Spherical shell tectonics: buckling of subducting lithosphere

Abstract

The lithospheric plate is a spherical shell rather than a plane plate. A spherical shell must buckle when it is bent inward. We examined the possibility of lithospheric buckling upon subduction. The lithosphere with its subducted portion is simulated by a hemispherical elastic shell bent inward at its circumferential edge by a uniform radial load. The buoyancy force acting on the lithosphere seaward of the trench is simulated by clamping the shell along a parallel. The deformable portion between the loaded and clamped edges corresponds to the subducting slab of lithosphere. Buckling analyses were made using the techniques of a linear stability analysis and a finite element method. The wavelength of buckling depends on the thickness of the shell and the length of its deformable portion: a longer wavelength is associated with a thicker shell and a longer deformable portion. By scaling the shell thickness and the length of the deformable portion to the elastic thickness of lithosphere and the length of subducting slab, respectively, the wavelength of buckling can be compared favourably to the length of one unit of arcuate trench in a chain-like continuation of island arcs. The load to be applied for initiation of buckling is called the critical load: a lower critical load is associated with a thinner shell with a longer deformable portion. The excess weight of subducting slab provides a load large enough to initiate lithospheric buckling at a relatively early stage of subduction. Radial displacement of the circumferential edge at the critical state is an order of magnitude smaller than the depth of the leading edge of the Wadati-Benioff zone, indicating that most of the present subducting lithospheres are under a postbuckling state. Undulation of the shell in the postbuckling state is not purely sinusoidal but a successive continuation of arcs with cusps in between, invoking the continuation of arcuate deep-sea trenches with cusps at their junctions. The cuspate feature of island arc chains is thus a natural consequence of lithospheric buckling and does not require any such irregularities as seamounts colliding with a trench. Collision of seamounts, however, can aid buckling greatly if they are aligned along a trench at an interval not very different from the inherent buckling wavelength.