Source-receiver Marchenko redatuming: Obtaining virtual receivers and virtual sources in the subsurface

Abstract

By solving the Marchenko equations, one can retrieve the Green’s function (Marchenko Green’s function) between a virtual receiver in the subsurface and points at the surface (no physical receiver is required at the virtual location). We extend the idea behind 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 it includes all primary, internal, and free-surface multiples. Similar to the Marchenko Green’s function, this virtual Green’s function requires the reflection response at the surface (single-sided illumination) and an estimate of the first-arrival traveltime from the virtual locations to the surface. These Green’s functions can be used to image the interfaces from above and below.