An analytic decomposition for modeling evanescent transient plane waves in a fluid/isotropic–solid configuration: Application to Rayleigh waves

This work is based on a complex-variable analytic decomposition method recently proposed for modeling transient propagating and evanescent wave phenomena without resorting to the usual integral techniques, such as the Fourier and Hilbert transforms. Its efficiency was previously demonstrated through a study of the interaction of transient acoustic plane waves with a plane interface between two fluids of different properties. The purpose of the present paper is to extend this approach to a fluid/isotropic–solid interface, involving longitudinal and transverse transmitted waves and the two associated critical angles beyond which one or both waves become evanescent. Furthermore, the particular case of Rayleigh waves is investigated in detail. The relative simplicity and efficiency of the method make it possible to obtain displacement and stress fields, together with an analysis of several characteristic properties, including precursor and successor phenomena. The results are illustrated by means of field maps, diagrams, particle trajectories, and animations of the deformation of the medium (Multimedia available online). All these results are quantitative. While the method applies to the classical monochromatic regime, its main advantages become apparent for transient finite-duration signals, including oscillatory, Lorentzian, and rectangular waveforms. In particular, the transient Rayleigh-wave analysis shows that, although the underlying Rayleigh-wave structure remains unchanged, the particle trajectories depend strongly on the signal waveform and may differ markedly from the classical monochromatic elliptical motion. Moreover, the specific symmetry and antisymmetry properties of the evanescent displacement and stress fields are established analytically and applied to the Rayleigh-wave case.