Influences of Initial Stress and Gravity on SH-Wave Propagation in a Transversely Isotropic Medium

Abstract

This study delves into the impact of gravity on the propagation of SH-surface waves within transversely isotropic half-spaces, examining both initially stressed heterogeneous and homogeneous scenarios. The investigation centers on the dispersion equation for SH-surface waves, with a specific focus on stress-free boundary surfaces.  The establishment of the dispersion relation for SH-surface waves serves as the foundational methodology. This involves a comprehensive analysis of both initially stressed heterogeneous and homogeneous transversely isotropic half-spaces. The theoretical findings established are rigorously compared with deduced results obtained through analytical means. Furthermore, numerical simulations are performed using MATHEMATICA software to provide a detailed exploration of the effects of various influencing parameters. The study presents analytical results that illuminate the behavior of SH-surface waves under the influence of gravity. These findings are not only theoretically derived but also verified through numerical simulations. The comparison between analytical and numerical results enhances the robustness of the study, offering a comprehensive understanding of how gravity influences wave propagation in transversely isotropic half-spaces. This study uniquely explores how gravity influences SH-surface waves in initially stressed transversely isotropic half-spaces, introducing a novel dimension through the derivation of dispersion relations for stress-free boundaries. The integration of analytical and numerical methods enhances reliability, with practical applications in geophysics, seismology, and materials science, providing insights into seismic data interpretation, event prediction, and broader engineering contexts.