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.

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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.

Based on poroelasticity analysis, we developed a new concept of frequency-dependent dynamic fluid modulus (DFM) to understand the velocity dispersion and wave attenuation due to wave-induced fluid flow. Conventional applications of Gassmann’s equation require a complete homogeneity inside the porous media (or equivalently, at zero frequency) and closed boundary condition. We first analyzed the fluid effect on the bulk modulus in homogeneous porous media with a nonclosed condition. The partial drainage of pore fluid causes additional pore volume change under applied stress. An incoming fluid flow stiffens the porous system, and an outgoing flow softens it. Such a phenomenon can still be effectively formulated as a closed system with Gassmann’s equation, by introducing a DFM, which adds a flow term into the original fluid modulus. We further proved that in heterogeneous porous media, the wave-induced internal fluid flow caused additional bulk volume deformation. It equals the amount of the fluid flow from a soft phase to a stiff phase times the difference of Skempton coefficients between the two phases. Again, with a frequency-dependent complex number DFM, the use of Gassmann’s equation can be extended into heterogeneous porous media at nonzero frequencies to fully characterize its viscoelastic behavior on rock’s bulk modulus. We evaluated three examples to show how to model the P-wave attenuation and velocity dispersion in porous media due to microscopic and mesoscopic scale heterogeneities, as well as in the presence of multiple sets of heterogeneities. Finally, we demonstrated that the DFM can be conveniently and deterministically inverted from the measured lab data. The inverted results can be used to identify the possible mechanisms behind the observed wave attenuation and velocity dispersion, and they were good indicators of the degree and distribution of heterogeneities inside the rocks.

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.