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 , , and , and the tilt angle 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 dominated the inversion, and so it was weighted less than and in the parameter updates. Estimates of and were influenced if the error in was ; estimates of were also influenced if the error in was . 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 , , and 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.