Free-field dynamic response of an inhomogeneous half-space

In this work, elastic wave propagation in the inhomogeneous half-space is solved by an analytical approach based on plane wave decomposition in conjunction with appropriate functional transformations for the displacement vector. Specifically, free-field motions are recovered at the surface of a half-space with either quadratic or exponential type of depth-dependent material parameters. The incident wave is a time harmonic, planar pressure wave and the resulting free-field motions are obtained in closed form, first for the full-space and then for the half-space by adding the reflected waves. Parametric studies show marked differences in the results when compared against the corresponding ones for a homogeneous background. Finally, sensitivities of the free-field waves on the basic characteristics of the underlying inhomogeneous material and of the incoming wave are investigated.