A method based on 3D stiffness matrices in Cartesian coordinates for computation of 2.5D elastodynamic Green's functions of layered half-spaces

This article elaborates on an extension to the classical stiffness matrix method to obtain the Green's functions for two-and-a-half dimensional (2.5D) elastodynamic problems in homogeneous and horizontally layered half-spaces. Exact expressions for the three-dimensional (3D) stiffness matrix method for isotropic layered media in Cartesian coordinates are used to determine the stiffness matrices for a system of horizontal layers underlain by an elastic half-space. In the absence of interfaces, virtual interfaces are considered at the positions of external loads. The analytic continuation is used to find the displacements at any receiver point placed within a layer. The responses of a horizontally layered half-space subjected to a unit harmonic load obtained using the present method are compared with those calculated using a well-established methodology, achieving good agreement.