AVO-A response of an anisotropic half-space bounded by a dipping surface for P-P, P-SV and P-SH data

We analyze amplitude variations with offsets and azimuths (AVO-A) of an ani sotropic half-space bounded by a dipping surface. By analyzing the response of a dipping reflector instead of a horizontal one, we integrate the funda mental problem of lateral heterogeneity vs. anisotropy into our study. This analysis is limited to the three scattering modes that dominate ocean bott om seismic (OBS) data: P-P, P-SV and P-SH. When the overburden is assumed i sotropic, the AVO-A of each of these three scattering modes can be cast in terms of a Fourier series of azimuths, phi, in general form. [GRAPHICS] where F-o, F-n and G(n) are the functions that describe the seismic amplitu de variations with offsets (AVO) for a given azimuth. The forms of AVO func tions are similar to those of classical AVO formulae; for instance, the AVO functions corresponding to the P-P scattering mode can be interpreted in t erms of the intercept and gradient, although the resulting numerical values can differ significantly from those of isotropic cases or horizontal refle ctors. One of the benefits of describing the AVO-A as a Fourier series is that the contribution of amplitude variations with azimuths (AVAZ) is distinguishab le from that of AVO. The AVAZ is characterized by the functions {1, cos phi , sin phi, cos2 phi, sin2 phi, cos3 phi, sin3 phi, cos4 phi, sin4 phi}, tha t are mutually orthogonal. Thus, the AVO-A inversion can be formulated as a series of AVO inversions where the AVO behaviors are represented by the fu nctions F-o, F-n and G(n). When the coordinate system of seismic acquisition geometry coincides with t he symmetry planes of the rock formations. the series corresponding to P-P and P-SV simplify even further; they reduce to F-o for azimuthally isotropi c symmetry and to F-o, F-2, F-4, G(2) and G(4) for orthorhombic symmetry. T he series corresponding to P-SH scattering is reduced to G(2) and G(4) for these two symmetries. Unfortunately, the coordinate system of seismic acqusition geometry rarely coincides with the symmetry planes of the rock formations: therefore, the o ther terms are rarely zero. In particular, the functions F-1, F-3, G(1) and G(3) become important for large dips and are actually largely dependent on the angle of the dipping reflector. For P-P scattering, these functions ar e zero if the reflector is horizontal, irrespective of the anisotropic beha vior. For P-SV and P-SH scattering, these functions are not necessarily zer o for horizontal reflectors because they are affected by the asymmetry of t he P-S reflection in addition to the effect of dip. (C) 2001 Elsevier Scien ce B.V. All rights reserved.