Fowler DMO and time migration for transversely isotropic media

The main advantage of Fowler's dip-moveout (DMO) method is the ability to perform velocity analysis along with the DMO removal. This feature of Fowler DMO becomes even more attractive in anisotropic media, where imaging methods are hampered by the difficulty in reconstructing the velocity field from surface data. We have devised a Fowler-type DMO algorithm for transversely isotropic media using the analytic expression for normal-moveout velocity. The parameter-estimation procedure is based on the results of Alkhalifah and Tsvankin showing 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 described fully by just two coefficients: the zero-dip NMO velocity V-nmo(0) and the anisotropic parameter eta (eta reduces to the difference between Thomsen parameters epsilon and delta in the limit of weak anisotropy). In this extension of Fowler DMO, resampling in the frequency-wavenumber domain makes it possible to obtain the values of V-nmo(0) and eta by inspecting zero-offset (stacked) panels for different pairs of the two parameters. Since most of the computing time is spent on generating constant-velocity stacks, the added computational effort caused by the presence of anisotropy is relatively minor. Synthetic and field-data examples demonstrate that the isotropic Fowler DMO technique fails to generate an accurate zero-offset section and to obtain the zero-dip NMO velocity for nonelliptical VTI models. In contrast, this anisotropic algorithm allows one to find the values of the parameters V-nmo(0) and eta (sufficient to perform time migration as well) and to correct for the influence of transverse isotropy in the DMO processing. When combined with poststack F-K Stolt migration, this method represents a complete inversion-processing sequence capable of recovering the effective parameters of transversely isotropic media and producing migrated images for the best-fit homogeneous anisotropic model.