Displacement field for an edge dislocation in a layered half-space

The displacement field for an edge dislocation in an Earth model consisting of a layer welded to a half-space of different material is found in the form of a Fourier integral following the method given by Weeks et al. [1968]. There are four elementary solutions to be considered: the dislocation is either in the half-space or the layer and the Burgers vector is either parallel or perpendicular to the layer. A general two-dimensional solution for a dip-slip faulting or dike injection (arbitrary dip) can be constructed from a superposition of these elementary solutions. Surface deformations have been calculated for an edge dislocation located at the interface with Burgers vector inclined 0°, 30°, 60°, and 90° to the interface for the case where the rigidity of the layer is half of that of the half-space and the Poisson ratios are the same. Those displacement fields have been compared to the displacement fields generated by similarly situated edge dislocations in a uniform half-space. The surface displacement field produced by the edge dislocation in the layered half-space is very similar to that produced by an edge dislocation at a different depth in a uniform half-space. In general, a low-modulus (high-modulus) layer causes the half-space equivalent dislocation to appear shallower (deeper) than the actual dislocation in the layered half-space.