Seismic, petrological and geodynamical constraints on thermal and compositional structure of the upper mantle: global thermochemical models

Mapping the thermal and compositional structure of the upper mantle requires a combined interpretation of geophysical and petrological observations. Based on current knowledge of material properties, we interpret available global seismic models for temperature assuming end-member compositional structures. In particular, we test the effects of modelling a depleted lithosphere, which accounts for petrological constraints on continents. Differences between seismic models translate into large temperature and density variations, respectively, up to 400 K and 0.06 g cm-3 at 150 km depth. Introducing lateral compositional variations does not change significantly the thermal interpretation of seismic models, but gives a more realistic density structure. Modelling a petrological lithosphere gives cratonic temperatures at 150 km depth that are only 100 K hotter than those obtained assuming pyrolite, but density is ~0.1 g cm-3 lower. We determined the geoid and topography associated with the density distributions by computing the instantaneous flow with an existing code of mantle convection, STAG-YY. Models with and without lateral variations in viscosity have been tested. We found that the differences between seismic models in the deeper part of the upper mantle significantly affect the global geoid, even at harmonic degree 2. The range of variance reduction for geoid due to differences in the transition zone structure (i.e. from 410 to 660 km) is comparable with the range due to differences in the whole mantle seismic structure. Since geoid is dominated by very long wavelengths (the lowest five harmonic degrees account for more than 90 per cent of the signal power), the lithospheric density contrasts do not strongly affect its overall pattern. Models that include a petrological lithosphere, however, fit the geoid and topography better. Most of the long-wavelength contribution that helps to improve the fit comes from the oceanic lithosphere. The signature of continental lithosphere worsens the fit, even in simulations that assume an extremely viscous lithosphere. Therefore, a less depleted, and thus less buoyant, continental lithosphere is required to explain gravity data. None of the seismic tomography models we analyse is able to reproduce accurately the thermal structure of the oceanic lithosphere. All of them show their lowest seismic velocities at ~100 km depth beneath mid-oceanic ridges and have much higher velocities at shallower depths compared to what is predicted with standard cooling models. Despite the limited resolution of global seismic models, this seems to suggest the presence of an additional compositional complexity in the lithospher

Temperature and heat flux scalings for isoviscous thermal convection in spherical geometry

Parametrized convection, which has long been used to reconstruct the thermal history of planetary mantles, is based on scaling relationships between observables (including heat flux) and controlling parameters (the most important being the Rayleigh number, Ra). To explore the influence of spherical geometry on heat transfer, we have conducted two series of numerical experiments of thermal convection (one with bottom heating and the other with mixed heating) in an isoviscous spherical shell with various curvatures. Using these calculations and a generalized non-linear inversion, we then derive scaling laws for the average temperature and for the surface heat flux. In the case of bottom heating, we found that the non-dimensional average temperature is given by θm=f2/(1 +f2), where f is the ratio between the core and total radii. The non-dimensional surface heat flux is fitted well by Nutop= 0.36f0.32 Ra(0.273+0.05f)θ0.6m. This scaling indicates that the available heating power decreases with increasing curvature (decreasing f). There exist strong trade-offs between the inverted parameters, that is, different sets of parameters explain our calculations well within error bars. For mixed heating, the non-dimensional average temperature and surface heat flux are well explained by θH=θm+ (1.68 − 0.8f)[(1 +f+f2)/3]0.79 h0.79/Ra0.234, where h is the non-dimensional rate of internal heating, and Nutop= 0.59f0.05 Ra(0.300−0.003f)θ1.23H. Due to a competition between the radiogenic and convective powers, and for given values of h and Ra, there is a curvature for which the Urey ratio reaches a minimum. Applied to the Earth's mantle, the mixed heating scaling predicts a Urey ratio between 0.4 and 0.6, depending on the Rayleigh number. Additional parameters, including the thermal viscosity ratio, phase transitions, the presence of dense material in the deep mantle, and variability of the flow pattern in time, may enter an appropriate modelling of the Earth's mantle thermal histor

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

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

The stability and structure of primordial reservoirs in the lower mantle: insights from models of thermochemical convection in three-dimensional spherical geometry

Large-scale chemical lateral heterogeneities are inferred in the Earth's lowermost mantle by seismological studies. We explore the model space of thermochemical convection that can maintain reservoirs of dense material for a long period of time, by using similar analysis in 3-D spherical geometry. In this study, we focus on the parameters thought to be important in controlling the stability and structure of primordial dense reservoirs in the lower mantle, including the chemical density contrast between the primordial dense material and the regular mantle material (buoyancy ratio), thermal and chemical viscosity contrasts, volume fraction of primordial dense material and the Clapeyron slope of the phase transition at 660 km depth. We find that most of the findings from the 3-D Cartesian study still apply to 3-D spherical cases after slight modifications. Varying buoyancy ratio leads to different flow patterns, from rapid upwelling to stable layering; and large thermal viscosity contrasts are required to generate long wavelength chemical structures in the lower mantle. Chemical viscosity contrasts in a reasonable range have a second-order role in modifying the stability of the dense anomalies. The volume fraction of the initial primordial dense material does not effect the results with large thermal viscosity contrasts, but has significant effects on calculations with intermediate and small thermal viscosity contrasts. The volume fraction of dense material at which the flow pattern changes from unstable to stable depends on buoyancy ratio and thermal viscosity contrast. An endothermic phase transition at 660 km depth acts as a ‘filter' allowing cold slabs to penetrate while blocking most of the dense material from penetrating to the upper mantl

Earth curvature effects on subduction morphology: Modeling subduction in a spherical setting

We present the first application in geodynamics of a (Fast Multipole) Accelerated Boundary Element Method (Accelerated-BEM) for Stokes flow. The approach offers the advantages of a reduced number of computational elements and linear scaling with the problem size. We show that this numerical method can be fruitfully applied for the simulation of several geodynamic systems at the planetary scale in spherical coordinates, and we suggest a general approach for modeling combined mantle convection and plate tectonics. The first part of the paper is devoted to the technical exposition of the new approach, while the second part focuses on the effect played by Earth curvature on the subduction of a very wide oceanic lithosphere (W=6,000km and W=9,000km), comparing the effects of two different planetary radii (ER=6,371km, 2ER=2×6,371km), corresponding to an "Earth-like" model (ER) and to a "flat Earth" one (2ER). The results show a distinct difference between the two models: while the slab on a "flat Earth" shows a slight undulation, the same subducting plate on the "Earth-like" setting presents a dual behavior characterized by concave curvature at the edges and by a folding with wavelength of the order of magnitude of 1,000km at the center of the sla

Melting-induced crustal production helps plate tectonics on Earth-like planets

AbstractWithin our Solar System, Earth is the only planet to be in a mobile-lid regime. It is generally accepted that the other terrestrial planets are currently in a stagnant-lid regime, with the possible exception of Venus that may be in an episodic-lid regime. In this study, we use numerical simulations to address the question of whether melting-induced crustal production changes the critical yield stress needed to obtain mobile-lid behaviour (plate tectonics). Our results show that melting-induced crustal production strongly influences plate tectonics on Earth-like planets by strongly enhancing the mobility of the lid, replacing a stagnant lid with an episodic lid, or greatly extending the time in which a smoothly evolving mobile lid is present in a planet. Finally, we show that our results are consistent with analytically predicted critical yield stress obtained with boundary layer theory, whether melting-induced crustal production is considered or not

The Tectonics and Volcanism of Venus: New Modes Facilitated by Realistic Crustal Rheology and Intrusive Magmatism

To explain Venus' young surface age and lack of plate tectonics, Venus' tectonic regime has often been proposed to be either an episodic-lid regime with global lithospheric overturns, or an equilibrium resurfacing regime with numerous volcanic and tectonic activities. Here, we use global 2-D thermochemical convection models with realistic parameters, including rheology (dislocation creep, diffusion creep, and plastic yielding), an experiment-based plagioclase (An$_{75}$) crustal rheology, and intrusive magmatism, to investigate the tectonics and mantle evolution of Venus. We find that surface tectonics is strongly affected by crustal rheology. With a ''weak'' plagioclase-rheology crust, models exhibit episodic overturns but with continuously high surface mobility and high distributed surface strain rates between overturns, leading to a new tectonic regime that we name ''deformable episodic lid''. On the other hand, olivine-crustal-rheology models exhibit either standard episodic-lid tectonics, i.e. with mobility that is high during overturns and near zero between overturns, or stagnant-lid tectonics, i.e. with near-zero mobility over the entire model time. Also, a combination of plagioclase crustal rheology and dislocation creep can weaken the lithosphere sufficiently to facilitate lithospheric overturns without applying plastic yielding. Internally, the composition-dependent density profile results in a ''basalt barrier'' at the mantle transition zone, which strongly affects Venus' mantle evolution. Only strong plumes can penetrate this basalt barrier and cause global lithospheric overturns. This basalt barrier also causes global internal episodic overturns that generate global volcanic resurfacing in stagnant-lid models, which suggests a new resurfacing mechanism (we name it ''stagnant episodic-volcanic-resurfacing'') that does not involve lithospheric overturns.Comment: Minor changes to previous version. Accepted by Icarus. Main text 54 pages, 17 figures, abstract abbreviate

Can we constrain interior structure of rocky exoplanets from mass and radius measurements?

We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii as well as to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Our main conclusions are: (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are key constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. [...]Comment: 19 pages, 18 figures, accepted in Astronomy & Astrophysics (no changes to previous version

A sequential data assimilation approach for the joint reconstruction of mantle convection and surface tectonics

International audienceWith the progress of mantle convection modelling over the last decade, it now becomes possible to solve for the dynamics of the interior flow and the surface tectonics to first order. We show here that tectonic data (like surface kinematics and seafloor age distribution) and mantle convection models with plate-like behaviour can in principle be combined to reconstruct mantle convection. We present a sequential data assimilation method, based on suboptimal schemes derived from the Kalman filter, where surface velocities and seafloor age maps are not used as boundary conditions for the flow, but as data to assimilate. Two stages (a forecast followed by an analysis) are repeated sequentially to take into account data observed at different times. Whenever observations are available, an analysis infers the most probable state of the mantle at this time, considering a prior guess (supplied by the forecast) and the new observations at hand, using the classical best linear unbiased estimate. Between two observation times, the evolution of the mantle is governed by the forward model of mantle convection. This method is applied to synthetic 2-D spherical annulus mantle cases to evaluate its efficiency. We compare the reference evolutions to the estimations obtained by data assimilation. Two parameters control the behaviour of the scheme: the time between two analyses, and the amplitude of noise in the synthetic observations. Our technique proves to be efficient in retrieving temperature field evolutions provided the time between two analyses is 10 Myr. If the amplitude of the a priori error on the observations is large (30 per cent), our method provides a better estimate of surface tectonics than the observations, taking advantage of the information within the physics of convection