'anomalies gravimétriques ou encore les variations du niveau marin.Cette thèse propose de développer des modèles numériques de convection mantellique générant defaçon auto-organisée de la tectonique des plaques en surface an d'étudier la façon dont le développement et la dynamique d'instabilités convectives telles que les panneaux de subduction ou les panaches mantelliques modifient la surface, dans un contexte de tectonique de surface approchant le régime terrestre.Dans une première partie, je m'intéresse à l'influence du couplage des mouvements de convection mantellique et de tectonique des plaques sur le développement de topographie dynamique (i.e. les mouvements verticaux de la lithosphère induits par la convection mantellique) à différentes échelles spatio-temporelles. Mes résultats suggèrent que la surface terrestre peut se déformer à toutes les échelles spatiales, du fait de mouvements convectifs de grande ampleur faisant intervenir le manteau entier (> 104 km) ou encore de convection à petite échelle sub-lithosphérique (< 500 km). Les variations temporelles de topographie dynamique s‘étendent de cinq à plusieurs centaines de millions d'années selon la nature des processus convectifs dont elles dérivent. En particulier, la dynamique d'initiation ou d'arrêt des zones de subduction contrôle l'existence d'échelles intermédiaires de topographie dynamique (longueurs d'onde variant entre 500 et 104 km). Ces résultats montrent donc que les interactions entre la dynamique de la lithosphère et la convection mantellique génèrent des motifs spatio-temporels de topographie dynamique complexes et cohérents par rapport aux observations terrestres.Dans un deuxième temps, cette thèse se focalise sur la dynamique des panaches mantelliques, et leurs interactions avec la surface. Je caractérise d'abord précisement le comportement des panaches générés dans nos modèles de convection à la lumière d'observations de surface. Puis, j'étudie la façon dont leurs interactions avec la tectonique de surface et les différentes échelles convectives modifient leurs mouvements latéraux. Enfin, la compréhension de la signature thermique des interactions entre panaches et rides océaniques me permet de proposer une reconstitution des mouvements relatifs entre le panache des Açores et la ride médio-Atlantique. / Earth's lithosphere, which is the upper boundary layer of mantle convection, represents the interface between the external and internal envelopes of our Planet. The multiple interactions between the mantle and lithosphere generate lateral (plate tectonics) and vertical (dynamic topography) deformations of Earth's surface. Understanding the influence of the dynamics of mantle convective instabilities on the surface is fundamental to improve our interpretations of a large range of surface observations, such as the formation of sedimentary basins, continental motions, the location of hotspots, the presence of gravity anomalies or sea-level variations.This thesis aims at developing numerical models of whole-mantle convection self-generating plate-like tectonics in order to study the impacts of the development and the dynamics of mantle convective instabilities (such as slabs or mantle plumes) on the continuous reshaping of the surface.First, I focus on the influence of the coupling between mantle convective motions and plate tectonics on the development of dynamic topography (i.e. surface vertical deformations induced by mantle convection) at different spatial and temporal scales. The results suggest that Earth's surface can deform over large spatial scales (> 104 km) induced by whole-mantle convection to small-scales (< 500 km) arising from small-scale sub-lithospheric convection. The temporal variations of dynamic topography range between five and several hundreds of millions of years depending on the convective instabilities from which they originate. In particular, subduction initiation and slab break-off events control the existence of intermediate scales of dynamic topography (between 500 and 104 km). This reflects that the interplay between mantle convection and lithosphere dynamics generates complex spatial and temporal patterns of dynamic topography consistent with constraints for Earth.A second aim of this thesis is to understand the dynamics of mantle plumes and their interactionswith surface. I first characterize in detail the behaviour of mantle plumes arising in models ofwhole-mantle convection self-generating plate-like tectonics, in light of surface observations. Then, I study how the interactions between surface plate tectonics and mantle convection affect plume motions. Finally, I use observations of the thermal signature of plume/ridge interactions to propose a reconstruction of the relative motions between the Azores mantle plume and the Mid-Atlantic Ridge.

No description available.

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.