The main difficulty in extending seismic processing to anisotropic media is the recovery of anisotropic velocity fields from surface reflection data. We suggest carrying out velocity analysis for transversely isotropic (TI) media by inverting the dependence of P-wave moveout velocities on the ray parameter. The inversion technique is based on the exact analytic equation for the normal-moveout (NMO) velocity for dipping reflectors in anisotropic media.We show that P-wave NMO velocity for dipping reflectors in homogeneous TI media with a vertical symmetry axis depends just on the zero-dip value V nmo (0) and a new effective parameter eta that reduces to the difference between Thomsen parameters epsilon and delta in the limit of weak anisotropy. Our inversion procedure makes it possible to obtain eta and reconstruct the NMO velocity as a function of ray parameter using moveout velocities for two different dips. Moreover, V nmo (0) and eta determine not only the NMO velocity, but also long-spread (nonhyperbolic) P-wave moveout for horizontal reflectors and the time-migration impulse response. This means that inversion of dip-moveout information allows one to perform all time-processing steps in TI media using only surface P-wave data. For elliptical anisotropy (epsilon = delta ), isotropic time-processing methods remain entirely valid. We show the performance of our velocity-analysis method not only on synthetic, but also on field data from offshore Africa.Accurate time-to-depth conversion, however, requires that the vertical velocity V P0 be resolved independently. Unfortunately, it cannot be done using P-wave surface moveout data alone, no matter how many dips are available. In some cases V P0 is known (e.g., from check shots or well logs); then the anisotropy parameters epsilon and delta can be found by inverting two P-wave NMO velocities corresponding to a horizontal and a dipping reflector. If no well information is available, all three parameters (V P0 , epsilon , and delta ) can be obtained by combining our inversion results with shear-wave information, such as the P-SV or SV-SV wave NMO velocities for a horizontal reflector.Generalization of the single-layer NMO equation to layered anisotropic media with a dipping reflector provides a basis for extending anisotropic velocity analysis to vertically inhomogeneous media. We demonstrate how the influence of a stratified anisotropic overburden on moveout velocity can be stripped through a Dix-type differentiation procedure.

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