Seismic anisotropy can help to extract azimuthal information for predicting crack alignment, but the accurate evaluation of cracked reservoir requires knowledge of degree of crack development, which is achieved through determining the crack density from seismic or VSP data. In this research we study the dependence of seismic anisotropy on crack density, using synthetic rocks with controlled crack geometries. A set of four synthetic rocks containing different crack densities are used in laboratory measurements. The crack thickness is 0.06 2 / 32 mm and the crack diameter is 3 mm in all the cracked rocks, while the crack densities are 0.00, 0.0243, 0.0486 and 0.0729. P and S wave velocities are measured by an ultrasonic investigation system at 0.5 MHz while the rocks are saturated with water. The measurements show the impact of crack density on the P and S wave velocities. Our results are compared to the theoretical prediction of (Chapman, 2003) and (Hudson, 1981). The comparison shows that measured velocities and theoretical results are in good quantitative agreement in all three cracked rocks, although Chapman's model fits the experimental results better. The measured anisotropy of the P and S wave in the four synthetic rocks shows that seismic anisotropy is directly proportional to increasing crack density, as predicted by several theoretical models. The laboratory measurements indicate that it would be effective to use seismic anisotropy to determine the crack density and estimate the intensity of crack density in seismology and seismic exploration.

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Fractures often play an important role in controlling the fluid flow in hydrocarbon reservoirs. When the seismic wave propagates through media containing fracture corridors, significant scattering dispersion and attenuation can occur. In this work, we study the P-wave dispersion and attenuation due to the scattering caused by 2-D fluid-saturated aligned fractures with finite thickness, which are embedded in an isotropic elastic background medium. Using the Foldy approximation and the representation theorem, the P-wave dispersion and attenuation are related to the displacement discontinuities across the fractures. These fracture displacement discontinuities are obtained from the boundary conditions and the P-wave dispersion and attenuation can thus be calculated. A numerical example shows that the fracture thickness has significant influence on the dispersion and attenuation, especially in the low-frequency regime when the fracture size is smaller than the seismic wavelength. The effects of the fluid bulk modulus are also significant, which are opposite to those of the fracture thickness. However, the effect of the fluid viscosity is found to be negligible for the studied configurations. To validate the proposed model, the theoretical predictions are compared with ultrasonic measurements on fractured samples. The comparison shows overall good agreement between theory and experiment. This work reveals the important influence of fracture thickness and saturating fluid properties on the P-wave scattering dispersion and attenuation. Hence, it shows a potential to extract these parameters from seismic data.

We used a laboratory scale model to study the effects aligned fractures might have on seismic wave propagation at a larger scale in real Earth imaging. Our main objective was to investigate the effect of aligned fractures on seismic P‐wave amplitude through the estimation of the induced attenuation. The physical model was constructed from a mixture of epoxy resin and silicon rubber, with inclusions designed to simulate two sets of inclined fractures at an angle of 29.2° with each other. Two‐dimensional reflection data were acquired using the pulse and transmission method in three principal directions relative to the fracture strike azimuth with the model submerged in a water tank. We used the Quality Versus Offset (QVO) method, an extension of the classical spectral ratio method for determining attenuation to estimate the induced attenuation (inverse of the seismic quality factor) from the Common Mid Point (CMP) pre‐processed gathers. The results of our analysis show that the induced P‐wave attenuation is anisotropic, with elliptical (cos2θ) variations with respect to the survey azimuth angle θ. The minor axis of the Q ellipse corresponds to the fracture normal. In this direction, i.e. across the material grain, the attenuation is a maximum. The major axis corresponds to the fracture strike direction (parallel to the material grain) where minimum attenuation occurs. These attenuation results show consistency with the azimuthal anisotropy observed in the stacking velocities in the fractured‐layer and are all consistent with the physical model, and thus provide a physical basis for using attenuation anisotropy to derive fracture properties from seismic data.

Effects of quenching process on dielectric, ferroelectric, and piezoelectric properties of 0.71BiFeO3−0.29BaTiO3 ceramics with Mn modification (BF–BT−xmol%Mn) were investigated. The dielectric, ferroelectric, and piezoelectric properties of BF–BT−xmol%Mn were improved by quenching, especially to the BF–BT−0.3 mol%Mn ceramics. The dielectric loss tanδ of quenched BF–BT−0.3 mol%Mn ceramics was only 0.28 at 500°C, which was half of the slow cooling one. Meanwhile, the remnant polarization Pr of quenched BF–BT−0.3 mol%Mn ceramics increased to 21 μC/cm2. It was notable that the piezoelectric constant d33 of quenched BF–BT−0.3 mol%Mn ceramics reached up to 191 pC/N, while the TC was 530°C, showing excellent compatible properties. The BF–BT−xmol%Mn system ceramics showed to obey the Rayleigh law within suitable field regions. The Rayleigh law results indicated that the extrinsic contributions to the dielectric and piezoelectric responses of quenched BF–BT−xmol%Mn ceramics were larger than the unquenched ceramics. These results presented that the quenched BF–BT−xmol%Mn ceramics were promising candidates for high‐temperature piezoelectric devices.