Reflection tomography in the migrated domain can help reconstruct heterogeneous, anisotropic velocity fields needed for accurate depth imaging of complex geologic structures. The presence of anisotropy, however, increases the uncertainty in velocity analysis and typically requires a priori constraints on the model parameters. Here, we develop a 2D P-wave tomographic algorithm for heterogeneous transversely isotropic media with a tilted symmetry axis (TTI) and investigate the conditions necessary for stable estimation of the symmetry-direction velocity VP0 and the anisotropy parameters ε and δ. The model is divided into rectangular cells, and the parameters VP0, ε, δ, and the tilt ν of the symmetry axis are defined at the grid points. To increase the stability of the inversion, the symmetry axis is set orthogonal to the imaged reflectors, with the tilt interpolated inside each layer. The iterative migration velocity analysis involves efficient linearized parameter updating designed to minimize the residual moveout in image gathers for all available reflection events. The moveout equation in the depth-migrated domain includes a nonhyperbolic term that describes long-offset data, which are particularly sensitive to ε. Synthetic tests for models with a “quasi-factorized” TTI syncline (i.e., ε and δ are constant inside the anisotropic layer) and a TTI thrust sheet demonstrate that stable parameter estimation requires either strong smoothness constraints or additional information from walkaway VSP (vertical seismic profiling) traveltimes. If the model is quasi-factorized with a linear spatial variation of VP0, it may be possible to obtain the interval TTI parameters just from long-spread reflection data.

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