Abstract
SUMMARY The variation of P-wave speed with direction in a weakly anisotropic homogeneous elastic medium of arbitrary symmetry is expanded as a series of spherical harmonics. The results given may be used to assess the information content of measurements of the P-wave speed acquired over a restricted angular range, and to design experiments with the objective of imaging a limited number of anisotropy parameters. Simplifications which occur for various symmetries typical of sedimentary rocks with and without fractures are discussed. Application is made to the determination of the azimuthal anisotropy of sedimentary rocks. For propagation direction n with polar angle χ and azimuthal angle χ defined with respect to some convenient choice of reference axes Ox1x2x3, the variation of P-wave speed νp(χ, η) with η for fixed χ is described by 12 parameters in the absence of symmetry. If the material contains a plane of mirror symmetry, and the axes are chosen with OX3 perpendicular to the symmetry plane, the variation of νp(χ, η) with η for fixed χ depends on six anisotropy parameters. For orthotropic symmetry the number of required parameters is reduced to three. For small polar angles χ, νp(χ, η) then varies with azimuth as cos 2η, with amplitude determined by a single anisotropy parameter (c13–c23–2c44+ 2c55).
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