Effective P-and S-wave moduli in finely layered thermoelastic media

P waves traveling in thermoelastic materials suffer attenuation and dispersion due to the existence of the thermal (T) wave, which is diffusive at low frequencies and is a propagation wave at high frequencies. Thus, this wave behaves similarly to the slow P wave in Biot (poroelastic) media. We presents a finiteelement (FE) procedure to determine an effective viscoelastic medium long-wave equivalent to a thermoelastic material, by applying compressibility and shear tests. Each test is defined by a boundary-value problem and the procedure is validated by comparison with an analytical solution for a periodic sequence of two layers of equal thickness and different Grüneisen ratios. The S wave is not sensitive to variations of this ratio, so that only the S-wave velocity is determined. Next, we consider a layered medium with varying Grüneisen ratios and random layer thicknesses, for which there is no analytical solution available. This case shows a decrease in the P-wave phase velocities and an increase in the dissipation factors, with respect to the previous case. Representations of the real an imaginary parts of the temperature illustrate the attenuation effects.