Kl. Larner et Jk. Cohen, MIGRATION ERROR IN TRANSVERSELY ISOTROPIC MEDIA WITH LINEAR VELOCITY VARIATION IN-DEPTH, Geophysics, 58(10), 1993, pp. 1454-1467
Given the sensitivity of imaging accuracy to the velocity used in migr
ation, 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 an
d lateral position as a function of reflector dip for transversely iso
tropic 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 anisotro
pic 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 wave
lengths as dip passes beyond 90 degrees. These errors depend on reflec
tor depth and average velocity to the reflector only through their rat
io, 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 tho
se encountered when inhomogeneity is ignored in migrating data from is
otropic, inhomogeneous media.