Curvature of subducted lithosphere from earthquake locations in the Wadati-Benioff zone

Estimates of slab curvature from 133 profiles across 12 major subduction zones are obtained by fitting splines through earthquakes locations. Several geometric quantities are computed from the spline fits, including the minimum radius of curvature. We also introduce a quantity called the equivalent radius of curvature to precisely define the bending dissipation in either a viscous or a plastic slab. The minimum and equivalent radius of curvature are approximately equal in slabs with simple geometry (i.e., a single bend) but deviate substantially when the geometry is more complicated. A compilation of estimates shows that the equivalent radius of curvature is insensitive to the age of the plate at the trench. Mean values are 175 km or 191 km, depending on the rheology of the slab. When bending occurs by viscous deformation, the resulting dissipation can exceed the power available from subduction with reasonable choices for viscosity. A more consistent description of the energetics is obtained by assuming a plastic rheology.