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In conventional seismic data processing, reflection traveltime is often assumed to be described by a hyperbolic equation with the quadratic term determined by NMO velocity. However, the influence of heterogeneity (either lateral or vertical) and non-elliptical anisotropy causes deviations from hyperbolic moveout, which typically become substantial for offset-to-depth ratios exceeding unity. Practical difficulties in working with long-spread data and insufficient understanding of nonhyperbolic move-out often force seismic processors to mute out the large-offset portion of the moveout curve. Nonetheless, advances in acquisition technology have significantly increased the range of source-receiver offsets in 3D surveys, and nonhyperbolic moveout has proved useful in such applications as anisotropic parameter estimation, suppression of multiples, and large-angle AVO (amplitude-variation-with-offset) analysis. Among the first to recognize the benefits of employing nonhyperbolic moveout in interval anisotropic velocity parameter estimation was Sena (1991), who developed travel-time approximations for multilayered VTI and HTI media based upon the so-called “skewed” hyperbolic moveout formulation of Byun et al. (1989). A detailed overview of nonhyperbolic moveout analysis for pure (PP and SS) modes and PS-waves in layered VTI models can be found in Tsvankin (2005).

This chapter discusses the influence of azimuthal anisotropy on nonhyperbolic moveout and introduces an efficient moveout-inversion algorithm for wide-azimuth P-wave data from orthorhombic and HTI media. We start with a brief description of nonhyperbolic moveout equations for layered anisotropic models. Deviation from hyperbolic moveout for pure reflected waves is largely governed by the quartic coefficient A4 of the traveltime series t2(x2).

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