A Radiation Condition for Layered Elastic Media

This study aims to establish a generalized radiation condition for time-harmonic elastodynamic states in a piecewise-homogeneous, semi-infinite solid wherein the “bottom” homogeneous half-space is overlain by an arbitrary number of bonded parallel layers. To consistently deal with both body and interfacial (e.g. Rayleigh, Love and Stoneley) waves comprising the far-field patterns, the radiation condition is formulated in terms of an integral over a sufficiently large hemisphere involving elastodynamic Green's functions for the featured layered medium. On explicitly proving the reciprocity identity for the latter set of point-load solutions, it is first shown that the layered Green's functions themselves satisfy the generalized radiation condition. By virtue of this result it is further demonstrated that the entire class of layered elastodynamic solutions, admitting a representation in terms of the single-layer, double-layer, and volume potentials (distributed over finite domains), satisfy the generalized radiation condition as well. For a rigorous treatment of the problem, fundamental results such as the uniqueness theorem for radiating elastodynamic states, Graffi's reciprocity theorem for piecewise-homogeneous domains, and the integral representation theorem for semi-infinite layered media are also established.