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Vertical and near-vertical incidence of P waves in a layered solid


 This article gives two analytical expressions of the displacement in a flat structure: one based on Cagniard's method for simpler cases, the other using a Fourier integral for more general cases. The numerical experiments aimed to check the methods by comparing zero-offset cases with cases of near-vertical incidence confirm the existence of longitudinal PS waves as obtained by Hron and his collaborators. In addition, the experiments reveal that the longitudinal motion of the PS waves is the limit of an elliptical-like particle motion associated with the PS waves for near-vertical incidence. It turns out that this unusual particle motion tends to the classical transverse rectilinear motion when the source-receiver offset is large enough. A similar behavior was found for the particle motion associated with the reflected PS, P2S, and PS2 for small offset receivers located on the free surface of a solid consisting of one homogeneous layer over a half-space.