Ray-based gridded tomography for tilted TI media

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 square cells, and the TTI parameters including 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 minimizes long-spread residual moveout in image gathers throughout the medium. Synthetic tests for a model with a “quasi-factorized” TTI syncline (i.e., ε and δ are constant inside the TTI layer) demonstrate that convergence toward the correct velocity model requires either strong smoothness constraints or additional information from walkaway VSP (vertical seismic profiling) traveltimes.