The elastic anisotrophy of shales

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Abstract
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.