Marchenko redatuming, imaging and multiple elimination, and their mutual relations

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With the Marchenko method it is possible to retrieve Green's functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusing functions. A macro model of the subsurface is needed to estimate the first arrival; the internal multiples are retrieved entirely from the reflection data. The retrieved Green's functions form the input for redatuming by multidimensional deconvolution (MDD). The redatumed reflection response is free of internal multiples related to the overburden. Alternatively, the redatumed response can be obtained by applying a second focusing function to the retrieved Green's functions. This process is called Marchenko redatuming by double focusing. It is more stable and better suited for an adaptive implementation than Marchenko redatuming by MDD, but it does not eliminate the multiples between the target and the overburden. An attractive efficient alternative is plane-wave Marchenko redatuming, which retrieves the responses to a limited number of plane-wave sources at the redatuming level. In all cases, an image of the subsurface can be obtained from the redatumed data, free of artefacts caused by internal multiples. Another class of Marchenko methods aims at eliminating the internal multiples from the reflection data, while keeping the sources and receivers at the surface. A specific characteristic of this form of multiple elimination is that it predicts and subtracts all orders of internal multiples with the correct amplitude, without needing a macro subsurface model. Like Marchenko redatuming, Marchenko multiple elimination can be implemented as an MDD process, a double dereverberation process, or an efficient plane-wave oriented process. We systematically discuss the different approaches to Marchenko redatuming, imaging and multiple elimination, using a common mathematical framework.