Tilted transversely isotropic (TTI) formations cause serious imaging distortions in active tectonic areas (e.g., fold-and-thrust belts) and in subsalt exploration. Here, we introduce a methodology for P-wave prestack depth imaging in TTI media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis (MVA), the model is divided into blocks with constant values of the anisotropy parameters ǫ and δ and linearly varying symmetry-direction velocity V P 0 controlled by the vertical (k z) and lateral (k x) gradients. Since estimation of tilt from P-wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity V P 0 is either known at the top of each block or remains continuous in the vertical direction. The MVA algorithm estimates the velocity gradients k z and k x and the anisotropy parameters ǫ and δ in the layer-stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized VTI media. Synthetic tests for several TTI models typical in exploration (a syncline, uptilted shale layers near a salt dome, and a bending shale layer) confirm that if the symmetry-axis direction is fixed, the parameters k z , k x , ǫ, and δ can be resolved from reflection data. It should be emphasized that estimation of ǫ (with known V P 0) in TTI media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of VTI processing algorithms to data from TTI media may lead to significant image distortions and errors in parameter estimation, even when tilt is moderate (e.g., 20-30 •). The ability of our MVA algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.

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