Conclusions

We have extended the concept of velocity continuation in isotropic media to continuations in both the NMO velocity and the anisotropy parameter $\eta$ for VTI media. Despite the fact that we have considered the simple case of post-stack migration separately, the exact kinematic equations describing the continuation process are anything but simple. However, useful insights into this problem are deduced from linearized approximations of the continuation equations. These insights include the following conclusions:

• The leading order behavior of the velocity continuation is proportional to $\tau_x^2$, which corresponds to small or moderate dips.
• The leading order behavior of the $\eta$ continuation is proportional to $\tau_x^4$, which corresponds to moderate or steep dips.
• Both leading terms are independent of the strength of anisotropy ($\eta$).

In practical applications, the initial migrated section is obtained by isotropic migration, and, therefore, the residual process is used to correct for anisotropy. Setting $\eta=0$ in the continuation equations for this type of an application is a reasonable approximation, given that $\eta$=0 is the starting point and we consider only weak to moderate degrees of anisotropy ($\eta \approx 0.1$). Numerical experiments with synthetically generated operators confirm this conclusion.

Future directions of research will focus on a practical implementation of anisotropy continuation as well as on extending the theory to the case of residual prestack migration.