We have developed a common-reflection-point (CRP)-based kinematic migration velocity analysis for 2D P-wave reflection data to estimate the four transversely isotropic (TI) parameters VPo, δ, and ε, and the tilt angle ϕ of the symmetry axis in a TI medium. In each iteration, the tomographic parameter was updated alternately with prestack anisotropic ray-based migration. Iterations initially used layer stripping to reduce the number of degrees of freedom; after convergence was reached, a couple of more iterations over all parameters and all CRPs ensured global interlayer coupling and parameter interaction. The TI symmetry axis orientation was constrained to be locally perpendicular to the reflectors. The VPo dominated the inversion, and so it was weighted less than δ and ε in the parameter updates. Estimates of δ and ε were influenced if the error in ϕ was >5°; estimates of VPo were also influenced if the error in ϕ was >10°. Examples included data for a simple model with a homogeneous TI layer whose dips allowed recovery of all anisotropy parameters from noise-free data, and a more realistic model (the BP tilted transversely isotropic (TTI) model) for which only VPo, δ, and ϕ were recoverable. The adequacy of the traveltimes predicted by the inverted anisotropic models was tested by comparing migrated images and common image gathers, with those produced using the known velocity models.

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