Point Loads in Cross‐Anisotropic, Layered Halfspaces

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Abstract
The airn in this paper is to present an explicit solution for the Green's functions associated with static and dynamic loads and dislocations acting on, or within, elastic cross‐anisotropic halfspaces and full spaces. The methodology employed represents a generalization of a procedure described by Kausel and Peek in 1982 for dynamic loads acting within isotropic strata of finite depth. In essence, the method consists of a discretization of the medium in the direction of layering and an idealization of the underlying halfspace, in the case of dynamic loads, in terms of paraaxial approximations. For static loads, on the other hand, the halfspace can be modeled exactly. The Green's functions are obtained, as before, with an integral transform evaluated in closed form. As a result, no numerical integrations are necessary, which constitutes a significant advantage over other numerical procedures currently available for this problem. Since the resulting equations for displacements are expressed in the spatial domain, they can be used directly as kernels in integral representations of problems in elastodynamics, such as seismic sources, soil‐structure interaction, and scattering of waves.

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