Based on the theory of anisotropic elasticity and observation of static mechanic measurement of transversely isotropic hydrocarbon source rocks or rock‐like materials, we reasoned that one of the three principal Poisson's ratios of transversely isotropic hydrocarbon source rocks should always be greater than the other two and they should be generally positive. From these relations, we derived tight physical constraints on c13, Thomsen parameter δ, and anellipticity parameter η. Some of the published data from laboratory velocity anisotropy measurement are lying outside of the constraints. We analysed that they are primarily caused by substantial uncertainty associated with the oblique velocity measurement. These physical constraints will be useful for our understanding of Thomsen parameter δ, data quality checking, and predicting δ from measurements perpendicular and parallel to the symmetrical axis of transversely isotropic medium. The physical constraints should also have potential application in anisotropic seismic data processing.

We have investigated the impact of wave-induced fluid flow, including Biot flow and mesoscopic flow, on the signatures of seismic reflectivity in heterogeneous reservoir rocks. We have incorporated the dynamic poroelastic responses of mesoscopic flow into the classical Biot theory. The resulting effective Biot media could capture the characteristics of velocity dispersion and wave attenuation in heterogeneous poroelastic media. On the basis of this effective Biot media, an approach was developed to compute the poroelastic reflection at arbitrary angles and frequencies from the boundary of two heterogeneous porous media. The computed poroelastic reflections not only depended on the elastic properties' contrast and incident angle, but also relied on the fluid mobility and observational frequency. For a typical sand-shale reflector, with the given rock and fluid properties, we found that the effect of mesoscopic flow causes Pwave reflection amplitude variations with the frequency being as high as 40% and a maximum phase shift as high as 16°at the seismic exploration frequency band. In addition, it was found that the amplitude variation with offset intercept and the gradient at the poroelastic interface were impacted by the mesoscopic flow and had a decreasing trend with frequency. Therefore, ignoring the impact of mesoscopic flow could possibly lead to uncertainty in seismic imaging as well as quantitative interpretation of reservoir properties. In comparison, the Biot flowinduced seismic dispersion effect, which occured at a very highfrequency range, was almost negligible.

A B S T R A C TElastic interactions between pores and cracks reflect how they are organized or spatially distributed in porous rocks. The principle goal of this paper is to understand and characterize the effect of elastic interactions on the effective elastic properties. We perform finite element modelling to quantitatively study how the spatial arrangement of inclusions affects stress distribution and the resulting overall elasticity. It is found that the stress field can be significantly altered by elastic interactions. Compared with a non-interacting situation, stress shielding considerably stiffens the effective media, while stress amplification appreciably reduces the effective elasticity. We also demonstrate that the T-matrix approach, which takes into account the ellipsoid distribution of pores or cracks, can successfully characterize the competing effects between stress shielding and stress amplification. Numerical results suggest that, when the concentrations of cracks increase beyond the dilute limit, the single parameter crack density is not sufficient to characterize the contribution of the cracks to the effective elasticity. In order to obtain more reliable and accurate predictions for the effective elastic responses and seismic anisotropies, the spatial distribution of pores and cracks should be included. Additionally, such elastic interaction effects are also dependent on both the pore shapes and the fluid infill.

By evaluating the consistency of the Gassmann theory with various inclusion‐based effective medium theories, we investigate the impact of elastic interactions between ellipsoidal pores on the poroelasticity. To rule out any factors that can violate the Gassmann condition, other than elastic interactions, we first construct idealized models that contain only a single set of isolated, identical, and vertically aligned ellipsoidal pores. The numerical simulation suggests that the periodic distribution of ellipsoidal pores generate uniform pore pressure distribution, whereas random distribution of ellipsoidal pores generates heterogeneous pore pressure distributions. Then we analyze the precise conditions under which the underlying Gassmann relationship is valid for various inclusion‐based models. The results reveal the following: (1) Noninteracting effective medium theories are always consistent with the Gassmann prediction, simply because the elastic interactions are ignored. (2) The elastic interactions between randomly distributed pores cause heterogeneous pore pressure that violates the essential requirement of the Gassmann theory. The differential effective medium and self‐consistent approximation theories corresponding to this model thus are inconsistent with the Gassmann prediction. (3) The elastic interactions between periodically distributed pores cause uniform pore pressure; therefore, the Gassmann condition is fully satisfied. The T‐matrix approach explicitly takes into account such elastic interactions and thus is consistent with the Gassmann theory. It is interesting to notice that on top of other well‐known common types of heterogeneities, like pore structure or fluid heterogeneities, the distribution of pores and its associated elastic interactions can be a separate source of heterogeneity, and this makes Gassmann equations not valid anymore.

Conventional seismic analysis in partially saturated rocks normally lays emphasis on estimating pore fluid content and saturation, typically ignoring the effect of mobility, which decides the ability of fluids moving in the porous rocks. Deformation resulting from a seismic wave in heterogeneous partially saturated media can cause pore fluid pressure relaxation at mesoscopic scale, thereby making the fluid mobility inherently associated with poroelastic reflectivity. For two typical gas‐brine reservoir models, with the given rock and fluid properties, the numerical analysis suggests that variations of patchy fluid saturation, fluid compressibility contrast, and acoustic stiffness of rock frame collectively affect the seismic reflection dependence on mobility. In particular, the realistic compressibility contrast of fluid patches in shallow and deep reservoir environments plays an important role in determining the reflection sensitivity to mobility. We also use a time‐lapse seismic data set from a Steam‐Assisted Gravity Drainage producing heavy oil reservoir to demonstrate that mobility change coupled with patchy saturation possibly leads to seismic spectral energy shifting from the baseline to monitor line. Our workflow starts from performing seismic spectral analysis on the targeted reflectivity interface. Then, on the basis of mesoscopic fluid pressure diffusion between patches of steam and heavy oil, poroelastic reflectivity modeling is conducted to understand the shift of the central frequency toward low frequencies after the steam injection. The presented results open the possibility of monitoring mobility change of a partially saturated geological formation from dissipation‐related seismic attributes.

With more core samples measured in laboratory, we observed wide scattering of velocity on heavy oil sand samples from different fields. A simple universal modeling for heavy oil sand velocity is unrealistic at this stage. However, with improvements on measurement techniques, plus additional information from heavy oil study and other sources, we have better understanding on each factor controlling velocities of heavy oil sands, which include: rock texture, pore fluid properties, and interaction between pore fluids and rock frame at different temperatures.

We have measured velocity anisotropy on 13 core samples from an organic shale oil reservoir with differential pressure up to 3000 psi. The pressure effect on velocities is generally stronger in direction normal to the bedding than along the bedding, and thus the anisotropy decreases with increasing differential pressure. P-wave anisotropy and vertical Vp/Vs ratio have good correlation with TOC content: the higher is the TOC content, the stronger is Pwave anisotropy and the lower is Vp/Vs ratio. The measured P-wave anisotropy is generally greater than Swave anisotropy. Sensitivity of c 13 and  to errors in

Dispersion and attenuation are important attributes of seismic data that can provide important information about reservoir rock lithology, pore fluid type, and pore structure. Based on Cheng’s pore-aspect-ratio spectrum inversion methodology, we related the closure and deformation of soft pores to the measured pressure-dependent porosity data. With this additional constraint, the inverted pore-aspect-ratio spectrum and concentrations are more realistic. The complex pore structure controls two important intrinsic dispersion and attenuation mechanisms: Biot flow and squirt flow. We modified and extended Tang’s unified velocity dispersion and attenuation model and made it applicable to poroelastic media with a complex pore structure under the undrained condition. The inverted pore-aspect-ratio spectra from pressure-dependent ultrasonic velocity measurements were put into the modified Tang’s model to predict velocity dispersion and attenuation in full frequency range at various differential pressure conditions.