Generalized Thermo-poroelasticity Equations and Wave Simulation

We establish a generalization of the thermoelasticity wave equation to the porous case, including the Lord–Shulman (LS) and Green–Lindsay (GL) theories that involve a set of relaxation times (τi,i=1,…,4). The dynamical equations predict four propagation modes, namely, a fast P wave, a Biot slow wave, a thermal wave, and a shear wave. The plane-wave analysis shows that the GL theory predicts a higher attenuation of the fast P wave, and consequently a higher velocity dispersion than the LS theory if τ1= τ2> τ3, whereas both models predict the same anelasticity for τ1= τ2= τ3. We also propose a generalization of the LS theory by applying two different Maxwell–Vernotte–Cattaneo relaxation times related to the temperature increment (τ3) and solid/fluid strain components (τ4), respectively. The generalization predicts positive quality factors when τ4≥ τ3, and increasing τ4 further enhances the attenuation. The wavefields are computed with a direct meshing algorithm using the Fourier pseudosp...