Design, implementation and application of the Marchenko plane-wave algorithm

The Marchenko algorithm can suppress the disturbing effects of internal multiples that are present in seismic reflection data. To achieve this, a set of coupled equations with four unknowns is solved. These coupled equations are separated into a set of two equations with two unknowns using a time window. The two unknown focusing functions can...

Implementation of the Marchenko multiple elimination algorithm

The Marchenko multiple elimination (MME) and transmission compensation schemes retrieve primary reflections in the two-way traveltime domain without model information or using adaptive subtraction. Both schemes are derived from projected Marchenko equations and are similar to each other, but they use different time-domain truncation operators...

Marchenko redatuming, imaging and multiple elimination, and their mutual relations

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....

Data-driven retrieval of primary plane-wave responses

Seismic images provided by reverse time migration can be contaminated by artefacts associated with the migration of multiples. Multiples can corrupt seismic images, producing both false positives, that is by focusing energy at unphysical interfaces, and false negatives, that is by destructively interfering with primaries. Multiple prediction...

Transmission compensated primary reflection retrieval in the data domain and consequences for imaging

We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require...

Data-driven internal multiple elimination and its consequences for imaging: A comparison of strategies

We have compared three data-driven internal multiple reflection elimination schemes derived from the Marchenko equations and inverse scattering series (ISS). The two schemes derived from Marchenko equations are similar but use different truncation operators. The first scheme creates a new data set without internal multiple reflections. The...

Marchenko equations for acoustic Green's function retrieval and imaging in dissipative media

We present a scheme for Marchenko imaging in a dissipative heterogeneous medium. The scheme requires measured reflection and transmission data at two sides of the dissipative medium. The effectual medium is the same as the dissipative medium, but with negative dissipation. We show how the measured double-sided data can be combined to obtain the...

From closed-boundary to single-sided homogeneous Green's function representations

The homogeneous Green’s function (i.e., the Green’s function and its time-reversed counterpart) plays an important role in optical, acoustic and seismic holography, in inverse scattering methods, in the field of time-reversal acoustics, in reversetime migration and in seismic interferometry. Starting with the classical closed-boundary...

On the focusing conditions in time-reversed acoustics, seismic interferometry, and Marchenko imaging

Despite the close links between the fields of time-reversed acoustics, seismic interferometry and Marchenko imaging, a number of subtle differences exist. This paper reviews the various focusing conditions of these methods, the causality/acausality aspects of the corresponding focusing wavefields, and the requirements with respect to...

Internal multiple suppression by adaptive Marchenko redatuming

Recently, a novel iterative scheme was proposed to retrieve Green's functions in an unknown medium from its single-sided reflection response and an estimate of the propagation velocity. In Marchenko imaging, these Green's functions are used for seismic imaging with complete wavefields, including internal multiple reflections. In this way, common...

Marchenko imaging

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic...

Green's function retrieval with Marchenko equations: A sensitivity analysis

Recent research showed that the Marchenko equation can be used to construct the Green’s function for a virtual source position in the subsurface. The method requires the reflection response at the surface and an estimate of the direct arrival of the wavefield, traveling from the virtual source location to the acquisition surface. In this paper,...

Three-dimensional Marchenko equation for Green's function retrieval “beyond seismic interferometry”

In recent work we showed with heuristic arguments that the Green's response to a virtual source in the subsurface can be obtained from reflection data at the surface. This method is called “Green's function retrieval beyond seismic interferometry”, because, unlike in seismic interferometry, no receiver is needed at the position of the virtual...