Linearized wave-equation migration velocity analysis by image warping

Seismic imaging produces images of contrasts in physical parameters in the subsurface, e.g., velocity or impedance. To build such images, a background model describing the wave kinematics in the earth is necessary. In practice, the structural image and background velocity model are unknown and have to be estimated from the acquired data. Migration velocity analysis deals with estimation of the background model in the framework of seismic migration and relies on two main elements: data redundancy and invariance of the structures with respect to different seismic experiments. Because all the experiments probe the same model, the reflectors must be invariant in suitable domains (e.g., shots or reflection angle); the semblance principle is the tool used to measure the invariance of a set of multiple images. We measure the similarity of the structural features between pairs of single-shot migrated images obtained from adjacent experiments. By using the estimated warping vector field between two migrated images, we construct an image perturbation which describes the difference in reflectivity observed by two shots. We derive an expression for the image perturbation that drives a migration velocity analysis procedure based on a linearization of the wave-equation with respect to the model parameters. Synthetic 2D examples show promising results in retrieving errors in the velocity model. This methodology can be directly applied to 3D.