With the Marchenko method, it is possible to retrieve Green’s functions between virtual sources in subsurface and receivers at surface from reflection data focusing functions. A macro model of needed estimate first arrival; internal multiples are retrieved entirely data. The form input for redatuming by multidimensional deconvolution (MDD). redatumed response free related overburden. Alternatively, can be obtained applying a second function This process called double focusing. It more stable...

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 be kinematically predicted, for example by the Jakubowicz method or inverse series (ISS), as long monotonicity, that is, “correct” temporal event ordering, is obeyed. Alternatively, (conventional) Marchenko removes all overburden-related wavefield interactions formulating an...

Correct handling of strong elastic internal multiples remains a challenge for seismic imaging. Methods aimed at eliminating them are currently limited by monotonicity violations, lack a-priori knowledge about mode conversions, or unavailability multicomponent sources and receivers not only particle velocities but also the traction vector. Most these challenges vanish in acoustic media such that Marchenko-equation-based methods able, theory, to remove exactly (within certain...

Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into subsurface. We discuss that account for internal multiple reflections, in particular propagator matrices, transfer matrices Marchenko focusing functions. A matrix is a square `propagates' wave-field vector one depth level another. It accounts primaries multiples holds propagating evanescent waves. function focuses at designated point space zero time. functions are useful...

Marchenko equation-based methods promise data-driven, true-amplitude internal multiple elimination. The method is exact in 1-D acoustic media, however it needs to be expanded account for the presence of 2- and 3-D elastodynamic wave-field phenomena, such as compressional (P) shear (S) mode conversions, total reflections or evanescent waves. Mastering high waveform-fidelity this, could further advance amplitude vs offset analysis lead improved reservoir characterization. This method-expansion...

Summary Deposition processes result in an almost length-scale-independent layering, which gives rise to many (usually weak) internal multiples. In frequently (and strongly) scattering media these multiples can have a (very) strong collective effect and is complex interference pattern (one that typically characterized by specific frequencies) rather than stand-alone events. This contradictory event-based multiple estimation (IME) strategies (e.g. the Jakubowicz IME). cases such approaches do...

Standard Marchenko redatuming and imaging schemes neglect evanescent waves are based on the assumption that decomposition into downgoing upgoing is possible in subsurface. Recently we have shown propagator matrices, which circumvent these assumptions, can be expressed terms of focusing functions. In this paper generalize relation between matrix functions for a 3D inhomogeneous dissipative medium. Moreover, same type medium discuss transfer

Summary The elastodynamic Marchenko method removes overburden interactions obscuring the target information. This either relies on separability of so-called focusing and Green's functions or requires an accurate initial estimate function overlap. Hitherto, F1- G-+ have been assumed separable, whereas F1+ (G--)* share unavoidable overlap, which has considered understood but hard to predict without knowing model. However, velocity differences between P- S-waves cause so far unexplored...

Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where scattering is strong. Marchenko has recently been introduced as a data-driven way deal with internal Given the increasing interest non-reciprocal materials, both for acoustic and electromagnetic applications, modification method proposed such materials. A unified wave equation formulated exploiting similarity between phenomena. forms basis deriving reciprocity theorems that interrelate fields...

Summary The presence of evanescent modes and their impact on the Marchenko method has been until very recently a topic that received little attention. In this contribution we link concept transfer matrix to fields usually associated with method. Using formalism, introduce path reversal - generalization time for travelling waves, which also encompasses modes. We take first look at implications latter may have "standard" It appears scheme should perform well, as long one does not attempt...

SUMMARY Minimum-phase properties are well-understood for scalar functions where they can be used as physical constraint phase reconstruction. Existing applications of the latter in geophysics include, example reconstruction transmission from acoustic reflection data, or multiple elimination via augmented Marchenko method. We review minimum-phase conventional Kolmogorov relation, well a less-known factorization Motivated to solve practice-relevant problems beyond case, we investigate (1) and...

Summary Amplitude fidelity is critical for data-driven and wave equation-based methods. In particular, the more advanced methods are often (first) applied on (2-D) sail lines, due to a sparse cross-line sampling, high computational cost or both. Hence, acquired seismic data needs be correctly converted from 3-D 2-D. This particularly true Marchenko method, as it only method capable of suppressing internal multiple without need adaptive subtraction, but at correct global time-...

Summary The Marchenko method is capable to create virtual sources inside a medium that only accessible from an open-boundary. resulting data can be used retrieve images free of artefacts caused by internal multiples. Conventionally, the retrieves so-called focusing wavefield focuses recording surface point medium. Recently, it was suggested modify condition such new creates plane wave source medium, instead source. image entire in single step rather than imaging individual points on surface....

Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into subsurface. We discuss that account for internal multiple reflections, in particular propagator matrices, transfer matrices Marchenko focusing functions. A matrix is a square `propagates' wave-field vector one depth level another. It accounts primaries multiples holds propagating evanescent waves. function focuses at designated point space zero time. functions are useful...

Marchenko imaging allows retrieving images from single-sided reflection measurements without artefacts due to internal multiples. A key step in is the retrieval of so-called focusing function and a background model. The conventional obeys point condition, i.e. it focuses inside medium interest both space time. Based on this property one can retrieve up- downgoing Green’s functions that are associated with virtual source or receiver medium, which be used for imaging. Recently, new has been...

Given the increasing interest for non-reciprocal materials, we propose a novel acoustic imaging method layered media. The is modification of Marchenko method, which handles multiple scattering between layer interfaces in data-driven way. We start by reviewing basic equations wave propagation medium. Next, discuss Green's functions, focusing and their mutual relations, horizontally These relations form basis deriving modified retrieves field inside medium from reflection measurements at...

Summary Current seismic imaging methods require data that is free of multiple reflections, which why a range multiple-removal algorithms have been developed. However, state-of-the-art for internal removal are based on single event identification. They fail in the presence finely layered (sub-wavelength) media cause short-period since these cannot be resolved individually. We present method 2D and 3D as an extension recent 1D work, Marchenko theory. If we can separate medium into horizontally...

Summary Marchenko redatuming retrieves Green's functions inside an unknown medium, by solving a set of coupled equations, which are derived from under-determined system equation and two temporal truncations. To constrain the problem, assumptions made, hold reasonably well for acoustic, but not elastodynamic waves. First, early part inverse transmission field is needed can be estimated sufficiently-simple acoustic cases, remains hard to predict elastic media without detailed overburden...