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

Abstract

[1] 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.Citation: Quiroga-Goode, G., S. Jiménez-Hernández, M. A. Pérez-Flores, and R. Padilla-Hernández (2005), Computational study of seismic waves in homogeneous dynamic-porosity media with thermal and fluid relaxation: Gauging Biot theory,

Seismic wave properties in time-dependent porosity homogeneous media

“…The numerical results of Quiroga-Goode et al (2005) confirm that Hickey's modifications to de la Cruz and Spanos theory (Hickey et al 1995) produce waveforms that are remarkably similar to those of Biot. Nonetheless, that does not provide clear answers for what the sources of energy loss could be since Biot theory is known, among other things, for misrepresenting the magnitude and behaviour of attenuation and dispersion.…”

“…Nonetheless, that does not provide clear answers for what the sources of energy loss could be since Biot theory is known, among other things, for misrepresenting the magnitude and behaviour of attenuation and dispersion. Therefore, it was concluded in Quiroga-Goode et al (2005), though only by inference, that the dynamic porosity in de la Cruz and Spanos theory (Hickey et al 1995) may not have, ultimately, a strong nexus to dissipation. This is one of the issues to investigate in the present work.…”

“…The first is represented by the large body of work associated to Biot (Biot 1956, 1962; White 1975; Bourbie et al 1987; Pride et al 1992; Dvorkin et al 1994; Carcione & Quiroga‐Goode 1995). The second corresponds to de la Cruz and Spanos theory (de la Cruz & Spanos 1985, 1989; de la Cruz et al 1993; Hickey 1994; Hickey et al 1995; Sahay 1996; Sahay et al 2001; Sahay 2001; Quiroga‐Goode et al 2005).…”

Numerical evidence of elliptical polarization in homogeneous fluid‐saturated porous sandstone and the nexus to inhomogeneous plane waves

“…The wave solution is obtained by solving numerically equation (4) with a pseudospectral algorithm [ Carcione and Quiroga‐Goode , 1995]. This numerical scheme is completely different than the finite difference algorithm used in Quiroga‐Goode et al [2005]. Due to computational constraints, the numerical solution is calculated in two dimensions, producing thus cylindrical waves, as opposed to spherical waves obtained with the Green's function.…”

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

“…The slow S wave damped so strongly that it dies off near its source, but it draws the energy from fast waves via mode conversion at interfaces and at materials with discontinuities and inhomogeneities. Quiroga-Goode et al (2005) numerically solved the Hickey's nonlinear system of partial differential equations in homogeneous dynamic porosity media with thermal and fluid relaxation to investigate the attenuation effects. Their numerical results show that thermomechanical coupling affects the fast P wave in a minor degree: compared with isothermal case, seismic amplitudes are diminished by less than 1% in the oilpermeated case but have no effects on the fast S or the slow P wave.…”