Reflection of inhomogeneous plane waves at the surface of a thermo-poroelastic medium

Abstract

Summary We analyze the reflection coefficient of an inhomogeneous plane wave incident on the thermally insulated surface of a thermo-poroelastic medium. The theory, which includes the classic Lord-Shulman (LS) and Green-Lindsay (GL) theories as well as a generalization of the LS model, predicts three inhomogeneous longitudinal waves and one transverse wave, described by potential functions specified by the propagation direction and inhomogeneity angle. The GL model can give a stronger P1-wave thermal attenuation and consequently a stronger velocity dispersion than the LS model. We investigate the influence of inhomogeneity angle, type of incident wave, frequency and surface boundary conditions. The generalized LS model exhibits increased P1-wave thermal attenuation with increasing Maxwell-Vernotte-Cattaneo (MVC) relaxation time and consequently predicts more interference energy, irrespective if the surface is open or sealed. The inhomogeneity angle affects the energy partitions particularly near the grazing incidence, with a significant interference energy, which must be taken into account to satisfy the energy conservation. The thermal dispersion occurs at frequencies around the thermal relaxation peak, which moves to low frequencies when the conductivity increases.

Amplitude-variation-with-offset in thermoelastic media

“…Following chapter 3 of Carcione (2014) and notations of Wang et al (2021), we consider the plane-wave solution…”

“…However, these authors ignore the presence of inhomogeneous (body) plane waves, thus violating the Snell law. On the other hand, Sharma (2018) and Wang et al (2021), by using the theory of thermo-poroelasticity, consider the inhomogeneous waves to study the scattering (reflection-transmission, R/T) coefficients.…”

Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

“…An attenuated wave is commonly specified by both directions i.e. direction of maximum attenuation and direction of propagation (Carcione, 2006, 2014; Wang et al , 2021). The displacement potentials of the incident wave are written as: where q 0 ( p 0 ) specifies the complex vertical (horizontal) slowness vector.…”

“…Furthermore, the gradient of T along the z -direction is zero when the surface is thermally insulated. Hence, the appropriate boundary conditions (Wang et al , 2021) for the considered medium are given by: Permeable boundary conditions: σzz=0, σzx=0, −Pl=0, −Pg=0, ∂T∂z=0. Impermeable boundary conditions: σzz=0, σzx=0, uzl=0, uzg=0, ∂T∂z=0. …”

“…Sheoran et al (2020) discussed the plane waves propagation in an initially stressed rotating thermo-elastic diffusive medium along two-temperature and micro-concentrations. Recently, Wang et al (2021) examined the reflection characteristics of inhomogeneous waves at the stress-free thermally insulated surface of the thermo-poroelastic medium. They investigated the impacts of inhomogeneity angle, wave frequency, surface pore characteristics and type of incident wave on the splitting of incident energy.…”