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. Here, we compute 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, we find quite contrary sensitivities of the error behavior to the values of δ and ε. 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, we show migrations of synthetic data that exemplify the mispositioning that results from ignoring anisotropy for P‐wave data. When migration is done using velocities derived from stacking velocity and when medium velocity increases with depth at rates typically encountered in practice, δ alone is sufficient to describe the position error. This is fortunate since the value of δ, unlike ε, can be obtained from combined vertical seismic profile (VSP) and surface seismic data. In contrast, when the migration velocity is obtained from the vertical rms velocity, the position errors depend strongly on ε, suggesting the importance of having an accurate estimate of ε when using an anisotropic migration algorithm.