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 the artifacts 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 have systematically examined the different approaches to Marchenko redatuming, imaging, and multiple elimination using a common mathematical framework.

中文翻译：

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马尔琴科重定、成像和多重消除及其相互关系

使用 Marchenko 方法，可以从地表反射数据和聚焦函数中检索地表下虚拟源和地表接收器之间的格林函数。需要地下的宏观模型来估计初到；内部倍数完全从反射数据中检索。检索到的格林函数通过多维反卷积 (MDD) 形成重新定标的输入。重新校准的反射响应没有与覆盖层相关的内部多次波。或者，可以通过将第二个聚焦函数应用于检索到的格林函数来获得重新校准的响应。该过程称为通过双聚焦进行的马尔琴科重定。它比 MDD 的 Marchenko redatuming 更稳定，更适合自适应实现，但它并没有消除目标和覆盖层之间的倍数。一个有吸引力的有效替代方法是平面波 Marchenko 重定点，它在重定点级别检索对有限数量的平面波源的响应。在所有情况下，都可以从重定基准数据中获得地下图像，而没有内部多次波造成的伪影。另一类马尔琴科方法旨在消除反射数据中的内部多次波，同时将源和接收器保持在表面。这种多次消去形式的一个具体特征是它以正确的幅度预测和减去内部多次波的所有阶数，而无需宏观地下模型。和 Marchenko redatuming 一样，Marchenko 多重消除可以作为一个 MDD 过程来实现，双去混响过程，或高效的平面波导向过程。我们使用通用数学框架系统地研究了马尔琴科重定标、成像和多重消除的不同方法。