Anelliptic time processing based on a shifted hyperbola approach

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

“…In principle, it may be possible to extend the formalism based on shifted hyperbolas (Siliqi and Bousqué, 2000) and other existing VTI moveout equations (e.g., Fomel, 2004;van der Baan 2004;Douma and Calvert, 2006) to orthorhombic media by making the pertinent moveout parameters azimuthally dependent. However, such generalized equations for wide-azimuth data still have to be developed.…”

“…Siliqi and Bousqué (2000) apply the shifted-hyperbola formalism to nonhyperbolic moveout inversion and time-domain processing in VTI media. Also, Sayers and Ebrom (1997) propose to describe nonhyperbolic moveout in azimuthally anisotropic media by expanding group velocity in spherical harmonics.…”

Automatic nonhyperbolic velocity analysis

“…To use this equation in nonhyperbolic velocity analysis, the parameters and couple is used to construct a time gate using equation (1). To enhance accuracy and appropriate sampling in the estimated parameters, different parameterizations can be employed to make the search optimal (Alkhalifah and Tsvankin, 1995;Alkhalifah, 1997;Grechka andTsvankin, 1998, Siliqi andBousquié, 2000).…”

Shifted hyperbola moveout approximation revisited

“…This approximation requires three traveltime parameters to be defined: two‐way vertical traveltime, normal moveout velocity and heterogeneity coefficient. The interpretation of the heterogeneity coefficient within the framework of the shifted hyperbola approximation was done by Siliqi and Bousquie (2000). The role of the shifted hyperbola approximation as a special case of more general approximations is discussed by Fomel and Stovas (2010) for a generalized moveout approximation, by Jäger et al (2001) for common reflection surface and by Landa, Gurevich and Trachtman (1999) for the multifocusing method.…”