A finite-element method to compute the seismic response in non-isothermal poroelastic media

We analyze the seismic response in fluid saturated poroelastic media based on the non-isothermal wave equation, which includes the temperature field other than those of stress and deformation. The model, which combines the Biot and Lord-Shulman (LS) theories, predicts the propagation of four waves: two compressional P waves, one fast and one slow, a thermal wave, and a shear wave. An initial boundary-value problem (IBVP) for the thermo-poroelastic wave equation is formulated and solved by applying the finite-element (FE) method. The FE procedure is formulated for the 1D case on an open bounded interval with absorbing boundary conditions at the artificial boundaries. We discretize the solid and fluid displacements and the temperature using piecewise linear globally continuous polynomials. The theory is used to study the propagation of the two compressional P waves and the thermal wave. We compare the coupled and uncoupled cases, including and neglecting viscosity. The algorithms may become useful for a better understanding of the behavior of seismic waves in hydrocarbon reservoirs and crustal rocks, because the assumption of isothermal wave propagation is now removed.