Correct procedure to study reflection in orthotropic thermoelastic medium: Inhomogeneous propagation of waves

Any study on reflection in anisotropic thermoelastic media, as available in literature, is either incorrect or incomplete. At the best, the earlier studies on this topic avoided the incidence of inhomogeneous waves. On the other hand, in recent times, each study is found to be forcing the isotropic elastic Snell’s law to define the anisotropic propagation of inhomogeneous reflected waves. To illustrate the common mistakes committed, this study revisits and corrects a previous work on reflection at the boundary of an orthotropic thermoelastic medium. For chosen directions of propagation with attenuation, a real finite parameter represents the inhomogeneity. A complex slowness vector is specified to define the propagation of inhomogeneous incident wave. In this incidence, horizontal slowness determines the slowness vectors for all reflected waves. For each reflected wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation coefficients. The slowness vectors of incident and reflected waves define the aggregate wave-field in thermoelastic medium. Appropriate boundary conditions on this wave-field determines the amplitude ratios and phase shifts for reflected waves relative to the incident wave. A square matrix of order four determines the partition of incident energy flux among the reflected waves.