Decomposition of the Green's function using the Marchenko equation

The Marchenko equation can be used to retrieve the Green’s function at depth as a full function or decomposed into its upand downgoing parts. We show that the equation can be rewritten to create a decomposition scheme that can decompose a full wavefield, that was recorded at depth, into its up- and downgoing parts. We show that this can be done without a smooth velocity model that the Marchenko scheme requires and without any knowledge of the medium properties that traditional decomposition methods require. Instead we only need a the reflection response and a wavefield that has been recorded at thesurface due to a source at depth or (by using source-receiver reciprocity) that was measured down in a borehole due to a source at the surface. We also validate our results by comparing them to directly modeled up- and downgoing wavefields