Migration error in transversely isotropic media with linear velocity variation in depth

Given the sensitivity of imaging accuracy to the velocity used in migration, migration founded (as in practice) on the erroneous assumption that a medium is isotropic can be expected to be inaccurate for steep reflectors. Here, we estimate errors in interpreted reflection time and lateral position as a function of reflector dip for transversely isotropic models in which the axis of symmetry is vertical and the medium velocity varies linearly with depth. We limit consideration to media in which ratios of the various elastic moduli are independent of depth. Tests with reflector dips up to 120 degrees on a variety of anisotropic media show errors that are tens of wavelengths for dips beyond 90 degrees when the medium (unrealistically) is homogeneous. For a given anisotropy, the errors are smaller for inhomogeneous media; the larger the velocity gradient, the smaller the errors. For gradients that are representative of the subsurface, lateral‐position errors tend to be minor for dips less than about 60 degrees, growing to two to five wavelengths as dip passes beyond 90 degrees. These errors depend on reflector depth and average velocity to the reflector only through their ratio, i.e., migrated reflection time. Migration error, which is found to be unrelated to the ratio of horizontal to vertical velocity, is such that reflections with later migrated reflection times tend to be more severely overmigrated than are those with earlier times. Over a large range of dips, migration errors that arise when anisotropy is ignored but inhomogeneity is honored tend to be considerably smaller than those encountered when inhomogeneity is ignored in migrating data from isotropic, inhomogeneous media.