Seismic anisotropy

Seismic anisotropy is a term used in seismology to describe the directional dependence of the velocity of seismic waves in a medium (rock) within the Earth.

A material is said to be anisotropic if the value of a vector measurement of a rock property varies with direction. Anisotropy differs from the rock property called heterogeneity in that anisotropy is the variation in vectorial values with direction at a point while heterogeneity is the variation in scalar or vectorial values between two or more points.

Seismic Anisotropy can be defined as the dependence of velocity on direction or upon angle. There are two main types of anisotropy, both of them are called transverse isotropy (it is called transverse isotropy because there is isotropy in the horizontal or vertical plane) or polar anisotropy. The difference between them is in their axis of symmetry, which is an axis of rotational invariance such that if we rotate the formation about the axis, the material is still indistinguishable from what it was before. The symmetry axis is usually associated with regional stress or gravity.

The transverse anisotropic matrix has the same form as the isotropic matrix, except that it has five non-zero values distributed among 12 non-zero elements.

Anisotropy dates back to the 19th century following the theory of Elastic wave propagation. Green (1838) and Lord Kelvin (1856) took anisotropy into account in their articles on wave propagation. Anisotropy entered seismology in the late 19th century and was introduced by Maurice Rudzki. From 1898 till his death in 1916, Rudzki attempted to advance the theory of anisotropy, he attempted to determine the wavefront of a transversely isotropic medium (TI) in 1898 and in 1912 and 1913 he wrote on surface waves in transversely isotropic half space and on Fermat’s principle in anisotropic media respectively.

With all these, the advancement of anisotropy was still slow and in the first 30 years (1920-1950) of exploration seismology only a few papers were written on the subject. More work was done by several scientists such as Helbig (1956) who observed while doing seismic work on Devonian schists that velocities along the foliation were about 20% higher than those across the foliation. However the appreciation of anisotropy increased with the proposition of a new model for the generation of anisotropy in an originally isotropic background and a new exploration concept by Crampin (1987). One of the main points by Crampin was that the polarization of three component shear waves carries unique information about the internal structure of the rock through which they pass, and that shear wave splitting may contain information about the distribution of crack orientations.

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