Migration error in 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. This study computes curves of such position error as a function of reflector dip for transversely isotropic (TI) media characterized by Thomsen's anisotropy parameters δ and ε. Depending on whether the migration velocity is derived from stacking velocity or vertical root-mean-square (rms) velocity, quite contrary sensitivities of the error behavior to the values of δ and ε are found. Likewise error-versus-dip behavior depends in a complicated way on vertical velocity gradient and vertical time, as well as orientation of the symmetry axis. Moreover, error behavior is dependent on just how δ and ε vary with depth. In addition to presenting such error curves, the paper shows migrations of synthetic data that exemplify the mispositioning that results from ignoring anisotropy for P-wave data. -from Authors