Why subduction zones are curved.

We give an explanation for the polarity, localization, shape, size, and initiation of subduction zones on Earth. By considering a soft, thin, curved lithospheric cap with either elastic or viscous rheology supported by a thick, nearly incompressible mantle, we find two different characteristic subduction geometries arise depending on boundary conditions: (1) plate boundaries where subduction results primarily from the gravitational body force (free subduction) have characteristic plate lengths and form arc-shaped dimpled segments resulting from the competition between bending and stretching in edge buckling modes of thin spherical shells, and (2) subduction zones due to localized applied loads that push one slab of thin, positively buoyant lithosphere beneath an overriding plate (forced subduction) form localized straight segments, consistent with the deformation of indented spherical shells. Both types of subduction are nonlinear subcritical instabilities, so small perturbations in the mechanical properties of the lithosphere have pronounced effects on subduction initiation and evolution. Yet in both cases, geometric relationships determined by the shape of the Earth itself play the most critical role in controlling the basic morphology and characteristic length scales of subduction zones. [ABSTRACT FROM AUTHOR]