Computational study of seismic waves in homogeneous dynamic-porosity media with thermal and fluid relaxation: Gauging Biot theory

摘要

The attenuation effects predicted by Hickey's poroelastic theory (Hpt) are quantified by means of seismic modeling in an unbounded, homogeneous, isotropic porous model fully saturated with water and with oil. The numerical results are compared to those predicted by Biot poroelastic theory (Bpt). As opposed to Bpt, Hpt accounts for thermomechanical coupling and viscous fluid relaxation and adequately models the transient fluctuations of porosity and mass densities as the wave compresses and dilates the porous medium during propagation. Despite all these theoretical improvements over Bpt, the numerical results show that both theories produce remarkably similar waveforms. Without considering thermal relaxation, Hpt produces less than 1% higher-amplitude attenuation and velocity dispersion than Bpt. The major contrasts correspond to the slow P wave. Thermomechanical coupling affects the fast P wave: seismic amplitudes are 1% smaller and some dispersion for the oil-permeated case can be observed. It produces no effects on the fast S or the slow P wave. Therefore these numerical experiments appear to substantiate what Biot assumed at the outset of his theoretical developments: that the effects of transient oscillations of porosity during wave propagation are negligible in terms of velocity dispersion and amplitude attenuation. Furthermore it is confirmed that in a homogeneous porous medium, the combined dissipation mechanisms mentioned are not adequate to explain the total amount of energy dissipation observed in the field or laboratory.