Thermoelastic-Diffusive Wave Reflection with Impedance, Hyperbolic Two-Temperature, and Temperature-Dependent Properties under the MGT Model

Abstract

Plane-wave reflection from a homogeneous, isotropic thermoelastic-diffusion half-space is investigated within the Moore–Gibson–Thompson heat-conduction framework. The model incorporates hyperbolic two-temperature effects, temperature-dependent material properties, nonlocality, and mechanical, thermal, and diffusive impedance boundary conditions. Using potential-function decomposition and time-harmonic solutions, the governing equations are reduced to a dispersion relation describing coupled longitudinal (P), thermal (T), diffusive (P₀), and transverse shear (SV) modes. The corresponding reflection amplitude ratios are obtained from the boundary system for different incident waves. Numerical results demonstrate that the reflected amplitudes and their angular extrema are significantly affected by the thermal model, impedance parameters, temperature dependence, and nonlocal parameter. The formulation also recovers the temperature-independent, diffusion-free, elastic-diffusive, and zero-impedance limits. The results provide a basis for advanced material characterization and interpretation of geophysical wave responses.