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...

Marchenko wavefield redatuming, imaging conditions, and the effect of model errors

Recently, a novel method to redatum the wavefield in the sub-surface from a reflection response measured at the surface has gained interest for imaging primaries in the presence of strong internal multiples. A prerequisite for the algorithm is an accurate and correct estimate of the direct-wave Green's function. However, usually we use an...

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

Recent work on retrieving the Green’s function with the Marchenko equation shows how these functions 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...

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...

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...

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,...