Impact of triangular irregularity, material heterogeneity and initial stress on the propagation of shear waves in a transversely isotropic porous layer

In this work, the behaviour of shear waves in a FSPL that is initially stressed exhibits transverse isotropy is investigated. The layer is located on an elastic half-space, characterized by a triangular shaped irregularity at interface of contact. This research derives the dispersion equation of shear waves utilizing elasticity theory by Biot, combined with perturbation techniques and Fourier transformations. Computational simulations of the dispersion equation, performed using MATLAB, highlight important findings, such as when inhomogeneity, anisotropy, and porosity increase, a noticeable decrease in phase velocity is observed. Additionally, phase velocity drops significantly with rising wave numbers. The graphical results reveal that there is a significant influence on the dimensionless phase velocity by the wave number, irregularity depth, initial stress, and anisotropy, highlighting the complex interplay between these factors in wave propagation in such layered media. This research provides deeper insight into the behaviour of shear waves in complex geological formations, with potential applications in geophysical exploration and material science.