The DMO operation is usually thought of as being velocity independent, then why residual DMO?
The DMO operator in isotropic homogeneous media has an elliptical shape. This ellipse shape along with the fact that the operator is considerably smaller than the one associated with migration is the reason why DMO implementations are fast and robust. Numerous techniques that benefit from the simple geometry of the DMO ellipse has been employed through the years to further enhance the efficiency of DMO operation. However, such a DMO, although efficient, will yield inaccurate results when the medium is $v(z)$, anisotropic, or both. This is where the concept of residual DMO steps in. Rather then apply a DMO that handles $v(z)$ or anisotropic media, why not apply the efficient isotropic homogeneous DMO and then use the residual operator to correct for any additional complexity in the medium. The residual operator, in most cases, should be even smaller than the DMO operator itself, and therfore its implementation should be effecient (may not be as effeciant as the ellipse DMO operator because of all the complexity involved in its shape, however it should be close enough). The residual operator has huge applications in velocity analysis.
Bellow are residual DMO operators:
First, for going from isotropic homogeneous (eta=0) to an anisotropic one (eta=0.2):
Second, for going from an isotropic homogeneous model to an isotropic $v(z)$ one:
Third, for going from an isotropic homogeneous model to a more complicated $v(z)$ one:
3-D ones are coming soon.