SEISMIC ANISOTROPY

Variation of seismic velocity depending on either the direction of travel for P- or Swaves  or the direction of polarization for S-waves. Velocity anisotropy (or coefficient of anisotropy) is sometimes taken as the fractional difference between the maximum and minimum velocities in different directions, (Vmax-Vmin)/Vmax, often expressed as a percentage, sometimes as the ratio of maximum and minimum velocities, Vmax/Vmin; the numerical value usually makes clear which is meant. P-wave anisotropy is usually meant unless S-wave anisotropy is specified, but anisotropy of P-waves usually implies anisotropy for S-waves and vice-versa.

a) The general elasticity tensor stiffness or its inverse compliance, relating stress and strain contains up to 21 independent constants, the number depending on the symmetry see symmetry systems. Because of symmetries, this 3X3X3X3 tensor may be written as a 6X6 matrix (Fig. 1). In isotropic media there are only two independent constants among 12 nonzero elements of this matrix.

b) Polar anisotropy (transverse isotropy) involves elastic properties that are the same in any direction perpendicular to a symmetry axis but different parallel to the axis. Layering is the most common cause of this situation; see Fig. 2 and polar anisotropy. Polar anisotropy involves five independent elastic constants. This symmetry is similar to that of a crystal having hexagonal symmetry.

c) Azimuthal asymmetry involving orthorhombic symmetry the symmetry of a brick gives a different P-wave velocity along the three orthogonal symmetry axes and different shear-wave splitting (see d below) in the three directions. Vertically fractured horizontal layering may produce this situation. Orthorhombic asymmetry involves nine independent elastic constants.

d) In an arbitrary polar or orthorhombic anisotropic medium, for each travel direction only two orthogonal polarizations of plane shear-waves are allowed although they are not necessarily transverse to the propagation direction; they may travel with different velocities. An S-wave of arbitrary polarization entering such a region in a direction other than along the symmetry axis splits into two S-waves; this is called shearwave splitting, birefringence, S-wave splitting, or double refraction.

e) Monoclinic anisotropy is similar to orthorhombic anisotropy except that one of the three axes is not orthogonal to the other axes. It involves eleven independent elastic constants.