Inversion versus migration: A new perspective to an old discussion
Seismic imaging techniques can be subdivided into inversion and migration. The object functions for inversion and migration are, respectively, the medium contrast parameters and reflectivity. In this paper, the relationship between inversion and migration is approached by analyzing the underlying representations (the forward models). It appears that the “two‐way representation” (which underlies inversion) as well as the “one‐way representation” (which underlies migration) can both be expressed in terms of a volume integral over the appropriate object function. In their linearized form, these representations account for primaries only. In this case, the one‐way representation in terms of reflectivity is the most accurate of the two, which implies that proper migration is more accurate than linearized inversion. Internal multiples can be taken into account by the nonlinear representations. As an alternative, however, the “generalized primary representation” is introduced. In its explicit form, this one‐way representation is linear in the reflectivity (opposed to linearized). Nonlinear effects are implicitly accounted for by the generalized primary propagators. The generalized primary representation is a suitable basis for true amplitude migration, taking the angle‐dependent dispersive effects of fine layering into account.