Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

Many seismic imaging methods use wavefield extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wavefield extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a...

Target-oriented least-squares reverse-time migration using Marchenko double-focusing: reducing the artefacts caused by overburden multiples

Geophysicists have widely used least-squares reverse-time migration (LSRTM) to obtain high-resolution images of the subsurface. However, LSRTM is computationally expensive and it can suffer from multiple reflections. Recently, a target-oriented approach to LSRTM has been proposed, which focuses the wavefield above the target of interest....

Green’s function representations for Marchenko imaging without up/down decomposition

Marchenko methods are based on integral representations which express Green’s functions for virtual sources and/or receivers in the subsurface in terms of the reflection response at the surface. An underlying assumption is that inside the medium the wave field can be decomposed into downgoing and upgoing waves and that evanescent waves can be...

Adaptation of the iterative Marchenko scheme for imperfectly sampled data

The Marchenko method retrieves the responses to virtual sources in the Earth's subsurface from reflection data at the surface, accounting for all orders of multiple reflections. The method is based on two integral representations for focusing- A nd Green's functions. In discretized form, these integrals are represented by finite summations...

Automated seismic acquisition geometry design for optimized illumination at the target: a linearized approach

In seismic exploration methods, imperfect spatial sampling at the surface causes a lack of illumination at the target in the subsurface. The hampered image quality at the target area of interest causes uncertainties in reservoir monitoring and production, which can have a substantial economic impact. Especially in the case of a complex...

Seismic inversion of soil damping and stiffness using multichannel analysis of surface wave measurements in the marine environment

Determination of soil material damping is known to be difficult and uncertain, especially in the offshore environment. Using an advanced inversion methodology based on multichannel spectral analysis, Scholte and Love wave measurements are used to characterize subsea soil from a North Sea site. After normalization, a determinant-based objective...

Marchenko multiple elimination of a laboratory example

The Marchenko multiple elimination (MME) scheme is derived from the coupled Marchenko equations. It is proposed for filtering primary reflections with two-way traveltime from the measured acoustic data. The measured acoustic reflection data are used as its own filter and no model information or adaptive subtraction is required to apply the...

A fast algorithm for multiple elimination and transmission compensation in primary reflections

The transmission compensated primary reflections can be obtained from the single-sided acoustic reflection response in the two-way traveltime domain. This is achieved by eliminating free-surface and internal multiple reflections and compensating for transmission losses in primary reflections without model information. The substantial...

The Marchenko method for evanescent waves

With the Marchenko method, Green’s functions in the subsurface can be retrieved from seismic reflection data at the surface. State-of-the-art Marchenko methods work well for propagating waves but break down for evanescent waves. This paper discusses a first step towards extending the Marchenko method for evanescent waves and analyses its...

Virtual plane-wave imaging via Marchenko redatuming

Marchenko redatuming is a novel scheme used to retrieve up- and downgoing Green's functions in an unknown medium.Marchenko equations are based on reciprocity theorems and are derived on the assumption of the existence of functions exhibiting space-time focusing properties once injected in the subsurface. In contrast to interferometry but...

Velocity analysis of simultaneous-source data using high-resolution semblance: Coping with the strong noise

Direct imaging of simultaneous-source (or blended) data, without the need of deblending, requires a precise subsurface velocity model. In this paper, we focus on the velocity analysis of simultaneous-source data using the normal moveout-based velocity picking approach.We demonstrate that it is possible to obtain a precise velocity model directly...

A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a...

On Green’s function retrieval by iterative substitution of the coupled Marchenko equations

Iterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing...

On the Marchenko equation for multicomponent single-sided reflection data

Recent work on the Marchenko equation has shown that the scalar 3-D Green’s function for a virtual source in the subsurface can be retrieved from the single-sided reflection response at the surface and an estimate of the direct arrival. Here, we discuss the first steps towards extending this result to multicomponent data. After introducing a...

Monitoring changes in velocity and Q using non-physical arrivals in seismic interferometry

Application of seismic interferometry to records from receivers at the Earth’s surface from sources in wells retrieves the reflection response measured at the receivers as if from virtual sources located also at the surface. When the wavefields experience intrinsic losses during propagation, non-physical arrivals (ghosts) would appear in the...

Interferometric redatuming by sparse inversion

Assuming that transmission responses are known between the surface and a particular depth level in the subsurface, seismic sources can be effectively mapped to this level by a process called interferometric redatuming. After redatuming, the obtained wavefields can be used for imaging below this particular depth level. Interferometric redatuming...

Data matching for free-surface multiple attenuation by multidimensional deconvolution

A common strategy for surface-related multiple elimination of seismic data is to predict multiples by a convolutional model and subtract these adaptively from the input gathers. Problems can be posed by interfering multiples and primaries. Removing multiples by multidimensional deconvolution (MDD) (inversion) does not suffer from these problems....