Love-Wave Propagation in an Inhomogeneous Orthotropic Medium Obeying the Exponential and Generalized Power Law Models

Abstract

Based on the theory of elasticity, the analytical solutions of the Love-wave dispersion equation are generated for the inhomogeneous orthotropic medium, for which the Young’s modulus (Ex, Ey, Ez), shear modulus (Gxy, Gyz, Gxz), and medium density (ρ) are obeying the exponential law model (Exeαz, Eyeαz, Ezeαz, Gxyeαz, Gyzeαz, Gxzeαz, and ρeαz) and the generalized power model [Ex(a + bz)m, Ey(a + bz)m, Ez(a + bz)m, Gxy(a + bz)m, Gyz(a + bz)m, Gxz(a + bz)m, and ρ(a + bz)m]; however, three Poisson’s ratios (υxy, υyz, υxz) are constants regardless of depth. In other words, the aforementioned moduli and density of the upper orthotropic layer [with thickness (H)] and lower orthotropic half-space are assumed to vary exponentially and generalized power laws as depth increased. To explore the influence of the inhomogeneous characteristics of the orthotropic materials on Love-wave velocity, a parametric study was conducted by utilizing the granite’s parameters. The results reveal that the Love-wave velocity is markedly influenced by the inhomogeneity parameters (α, a, b, and m) but is unaffected by the presented isotropic/orthotropic rock types. Hence, it is imperative to consider the effect of inhomogeneities when investigating the behaviors of Love-wave propagation in the orthotropic medium.