Synthesising singly-scattered waves (primaries) from multiply-scattered data

One-dimensional inverse scattering problems are governed by the Marchenko equation which relates scattered wavefields to perturbations in the medium of propagation.The same equation also governs the theory of focusing - the ability to craft an incident wavefield which focuses at a specific time and place in the medium.Focusing wavefields may be obtained by solving the Marchenko equation using a method that requires only a reflection response measured at one side of the medium, and an estimate of the traveltime of the wave to the focusing location.We show how these focusing wavefields can be used to estimate new reflection responses which only involve primaries in two different ways.We demonstrate our method in a 1D medium with 10 discrete velocity contrasts.The resulting primaries-only wavefields produce excellent images of the medium using standard reverse-time migration.