General expressions for internal deformation fields due to a dislocation source in a multilayered elastic half-space

Abstract

SUMMARY We have obtained general expressions for internal displacement and stress fields due to a point dislocation source in a multilayered elastic half-space under gravity. Most previous expressions for the internal deformation fields were obtained by applying one of two different types of Thomson‐Haskell propagator matrix, namely the up-going propagator matrix proposed by Singh (1970) and the down-going propagator matrix proposed by Sato (1971). The solution derived with the up-going propagator matrix is stable below the source, but becomes unstable above the source. In contrast, the solution derived with the down-going propagator matrix is stable above the source, but becomes unstable below the source. We succeeded in unifying the up-going and the down-going propagator matrices into a generalized propagator matrix, and applied it to obtain general expressions that are stable at any depth. By integrating the effects of point sources distributed along an infinitely long horizontal line, we also obtained general expressions for a line dislocation source. We give some examples of internal displacement fields computed with these expressions to examine the effects of layering. Applying the correspondence principle of linear viscoelasticity to the derived elastic solutions, we can obtain the internal viscoelastic displacement and stress fields due to dislocation sources.