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Generally, local stress induced by individual crack hardly disturbs their neighbours for small crack densities, which, however, could not be neglected as the crack density increases. The disturbance becomes rather complex in saturated porous rocks due to the wave‐induced diffusion of fluid pressures. The problem is addressed in this study by the comparison of two solutions: the analytical solution without stress interactions and the numerical method with stress interactions. The resultant difference of effective properties can be used to estimate the effect of stress interactions quantitatively. Numerical experiments demonstrate that the spatial distribution pattern of cracks strongly affects stress interactions. For regularly distributed cracks, the resulting stress interaction (shielding or amplification) shows strong anisotropy, depending on the arrangement and density of cracks. It has an important role in the estimation of effective anisotropic parameters as well as the incident‐angle‐dependency of P‐ and SV‐wave velocities. Contrarily, randomly distributed cracks with a relative small crack density generally lead to a strong cancellation of stress interactions across cracks, where both the numerical and analytical solutions show a good agreement for the estimation of effective parameters. However, for a higher crack density, the incomplete cancellation of stress interactions is expected, exhibiting an incidence‐angle dependency, slightly affecting effective parameters, and differentiating the numerical and analytical solutions.

We examine the effect of poroelastic boundary conditions when determining elastic properties of fluid‐saturated porous rocks from forced‐oscillation laboratory experiments. One undesired yet often unavoidable complication in the estimation of the undrained bulk modulus is due to the presence of the so‐called dead volume. It implies that some fluid mass can escape the rock sample under applying a confining pressure perturbation. Thus, the dead volume compromises the undrained state required to unambiguously determine the undrained bulk modulus. In this paper, we model data of recently performed low‐frequency (0.1 Hz) measurements. Therein, the dead volume has been systematically varied from 10% to 1000% of the pore volume. For the smallest dead volume, the inferred bulk modulus is close to the Biot–Gassmann undrained bulk modulus. With increasing dead volume, the experimentally inferred bulk modulus approaches the drained bulk modulus. We show that the transition from undrained to drained state as a function of dead volume can be modelled with a 1D poroelastic model for the rock sample‐dead volume system with a boundary condition that honours the continuity of the fluid volume flux. We discuss the limitations of the 1D model when applied to data recorded at higher frequencies (up to 100 Hz).

The effect of stress interactions on the effective poroelastic properties in saturated porous media has not been well-understood, especially for rocks with a fracture density larger than the dilute limit assumption. Frequency- and angle-dependent characteristics of stress interactions are analyzed by finite-element numerical tests with a least-squares procedure. We have investigated two types of fractured media: a stacked fractured model with stress shielding and a coplanar fractured model with stress amplification. We evaluate the effect of stress interactions from different spatial distributions of fractures on seismic attenuation and dispersion, with a specific focus on their frequency- and angle-dependent characteristics. We determine with numerical examples that a greater shielding effect corresponds to a larger frequency corresponding to maximum attenuation but a smaller peak attenuation. In contrast, a larger amplification effect leads to a higher attenuation. Due to the excluded diffusion energy outside the representative volume element, increasing the incidence angle ([Formula: see text]) leads to decreasing attenuation, whereas stress amplification is enhanced as the incidence angle increases continuously ([Formula: see text]), corresponding to increasing attenuation. This suggests that different incidence angles reshape the spatial distribution of stress interactions, in turn contributing to different frequency-dependent behaviors.

Elastic interactions between fractures will greatly affect the effective elasticity, which, in turn, reshape the effective fracture parameters. The disturbance will be more complex in the fault zone due to the complicated fracture distributions. The problem is addressed in this study by the comparison of two solutions: the analytical solution without stress interactions and the numerical method considering the stress interactions. The resultant difference between the two solutions allows the estimation of stress interactions on elasticity quantitatively. Furthermore, based on the orthorhombic assumption for fracture clustering in the damage zone, effect of stress interaction on the equivalent fractures parameter is estimated. We firstly characterize the fracture parameters in the fault damage zone considering more realistic distributions of fractures. Then, a series of numerical simulations are conducted to study the effective parameters of the fractured model. Finally, assuming the orthorhombic system of the fracture clustering, we invert the crack density and validate the accuracy of the inversion through the incidence-angle seismic velocities. Our numerical results suggest that, the size of fractures will determine the dominated type of stress interactions, and thus significantly reshape the effective properties of the models regardless of the fracture spatial distribution. Furthermore, the stress interactions tend to underestimate the fracture density for models containing long fractures, but generate a relatively satisfactory inverted fracture density for short fractures.

Crack surfaces are usually rough on various scales, and are sensitive to loading stresses and hence significantly affecting the mechanical properties of cracked rocks. We design a number of dry- and fluid-saturated numerical cracked samples to investigate the roughness influence of crack surfaces on the elastic stiffness. The fracture surface roughness is characterized by non-uniform fracture radii. We calculate the elastic moduli of cracked samples by finite-element simulation. Comparisons with the theoretical predictions by Gassmann and C&S (Ciz and Shapiro) (Ciz and Shapiro, Geophysics, 2007, 72(6), A75–A79) substitution equations demonstrate that the rough crack surfaces for both dry- and fluid-saturated samples can induce a stress concentration around the crack that reduces the elastic moduli and decreases the stiffness of rocks. For the fluid/solid-saturated cracks under the normal (shear) loading stresses, because the stress-concentration can induce shear (normal) strains around fracture, shear (bulk) modulus of the filling material will have contributions to the effective bulk (shear) modulus of rocks. The extra contribution, however, makes the Gassmann equation and C&S equation invalid.

The wave-induced interlayer flow between mesoscopic-scale heterogeneities (i.e., larger than pore scale but smaller than the predominant wavelengths) is the most important cause of attenuation at frequencies below 1 kHz. According to the White's layered model ( White et al., 1975 ), the wave-induced flow at an interface is symmetrical in periodically layered porous media due to its symmetrical structure. However, in one-dimensional (1-D) randomly layered porous rocks, layers of various thicknesses lead to different types of the interlayer flow. The coexistence of various wave-induced interlayer flow patterns at different interfaces results in interactions. The numerical creep test and a volume average of White's analytical solution were used to analyse the interactions in the two kinds of models (i.e., representative elementary volumes and randomly layered models). One of the parameters used to build a randomly layered model is the standard deviation of the thickness of the water-saturated layer, which could control the interaction strength of the interlayer flow. The detailed characteristics of the interlayer flow interaction were demonstrated by analysing the relative fluid velocity, while the statistical characteristics of the interlayer flow interaction were demonstrated by analysing the average solid velocity. We investigated the effect of the interaction on the amplitude versus the deviation at the interface between a non-dispersive medium and a patchy-saturated dispersive medium in three types of reservoirs. These results are beneficial for describing the distribution of oil/gas patches based on the statistical seismic properties in a layered formation with random disorder.

Multiparameter inversion for pre-stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem due to the non-unique results and unstable nature of the processing; the pre-stack seismic inversion problem is ill-posed and band-limited. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularisation can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge-preserving regularisation and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimisation problem. The method directly obtains reflectivity RPP values using the full Zoeppritz equation instead of its approximations and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S- and P-wave velocity ratio and using the generalised Gardner equation. We substituted the inverted parameters, i.e., the P-wave velocity, the fitting deviation of S-wave velocity, and the density were inverted instead of the P-wave velocity, the S-wave velocity, and the density, and the generalised Gardner equation was applied as a constraint. Test results on two-dimensional synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilising high-order anisotropic Markov random field neighbourhoods at early stages and low-order anisotropicMarkov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves.