Inhomogeneous waves propagation in double-porosity thermoelastic media

Abstract

Purpose The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium. Design/methodology/approach To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method. Findings The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium. Originality/value A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

Wave-induced fluid flow and reflection/transmission of seismic waves at a fluid/double-porosity thermoelastic medium interface

“…The P 1 , P 2 , P 3 , P 4 , SV waves phase velocities are of the order 4300, 300, 140, 10, 2765 m s −1 , respectively. Moreover, the velocity and attenuation of P 1 , P 2 , P 3 , P 4 , SV waves is plotted in figures 1-3 by Kumar et al [31]. These waves are discovered to move at distinct speeds that are complex-valued and frequency-dependent.…”

“…Inserting (1)-( 4) into equations ( 5)-( 8) and owing to the relations (11), we get two sets of equations: one corresponding to dilatational wave potentials and the other corresponding to shear wave potentials. Kumar et al [31] have already already solved the so-obtained system of equations and studied propagation characteristics of dilatational and shear waves double-porosity thermoelastic medium. They proved that five fundamental waves can propagate in the medium under consideration.…”

“…As a result, all waves have an attenuating and dispersive character. These waves' respective potentials are interconnected, and different couplings are provided by Kumar et al [31] relations (29) and (30). In mediums with dissipation, plane waves exhibit inhomogeneity, and the magnitudes of their phase speeds and attenuations depend on the angle between the direction of propagation and the direction of maximum attenuation.…”

“…In mediums with dissipation, plane waves exhibit inhomogeneity, and the magnitudes of their phase speeds and attenuations depend on the angle between the direction of propagation and the direction of maximum attenuation. As a result, using the formulas (32) and (33) in Kumar et al [31], the phase speeds ( ) v i  and maximum attenuations ( ) z i  for the relevant dilatation and shear waves are determined. The relation (34) in Kumar et al [31] provides the displacement components distinct phases of DPT medium in the two-dimensional x-z plane.…”

“…Therefore, in taking into account the significance of thermoelasticity, Li et al [30] combined the LS and BR equations to develop the double-porosity thermoelasticity (DPT) theory, which explains how thermal effects and local/global fluid flow influence the wave velocity and attenuation. Recently, Kumar et al [31] examined the propagation properties of seismic waves in a double-porosity thermoelasticity medium. They have calculated energy ratios, phase velocities and attenuation coefficients, propagation/attenuation directions, and phase shifts as a function of incidence direction.…”