Viscous Dissipation and Criticality of Subducting Slabs

Michael R. Riedel, Shun Karato, Dave A. Yuen

We calculate the amount of viscous dissipation during subduction of a lithospheric plate as constrained by experimental rock mechanics. The maximum bending moment Mcrit that can be sustained by a slab is of the order of 1019 Nm per m according to Mcrit ~ sp * h2/4, where sp is the Peierl's stress limit of slab materials and h is the slab thickness. Near Mcrit, the amount of viscous dissipation grows strongly as a consequence of a lattice instability of mantle minerals (dislocation glide in olivine). The value of Mcrit is about 1-2 orders of magnitude too high to be reached by a ridge push of typically 1012 N per m at convergent plate boundaries, but unusual tectonic settings like a thick sedimentary load of the lithosphere or a shallow angle of slab penetration at the transition zone can help to overstep this bending moment threshold. The immediate consequence is a sudden drop of the effective viscosity to below 1021 Pas, so that the observed weakening effect serves as a self-regulating mechanism to adjust plate tectonics on Earth against strong viscous resistance forces.

Strong growth of viscous dissipation DeltaQ in dependence of the bending moment M for 3 different sets of constitutive equations for olivine creep (subduction speed 10 cm/yr, slab thickness 85 km):
(a) complete set including Peierls mechanism
(b) reduced set: only diffusion and power-law creep included
(c) linear rheology: only diffusion creep included
Also shown is the minimum slab bending curvature Rmin in dependence of M.

Dominant deformation mechanisms in subducting slabs. Initial temperature distribution corresponds to that for a 100 myr oceanic lithosphere of 85 km thickness. The cases for subduction velocities of 4 cm/yr and 10 cm/yr are shown. Because stress, temperature, pressure and grain-size change significantly in space for a given slab, dominant mechanisms of deformation change in a complicated fashion. In high stress, low temperature regions, the Peierls mechanism dominates. In moderate stress, moderate to large grain-size-regions, power- law creep dominates. Diffusion creep plays an important role in cold, fine-grain regions in the center of labs after a phase tranformation. Note that such a pattern also depends on the velocity of subduction, which controls the temperature distribution and the magnitude of stress.

Domain diagram showing the critical range of bending moments for a slab with 85 km thickness where the lithosphere is subject to thermo-mechanical instabilities (peak shear-heating rate inside the slab larger than 10-5 W/m3). In this ``critical'' domain, the minimum local bending curvature of the slab Rmin drops down to values below the slab thickness h. Arrows indicate the possible effect of the presence of water in the mantle lithosphere (see discussion). Also shown is the range of plate-like tectonics on Earth as inferred from observation