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Abstract. We analyze amplitude variations with offsets and azimuths (AVO-A) of an anisotropic half-space for P-P, P-SV and P-SH scattering. When the overburden is assumed to be isotropic, the AVO-A of each of these three scattering modes can be cast in terms of a Fourier series of azimuths,φ, as follows:


where, and are the functions that describe the seismic amplitude variations with offsets (AVO) for a given azimuth. The forms of AVO functions are similar to those of classical AVO formulae; for instance, the AVO functions corresponding to the P-P scattering mode can be interpreted in terms of the intercept and gradient, although the resulting numerical values can differ significantly from those of isotropic cases. One of the benefits of describing the AVO-A as a Fourier series is that the contribution of amplitude variations with azimuths (AVAZ) is distinguishable from that of AVO. The AVAZ is characterized by the functions {1,cosφ,sinφ,cos2φ,sin2φ,cos3φ, sin3φ, cos4φ, sin4φ}, which are mutually orthogonal. Thus, the AVO-A inversion can be formulated as a series of AVO inversions in which the AVO behaviors are represented by the functions F0,Fn,Gn.

When the coordinate system of seismic acquisition geometry coincides with the symmetry planes of the rock formations, the series corresponding to P-P and P-SV simplify even further; they reduce to for F0 azimuthally isotropic symmetry and to F0, F2 and F4 for orthorhombic symmetry. The series corresponding to P-SH scattering is null for azimuthally isotropic symmetry and reduces to G2 and G4 for orthorhombic symmetry. Unfortunately, the coordinate system of seismic acqusition geometry rarely coincides with the symmetry planes of the rock formations; therefore, the other terms are rarely null. In particular, the functions F1 and G1 become important for P-SV and P-SH scattering because they are affected by the asymmetry of the P-S reflection. These functions are null for P-P scattering, irrespective of the symmetry planes.

The potential ambiguity between heterogeneity and anisotropy (which can be due to a dipping interface between the isotropic and anisotropic half-spaces) in the recontruction of elastic parameters from the AVO functions F0, Fn, and Gn is also discussed, as well as the sensitivity of these AVO functions to properties of fractured rock formations, including their fluid saturation.

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