The reflection response of strongly scattering media often contains complicated interferences between primaries and (internal) multiples, which can lead to imaging artifacts unless handled correctly. Internal multiples can be kinematically predicted, for example by the Jakubowicz method or by the inverse scattering series (ISS), as long as monotonicity, that is, "correct"temporal event ordering, is obeyed. Alternatively, the (conventional) Marchenko method removes all overburden-related wavefield interactions by formulating an inverse problem that can be solved if the Green's and the so-called focusing functions are separable in the time domain, except for an overlap that must be predicted. For acoustic waves, the assumptions of the aforementioned methods are often satisfied within the recording regimes used for seismic imaging. However, elastic media support wave propagation via coupled modes that travel with distinct velocities. Compared to the acoustic case, not only does the multiple issue become significantly more severe, but also violation of monotonicity becomes much more likely. By quantifying the assumptions of the conventional Marchenko method and the ISS, unexpected similarities as well as differences between the requirements of the two methods come to light. Our analysis demonstrates that the conventional Marchenko method relies on a weaker form of monotonicity. However, this advantage must be compensated by providing more prior information, which in the elastic case is an outstanding challenge. Rewriting, or remixing, the conventional Marchenko scheme removes the need for prior information but leads to a stricter monotonicity condition, which is now almost as strict as for the ISS. Finally, we introduce two strategies on how the remixed Marchenko solutions can be used for imperfect, but achievable, demultiple purposes.

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Marchenko methods aim to remove all overburden-related internal multiples. The acoustic and elastodynamic formulations observe identical equations, but different physics. The elastodynamic case highlights that the Marchenko method only handles overburden-generated reflections, i.e. forward-scattered transmitted waves (and so-called fast multiples) remain in the data. Moreover, to constrain an underdetermined problem, the Marchenko method makes two assumptions that are reasonable for acoustic, but not for elastodynamic waves. Firstly, the scheme requires an initial guess that can be realistically estimated for sufficiently-simple acoustic cases, but remains unpredictable for elastic media without detailed overburden knowledge. Secondly, the scheme assumes temporal separability of upgoing focusing and Green’s functions, which holds for many acoustic media but easily fails in presence of elastic effects. The latter limitation is nearly-identical to the monotonicity requirement of the inverse scattering series, indicating that this limitation may be due to the underlying physics and not algorithm dependent. Provided that monotonicity holds, the aforementioned initial estimate can be retrieved by augmenting the Marchenko method with energy conservation and a minimum-phase condition. However, the augmentation relies on the availability of an elastic minimum-phase reconstruction method, which is currently under investigation. Finally, we discuss a geological setting where an acoustic approximation suffices.@en