Impact of Substrate Inhomogeneity and Parabolic Interface on Horizontal Transverse Waves in Sandy Layer

This paper investigates the dispersion of transverse horizontal surface waves in a sandy layer overlying an inhomogeneous orthotropic half‐space with a parabolic interface irregularity. Two distinct gradient variations of the substrate, namely exponential and quadratic are considered to model different forms of material inhomogeneity. The study is motivated by the need to represent realistic geological structures such as sandy soil layers overlying heterogeneous rock formations commonly found in sedimentary basins, coastal regions, and seismic zones. The novelty of the present work lies in the unified treatment of sandy overlayers, orthotropic inhomogeneity, and parabolic interface irregularity, a combination scarcely addressed in existing literature. The governing equations are solved under appropriate boundary conditions at the interface and free surface, employing Fourier transforms and perturbation techniques to derive the dispersion relations. The formulation reduces to classical results in limiting cases, validating the model. Numerical computations elucidate the effects of the inhomogeneity parameter, sandy layer properties, and interface width ratio on phase velocity, while a comparative analysis highlights the contrasting influences of exponential and quadratic gradients. Benchmarking against the classical Love wave solution reveals a reduction in energy penetration into the substrate during propagation, with potential implications for seismic hazard mitigation.