Seismic excitation model of half-space propagation of rayleigh waves

Abstract

This article presents a scientific study of seismic oscillations and Rayleigh wave propagation models. The research details how Rayleigh waves propagate in a semi-infinite elastic medium, the types of motions they create on Earth’s surface, and how their amplitude decreases with depth. In the first section, the study examines Rayleigh waves and their mathematical representations, illustrating how these waves form and propagate in a semi-infinite medium. In addition, the relationships between wave amplitude and other parameters are expressed by mathematical equations. The following sections deal with the problem of defining the elastic properties of the medium taking boundary conditions into account. The study provides an analysis of strains and stress tensors, discusses their role in wave propagation, and describes in detail the components of stress and strain at each point. To solve problems with geometric symmetry, the Boundary Element Method (BEM) is used. Using the Morrow Point Dam model as an example, the study explains how this approach helps reduce computational effort by taking symmetry planes into account. It also describes the balance of hydrodynamic pressure and normal stresses at the interface between water and solid media. This article serves as a valuable resource for understanding the mathematical and physical principles, computational approaches, and boundary conditions in wave propagation that are critical to geophysical applications. Finally, the study highlights how the amplitude of Rayleigh waves changes with depth in a semi-infinite medium and discusses the importance of elastic constants in controlling these changes. This research provides essential theoretical insights useful for geological and engineering practices.