Nonhyperbolic moveout analysis of wide-azimuth P-wave data
Published:January 01, 2011
2011. "Nonhyperbolic moveout analysis of wide-azimuth P-wave data", Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization, Ilya Tsvankin, Vladimir Grechka
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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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Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization
Traveltimes of reflected waves (reflection moveout) in heterogeneous anisotropic media are usually modeled by multioffset and multiazimuth ray tracing (e.g., Gajewski and Pšenčĺk, 1987). Whereas anisotropic ray-tracing codes are sufficiently fast for forward modeling, their application in moveout inversion requires repeated generation of azimuthally-dependent traveltimes around many common-midpoint (CMP) locations, which makes the inversion procedure extremely time-consuming. Also, purely numerical solutions do not give insight into the influence of anisotropy on reflection traveltimes.
This chapter is devoted to analytic treatment of conventional-spread reflection moveout in anisotropic media. For models with moderate structural complexity and spreadlength-to-depth ratios close to unity, traveltimes in CMP geometry are welldescribed by normal-moveout (NMO) velocity defined in the zero-spread limit (Tsvankin and Thomsen, 1994; Tsvankin, 2005). Even in the presence of nonhyperbolic moveout, NMO velocity (Vnmo) is still responsible for the most stable, conventionaloffset portion of the moveout curve. The description of Vnmo given here provides an analytic basis for moveout inversion, helps evaluate the contribution of the anisotropy parameters to reflection traveltimes, and leads to a significant increase in the efficiency of traveltime modeling/inversion methods.