Seismic wave reflection characteristics and wave-induced fluid flow in unsaturated porous solid

Abstract

This study examines the characteristics of seismic wave reflection and wave-induced fluid flow (WIFF) in an unsaturated porous solid half-space confined beneath an impermeable plane surface. We first present the field equations and constitutive relations for partially saturated porous media. Next, we solve these equations in terms of the Christoffel equations, thereby addressing the propagation of a four-plane harmonic wave. These waves propagate as inhomogeneous waves at stress-free, impermeable boundary surfaces due to the medium's dissipative properties. Furthermore, we compute the reflection coefficients from stress-free impervious boundary surfaces at arbitrary angles. The incidence of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_1/SV$$\end{document} wave generates four reflected waves. The calculation of theoretical formulations for reflection coefficients involves a set of four non-homogeneous linear equations derived from boundary conditions. Subsequently, these reflection coefficients are utilized to calculate the WIFF and the partitioning of incident energy at the impervious boundary of the porous solid. A numerical example is considered to investigate the effects of wave frequency, incidence direction, and elastic parameters such as porosity, inclusion radius, and liquid saturation on energy partitioning and wave-induced fluid flow. The conservation of incident energy has been confirmed at every angle of incidence. The numerical results demonstrate a significant dependence of energy shares of distinct reflected waves on the incident direction, saturation, porosity, inclusion radius, wave frequency, and WIFF. This theoretical study serves as a valuable tool for subsurface reservoir characterization, with applications in hydrocarbon exploration, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO_2$$\end{document} sequestration monitoring, and other geological engineering fields.