A mathematical model for the deformations achievable by a slightly extensible spherical cap

Abstract

The shape of a deep seismic zone is thought to represent that of the descending slab of the lithosphere. The lithosphere before subduction is a spherical cap, and the shape of the descending slab is the result of the deformation of the spherical lithosphere at the subduction zone. It was found that the actual shape of the descending slab maybe approximated by a slightly extensible spherical cap for a shallow subduction zone, while for a deep subduction zone, the cap appears to be too inflexible to form a steep dipping angle. A technique was developed to explore the relationship between the subducted slab shape and the slab deformation.