f 3D Dip moveout in a inhomogeneous earth

In a constant velocity earth, 3-D DMO corrects for midpoint dispersal by moving data in the vertical plane of the source-to-receiver axis. In an inhomogeneous earth, the exact DMO operator becomes a complex surface and data has to be moved in 3-D space. In this paper we introduce an efficient and accurate construction of the 3-D DMO operator in two steps: a constant velocity DMO followed by 3-D residual modeling or migration. This construction leads to a relatively efficient implementation of DMO in the space-time domain, and no 3-D ray tracing is required. We demonstrate that the residual operator is accurate for the case of a medium with a linear velocity increase with depth. Other effects, such as transverse isotropy (TI), can be incorporated into our 3-D DMO construction. We also show with field data examples that in some cases of weak TI, anisotropy may counteract the effect of a vertical velocity increase, effectively reducing the DMO operator to the familiar source-to-receiver ellipse. This offers an explanation of why in certain sedimentary regimes a 3-D constant-velocity DMO works as well or better than a V(z) DMO algorithm.