SUMMAR YThe source terms that are meaningful in dynamic poroelasticity are those exciting the centre-of-mass field and the internal field. These fields are the sum of the mass weighted motion and the difference motion of the solid and fluid constituents, respectively. The corresponding homogeneous and isotropic Green's function valid for a uniform wholespace is obtained using Kupradze's method after the vector differential equations for these two fields are combined and expressed as a 6r6 matrix differential operator. The solution is quite amenable to numerical calculations and the results for a saturated Berea sandstone show that the fast P and S waves correspond to those usually detected by geophones at large distances from the source. The slow P wave, which is associated with fluid flow, is rapidly attenuated with distance from the source while the slow S wave, which is part of the solution, dies off rapidly in the near-neighbourhood of the source.

In a porous medium, the porosity perturbation, i.e., the change in porosity, is an integral part of a deformation process. Yet, there is no explicit statement about that in the Biot theory. By linking its constitutive relation to the continuity equations, the tacit assumption about the porosity perturbation in this theory is inferred. The linear dependence of the porosity perturbation on the pressure difference of the two phases is embedded in its constitutive relation. The solid and fluid pressures affect the change in porosity in equal magnitude but in opposite sense. By assuming that the fluid pressure may affect the porosity perturbation to an extent different than that of the solid pressure, the Biot constitutive relation is generalized. This introduces a nondimensional parameter. It could be named the porosity effective pressure coefficient, because the measure of the extent the fluid pressure affects the change in porosity relative to the solid pressure. In the regime in which the fluid pressure affects to a lesser extent, this parameter spans from unity, the state in which fluid resists the change in porosity in equal but opposite manner to solid, to zero, the state in which fluid ultimately ceases to affect the porosity change at all. As this parameter diminishes from unity, the undrained bulk modulus drops from being the Gassmann modulus. Ultimately, it becomes the series combination of the dry frame bulk modulus with the bulk modulus of fluid weighted by the Biot coefficient when the parameter is vanishing. The other regime is the one in which the fluid pressure affects to an extent greater than the solid pressure. Here, the parameter may span from unity to the ratio of bulk modulus of constituent solid mineral to fluid, which is its upper limit. At the upper limit, the undrained bulk modulus is the Voigt average: the upper bound of the modulus of a composite medium.

It is accepted widely that the Biot theory predicts only one shear wave representing the in-phase/unison shear motions of the solid and fluid constituent phases (fast S-wave). The Biot theory also contains a shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow S-wave). From the outset of the development of the Biot framework, the existence of this mode has remained unnoticed because of an oversight in decoupling its system of two coupled equations governing shear processes. Moreover, in the absence of the fluid strain-rate term in the Biot constitutive relation, the velocity of this mode is zero. Once the Biot constitutive relation is corrected for the missing fluid strain-rate term (i.e., fluid viscosity), this mode turns out to be, in the inertial regime, a diffusive process akin to a viscous wave in a Newtonian fluid. In the viscous regime, it degenerates to a process governed by a diffusion equation with a damping term. Although this mode is damped so heavily that it dies off rapidly near its source, overlooking its existence ignores a mechanism to draw energy from seismic waves (fast P- and S-waves) via mode conversion at interfaces and at other material discontinuities and inhomogeneities. To illustrate the consequence of generating this mode at an interface, I examine the case of a horizontally polarized fast S-wave normal incident upon a planar air-water interface in a porous medium. Contrary to the classical Biot framework, which suggests that the incident wave should be transmitted practically unchanged through such an interface, the viscosity-corrected Biot framework predicts a strong, fast S-wave reflection because of the slow S-wave generated at the interface.

Poroelastic modelling of micro‐inhomogeneous rocks is of interest for applications in rock physics and geomechanics. Laboratory measurements from both communities indicate that the Biot poroelasticity framework is not adequate. For the case of a macroscopically homogeneous and isotropic rock, we present the most general poroelasticity framework within the scope of equilibrium thermodynamics that is able to capture the effects of micro‐inhomogeneities in a natural way. Within this generalized poroelasticity framework, the concept of micro‐inhomogeneity is generically related to partial localization of the deformational potential energy either in the solid phase, including the interfacial region or in the fluid phase. The former case can occur in the presence of surface roughness or multi‐mineralic frame and the latter case can be related to suspended particles residing in the fluid phase. A measure for micro‐inhomogeneity is the coefficient that governs the effective pressure dependence of porosity changes as described by the porosity perturbation equation of this framework. It can be therefore equivalently interpreted as porosity effective pressure coefficient or as micro‐inhomogeneity parameter. We show how this parameter and the other poroelastic constants embedded in this framework can be expressed in terms of experimentally accessible poroelastic constants.

Quasistatic deformation experiments in the laboratory are key to determining the poroelastic moduli of rocks. For microinhomogeneous porous rocks, it is a challenge to determine a complete set of poroelastic parameters. This is because an additional parameter is required that quantifies the effect of microinhomogeneities because then the unjacketed bulk and pore moduli are no longer the same as the bulk modulus of the solid phase. We found that measurements for the drained and unjacketed bulk moduli together with Skempton’s pore-pressure build-up coefficient were sufficient to determine the solid-phase bulk modulus and the microinhomogeneity parameter. The latter served as a direct measure for the deviation from Biot-Gassmann prediction for the undrained bulk modulus. We applied the results to a set of measured poroelastic moduli in which microinhomogeneities have been made responsible for a non-Gassmann rock behavior. Accordingly, our estimate for the microinhomogeneity parameter quantified the deviation from the Biot-Gassmann prediction.