Convection in a two‐layer mantle with a strongly temperature‐dependent viscosity

Abstract

Recent geochemical and isotopic data support the hypothesis that the earth's mantle convects in two separate layers with an interface at the 650-km seismic discontinuity. This paper studies the implications of this hypothesis with regard to the thermal boundary layers that are expected to develop adjacent to the interface between the convecting layers. We are particularly concerned with a possible decrease in the mantle viscosity across this interface. In order to study the structure of the thermal boundary layers in a fluid with a strongly temperature-dependent viscosity we utilize an approximate method developed by Howard (1966). If the upper and lower mantle have the same viscosity law, we find that stratified convection requires a lower mantle viscosity which is several orders of magnitude lower than the upper mantle viscosity. This is not consistent with studies of postglacial rebound. It is possible to obtain a viscosity law for the lower mantle that gives a viscosity nearly equal to that of the upper mantle and reasonable temperatures. However, the required law is not consistent with the currently available experimental data on lower mantle materials. Therefore we conclude that thermal arguments favor whole mantle convection. INTRODUCTION It is generally accepted that mantle convection is the drivingmechanism for plate tectonics and continental drift; in fact, the lithospheric plates are the thermal boundary layers of mantle convection cells [Turcotte and Schubert, 1982, pp. 163-167]. However, two major uncertainties concerning mantle convection remain. These are (1) whether there are separate upper and lower mantle convection systems and (2) whether and in what form a second scale of mantle convection other than the plate motions occurs in the upper mantle. Arguments regarding upper versus whole mantle convection center on the role of the 650-km seismic discontinuity. If this discontinuity is caused by a change in mantle composition, it is unlikely that mantle convective flows could penetrate it. The higher density lower mantle would be stable with respect to the less dense upper mantle. The alternative is that the density change associated with the seismic discontinuity is due to a solid-solid phase change. A phase change may enhance convection, or hinder convection, depending upon its thermodynamic properties [Schubert and Turcotte, 1971]. Laboratory studies indicate that the spinel-basic oxide phase change may have the properties needed to account for the discontinuity [Ming and Bassett, 1975; Watt and O'Connell, 1978]. However, other authors disagree [Liu, 1980; Jeanloz and Thompson, 1981]. The fate of the subducted lithosphere is directly related to this problem. If an upper mantle convection system exists, the subducted lithosphere would be expected to lie on the 650-km compositional boundary. The termination of Benioff zones at this depth favors upper mantle convection. However, some seismologists believe that they can observe the propagation of seismic waves through subducted lithosphere at depths...

Igneous Petrogenesis

“…Details of the movements and the scale of convection remain uncertain, although there is no doubt that the rates are so slow that the mantle is effectively motionless within a human framework of time. Schemes have been proposed involving large convection cells extending through the entire mantle (Loper 1985) or independently convecting upper and lower mantle layers (Richter & McKenzie 1981, Kenyon & Turcotte 1983, O'Nions 1987Fig. 3.6).…”

Laboratory Studies of Mantle Convection

“…The presence of a deformable interface offers the possibility of Hopf bifurcations: since it introduces an additional degree of freedom, overstability can occur in the form of oscillatory interfacial instability (Richter and Johnson, 1974;Rasenat et al, 1989;Le Bars and Davaille, 2002;Jaupart et al, 2007). At first, numerical studies of two-layer convection at finite amplitude have typically focused on the mechanism of coupling (thermal vs. mechanical) between the layers, often treating the interface as impermeable (e.g., Richter and McKenzie, 1981;Kenyon and Turcotte, 1983;Christensen and Yuen, 1984;Cserepes and Rabinowicz, 1985;Boss and Sacks, 1986;Cserepes et al, 1988). At first, numerical studies of two-layer convection at finite amplitude have typically focused on the mechanism of coupling (thermal vs. mechanical) between the layers, often treating the interface as impermeable (e.g., Richter and McKenzie, 1981;Kenyon and Turcotte, 1983;Christensen and Yuen, 1984;Cserepes and Rabinowicz, 1985;Boss and Sacks, 1986;Cserepes et al, 1988).…”

Numerical models of thermally and mechanically coupled two-layer convection of highly viscous fluids

“…Previous stability analyses of two-layer convection have shown that a density contrast between chemically distinct layers of at least 1 per cent (Richter & Johnson 1974) and as much as 3 per cent (Olson & Yuen 1982) is required to prevent the layers from mixing. Perhaps the strongest argument in favour of whole mantle convection, put forward by Spohn & Schubert (1981), Davies (1981Davies ( ,1983Davies ( ,1984, and Kenyon & Turcotte (1983), is that steady-state, two-layer convection with the same rheology in both layers will lead to either widespread melting in the lower mantle or a large decrease in viscosity with depth across the interface thermal boundary layer; these conclusions are inconsistent with seismic data and current estimates of the earth's viscosity structure (Cathles 1975;Peltier 1981Peltier , 1982Sabadini & Peltier 1981;Wu & Peltier 1983Rubincam 1984;Hager 1984).…”