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.

Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where multiple scattering is strong. Marchenko imaging has recently been introduced as a data-driven way to deal with internal multiple scattering. Given the increasing interest in non-reciprocal materials, both for acoustic and electromagnetic applications, a modification to the Marchenko method is proposed for imaging such materials. A unified wave equation is formulated for non-reciprocal materials, exploiting the similarity between acoustic and electromagnetic wave phenomena. This unified wave equation forms the basis for deriving reciprocity theorems that interrelate wave fields in a non-reciprocal medium and its complementary version. Next, these theorems are reformulated for downgoing and upgoing wave fields. From these decomposed reciprocity theorems, representations of the Green's function inside the non-reciprocal medium are derived in terms of the reflection response at the surface and focusing functions inside the medium and its complementary version. These representations form the basis for deriving a modified version of the Marchenko method to retrieve the wave field inside a non-reciprocal medium and to form an image, free from artefacts related to multiple scattering. The proposed method is illustrated at the hand of the numerically modeled reflection response of a horizontally layered medium.

Current seismic imaging methods require data that is free of multiple reflections, which is why a range of multiple-removal algorithms have been developed. However, state-of-the-art algorithms for internal multiple removal are based on single event identification. They fail in the presence of finely layered (sub-wavelength) media which cause short-period internal multiple reflections, since these cannot be resolved individually. We present a method for seismic short-period internal multiple removal for 2D and 3D media as an extension of recent 1D work, based on the Marchenko theory. If we can separate the medium into a horizontally layered overburden and an arbitrary complex underburden we are able to remove the overburden-related effects of short-period (and long-period) internal multiples. We do not require an impedance model but achieve this with a smooth background velocity model, similar to what is used in other multiple removal algorithms. We give a 2D numerical example with a finely layered horizontal overburden and a laterally inhomogeneous underburden. Comparison of the image derived with our augmented Marchenko scheme with a conventional Marchenko image results in a considerable uplift. This is the first time that short-period internal multiples are removed correctly from 2D seismic data in a purely data-driven way.

The elastodynamic Marchenko method removes overburden interactions obscuring the target information. This method either relies on separability of the so-called focusing and Green's functions or requires an accurate initial estimate of the focusing and Green's function overlap. Hitherto, F1- and G-+ have been assumed separable, whereas F1+ and (G-)* share an unavoidable overlap, which has been considered understood but hard to predict without knowing the model. However, velocity differences between P- and S-waves cause so far unexplored fundamental challenges for elastodynamic Marchenko autofocusing. These challenges are analysed for horizontally-layered media. First, the F1-/G-+ separability assumption can be violated depending on the medium, the redatuming depth and the angle of incidence. Second, the initial estimate of the said unavoidable overlap can be even more complicated than originally thought, including some of the internal multiples. We propose a strategy where we trade-off this sophisticated initial estimate with a trivial one at the cost of a more restrictive F1-/G-+ separability assumption, or at the cost of introducing an overlap between F1- and G-+ instead. The proposed method finds the desired solutions convolved by an unknown matrix which we can hope to remove by exploiting energy conservation and minimum-phase properties of the focusing functions.