Beyond Marchenko – Obtaining virtual receivers and virtual sources in the subsurface

By solving the Marchenko equations, the Green’s function can be retrieved between a virtual receiver in the subsurface to points at the surface (no physical receiver is required at the virtual location). We extend the idea of these equations to retrieve the Green’s function between any two points in the subsurface; i.e, between a virtual source and a virtual receiver (no physical source or physical receiver is required at either of these locations). This Green’s function is called the virtual Green’s function and includes all the primaries, internal and free-surface multiples. Similar to the Marchenko Green’s function, we require the reflection response at the surface (single-sided illumination) and an estimate of the first arrival travel time from the virtual location to the surface.