Gerard T. Schuster
I start with the governing equation of a migration image for an arbitrary migration velocity. Perturbing this equation with respect to the migration velocity leads to a formula that generalizes the velocity continuation concept for any migration velocity. Further manipulation leads to an expression for a Frechet derivative of the migration image with respect to a perturbation in the velocity. This means that the velocity continuation procedure is now extended to lateral velocity variations and can use gradient optimization methods to search for the optimal migration velocity. The simple formulae derived in this report might give us fresh tools f or addressing other problems in exploration seismology.