Fowler DMO and time migration in transversely isotropic media

The main advantage cf Fowler's (1984) isotropic dip moveout (DMO) method is the ability to perform velocity analysis along with the DMO removal. Here, we devise a Fowler-type DMO algorithm for transversely isotropic media using the analytic expression for normal-moveout velocity given by Tsvankin (1994). Alkhalifah and Tsvankin (1994) have shown that in transversely isotropic media with a vertical axis of symmetry (VTI), the P-wave normal-moveout (NMO) velocity as a function of ray parameter can be fully described by the zero-dip NM0 velocity Vnmo(0) and the anisotropic parameter η (η reduces to the difference between Thomsen parameters ∈ and δ in the limit of weak anisotropy). In our extension of Fowler DMO, resampling in the frequencywavenumber domain makes it possible to obtain the values of V,(O) and η by inspecting zero-offset panels for different pairs of the two parameters. Synthetic examples demonstrate that the isotropic Fowler DMO technique fails to generate an accurate zero-offset section and obtain the zero-dip NM0 velocity for non-elliptical VTI models. In contrast, our anisotropic algorithm allows one to find the values of the parameters Vnmo(0) and η, and correct for the influence of transverse isotropy in the DMO processing. This method, combined with post-stack frequency-wavenumber (F-K) Stolt migration, represents a complete inversion-processing sequence capable of recovering the effective parameters of transversely isotropic media and producing migrated images for the best-fit anisotropic model. Since most of the computing time is spent on generating constant-velocity stacks, the added computational effort due to the presence of anisotropy is relatively minor.