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Published as Center for Wave Phenomena, CWP-372 (2001)

Nonhyperbolic reflection moveout of $P$-waves:
An overview and comparison of reasons

Sergey Fomel[*]and Vladimir Grechka[*]


The familiar hyperbolic approximation of $P$-wave reflection moveout is exact for homogeneous isotropic or elliptically anisotropic media above a planar reflector. Any realistic combination of heterogeneity, reflector curvature, and nonelliptic anisotropy will cause departures from hyperbolic moveout at large offsets. Here, we analyze the similarities and differences in the influence of those three factors on $P$-wave reflection traveltimes. Using the weak-anisotropy approximation for velocities in transversely isotropic media with a vertical symmetry axis (VTI model), we show that although the nonhyperbolic moveout due to both vertical heterogeneity and reflector curvature can be interpreted in terms of effective anisotropy, such anisotropy is inherently different from that of a generic homogeneous VTI model.