Migration Velocity Analysis with Reflected and Transmitted Waves

Migration Velocity Analysis techniques are classically associated to reflected data for the determination of the background velocity model. Based on the notion of extended models, we propose to define common image gathers function of depth-offset through a minimization problem. Extended images are obtained as the first gradient of a misfit functional defined in the time data domain. Within this framework, it is possible to simultaneously handle both reflected and transmitted waves modelled under the Born approximation. We examine the shape of events in common image gathers, especially for direct and diving waves. The convex shape of the differential semblance objective function is still observed on simple synthetic cases.