Generalized nonhyperbolic moveout approximation |

Reflection moveout approximations are commonly used for velocity analysis, stacking, and time migration (Yilmaz, 2000). The reflection traveltime as a function of the source-receiver offset has a well-known hyperbolic form in the case of plane reflectors in homogeneous isotropic (or elliptically anisotropic) overburden. A hyperbolic behavior of the PP moveout is always valid around the zero offset thanks to the source-receiver reciprocity and the first-order Taylor series expansion. However, any deviations from this simple model may cause nonhyperbolic behavior at large offsets (Fomel and Grechka, 2001).

Considerable research effort has been devoted to developing nonhyperbolic moveout approximations in both isotropic and anisotropic media. The work on isotropic approximations goes back to Bolshykh (1956), Taner and Koehler (1969), Malovichko (1978), de Bazelaire (1988), Castle (1994), and others. Fowler (2003) provides a comprehensive review of many different approximations developed for non-hyperbolic moveout in anisotropic (VTI - vertically transversally isotropic) media. A particularly simple ``velocity acceleration'' model for nonhyperbolic moveout is suggested by Taner et al. (2005,2007). Causse (2004) approximates nonhyperbolic moveout by expanding it into a sum of basis functions. Douma and Calvert (2006) and Douma and van der Baan (2008) build an accurate moveout approximation by using rational interpolation between several rays.

In this paper, we propose a general functional form for nonhyperbolic approximations that can be applied to different kinds of seismic media. The proposed form includes five coefficients as opposed to two coefficients in the classic hyperbolic approximation. In certain cases, the number of coefficients can be reduced. In the case of a homogeneous VTI medium and the ``acoustic approximation'' of Alkhalifah (1998), our approximation becomes identical to the one proposed previously by Fomel (2004). In the general case, determining the optimal coefficients requires tracing of only one non-zero-offset ray.

Using analytical ray-tracing solutions and numerical experiments, we compare the accuracy of our approximation with the accuracy of other known approximations and discover an improvement in accuracy of several orders of magnitude. Potential applications of the new approximation include velocity analysis and time-domain imaging.

Generalized nonhyperbolic moveout approximation |

2013-07-26