The failure of brittle rocks during compression is preceded by the formation, growth, and coalescence of microcracks. Elastic wave velocities are reduced in the presence of open microcracks and fractures and may therefore be used to monitor the progressive damage of the rock. In general, these microcracks are not randomly oriented, and the rock displays an elastic anisotropy. The elastic anisotropy due to cracks can be expressed in terms of a second-rank and fourthrank crack density tensor. For open cracks the contribution of the fourth-rank crack density tensor to the elastic wave velocities is small. These results are compared with recent measurements of the ultrasonic compressional and shear wave velocities for propagation parallel and perpendicular to an increasing axial stress applied at constant confining stress to Berea sandstone. Inversion of the velocity measurements indicates that the microcracks propagate parallel to the maximum compressive stress, in agreement with current rock mechanics theory. A reasonable fit to the data is obtained using only the second-rank crack density tensor even though, at high confining stress, the cracks are expected to be in partial contact along their length. This is consistent with the model of elastic wave propagation in a medium containing partially contacting fractures published by White. However, measurements of off-axis wave velocities are required to fully quantify the contribution of the fourth-rank crack density tensor.

A simple method for including the effects of geologically realistic fractures on the seismic propagation through fractured rocks can be obtained by writing the effective compliance tensor of the fractured rock as the sum of the compliance tensor of the unfractured background rock and the compliance tensors for each set of parallel fractures or aligned fractures. The compliance tensor of each fracture set is derivable from a second rank fracture compliance tensor. For a rotationally symmetric set of fractures, the fracture compliance tensor depends on only two fracture compliances, one controlling fracture compliance normal, the other, tangential, to the plane of the fractures. The stiffness tensor, which is more useful in the consideration of elastic wave propagation through rocks, can then be obtained by inversion. The components of the excess fracture compliance tensor represent the maximum amount of information that can be obtained from seismic data. If the background rock is isotropic and the normal and shear compliance of each fracture are equal, although different from those of other fractures, the effective elastic behavior of the fractured rock is orthorhombic for any orientation distribution of fractures. A comparison of the theory with recent ultrasonic experiments on a simulated fractured medium shows near equality of the normal and shear compliance for the case of air‐filled fractures.

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Shales constitute about 75% of the clastic fill of sedimentary basins and have a decisive effect on fluid flow and seismic wave propagation because of their low permeability and anisotropic microstructure. The elastic stiffnesses of a shale with partially oriented clay particles is expressed in terms of the coefficients Wlmn in an expansion of the clay‐particle orientation distribution function in generalized Legendre functions. Application is made to the determination of the anellipticity of shales. For transverse isotropy the anellipticity quantifies the deviation of the P wave slowness curve from an ellipse and is shown to depend on a single coefficient W400 in the expansion of the clay‐particle orientation distribution function. If W400 is small, the anellipticity may be neglected, as is apparently the case for a near‐surface late Tertiary shale studied by Winterstein and Paulson. Strongly aligned clay particles result in a positive value of W400 and a positive anellipticity, in agreement with the majority of field measurements. However, less well ordered shales could have a significantly positive second moment W200 but only a small positive or even negative value of W400 For such shales the anellipticity would be small or negative despite a preferred alignment of clay particles in the bedding plane. Numerical examples of clay particle orientation distribution functions leading to zero or negative anellipticity are given.

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