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

The angle dependence of the group velocity in equations (1)
and (5) is characterized by *small* anisotropic
coefficients. Therefore, we can assume that an analogous influence of
lateral heterogeneity might be caused by *small* velocity
perturbations. (Large lateral velocity changes can cause behavior too
complicated for analytic description.) An appropriate model is a plane
laterally heterogeneous layer with the velocity

where is the midpoint location and the integration limits correspond to the source and receiver locations. For simplicity and without loss of generality, we can set to zero. Linearizing equation (79) with respect to the small perturbation , we get

It is clear from equation (80) that lateral
heterogeneity can cause many different types of the nonhyperbolic moveout.
In particular, comparing equations (80) and
(11), we conclude that a pseudo-anisotropic behavior of
traveltimes is produced by lateral heterogeneity in the form

where and should be considered now as parameters, describing the

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

2014-01-27