Nicolas Coltice

Mantle convection shapes Earth's surface by generating dynamic topography. Observational constraints and regional convection models suggest that surface topography could be sensitive to mantle flow for wavelengths as short as 1,000 and 250 km, respectively. At these spatial scales, surface processes including sedimentation and relative sea-level change occur on million-year timescales. However, time-dependent global mantle flow models do not predict small-scale dynamic topography yet. Here we present 2-D spherical annulus numerical models of mantle convection with large radial and lateral viscosity contrasts. We first identify the range of Rayleigh number, internal heat production rate and yield stress for which models generate plate-like behavior, surface heat flow, surface velocities, and topography distribution comparable to Earth's. These models produce both whole-mantle convection and small-scale convection in the upper mantle, which results in small-scale (<500 km) to large-scale (>10 4 km) dynamic topography, with a spectral power for intermediate scales (500 to 10 4 km) comparable to estimates of present-day residual topography. Timescales of convection and the associated dynamic topography vary from five to several hundreds of millions of years. For a Rayleigh number of 10 7 , we investigate how lithosphere yield stress variations (10–50 MPa) and the presence of deep thermochemical heterogeneities favor small-scale (200–500 km) and intermediate-scale (500–10 4 km) dynamic topography by controlling the formation of small-scale convection and the number and distribution of subduction zones, respectively. The interplay between mantle convection and lithosphere dynamics generates a complex spatial and temporal pattern of dynamic topography consistent with constraints for Earth.

Over the past 15 yr, numerical models of convection in Earth's mantle have made a leap forward: they can now produce self-consistent plate-like behaviour at the surface together with deep mantle circulation. These digital tools provide a new window into the intimate connections between plate tectonics and mantle dynamics, and can therefore be used for tectonic predictions, in principle. This contribution explores this assumption. First, initial conditions at 30, 20, 10 and 0 Ma are generated by driving a convective flow with imposed plate velocities at the surface. We then compute instantaneous mantle flows in response to the guessed temperature fields without imposing any boundary conditions. Plate boundaries self-consistently emerge at correct locations with respect to reconstructions, except for small plates close to subduction zones. As already observed for other types of instantaneous flow calculations, the structure of the top boundary layer and upper-mantle slab is the dominant character that leads to accurate predictions of surface velocities. Perturbations of the rheological parameters have little impact on the resulting surface velocities. We then compute fully dynamic model evolution from 30 and 10 to 0 Ma, without imposing plate boundaries or plate velocities. Contrary to instantaneous calculations, errors in kinematic predictions are substantial, although the plate layout and kinematics in several areas remain consistent with the expectations for the Earth. For these calculations, varying the rheological parameters makes a difference for plate boundary evolution. Also, identified errors in initial conditions contribute to first-order kinematic errors. This experiment shows that the tectonic predictions of dynamic models over 10 My are highly sensitive to uncertainties of rheological parameters and initial temperature field in comparison to instantaneous flow calculations. Indeed, the initial conditions and the rheological parameters can be good enough for an accurate prediction of instantaneous flow, but not for a prediction after 10 My of evolution. Therefore, inverse methods (sequential or data assimilation methods) using short-term fully dynamic evolution that predict surface kinematics are promising tools for a better understanding of the state of the Earth's mantle.

The existence of undulations of the geoid, gravity and bathymetry in ocean basins, as well as anomalies in heat flow, point to the existence of small scale convection beneath tectonic plates. The instabilities that could develop at the base of the lithosphere are sufficiently small scale (<500km) that they remain mostly elusive from seismic detection. We take advantage of 3D spherical numerical geodynamic models displaying plate-like behavior to study the interaction between large-scale flow and small-scale convection. We find that finger-shaped instabilities develop at seafloor ages >60 Ma. They form networks that are shaped by the plate evolution, slabs, plumes and the geometry of continental boundaries. Plumes impacting the boundary layer from below have a particular influence through rejuvenating the thermal lithosphere. They create a wake in which new instabilities form downstream. These wakes form channels that are about 1000 km wide, and thus are possibly detectable by seismic tomography. Beneath fast plates, cold sinking instabilities are tilted in the direction opposite to plate motion, while they sink vertically for slow plates. These instabilities are too small to be detected by usual seismic methods, since they are about 200 km in lateral scale. However, this preferred orientation of instabilities below fast plates could produce a pattern of large-scale azimuthal anisotropy consistent with both plate motions and the large scale organisation of azimuthal anisotropy obtained from recent surface wave models.

The theory of plate tectonics describes how the surface of Earth is split into an organized jigsaw of seven large plates of similar sizes and a population of smaller plates whose areas follow a fractal distribution. The reconstruction of global tectonics during the past 200 million years 4 suggests that this layout is probably a long-term feature of Earth, but the forces governing it are unknown. Previous studies, primarily based on the statistical properties of plate distributions, were unable to resolve how the size of the plates is determined by the properties of the lithosphere and the underlying mantle convection. Here we demonstrate that the plate layout of Earth is produced by a dynamic feedback between mantle convection and the strength of the lithosphere. Using three-dimensional spherical models of mantle convection that self-consistently produce the plate size–frequency distribution observed for Earth, we show that subduction geometry drives the tectonic fragmentation that generates plates. The spacing between the slabs controls the layout of large plates, and the stresses caused by the bending of trenches break plates into smaller fragments. Our results explain why the fast evolution in small back-arc plates reflects the marked changes in plate motions during times of major reorganizations. Our study opens the way to using convection simulations with plate-like behaviour to unravel how global tectonics and mantle convection are dynamically connected.

Stresses acting on cold, thick and negatively buoyant oceanic lithosphere are thought to be crucial to the initiation of subduction and the operation of plate tectonics, which characterizes the present-day geodynamics of the Earth. Because the Earth’s interior was hotter in the Archaean eon, the oceanic crust may have been thicker, thereby making the oceanic lithosphere more buoyant than at present, and whether subduction and plate tectonics occurred during this time is ambiguous, both in the geological record and in geodynamic models. Here we show that because the oceanic crust was thick and buoyant, early continents may have produced intra-lithospheric gravitational stresses large enough to drive their gravitational spreading, to initiate subduction at their margins and to trigger episodes of subduction. Our model predicts the co-occurrence of deep to progressively shallower mafic volcanics and arc magmatism within continents in a self-consistent geodynamic framework, explaining the enigmatic multimodal volcanism and tectonic record of Archaean cratons. Moreover, our model predicts a petrological stratification and tectonic structure of the sub-continental lithospheric mantle, two predictions that are consistent with xenolith and seismic studies, respectively, and consistent with the existence of a mid-lithospheric seismic discontinuity. The slow gravitational collapse of early continents could have kick-started transient episodes of plate tectonics until, as the Earth’s interior cooled and oceanic lithosphere became heavier, plate tectonics became self-sustaining.

Reconstructing convective flow in the Earth’s mantle is a crucial issue for a diversity of disci- plines, from seismology to sedimentology. The common and fundamental limitation of these reconstruc- tions based on geodynamic modeling is the unknown initial conditions. Because of the chaotic nature of convection in the Earth’s mantle, errors in initial conditions grow exponentially with time and limit forecast- ing and hindcasting abilities. In this work, we estimate for the first time the limit of predictability of Earth’s mantle convection. Following the twin experiment method, we compute the Lyapunov time (i.e., e-folding time) for state of the art 3-D spherical convection models, varying rheology, and Rayleigh number. Our most Earth-like and optimistic solution gives a Lyapunov time of 136 6 13 Myr. Rough estimates of the uncertainties in best guessed initial conditions are around 5%, leading to a limit of predictability for mantle convection of 95 Myr. Our results suggest that error growth could produce unrealistic convective structures over time scales shorter than that of Pangea dispersal.

Supercontinents like Pangea impose a first-order control on Earth’s evolution as they modulate global heat loss, sea level, climate, and biodiversity. In a traditional view, supercontinents form and break up in a regular, perhaps periodic, manner in a cycle lasting several 100 Myr as reflected in the assembly times of Earth’s major continental aggregations: Columbia, Rodinia, and Pangea. However, modern views of the supercontinent cycle propose a more irregular evolution on the basis of an improved understanding of the Precambrian geologic record. Here we use fully dynamic spherical mantle convection models featuring plate-like behavior and continental drift to investigate supercontinent formation and breakup. We further dismiss the concept of regularity but suggest a statistical cyclicity in which the supercontinent cycle may have a characteristic period imposed by mantle and lithosphere properties, but this is hidden in immense fluctuations between different cycles that arise from the chaotic nature of mantle flow.

The growth of the continental crust has shaped the evolution of the Earth from its interior
to its fluid envelopes. Continents have played a major role in the evolution of global tecton- ics through their interaction with mantle convection. The feedback between continents and mantle convection has been studied for the past 25 years, but it is only recently that the dynamic influence of continents on seafloor spreading can be explored thanks to progress in convection modeling. In this work, we investigate how continental size impacts seafloor spreading activity with state-of-the-art three-dimensional spherical convection models. We show that increasing the continental area forces higher production rates of new seafloor with stronger fluctuations. As a consequence, the average age of the seafloor decreases with increasing continental area. This study suggests that mantle heat loss experienced signifi- cant fluctuations through continental growth and reinforces the estimate of <10% continen- tal growth since the late Archean.

For 50 years of data collection and kinematic reconstruction efforts, plate models have provided alternative scenarios for plate motions and seafloor spreading for the past 200 My. However, these efforts are naturally limited by the incomplete preservation of very old seafloor, and therefore the time-dependence of the production of new seafloor is controversial. There is no consensus on how much it has varied in the past 200 My, and how it could have fluctuated over longer timescales. We explore how seafloor spreading and continental drift evolve over long geological periods using independently derived models: a recently developed geodynamic modelling approach and state-of-the-art plate reconstructions. Both kinematic reconstructions and geodynamic models converge on variations by a factor of 2 in the rate of production of new seafloor over a Wilson cycle, with concomitant changes of the shape of the area–age distribution of the seafloor between end members of rectangular, triangular and skewed distributions. Convection models show that significant fluctuations over longer periods (∼1 Gy) should exist, involving changes in ridge length and global tectonic reorganisations. Although independent, both convection models and kinematic reconstructions suggest that changes in ridge length are at least as significant as spreading rate fluctuations in driving changes in the seafloor area–age distribution through time.

On 15 February 2013 around 03:20:00 UTC, the largest meteor reported since the 1908 Tunguska event was observed as a fireball traveling through the Earth’s atmosphere, exploding in an air burst near the city of Chelyabinsk, Russia. The rarity of such an event provides a unique window on the physics of meteoroid collision. We report the fine seismic detection of Rayleigh waves produced by the coupling of ground motion with the incident shock wave at distances up to 4000 km from the event. Combining information from seismic beam-forming analysis, reconstructed trajectory from casual video records, and remote sensing, we identify the Rayleigh waves as being initiated by the shock wave produced by the main blast that occasioned damages and injuries in Chelyabinsk. From the Rayleigh wave observations, we report a magnitude Ms 􏰁 3.7 seismic source.

Many continental growth models have been proposed over the years to explain geological and geochemical data. Amongst these data, the evolution of the 87Sr/86Sr of marine carbonates has been used as an argument in favour of delayed continental growth models and of a Neoarchean pulse in continental growth. This interpretation requires that continental freeboard and continental hypsometry have remained constant throughout Earth's history. However, recent studies suggest that Archean sea levels were higher, and Archean relief lower, than present-day ones.

To assess the validity of the evolution of the 87Sr/86Sr of marine carbonates as a proxy for continental growth, we have developed a model that evaluates the co-evolution of mantle temperature, continental hypsometry, sea level, ridge depth, emerged area of continental crust and the 87Sr/86Sr of ocean water as a function of continental growth. We show that Archean sea levels were between ∼500 m and ∼1800 m higher than present-day ones, that Archean mid-oceanic ridges were between ∼700 m and ∼1900 m shallower than present-day ones, and that the Archean emerged land area was less than ∼4% of Earth's area. Importantly, the evolution of the area of emerged land, contrary to that of sea level and ridge depth, barely depends on continental growth models. This suggests that the evolution of surface geochemical proxies for felsic lithologies does not constrain continental growth. In particular, the evolution of the 87Sr/86Sr of ocean water predicted for an early continental growth model is in broad agreement with the 87Sr/86Sr data on marine carbonates when changes in continental freeboard and continental hypsometry are taken into account. We propose that the Neoarchean shift in the 87Sr/86Sr of marine carbonates recorded the emergence of the continents rather than a pulse in continental growth. Since the evolution of other geochemical indicators for felsic crust used as proxies for continental growth is equally well explained by continental emergence, we suggest that there could be no need for delayed continental growth models.

Continents slowly drift at the top of the mantle, sometimes colliding, splitting and aggregating. The evolutions of the continent configuration, as well as oceanic plate tectonics, are surface expressions of mantle convection and closely linked to the thermal state of the mantle; however, quantitative studies are so far lacking. In the present study we use 3D spherical numerical simulations with self-consistently generated plates and compositionally and rheologically distinct continents floating at the top of the mantle in order to investigate the feedbacks between continental drift, oceanic plate tectonics and the thermal state of the Earth's mantle, by using different continent configurations ranging from one supercontinent to six small continents. With the presence of a supercontinent we find a strong time-dependence of the oceanic surface heat flow and suboceanic mantle temperature, driven by the generation of new plate boundaries. Very large oceanic plates correlate with periods of hot suboceanic mantle, while the mantle below smaller oceanic plates tends to be colder. Temperature fluctuations of subcontinental mantle are significantly smaller than in oceanic regions and are caused by a time-variable efficiency of thermal insulation of the continental convection cell. With the presence of multiple continents the temperature below individual continents is generally lower than below supercontinent and is more time-dependent, with fluctuations as large as 15% that are caused by continental assembly and dispersal. The periods featuring a hot subcontinental mantle correlate with strong clustering of the continents and periods characterized by cold subcontinental mantle, at which it can even be colder than suboceanic mantle, with a more dispersed continent configuration. Our findings with multiple continents imply that periods of partial melting and strong magmatic activity inside the continents, which may contribute to continental rifting and pronounced growth of continental crust, might be episodic processes related to the supercontinent cycle. Finally, we observe an influence of continents on the wavelength of convection: for a given strength of the lithosphere we observe longer-wavelength flow components, when continents are present. This observation is regardless of the number of continents, but most pronounced for a single supercontinent.

Melting and solidification are fundamental to geodynamical processes like inner core growth, magma chamber dynamics, and ice and lava lake evolution. Very often, the thermal history of these systems is controlled by convective motions in the melt. Computing the evolution of convection with a solid–liquid phase change requires specific numerical methods to track the phase boundary and resolve the heat transfer within and between the two separate phases. Here we present two classes of method to model the phase transition coupled with convection. The first, referred to as the moving boundary method, uses the finite element method and treats the liquid and the solid as two distinct grid domains. In the second approach, based on the enthalpy method, the governing equations are solved on a regular rectangular grid with the finite volume method. In this case, the solid and the liquid are regarded as one domain in which the phase change is incorporated implicitly by imposing the liquid fraction fL as a function of temperature and a viscosity that varies strongly with fL. We subject the two modelling frameworks to thorough evaluation by performing benchmarks, in order to ascertain their range of applicability. With these tools we perform a systematic study to infer heat transfer characteristics of a solidifying convecting layer. Parametrized relations are then used to estimate the super-isentropic temperature difference maintained across a basal magma ocean (BMO) (Labrosse et al., 2007), which happens to be minute (< 0:1 K), implying that the Earth’s core must cool at the same pace as the BMO.

The 3.46 Ga Marble Bar Chert Member of the East Pilbara Craton, Western Australia, is one of the earliest and best- preserved sedimentary successions on Earth. Here, we interpret the finely laminated thin-bedded cherts, mixed conglomeratic beds, chert breccia beds and chert folded beds of the Marble Bar Chert Member as the product of low-density turbidity currents, high-density turbidity currents, mass transport complexes and slumps, respectively. Integrated into a channel-levee depositional model, the Marble Bar Chert Member constitutes the oldest documented deep-sea fan on Earth, with thin-bedded cherts, breccia beds and slumps composing the outer levee facies tracts, and scours and conglomeratic beds representing the channel systems.

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.

Large basaltic provinces as much as 15 km thick are common in Archean cratons. Many of
these flood basalts erupted through continental crust but remained at sea level. Although com- mon in the Archean record, subaqueous continental flood basalts (CFBs) are rare to absent in the post-Archean. Here we show that gravity-driven lower crustal flow may have contributed to maintaining Archean CFBs close to sea level. Our numerical experiments reveal that the characteristic time to remove the thickness anomaly associated with a CFB decreases with increasing Moho temperature (TM), from 500 m.y. for TM ≈ 320 °C to 1 m.y. for TM ≈ 900 °C. This strong dependency offers the opportunity to assess, from the subsidence history of CFBs, whether continental geotherms were significantly hotter in the Archean. In particular, we show that the subsidence history of the ca. 2.7 Ga upper Fortescue Group in the East Pilbara Craton, Western Australia, requires Moho temperatures >>700 °C. Applied to eight other unambiguous subaqueous Archean CFBs, our results indicate Moho temperatures >>650 °C at the time of eruption. We suggest that the decrease in the relative abundance of subaqueous CFBs over Earth’s history could reflect the secular cooling of the continental lithosphere due to the decrease in radiogenic heat production.

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.

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). Here we explore the consequences of the crystallization of a BMO for the noble gas evolution of the mantle. The crystals extracted from a BMO upon cooling generate dense chemical piles at the base of the mantle. We show that if the solid–melt partition coefficients of He and Ne are N 0.01 at high pressure and temperature, He and Ne isotopic ratios in pile cumulates can be pristine like. Hence, the entrainment of modest amounts of BMO cumulate in mantle plumes (b10%) potentially explains the primitive-like He and Ne signatures in hotspots. Because pile material can be depleted in refractory elements while simultaneously enriched in noble gasses, our model forms a viable hypothesis to explain the complex relationship between He and refractory isotopic systems in Earth's interior.

Stresses acting on cold, thick and negatively buoyant oceanic lithosphere are thought to be crucial to the initiation of subduction and the operation of plate tectonics, which characterizes the present-day geodynamics of the Earth. Because the Earth’s interior was hotter in the Archaean eon, the oceanic crust may have been thicker, thereby making the oceanic lithosphere more buoyant than at present, and whether subduction and plate tectonics occurred during this time is ambiguous, both in the geological record and in geodynamic models. Here we show that because the oceanic crust was thick and buoyant, early continents may have produced intra-lithospheric gravitational stresses large enough to drive their gravitational spreading, to initiate subduction at their margins and to trigger episodes of subduction. Our model predicts the co-occurrence of deep to progressively shallower mafic volcanics and arc magmatism within continents in a self-consistent geodynamic framework, explaining the enigmatic multimodal volcanism and tectonic record of Archaean cratons. Moreover, our model predicts a petrological stratification and tectonic structure of the sub-continental lithospheric mantle, two predictions that are consistent with xenolith5 and seismic studies, respectively, and consistent with the existence of a mid-lithospheric seismic discontinuity. The slow gravitational collapse of early continents could have kick-started transient episodes of plate tectonics until, as the Earth’s interior cooled and oceanic lithosphere became heavier, plate tectonics became self-sustaining.

Isotopic signatures of He and Ne in basalt glasses and phenocrysts require that the OIB source has retained a fair amount of primordial gases whereas the MORB source is extensively outgassed according to its mostly radiogenic composition. Unexpectedly, all basalt glasses recovered from oceanic islands (seamounts) exhibit low noble-gas contents when compared to MORB glasses erupted at similar depths.

The thermal evolution of planets during their accretionary growth is strongly influenced by impact heating. The temperature increase following a collision takes place mostly below the impact location in a volume a few times larger than that of the impactor. Impact heating depends essentially on the radius of the impacted planet. When this radius exceeds~ 1000km, the metal phase melts and forms a shallow and dense pool that penetrates the deep mantle as a diapir.

In the long term, the total amount of emerged land at Earth's surface and the depth of mid-oceanic ridges are controlled by the growth of the continental crust and by the secular cooling of Earth's mantle that implies changes in the isostatic balance between continents and oceans. The evolution of the area of emerged land and of oceanic bathymetry are of fundamental importance to the geochemical coupling of mantle, continental crust, ocean and atmosphere.

Résumé: L'objectif de cette recherche est d'analyser le processus de professionnalisation de futurs enseignants de Français Langue Etrangère, lors de l'exercice d'activités nouvelles liées à un tutorat synchrone à distance, auprès d'étudiants américains. Ce processus a été envisagé sous l'angle du développement de différentes compétences-clés, liées à la prise d'autonomie dans l'exercice de l'activité.

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 longevity of the continental lithosphere mantle is explained by its unusual composition. This part of the mantle is made up mainly of forsterite-rich olivine (Fo92–94), with or without orthopyroxene, and it is essentially anhydrous. The former characteristic makes it buoyant, the latter makes it viscous, and the combination of these features that allow it to remain isolated from the convecting mantle. Highly forsteritic olivine is not normally produced during mantle melting.

The boron geochemical cycle has been simulated using a time-dependent geochemical box model that was coupled to a one-dimension model of seawater–oceanic crust interactions. Boron elemental and isotopic compositions of oceanic rocks as a function of depth were calculated by mass balance, using the temperature and porosity profiles of the crust as well as the available experimental and empirical distribution coefficients and fractionation factors between mineral and water.