Wave propagation in inhomogeneous orthotropic rocks

Abstract

Analytical solutions for body wave velocities are yielded for a continuously inhomogeneous orthotropic rock, in whichYoung\'s moduli (E-x, E-y, E-z), shear modulus (G(xy), G(yz), G(xz)), and the medium density (rho) all varied exponentially as depth increased. However, three Poison\'s ratios (u(xy), u(yz), u(xz)) of the orthotropic rocks are remained constants regardless of depth. The generalized Hooke\'s law, strain-displacement relationships, and equilibrium equations are integrated to constitute the governing equations. In these equations, displacement components are fundamental variables, and hence, the solutions of three quasi-wave velocities, V-P, V-SV, andV(SH), are generated for the inhomogeneous orthotropic media. The proposed solutions correlate well with the orthotropic solutions when the inhomogeneity parameter, alpha, is 0. In addition, parametric study results indicate that the magnitudes of wave velocity are markedly affected by (1) the inhomogeneity parameter; (2) the type and degree of geomaterial anisotropy; (3) the phase angle; and (4) the medium density. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in orthotropic rocks.