Because of their distinct chemical signatures, ocean-island and mid-ocean-ridge basalts are traditionally inferred to arise from separate, isolated reservoirs in the Earth's mantle. Such mantle reservoir models, however, typically satisfy geochemical constraints, but not geophysical observations. Here we propose an alternative hypothesis that, rather than being divided into isolated reservoirs, the mantle is filtered at the 410-km-deep discontinuity. We propose that, as the ascending ambient mantle (forced up by the downward flux of subducting slabs) rises out of the high-water-solubility transition zone (between the 660 km and 410 km discontinuities) into the low-solubility upper mantle above 410 km, it undergoes dehydration-induced partial melting that filters out incompatible elements. The filtered, dry and depleted solid phase continues to rise to become the source material for mid-ocean-ridge basalts. The wet, enriched melt residue may be denser than the surrounding solid and accordingly trapped at the 410 km boundary until slab entrainment returns it to the deeper mantle. The filter could be suppressed for both mantle plumes (which therefore generate wetter and more enriched ocean-island basalts) as well as the hotter Archaean mantle (thereby allowing for early production of enriched continental crust). We propose that the transition-zone water-filter model can explain many geochemical observations while avoiding the major pitfalls of invoking isolated mantle reservoirs.

Abstract. A theoretical model for the dynamics of a simple two-phase mixture is presented. A classical averaging approach combined with symmetry arguments is used to derive the mass, momentum, and energy equations for the mixture. The theory accounts for surficial energy at the interface and employs a nonequilibrium equation to relate the rate of work done by surface tension to the rates of both pressure work and viscous deformational work. The resulting equations provide a basic model for compaction with and without surface tension. Moreover, use of the full nonequilibrium surface energy relation allows for isotropic damage, i.e., creation of surface energy through void generation and growth (e.g., microcracking), and thus a continuum description of weakening and shear localization. Applications to compaction, damage, and shear localization are investigated in two companion papers.

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The initiation of plate tectonics on Earth is a critical event in our planet's history. The time lag between the first proto-subduction (about 4 billion years ago) and global tectonics (approximately 3 billion years ago) suggests that plates and plate boundaries became widespread over a period of 1 billion years. The reason for this time lag is unknown but fundamental to understanding the origin of plate tectonics. Here we suggest that when sufficient lithospheric damage (which promotes shear localization and long-lived weak zones) combines with transient mantle flow and migrating proto-subduction, it leads to the accumulation of weak plate boundaries and eventually to fully formed tectonic plates driven by subduction alone. We simulate this process using a grain evolution and damage mechanism with a composite rheology (which is compatible with field and laboratory observations of polycrystalline rocks), coupled to an idealized model of pressure-driven lithospheric flow in which a low-pressure zone is equivalent to the suction of convective downwellings. In the simplest case, for Earth-like conditions, a few successive rotations of the driving pressure field yield relic damaged weak zones that are inherited by the lithospheric flow to form a nearly perfect plate, with passive spreading and strike-slip margins that persist and localize further, even though flow is driven only by subduction. But for hotter surface conditions, such as those on Venus, accumulation and inheritance of damage is negligible; hence only subduction zones survive and plate tectonics does not spread, which corresponds to observations. After plates have developed, continued changes in driving forces, combined with inherited damage and weak zones, promote increased tectonic complexity, such as oblique subduction, strike-slip boundaries that are subparallel to plate motion, and spalling of minor plates.

SUMMARY The two‐phase theory for compaction and damage proposed by Bercovici et al. (2001a, J. Geophys. Res.,106, 8887–8906) employs a nonequilibrium relation between interfacial surface energy, pressure and viscous deformation, thereby providing a model for damage (void generation and microcracking) and a continuum description of weakening, failure and shear localization. Here we examine further variations of the model which consider (1) how interfacial surface energy, when averaged over the mixture, appears to be partitioned between phases; (2) how variability in deformational‐work partitioning greatly facilitates localization; and (3) how damage and localization are manifested in heat output and bulk energy exchange. Microphysical considerations of molecular bonding and activation energy suggest that the apparent partitioning of surface energy between phases goes as the viscosity of the phases. When such partitioning is used in the two‐phase theory, it captures the melt‐compaction theory of McKenzie (1984, J. Petrol.,25, 713–765) exactly, as well as the void‐damage theory proposed in a companion paper (Ricard & Bercovici, submitted). Calculations of 1‐D shear localization with this variation of the theory still show at least three possible regimes of damage and localization: at low stress is weak localization with diffuse slowly evolving shear bands; at higher stress strong localization with narrow rapidly growing bands exists; and at yet higher shear stress it is possible for the system to undergo broadly distributed damage and no localization. However, the intensity of localization is strongly controlled by the variability of the deformational‐work partitioning with dilation rate, represented by the parameter γ. For γ≫ 1, extreme localization is allowed, with sharp profiles in porosity (weak zones), nearly discontinuous separation velocities and effectively singular dilation rates. Finally, the bulk heat output is examined for the 1‐D system to discern how much deformational work is effectively stored as surface energy. In the high‐stress, distributed‐damage cases, heat output is reduced as more interfacial surface energy is created. Yet, in either the weak or strong localizing cases, the system always releases surface energy, regardless of the presence of damage or not, and thus slightly more heat is in fact released than energy is input through external work. Moreover, increased levels of damage (represented by the maximum work‐partitioning f*) make the localizing system release surface energy faster as damage enhances phase separation and focusing of the porosity field, thus yielding more rapid loss of net interfacial surface area. However, when cases with different levels of damage are compared at similar stages of development (say, the peak porosity of the localization) it is apparent that increased damage causes smaller relative heat release and retards loss of net interfacial surface energy. The energetics and energy partitioning of this damage and shear‐localization model are applied to estimating th...

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International audienceP>We employ basic non-equilibrium thermodynamics to propose a general equation for the mean grain size evolution in a deforming medium, under the assumption that the whole grain size distribution remains self-similar. We show that the grain size reduction is controlled by the rate of mechanical dissipation in agreement with recent findings. Our formalism is self consistent with mass and energy conservation laws and allows a mixed rheology. As an example, we consider the case where the grain size distribution is lognormal, as is often experimentally observed. This distribution can be used to compute both the kinetics of diffusion between grains and of dynamic recrystallization. The experimentally deduced kinetics of grain size coarsening indicates that large grains grow faster than what is assumed in classical normal grain growth theory. We discuss the implications of this model for a mineral that can be deformed under both dislocation creep and grain size sensitive diffusion creep using experimental data of olivine. Our predictions of the piezometric equilibrium in the dislocation-creep regime are in very good agreement with the observations for this major mantle-forming mineral. We show that grain size reduction occurs even when the average grain size is in diffusion creep, because the largest grains of the grain size distribution can still undergo recrystallization. The resulting rheology that we predict for olivine is time-dependent and more non-linear than in dislocation creep. As the deformation rate remains an increasing function of the deviatoric stress, this rheology is not localizing