There is no doubt that replacing the constant-velocity dip moveout step by a variable-velocity dip moveout step improves the zero-offset section after stack. However, the final result of a standard processing flow is the post-stack migrated section. Thus, the idea of comparing the pre-stack migrated section to the post-stack migrated sections with and without the constant velocity assumption is natural. David Lumley provided the synthetic data example that appears in the next three figures. The synthetic model includes four diffractors at various depth and midpoint positions, two horizontal events, and a 45-degree dipping event, overlaid by a strong constant RMS-velocity gradient (). The processing flow involving a constant-velocity dip moveout step is displayed in Figure . The three deepest diffractors are unfocused whereas the shallow diffractor is focused but low-amplitude. The horizontal reflectors are well imaged but the dipping event has lower amplitude than expected though it is not mispositioned. As shown in Figure , the variable-velocity step corrects for these inaccuracies and yields a post-stack migrated section hardly differentiable from the pre-stack migration (Figure ).
The similarity between the pre-stack migration and the post-stack migration after depth-variable velocity dip moveout is not surprising because the two processing are equivalent when there is no lateral velocity variation. However, the clear improvement with respect the a standard processing makes the variable-velocity dip moveout a very useful tool.