Inversion velocity analysis in the subsurface-offset domain

Optimization-based migration velocity analysis updates long-wavelength velocity information by minimizing an objective function that measures the violation of a focusing criterion, applied to an image volume. Differential semblance optimization forms a smooth objective function in velocity and data, regardless of the data-frequency content. Depending on how the image volume is formed, however, the objective function may not be minimized at a kinematically correct velocity, a phenomenon characterized in the literature (somewhat inaccurately) as "gradient artifacts." We find that the root of this pathology is imperfect image volume formation resulting from reverse time migration (RTM), and that the use of linearized inversion (least-squares migration) more or less eliminates it. A synthetic Marmousi example and a 2D real data example are used to demonstrate that an approximate inverse operator, a little more expensive than RTM, leads to recovery of a kinematically correct velocity.