Comparative Analysis of the Effects of Initial Stress, Heterogeneity and Directional Rigidities on Torsional Surface Waves Using Analytical and Computational Approaches

<title>Abstract</title> <p> This study investigates the propagation characteristics of torsional surface waves in an initially stressed anisotropic layer embedded between two anisotropic semi-infinite media. The effects of initial stress, heterogeneity, directional rigidities, sandy parameter, and exponent number on wave propagation are examined in detail. It is assumed that the directional rigidities, density, and initial stress remain homogeneous in the upper half-space, exhibit exponential variation within the intermediate layer, and vary linearly in the lower half-space. By employing the appropriate governing equations and boundary conditions, a closed-form dispersion relation for torsional surface waves has been derived. A corresponding velocity equation is also obtained as a special case in the absence of heterogeneity. Numerical computations and graphical analyses reveal that the propagation behavior of torsional surface waves is significantly influenced by the initial stress, heterogeneity parameters, ratios of directional rigidities, sandy parameter, and exponent number. Variations in these parameters produce notable changes in the phase velocity and dispersion characteristics of the waves, demonstrating their crucial role in controlling wave propagation in layered anisotropic media. Furthermore, it is shown that the derived velocity equation reduces to the classical Love-wave equation in the limiting case of a homogeneous medium, thereby validating the present formulation. The results obtained in this study provide valuable insights into the dynamic behavior of wave propagation in anisotropic geological formations and engineered layered structures. Consequently, the findings are expected to be of considerable interest to researchers in seismology, geophysics, earthquake engineering, and structural engineering, where understanding the influence of material heterogeneity and initial stress on wave motion is of significant practical importance. Mathematics Subject Classification – MSC2020: 86A15 Seismology(including tsunami modeling), earthquakes ^{1 2} </p>