Elastodynamic Marchenko Green's function retrieval from two-sided reflection and transmission data

Green’s functions in an unknown elastic layered medium can be retrieved from single-sided reflection data by solving a Marchenko equation. This methodology requires a priori knowledge of all forward-scattered (non-converted and converted) waveforms. Moreover, the medium should satisfy stringent monotonicity conditions, which are often not met in...

On the benefits of auxiliary transmission data for Marchenko-based Green’s function retrieval

Green’s functions in an unknown medium can be retrieved from single-sided reflection data by solving a multidimensional Marchenko equation. This methodology requires knowledge of the direct wavefield throughout the medium, which should include forward-scattered waveforms. In practice, the direct field is often computed in a smooth background...

A single-sided representation for the homogeneous Green's function, accounting for all multiples

Marchenko imaging is a novel imaging technique that is capable to retrieve images from single-sided reflection measurements free of artefacts related to internal multiples (e.g. Behura et al., 2014; Broggini et al., 2012). An essential ingredient of Marchenko imaging is the so-called focusing function which can<br/>be retrieved from reflection...

Artefact-Free Imaging by a Revised Marchenko Scheme

A revised Marchenko scheme that avoids the need to compute the Green’s function is presented for artefact-free image of the subsurface with single-sided reflection response as input. The initial downgoing Green’s function which can be modelled from a macro model is needed for solving the revised Marchenko equations instead of its inverse. The...

Why multiples do not contribute to deconvolution imaging

The question whether multiples are signal or noise is subject of ongoing debate. In this paper we consider correlation and deconvolution imaging methods and analyse to what extent multiples contribute to the image in these methods. Our starting point is the assumption that at a specific depth level the full downgoing and upgoing fields (both...

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...

Electromagnetic Marchenko imaging in 1D for dissipative media

We present a one-dimensional lossless scheme to compute an image of a dissipative medium from two single-sided reflection responses. One reflection response is measured at or above the top reflector of a dissipative medium and the other reflection response is computed as if measured at or above the top reflector of a medium with negative...

Inversion of the multidimensional marchenko equation

Focusing functions are defined as wavefields that focus at a specified location in a heterogeneous subsurface. These functions can be directly related to Green's functions and hence they can be used for seismic imaging of complete wavefields, including not only primary reflections but all orders of internal multiples. Recently, it has been shown...

Autofocusing imaging: Imaging with primaries, internal multiples and free-surface multiples

Recent work on autofocusing with the Marchenko equation has shown how the Green's function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green's function from the location of the virtual source to the surface. The Green's function is retrieved using only the reflection...

Marchenko imaging below an overburden with random scatterers

Marchenko imaging is a new way to deal with internal multiple scattering in migration. It has been designed for layered media with smooth interfaces. Here we analyze the performance of the Marchenko scheme for a medium with many point scatterers. Although the conditions for Marchenko imaging are violated, we observe from a numerical experiment...

Data-driven green's function retrieval from reflection data: Theory and example

Recently we introduced a new approach for retrieving the Green's response to a virtual source in the subsurface from reflection data at the surface. Unlike in seismic interferometry, no receiver is needed at the position of the virtual source. Here we present the theory behind this new method. First we introduce the Green's function G and a so...