On An Earthquake And Aftershock Mechanism Relating To A Model Of The Crust And Mantle

A layered half-space is presented as a model for the crust-mantle system of the earth. Elastic and inelastic properties are attributed to both media. The primary purpose of this report is to study time sequences of shallow earthquakes, with special consideration of the material properties of the crust and mantle. The earthquake mechanism is modelled after the San Andreas Fault in California, and is considered as a discrete Volterra type dislocation. A three-dimensional boundary value problem in static linear elasticity, where the material is assumed to be incompressible, is solved by means of a modified form of the Galerkin vector and use of double Fourier transforms. The solution is shown to reduce to the classical one obtained for the half-space. Time dependent properties are introduced into the system by means of Biot's correspondence principle of linear viscoelasticity. Solutions are obtained in quadrature for the surface displacements and some stresses at the interface. A brief discussion of postglacial uplift and its relation to the inelastic properties of the system is included. Experiments and observations which may be needed for numerical calculations are suggested. (Author).