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The anisotropic structure of the stiffness tensor influences not only traveltimes of seismic waves but also their polarizations and amplitudes. As follows from the Christoffel equation (1.10), the polarization vectors of plane waves in the presence of anisotropy are not strictly parallel or perpendicular to the propagation (slowness) or ray direction. This suggests that polarization directions of body waves with realistic curved wavefronts should also be distorted by anisotropic velocity fields. Analysis of both polarization and amplitude anomalies, however, requires going beyond plane-wave theory and investigating 3D wavefronts generated by such sources of seismic energy as a concentrated force, explosion, and dislocation.

The first section of this chapter gives a description of point-force radiation patterns and body-wave polarizations in anisotropic media. Numerical analysis based on the evaluation of Fourier-Bessel (Weyl-type) integrals is supported by a closed-form solution for the far-field displacement derived using the stationary-phase approximation. Both analytic and numerical results show that the amplitudes of P-waves and, in particular, S-waves in anisotropic media may be substantially distorted by focusing and defocusing of energy, usually associated with maxima and minima (respectively) in the angle-dependent velocity.

The second section is devoted to the basics of amplitude-variation-with-offset (AVO) analysis in transversely isotropic media with a vertical symmetry axis (VTI). The dependence of reflection coefficients on the incidence angle is quite sensitive to the presence of anisotropy on either side of the interface. Furthermore, if the overburden contains anisotropic (e.g., shale) layers, AVO signatures are also influenced by the amplitude focusing phenomena above

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