Incorporating free-surface multiples in Marchenko imaging

Imagine placing a receiver at any location in the Earth and recording the response at that location to sources on the surface. In such a world, we could place receivers around our reservoir to better image the reservoir and understand its properties. Realistically, this is not a feasible approach for understanding the subsurface. Here, we present an alternative and realizable approach to obtaining the response of a buried virtual receiver for sources at the surface. This method is capable of retrieving the Green’s function for a virtual point in the subsurface to the acquisition surface. In our case, a physical receiver is not required at the subsurface point; instead, we require the reflection measurements for sources and receivers at the surface of the Earth and a macro-model (no small-scale details of the model are necessary). We can interpret the retrieved Green’s function as the response to sources at the surface for a virtual receiver in the subsurface. We obtain this Green’s function by solving the Marchenko equation, an integral equation pertinent to inverse scattering problems. Our derivation of the Marchenko equation for the Green’s function retrieval takes into account the free-surface reflections. We decompose the Marchenko equation into upand down-going fields and solve for these fields iteratively. We use these upand down-going fields, which includes the free-surface multiples, to obtain a 2D image of our area of interest, in this case, below a synclinal structure. This imaging is called Marchenko imaging.