Except for the first 50-100 million years or so of the Earth's history, when most of the mantle may have been subjected to melting, the differentiation of Earth's silicate mantle has been controlled by solid-state convection. As the mantle upwells and decompresses across its solidus, it partially melts. These low-density melts rise to the surface and form the continental and oceanic crusts, driving the differentiation of the silicate part of the Earth. Because many trace elements, such as heat-producing U, Th and K, as well as the noble gases, preferentially partition into melts (here referred to as incompatible elements), melt extraction concentrates these elements into the crust (or atmosphere in the case of noble gases), where nearly half of the Earth's budget of these elements now resides. In contrast, the upper mantle, as sampled by mid-ocean ridge basalts, is highly depleted in incompatible elements, suggesting a complementary relationship with the crust. Mass balance arguments require that the other half of these incompatible elements be hidden in the Earth's interior. Hypotheses abound for the origin of this hidden reservoir. The most widely held view has been that this hidden reservoir represents primordial material never processed by melting or degassing. Here, we suggest that a necessary by-product of whole-mantle convection during the Earth's first billion years is deep and hot melting, resulting in the generation of dense liquids that crystallized and sank into the lower mantle. These sunken lithologies would have 'primordial' chemical signatures despite a non-primordial origin.

S U M M A R YMixed heated 3-D mantle convection simulations with a low-viscosity asthenosphere reveal relatively short and long wavelength regimes with different scalings in terms of surface velocity and surface heat flux and show that mantle flow in the lithosphere-asthenosphere region is a Poiseuille-Couette flow. The Poiseuille/Couette velocity magnitude ratio, D/U , allows us to characterize solid-state flow in the asthenosphere and to predict the regime transition. The transition from dominantly pressure-driven Poiseuille flow at shorter wavelengths to dominantly shear-driven Couette flow at long wavelengths depends on the relative strength of lithosphere and asthenosphere and is associated with a switch in the dominant resistance to convective motion. In the Poiseuille regime significant resistance is provided by platebending, whereas in the Couette regime most resistance is due to vertical shear in the bulk mantle. The Couette case corresponds to classical scaling ideas for mantle convection whereas the Poiseuille case, with asthenospheric velocities exceeding surface velocities, is an example of a sluggish lid mode of mantle convection that has more recently been invoked for thermal history models of the Earth. Our simulations show that both modes can exist for the same level of convective vigour (i.e. Rayleigh number) but at different convective wavelengths. Additional simulations with temperature-and yield-stress dependent viscosity show consistent behaviour and suggest an association of the regime crossover with the relative strength of plate margins. Our simulations establish a connection between the strength of plate margins, solid-state flow in the asthenosphere and the wavelength of mantle convection. This connection suggests that plate tectonics in the sluggish lid mode is wavelength dependent and potentially more robust than previously envisioned.

[1] Tectonic plate motions reflect dynamical contributions from subduction processes (i.e., classical "slabpull" forces) and lateral pressure gradients within the asthenosphere ("asthenosphere-drive" forces), which are distinct from gravity forces exerted by elevated mid-ocean ridges (i.e., classical "ridge-push" forces).Here we use scaling analysis to show that the extent to which asthenosphere-drive contributes to plate motions depends on the lateral dimension of plates and on the relative viscosities and thicknesses of the lithosphere and asthenosphere. Whereas slab-pull forces always govern the motions of plates with a lateral extent greater than the mantle depth, asthenosphere-drive forces can be relatively more important for smaller (shorter wavelength) plates, large relative asthenosphere viscosities or large asthenosphere thicknesses. Published plate velocities, tomographic images and age-binned mean shear wave velocity anomaly data allow us to estimate the relative contributions of slab-pull and asthenosphere-drive forces for the motions of the Atlantic and Pacific plates. Whereas the Pacific plate is driven largely by slab pull, the Atlantic plate is predicted to be strongly driven by basal forces related to viscous coupling to strong asthenospheric flow, consistent with recent observations related to the stress state of North America. In addition, compared to the East Pacific Rise (EPR), the relatively large lateral pressure gradient near the Mid-Atlantic Ridge (MAR) is expected to produce significantly steeper dynamic topography. Thus, the relative importance of this platedriving force may partly explain why the flanking topography at the EPR is smoother than at the MAR. Our analysis also indicates that this plate-driving force was more significant, and heat loss less efficient, in Earth's hotter past compared with its cooler present state. This type of trend is consistent with thermal history modeling results which require less efficient heat transfer in Earth's past.

SUMMARY Boundary layer theory is used to derive scaling relationships for plate stresses in a mantle convection system with a low‐viscosity asthenosphere. The theory assumes a plate tectonic like mode of mantle convection with flow driven by an active upper boundary layer. The theory predicts that the confinement of horizontal mantle flow within a low‐viscosity, sublithospheric channel can lead to an increase in plate stress compared to the case lacking a channel (even if the absolute viscosity of the sublithosphere mantle does not change between the two cases). The theory further predicts increasing shear stress with decreasing low‐viscosity channel thickness. If the thickness of tectonic plates is determined dominantly by a dehydrated chemical lithosphere, then the plate normal stress is predicted to also increase with decreasing channel thickness. We use 3‐D spherical shell simulations of mantle convection with temperature‐, depth‐ and stress dependent rheology to test scaling trends. The simulations and theoretical scalings demonstrate that a low‐viscosity layer (asthenosphere) can amplify convective stresses. If the level of convective stress plays a role in maintaining and/or reactivating plate boundaries, this suggests that a relatively thin low viscosity layer may help to maintain plate tectonics. The numerical simulations support this suggestion as they show that an increase in the thickness of a low viscosity channel can cause the system to transition from an active‐lid mode of convection to a stagnant lid state. Collectively, the simulations and theoretical scalings lead to the conclusion that the role of the asthenosphere in maintaining plate tectonics does not come principally from a basal lubrication effect, associated with a low absolute asthenosphere viscosity, but, instead, from a mantle flow channelization effect, associated with a high viscosity contrast from the asthenosphere to the mantle below.

[1] Numerical mantle convection simulations show that depth-dependent viscosity can increase the flow wavelength. A recent analysis demonstrates that flow channelization into a low-viscosity region lowers lateral dissipation. This allows long wavelength flow to more efficiently cool the interior mantle. We present three-dimensional, mixed heating mantle convection simulations with a thin lowviscosity channel for a range of aspect ratios to test the implications of the theoretical analysis. For reasonable viscosity contrasts between lithosphere, asthenosphere and bulk mantle we find that very large aspect ratios can develop. Velocity profiles quantify the degree of channelization for variable aspect ratios. Internal temperatures are found to decrease with increasing aspect ratio and both surface heat flux and velocity are found to increase with aspect ratio. Our results are consistent with the idea that the asthenosphere channels lateral mantle flow which, in turn, stabilizes long wavelength convection cells and makes long wavelength flow energetically favorable.Citation: Höink, T., and A. Lenardic (2008), Three-dimensional mantle convection simulations with a low-viscosity asthenosphere and the relationship between heat flow and the horizontal length scale of convection, Geophys. Res. Lett., 35, L10304,