Mantle rheology and the scaling of bending dissipation in plate tectonics

[1] Plate tectonics on Earth involves the bending deformation of plates at subduction zones, and because plates are generally considered to be stiff owning to the rheology of mantle minerals, the role of energy dissipation by plate bending in the global energy balance has been frequently debated in the recent literature. Here we consider how bending dissipation should scale with slab parameters such as dip angle, plate age, the radius of curvature, and plate velocity by systematically exploring the parameter space with instantaneous Stokes flow calculations. We derive the scaling of bending dissipation for a range of mantle viscosity functions, including pseudoplastic rheology with olivine flow laws. Our results indicate that, as we move away from the isoviscous case, the scaling gradually deviates from what has commonly been assumed in previous studies, most notably for the radius exponent, which exhibits more than threefold reduction and even a sign reversal in some cases. These modifications in scaling exponents originate in the complication of the deformation field caused by viscosity variations within the bending plate. Approximating the lithospheric rheology by a single effective viscosity in the dynamical models of subduction has been a common practice, but we suggest that such approximation may limit the geological relevance of modeling studies, in particular when estimating the significance of bending dissipation.