Wave Simulation in Partially Saturated Porothermoelastic Media

In wave propagation in rocks, the strain field affects the internal energy such that compressed regions become hotter and expanded regions cooler. This thermoelastic effect is that the lack of thermal equilibrium between various parts of the vibrating medium and energy is dissipated when irreversible heat flow driven by the temperature gradient occurs. Moreover, rocks are generally partially saturated and the interfacial tension between fluids affects the acoustic properties and induces additional slow P waves. To model these phenomena, we develop a generalized porothermoelasticity theory, including the Lord-Shulman (LS) and Green-Lindsay (GL) theories, for wave propagation in partially saturated nonisothermal media. The dynamical equations have as solutions the classical P1 and S waves and three slow waves modes, namely, the slow P2, slow P3, and the thermal (T) waves, which present diffusive behavior depending on the viscosity, frequency, and thermal properties. We compute the wavefields with a direct meshing algorithm by using an optimized finite- difference (FD) method to obtain the spatial derivatives and a first-order explicit Crank-Nicolson method for temporal extrapolation. The simulated snapshots and waveforms for the homogeneous and heterogeneous models with two different sets of thermal properties illustrate the characteristics of propagation as a function of frequency and saturation, which are consistent with the plane-wave analyses. The GL model can predict a higher thermal attenuation of the P1 wave and, consequently, a larger velocity dispersion than the LS theory. The thermal relaxation peak moves to low frequencies as the conductivity increases. This study is relevant to understand wave propagation in porous rocks and high temperature and pressure fields.