Mantle convection with strong subduction zones

Abstract

Because mantle viscosity is temperature‐dependent, cold subducting lithosphere should be strong, which implies that the rapid, localized deformation associated with subduction should strongly resist plate motions. Due to computational constraints, the deformation of a subducting plate cannot be accurately resolved in mantle‐scale convection models, so its effect on convection is difficult to investigate. We have developed a new method for implementing subduction that parametrizes the deformation of the oceanic lithosphere within a small region of a finite element grid. By imposing velocity boundary conditions in the vicinity of the subduction zone, we enforce a geometry for subduction, producing a slab with a realistic thermal structure. To make the model dynamically consistent, we specify a rate for subduction that balances the energy budget for convection, which includes an expression for the energy needed to deform the oceanic lithosphere as it subducts. This expression is determined here from a local model of bending for a strong viscous lithosphere. By implementing subduction in this way, we have demonstrated convection with plates and slabs that resemble those observed on Earth, but in which up to 40 per cent of the mantle's total convective resistance is associated with deformation occurring within the subduction zone. This additional resistance slows plate velocities by nearly a factor of two compared to models with a weak slab. For sufficiently strong lithosphere, the bending deformation slows surface plates sufficiently that they no longer actively participate in global‐scale convection, which occurs instead beneath a ‘sluggish lid’. By introducing a low‐viscosity asthenosphere beneath the oceanic plate, we demonstrate that small‐scale convection at the base of oceanic lithosphere may limit plate thickness, and thus the resistance to bending, and cause plate velocities to depend on the strength of the bending lithosphere rather than on the viscosity of the underlying mantle. For a cooling Earth, the effective lithosphere viscosity should be nearly constant, but the mantle viscosity should increase with time. Thus, subduction‐resisted convection should produce nearly constant plate velocities and heat flow over time, which has implications for the Earth's thermal evolution. We estimate that this style of convection should apply if the effective viscosity of the bending lithosphere is greater than about 10^(23) Pa s, but only if some mechanism, such as small‐scale convection, prevents the bending resistance from stopping plates altogether. Such a mechanism could be fundamental to plate tectonics and Earth's thermal history.