Marc Monnereau

Spherical shell models of mantle convection with tectonic plates

Abstract A simple three-dimensional spherical model of mantle convection, where plates are taken into account in the top boundary condition, allows to investigate the plate tectonics–mantle convection coupling in a self-consistent way. Avoiding the strong difficulties inherent in the numerical treatment of rheology, the plate condition appears efficient in reproducing the Earth-like features as subduction, mid-oceanic ridges and hotspots. Whereas the free-slip condition leads to a classical polygonal cell pattern with cylindrical hot plumes surrounded by downwellings, the plate condition favors the development of strong linear downwellings associated to passive diverging zones along plate boundaries. These cold currents, very similar to subductions, act the main role in mantle convection: they drive the whole circulation. In that context, hot plumes remain almost independent, except if on the long term, cold material spreading at the core surface induces a slight migration, below a few mm/yr, of their surface impingement. The main result is that plate tectonics appear to be more than a simple mode of organization of the surface movements, it is the essence of the Earth mantle dynamics.

Mechanical erosion and reheating of the lithosphere: A numerical model for hotspot swells

It is currently debated if either thermal erosion of the lithosphere or dynamical support is the source of topography and geoid anomalies. The origin of tins controversy lies probably in the difficulty to model simultaneously these two effects. For this purpose we have studied the time dependent behavior of two-dimensional convection with a temperature and pressure dependent viscosity. The use of a control volume method allows us to define a rigid zone simulating the mechanical lithosphere. The interface between the lithosphere and the convective mantle is determined by a viscosity cutoff. First, some experiments model the rise of a plume below the lithosphere in order to observe the evolution of the uplift and thus to appreciate the various processes involved in the swell formation. Before the plume reaches the base of the thermal lithosphere, an uplift a few hundred meters in amplitude develops which can only be ascribed to a pure dynamical support. The major uplift occurs when the ductile part of the lithosphere, the convective boundary layer, is squeezed by the plume. The reheating of the mechanical lithosphere takes place after this transient stage of dynamical erosion. However, this late process is very slow but can magnify the amplitude of the swell if the lithosphere stays long enough above the plume. These results shed some light on the different mechanisms occurring during the swell formation, but the configuration modeled does not correspond to the one expected for actual hotspot swells. They feature plume rising up to the lithosphere while natural situations correspond to lithosphere drifting above preexisting plumes. An experiment with a moving lithosphere was run and shows that thermal erosion does not affect significantly a moving lithosphere even for relatively slow drifting velocities (few centimeters/year). Indeed, the thermal structure of the lithosphere is not modified above the 800°C isotherm except for a motionless plate. In this case the resulting swell should be greater: this could explain why Azores, Crozet or Cap Verde swells are so high. On the other hand, the shape of a swell over a moving lithosphere is strikingly reminiscent of the Hawaiian swell.

Is the transition zone an empty water reservoir? Inferences from numerical model of mantle dynamics

Abstract Water is probably present everywhere in the Earth’s mantle today, with abundances ranging between scales of percent (%) to the parts per million (ppm). Mantle total water content is estimated to be between 10% to several times that of the present-day hydrosphere. Numerous studies have been devoted to the determination of water solubility in mantle material [D.R. Bell, G.R. Rossmann, Science 255 (1992) 1391–1397; J. Ingrin, H. Skogby, Eur. J. Mineral. 12 (2000) 543–570]. They all show strong solubility variations from one mineral phase to another. Principally, water partitioning has made the transition zone a probable trap for water from the Earth’s mantle [N. Bolfan-Casanova et al., Earth Planet. Sci. Lett. 182 (2000) 209–221; D.L. Kohlstedt et al., Contrib. Mineral. Petrol. 123 (1996) 345–357]. Nevertheless, water distribution within the mantle is still debated. We have studied the role of mantle dynamics in water distribution by modeling water transport and mantle convection in a two-dimensional (2-D) cartesian geometry. The model takes into account water partitioning between the mantle’s transition zone and the upper mantle of 10:1 and between the lower mantle and the transition zone of 1:100 (i.e. respectively between olivine and spinel and spinel and post-spinel). We have modeled the mantle temperature field using depth-dependent viscosity and plate-like surface conditions. Water injection at the trench has also been simulated. Our numerical experiments suggest that diffusivity of water has to be very high, at least two orders of magnitude higher than the one experimentally determined [D.R. Bell, G.R. Rossmann, Science 255 (1992) 1391–1397; J. Ingrin, H. Skogby, Eur. J. Mineral. 12 (2000) 543–570] to significantly influence water distribution in Earth’s mantle. In fact, the diffusion process is not efficient enough to balance the mixing due to mantle dynamics and to force water into the transition zone. We show that the distribution of water should be quite homogeneous throughout the mantle if advection and diffusion are the only processes involved in water transport in the mantle. This homogeneity implies that water below the transition zone could be in excess according to the lower mantle rocks solubility. This addresses the question of stability of free water in the lower mantle and its mobility by percolation process, which could be a very efficient transport process, previously unconsidered in this field of research.

Viscosity and thickness of the sub-lithospheric low-viscosity zone: constraints from geoid and depth over oceanic swells

Abstract The medium-wavelength geoid to depth anomalies ratio (GDR) at oceanic hotspot swells has been found to increase from ∼ −0.5 m/km to ∼ 5 m/km according to the age of the lithosphere they occur on. In order to interpret this trend, the geoid and topography anomalies associated with mantle convective plumes crossing a sublithospheric low viscosity zone (LVZ) have been derived from numerical models and a systematic investigation of the GDR dependence on the viscosity and depth extent of the LVZ, on the thickness and thermal structure of the lithosphere and on the Rayleigh number has been conducted. It is shown that, for viscosity drops across the base of the LVZ, greater than one order of magnitude, the GDR is strongly dependent on the depth of shallow interfaces such as the lithosphere/ athenosphere boundary and on the LVZs thickness. Consequently, the empirical trend can be accounted for by the thickening of the lithosphere with age provided it occurs at the expense of a LVZ whose base is at a fixed depth (around 200 km). In such a frame, no significant variation with age of the LVZs viscosity is required by the GDR data. Best fit with the empirical trend is found for a LVZ about 50 times less viscous than the underlying mantle. The mantle flow starts to fluctuate when the local Rayleigh number of the low-viscosity layer exceeds the Rayleigh number of the underlying mantle. The fluctuations are initiated in the upper boundary layer, in the diverging part of the plume, at a distance of a few hundreds of kilometers from the main ascending current. For viscosity contrasts in the range of 40–60, deduced from the present study, the conditions for the development of these small-scale instabilities are realized only where the lithosphere has not yet grown significantly downwards (ages

How flat is the lower-mantle temperature gradient?

Abstract The temperature gradient in the lower mantle is fundamental in prescribing many transport properties, such as the viscosity, thermal conductivity and electrical conductivity. The adiabatic temperature gradient is commonly employed for estimating these transport properties in the lower mantle. We have carried out a series of high-resolution 3-D anelastic compressible convections in a spherical shell with the PREM seismic model as the background density and bulk modulus and the thermal expansivity decreasing with depth. Our purpose was to assess how close under realistic conditions the horizontally averaged thermal gradient would lie to the adiabatic gradient derived from the convection model. These models all have an endothermic phase change at 660 km depth with a Clapeyron slope of around −3 MPa K −1 , uniform internal heating and a viscosity increase of 30 across the phase transition. The global Rayleigh number for basal heating is around 2×10 6 , while an internal heating Rayleigh number as high as 10 8 has been employed. The pattern of convection is generally partially layered with a jump of the geotherm across the phase change of at most 300 K. In all thermally equilibrated situations the geothermal gradients in the lower mantle are small, around 0.1 K km −1 , and are subadiabatic. Such a low gradient would produce a high peak in the lower-mantle viscosity, if the temperature is substituted into a recently proposed rheological law in the lower mantle. Although the endothermic phase transition may only cause partial layering in the present-day mantle, its presence can exert a profound influence on the state of adiabaticity over the entire mantle.

DYNAMICS OF SUPERPLUMES IN THE LOWER MANTLE

Superplumes in the lower mantle have been inferred for a long time by the presence of two very large provinces with slow seismic wave velocities. These extensive structures are not expected from numerical and laboratory experiments nor are they found in thermal convection with constant physical properties under high Rayleigh number conditions. Here we summarize our dynamical understanding of superplume structures within the framework of thermal convection. The numerical studies involve both two- and threedimensional models in Cartesian and spherical-shell geometries. The theoretical approach is based on models with increasing complexity, starting with the incompressible Boussinesq model and culminating with the anelastic compressible formulation. We focus here on the (1) depth-dependence of variable viscosity and thermal coefficient of expansion (2) radiative thermal conductivity and (3) both upper- and deep-mantle phase transitions. All these physical factors in thermal convection help to create conditions favorable for the formation of partially-layered convection and large-scale upwelling structures in the lower mantle.

Thermal and petrological consequences of melt migration within mantle plumes

The high temperatures and high degrees of melting expected in the core of mantle plumes have virtually no expression in the eruption temperatures of hotspot lavas, nor in the composition of their glasses, which is restricted in the basaltic field. A solution to this paradox is looked for in the melt migration processes within the melting region of mantle plumes. Three dimensional convective calculations at Rayleigh number of 106 allow estimates of the possible temperature, melt fraction and stress fields within a plume. Two regions with different melt migration patterns can be distinguished. A lower zone ranging in depth from the base of the melting region (150 km) to around 80—100 km where the first melt fraction is redistributed in a sub-horizontal vein network and convects in response to the steep horizontal temperature gradient. This process is able to homogenize the temperature within the melting region very efficiently. The high (300 °C) temperature contrast between the centre of the plume and the surrounding mantle can be reduced to a few tens of degrees at the top of this zone. Fractional crystallization of high pressure phases will strongly modify the composition of the melt as it circulates toward the periphery of the melting region. A second upper zone, where the sub-vertical vein orientation will make possible rapid melt migration toward the surface, extends to the base of the lithosphere. Due to the buffering of the plume temperature around a value close to the mean upper mantle temperature, the degree of adiabatic melting within this upper zone will not greatly exceed that beneath normal spreading centres, even in the case of on-ridge hotspots. The lavas erupted at hotspots are likely to result from the mixing in various proportions of these low pressure melts (basalts) with the highly evolved liquids (possibly with kimberlitic to alkalic affinities) resulting from fractional crystallization of the high-pressure melt fractions produced at the base of the melting region. This scenario could account for the low eruption temperatures and Mg contents of hotspot lavas, in spite of a complex high pressure, and thus high temperature, history evidenced by some geochemical trends.

Is the 670 km phase transition able to layer the Earth's convection in a mantle with depth‐dependent viscosity?

The effect of a viscosity stratification on phase change dynamics have been investigated with axi-spherical convection models. As in previous studies with a constant viscosity mantle an intermittent layering appears for a Clapeyron slope from −2 MPa/K to −3 MPa/K. A viscosity increase in lower mantle requires a more negative Clapeyron slope to produce the layering. This shift is sensitive to the mechanical boundary condition. With a viscosity contrast of 30, a no-slip top condition does not lead to layering in the range of the possible values for the Clapeyron slope. With a free-slip condition, the threshold is at −4 MPa/K. Just below this threshold, a whole mantle circulation driven by a cylindrical hot plume coexists with layered mantle domains over several billion years.