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The theory of wave propagation in non-isothermal porous rocks has been introduced in geophysics in recent years by combining the single-phase-lag (SPL) Lord-Shulman (LS) model of heat conduction with Biot’s poroelasticity theory. However, the theory of SPL thermoporoelasticity is inadequate in describing the lagging behavior of thermal relaxation for wave dissipation due to fluid and heat flow effects. We address this problem by incorporating a dual-phase-lags (DPL) model of heat conduction into thermoporoelasticity, utilizing analytical solutions and numerical simulations. The DPL model involves two lagging times: the (macroscopic) heat-flux lagging time  τ qfrom the LS model and an additionally introduced lagging time  τ Tof temperature gradient that characterizes the fluid phase. A plane-wave analysis predicts four propagation waves, namely, fast P, slow P, thermal (T), and shear (S). We calculate wavefield snapshots by using a finite-difference solver for the DPL thermoelastic equations and provide further insight into the physics of two lagging times for porous rocks. The simulations show that the DPL model induces higher thermal attenuation and larger velocity dispersion compared to the SPL model, especially at high frequencies. The influence of fluids is crucial for wave propagation within thermoporoelastic media.

Simulation of wave propagation in thermoporoelastic media with dual-phase-lag heat conduction