Migration error for transversely isotropic media

Most migration algorithms today are based on the assumption that the Earth is isotropic, an approximation that is often not valid and thus can lead to position errors on migrated images. Here, we compute curves of such position errors as a function of reflector dip for transversely isotropic (TI) media characterized by Thomsen's anisotropy parameters S and e. Depending on whether the migration velocity is derived from stacking velocity or from vertical rms velocity, we find quite contrary sensitivities of the error behavior to the values of 6 and e. Error-versus-dip behavior also depends in a complicated way on vertical velocity gradient and vertical time, as well as orientation of the symmetry axis. Moreover, error behavior is quite dependent on just how S and e vary with depth. In addition to presenting the error-versus-dip curves, we show migrations of synthetic data that exemplify the mispositioning that results from ignoring anisotropy.