Seismic reflector imaging using internal multiples with Marchenko-type equations

We present an imaging method that creates a map of reflection coefficients in correct one-way time with no contamination from internal multiples using purely a filtering approach. The filter is computed from the measured reflection response and does not require a background model. We demonstrate that the filter is a focusing wavefield that focuses inside a layered medium and removes all internal multiples between the surface and the focus depth. The reflection response and the focusing wavefield can then be used for retrieving virtual vertical seismic profile data, thereby redatuming the source to the focus depth. Deconvolving the upgoing by the downgoing vertical seismic profile data redatums the receiver to the focus depth and gives the desired image. We then show that, for oblique angles of incidence in horizontally layered media, the image of the same quality as for 1D waves can be constructed. This step can be followed by a linear operation to determine velocity and density as a function of depth. Numerical simulations show the method can handle finite frequency bandwidth data and the effect of tunneling through thin layers.