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