We develop a two-temperature dual-phase-lag (TT-DPL) thermoporoelasticity theory, that extends the classical single-temperature (ST) theory. The theory distinguishes between the solid and fluid temperatures and includes fluid-solid coupling terms, related to temperature-displacement and temperature-conductivity coefficients, that describe the interactions and heat conduction between the skeleton and the pore fluids. A plane-wave analysis predicts five waves, namely, fast P, slow P, fast thermal (T1), slow thermal (T2), and a shear wave. The results show that the slow P and slow T are mainly influenced by the pore fluid, while the fast P and fast T by the solid phase. The TT-DPL model leads to more velocity dispersion and thermal attenuation, particularly at high frequencies. A rotated staggered grids finite-difference (FD) method, combined with an effective absorbing boundary, is used to compute wavefield snapshots. The type of fluid in the rock affects the T-wave behavior, with the fluid viscosity playing an important role.
Liu et al. (2025) studied this question.