Purpose
The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media..
Design/methodology/approach
The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB.
Findings
In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix.
Originality/value
The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.
Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves (i.e., incident and reflected) in an elastic medium are considered as homogeneous (i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous (i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.
The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves (i.e., P 1 and SV) is considered. As a result of the incident waves, four reflected (three longitudinal and one shear) waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.
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