A three-dimensional analytical framework is presented to study the propagation of Rayleigh-type surface waves in layered media consisting of a transversely isotropic (TI) elastic layer perfectly bonded to an isotropic soil substrate. The formulation is based on a potential decomposition combined with Helmholtz representations, allowing the coupled effects of material anisotropy, geometric confinement, and elastic contrast to be captured in a unified manner. By imposing traction-free conditions at the free surface and enforcing continuity of displacement and stress across the interface, a dispersion relation for Rayleigh-type waves is obtained in closed analytical form. For numerical illustration, seven representative TI crystalline materials, viz., Beryl, Cadmium, Cobalt, Hafnium, Ice, Yttrium, and Zinc, are considered for the upper layer, covering a wide range of elastic stiffness and mass densities. This selection enables a comprehensive analysis of the sensitivity of surface-wave dispersion to anisotropic elastic parameters. The computed phase-velocity dispersion curves exhibit strong dependence on anisotropic stiffness, layer thickness, and substrate stiffness ratio and unravel distinct dispersion regimes and critical transitions in wave behavior. The proposed framework offers a clear and physically meaningful basis for modeling Rayleigh-type waves in layered anisotropic media, with direct applications in seismic characterization, geotechnical engineering, and nondestructive material evaluation.
Saha et al. (2026) studied this question.