Three-Dimensional Fields Produced by a Volterra Dislocation Imbedded in a Layered Half-Space: Analytical Representation of a Seismic Mechanism

摘要

A three-dimensional boundary value problem in static linear elasticity is presented as a restricted formal characterization of a conceptual model for the crust-mantle system of the earth. The system is considered as a two-layered half-space, where elastic and inelastic properties are attributed to both media. It is assumed that both materials are incompressible. A Volterra dislocation, representing a fault plane, is imbedded in the upper layer, lying in a vertical plane with slip parallel to the free surface. The problem is solved by means of a modified form of the Galerkin vector and use of double Fourier transforms. Solutions are obtained in quadrature for the surface displacements and some stresses at the interface. Time dependent properties are introduced into the system by means of Biot's correspondence principle of linear viscoelasticity. This investigation is a segment of a comprehensive study in geomechanics, based upon a more complete conceptual and ontological model of the crust and mantle, which may prove essential for implementing an effective shallow-earthquake prediction program. (Author)