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. We have developed an alternative and realizable approach to obtain the response of a buried virtual receiver for sources at the surface. Our 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 macromodel of the velocity (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 present in the reflection response (previous work considered a response without free-surface multiples). We decompose the Marchenko equation into up- and downgoing fields and solve for these fields iteratively. The retrieved Green’s function not only includes primaries and internal multiples as do previous methods, but it also includes freesurface multiples. We use these up- and downgoing fields to obtain a 2D image of our area of interest, in this case, below a synclinal structure. @en

From acoustics to medical imaging and seismology, one strives to make inferences about the structure of complex media from acoustic wave observations. This study proposes a solution that is derived from the multidimensional Marchenko equation, to learn about the acoustic source distribution inside a volume, given a set of observations outside the volume. Traditionally, this problem has been solved by backpropagation of the recorded signals. However, to achieve accurate results through backpropagation, a detailed model of the medium should be known and observations should be collected along a boundary that completely encloses the volume of excitation. In practice, these requirements are often not fulfilled and artifacts can emerge, especially in the presence of strong contrasts in the medium. On the contrary, the proposed methodology can be applied with a single observation boundary only, without the need of a detailed model. In order to achieve this, additional multi-offset ultrasound reflection data must be acquired at the observation boundary. The methodology is illustrated with one-dimensional synthetics of a photoacoustic imaging experiment. A distribution of simultaneously acting sources is recovered in the presence of sharp density perturbations both below and above the embedded sources, which result in significant scattering that complicates the use of conventional methods. @en

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.@en