Effects of plate bending and fault strength at subduction zones on plate dynamics

For subduction to occur, plates must bend and slide past overriding plates along fault zones. Because the lithosphere is strong, significant energy is required for this deformation to occur, energy that could otherwise be spent deforming the mantle. We have developed a finite element representation of a subduction zone in which we parameterize the bending plate and the fault zone using a viscous rheology. By increasing the effective viscosity of either the plate or the fault zone, we can increase the rates of energy dissipation within these regions and thus decrease the velocity of a plate driven by a given slab buoyancy. We have developed a simple physical theory that predicts this slowing by estimating a convecting cell's total energy balance while taking into account the energy required by inelastic deformation of the bending slab and shearing of the fault zone. The energy required to bend the slab is proportional to the slab's viscosity and to the cube of the ratio of its thickness to its radius of curvature. The distribution of dissipation among the mantle, lithosphere, and fault zone causes the speed of a plate to depend on its horizontal length scale. Using the observation that Earth's plate velocities are not correlated to plate size, we can constrain the lithosphere viscosity to be between 50 and 200 times the mantle viscosity, with higher values required if the fault zone can support shear tractions  50 MPa over 300 km. These subduction zone strengths imply that the mantle, fault zone, and lithosphere dissipate about 30%, 10%, and 60% of a descending slab's potential energy release if the slab is 100 km thick. The lithospheric component is highly dependent on slab thickness; it is smaller for thin plates but may be large enough to prevent bending in slabs that can grow thicker than 100 km. $ubduction zone strength should be more stable than mantle viscosity to changes in mantle temperature, so the controlling influence of subduction zones could serve to stabilize plate velocities over time as the Earth cools. Because the "details" of convergent plate boundaries are so important to the dynamics of plate motion, numerical models of mantle flow should treat subduction zones in a realistic way.