The Marchenko method can, in principle, retrieve full-wavefield subsurface responses using only surface reflection data and relatively little knowledge of the subsurface properties. In practice, however, existing versions of the method impose of the use of smooth background models, together with simplifications on the input focusing functions, in order to enable the numerical solution of the Marchenko integral equations. These choices, while simplifying the implementation of the approach, also limit how well the method performs in retrieving focusing functions and redatumed fields in the case of highly complex media, such as subsalt. In this study, we propose an alternative scattering-based scheme, where we account for arbitrarily complex reference models (e.g., discontinuous velocity models with salt interfaces) by incorporating an additional Marchenko system for the background model. We then propose a new least-squares optimization approach for the scattered focusing and Green's functions, while honoring the auxiliary background-medium Marchenko system as a constraint. Using a complex subsalt example, we show that our S-Marchenko approach can make use of the wavefield complexity from a discontinuous background model, yielding accurate estimates of redatumed fields and overcoming the complex-media limitations of previous versions of the Marchenko method.


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