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Nonhyperbolic reflection moveout of *P*-waves is an important
indicator of anisotropy. However, its correct interpretation is
impossible without taking other factors into account. In this paper,
we have considered three other important factors: vertical
heterogeneity, curvature of the reflector, and lateral
heterogeneity. Each of these three factors can have an effect on
nonhyperbolic behavior of the reflection moveout comparable with the
effect of anisotropy. In particular, vertical heterogeneity produces a
depth-variant anisotropic pattern, different from the pattern of VTI
media. In the isotropic case, this pattern is reasonably well
approximated by the shifted hyperbola formula. In the case of a VTI
vertically heterogeneous medium, the parameters of anisotropy should
be replaced with their effective values. For the case of a curved
reflector in a homogeneous VTI medium, we have developed an
approximation based on the Taylor series expansion of the traveltime
with both the reflector curvature and the anisotropic parameters
entering the nonhyperbolic term. In the case of a lateral
heterogeneity, virtually any effectively anisotropic effect can be
created.
The theoretical results of this paper are directly applicable for *
modeling* nonhyperbolic moveouts. Particularly attractive in this
context are the general formulas connecting the reflection traveltime
derivatives with the traveltime derivatives of a direct wave. For
smooth velocity models, these formulas may reduce the problem of
tracing a family of reflected rays to the problem of tracing one
central ray. Practical estimation and *inversion* of nonhyperbolic
moveout is a different and more difficult problem. Nevertheless, the
theoretical guidelines provided by the analytical theory are helpful
for a correct formulation of the inversion problem. They show us
explicitly what parameters of the medium we may hope to extract from
the kinematics of *P*-wave seismic reflection data.

** Next:** Acknowledgments
** Up:** Fomel & Grechka: Nonhyperbolic
** Previous:** TI MOVEOUT IN TERMS
Stanford Exploration Project

11/12/1997