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Abstract

A medium (or a region of a continuum) is called anisotropic with respect to a certain parameter if this parameter changes with the direction of a measurement. If an elastic medium is anisotropic, seismic waves of a given type propagate in different directions with different velocities. This velocity anisotropy implies the existence of a certain structure (order) on the scale of seismic wavelength imposed by various physical phenomena. In typical subsurface formations, velocity changes with both spatial position and propagation direction, which makes the medium heterogeneous and anisotropic. The notions of heterogeneity and anisotropy are scale-dependent, and the same medium may behave as heterogeneous for small wavelengths and as anisotropic for large wavelengths (e.g., Helbig, 1994). For example, such small-scale heterogeneity as fine layering detectable by well logs may create an effectively anisotropic model in the long-wavelength limit.

Anisotropy in sedimentary sequences is caused by the following main factors (e.g., Thomsen, 1986):

  • intrinsic anisotropy due to preferred orientation of anisotropic mineral grains or the shapes of isotropic minerals

  • thin bedding of isotropic layers on a scale small compared to the wavelength (the layers may be horizontal or tilted)

  • vertical or dipping fractures or microcracks

  • nonhydrostatic stress

It is common to see anisotropy produced by a certain combination of these factors. For instance, systems of vertical fractures may develop in finely layered sediments, or the thin layers themselves may be intrinsically anisotropic. As a result, subsurface formations may possess several anisotropic symmetries, each with a different character of wave propagation (subsection 1.1.4).

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