# Kees Wapenaar's research while affiliated with Delft University of Technology and other places

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## Publications (484)

By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and if...

By solving a Marchenko equation, Green's functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are to be collected at the top of the medium. So far, an exact solution could only be obtained if the medium obeys stringent monotonicity conditions and if all forw...

Least-squares reverse time migration (LSRTM) is a common imaging technique that geophysicists have been using to obtain high-resolution images. Nevertheless, the high computational cost shifted the focus of researchers to the target-oriented approach. In this approach, by limiting the computational grid to a relatively smaller region, the computati...

Seismic interferometry (SI) is a method that retrieves new seismic traces from the cross-correlation of existing traces, where one of the receivers acts as a virtual seismic source whose response is retrieved at other receivers. When using sources only at the surface, and so-called one-sided illumination of the receivers occurs, not only desired ph...

Geophysicists have widely used Least-squares reverse-time migration (LSRTM) to obtain high-resolution images of the subsurface. However, LSRTM needs an accurate velocity model similar to other migration methods. Otherwise, it suffers from depth estimation errors and out of focus images. Moreover, LSRTM is computationally expensive and it can suffer...

Geophysical monitoring of subsurface reservoirs relies on detecting small changes in the seismic response between a baseline and monitor study. However, internal multiples, related to the over- and underburden, can obstruct the view of the target response, hence complicating the time-lapse analysis. In order to retrieve a response that is free from...

A Green's function in an acoustic medium can be retrieved from reflection data by solving a multidimensional Marchenko equation. This procedure requires a-priori knowledge of the initial focusing function, which can be interpreted as the inverse of a transmitted wavefield as it would propagate through the medium, excluding (multiply) reflected wave...

A Green's function in an acoustic medium can be retrieved from reflection data by solving a multidimensional Marchenko equation. This procedure requires a-priori knowledge of the initial focusing function, which can be interpreted as the inverse of a transmitted wavefield as it would propagate through the medium, excluding (multiply) reflected wave...

Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions, and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, s...

The propagator matrix “propagates” a full wave field from one depth level to another, accounting for all propagation angles and evanescent waves. The Marchenko focusing function forms the nucleus of data-driven Marchenko redatuming and imaging schemes, accounting for internal multiples. These seemingly different concepts appear to be closely relate...

Classical acoustic wave-field representations consist of volume and boundary integrals, of which the integrands contain specific combinations of Green's functions, source distributions and wave fields. Using a unified matrix-vector wave equation for different wave phenomena, these representations can be reformulated in terms of Green's matrices, so...

The propagator matrix "propagates" a full wave field from one depth level to another, accounting for large propagation angles and evanescent waves. The Marchenko focusing function forms the nucleus of data-driven Marchenko redatuming and imaging schemes, accounting for internal multiples. These seemingly different concepts appear to be closely rela...

We implement the 3D Marchenko equations to retrieve responses to virtual sources inside the subsurface. For this, we require reflection data at the surface of the Earth that contain no free-surface multiples and are densely sampled in space. The required 3D reflection data volume is very large and solving the Marchenko equations requires a signific...

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 negle...

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. The...

We create virtual sources and receivers in a 3-D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at the Earth's surface, a macrovelocity model, and the Marchenko method. The homogeneous Green's function is Gre...

The Gel'fand-Levitan equation, the Gopinath-Sondhi equation, and the Marchenko equation are developed for one-dimensional inverse scattering problems. Recently, a version of the Marchenko equation based on wavefield decomposition has been introduced for focusing waves in multi dimensions. However, wavefield decomposition is a limitation when waves...

Correct handling of strong elastic, internal, multiples remains a challenge for seismic imaging. Methods aimed at eliminating them are currently limited by monotonicity violations, a lack of a-priori knowledge about mode conversions, or unavailability of multi-component sources and receivers for not only particle velocities but also the traction ve...

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 negle...

The Hessian matrix plays an important role in correct interpretation of the multiple scattered wave fields inside the FWI frame work. Due to the high computational costs, the computation of the Hessian matrix is not feasible. Consequently, FWI produces overburden related artifacts inside the target zone model, due to the lack of the exact Hessian m...

The Marchenko multiple elimination 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 similar to each other, but use different time-domain truncation operators. The Marchenko multi...

Suppression of surface-related and internal multiples is an outstanding challenge in seismic data processing. The former is particularly difficult in shallow water, whereas the latter is problematic for targets buried under complex, highly scattering overburdens. We propose a two-step, amplitude- and phase-preserving, inversion-based workflow, whic...

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 possibilit...

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- and Green’s functions. In discretized form, these integrals are represented by finite summations over the...

We create virtual sources and receivers in a 3D subsurface using the single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at the Earth's surface, a macro velocity model and the Marchenko method. The homogeneous Green's function is a Green's function supe...

With the Marchenko method, it is possible to retrieve the wave field inside a medium from its reflection response at the surface. To date, this method has predominantly been applied to naturally occurring materials. This study extends the Marchenko method for applications in layered metamaterials with, in the low-frequency limit, effective negative...

To quantitatively image fractures with high resolution, we develop an elastic least-squares migration (LSM) algorithm coupled with linear-slip theory, which accurately addresses seismic wave interaction with thin structures. We derive a linearized waveform inversion using the Born approximation to the boundary integral equation for scattered 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 possibilit...

The homogeneous Green's function is the difference between an impulse response and its time-reversal. According to existing representation theorems, the homogeneous Green's function associated with source-receiver pairs inside a medium can be computed from measurements at a boundary enclosing the medium. However, in many applications such as seismi...

The reflection response of strongly scattering media often contains complicated interferences between primaries and (internal) multiples, which can lead to imaging artefacts unless handled correctly. Internal multiples can be kinematically predicted, e.g. by the Jakubowicz method or by the inverse scattering series (ISS), as long as monotonicity, i...

With the Marchenko method it is possible to retrieve the wave field inside a medium from its reflection response at the surface. To date, this method has predominantly been applied to naturally occurring materials. In this paper we extend the Marchenko method for applications in metamaterials with, in the low-frequency limit, effective negative con...

Seismic images provided by reverse time migration can be contaminated by artefacts associated with the migration of multiples, which can corrupt seismic images producing both false positives and false negatives. Multiple prediction / primary synthesis methods are usually designed to operate on point source gathers, and can therefore be computationa...

In recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on 2D synthetic data and applied to 2D field data, but only little is known about their behaviour on 3D synthetic data and 3D field data. Particularly, it is not known whether Marchenko methods are...

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, i.e. by focusing energy at unphysical interfaces, and false negatives, i.e. by destructively interfering with primaries. Multiple prediction/primary synt...

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- and Green's functions. In discretized form, these integrals are represented by finite summations over the...

In recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on 2D synthetic data and applied to 2D field data, but only little is known about their behaviour on 3D synthetic data and 3D field data. Particularly, it is not known whether Marchenko methods are...

The Marchenko method can be applied on cross-sections of 3D data using a 2D algorithm, but only a full 3D implementation can properly retrieve all 3D effects present in the data. The 3D implementation of the iterative Marchenko method is in principle a straightforward extension of the 2D method, it only requires an additional surface integration di...

The Hessian matrix plays an important role in correct interpretation of the multiple scattered wave fields inside the FWI frame work. Due to the high computational costs, the computation of the Hessian matrix is not feasible. Consequently, FWI produces overburden related artifacts inside the target zone model, due to the lack of the exact Hessian m...

A geothermal well doublet, designed for two primary aims of research and commercial heat supply, is planned to be constructed on the campus of Delft University of Technology. The plans include a comprehensive research programme, including installation of a wide range of instruments alongside a comprehensive logging and coring programme and an exten...

The Marchenko method retrieves the responses to virtual sources in the subsurface, accounting for all orders of multiples. The method is based on two integral representations for focusing and Green's functions. In discretized form these integrals are represented by finite summations over the acquisition geometry. Consequently, the method requires i...

Since the introduction of the Marchenko method in geophysics, many variants have been developed. Using a compact unified notation, we review redatuming by multidimensional deconvolution and by double focusing, virtual seismology, double dereverberation and transmission-compensated Marchenko multiple elimination, and discuss the underlying assumptio...

Time-lapse seismic monitoring aims at resolving changes in a producing reservoir from changes in the reflection response. When the changes in the reservoir are very small, the changes in the seismic response can become too small to be reliably detected. In theory, multiple reflections can be used to improve the detectability of traveltime changes:...

We have seen many developments in Marchenko equation-based methods for internal multiple attenuation in the past years. Starting from a wave-equation based method that required a smooth velocity model, there are now Marchenko equation-based methods that do not require any model information or user-input. In principle, these methods accurately predi...

We consider reflection data that have been subsampled by 70% and use Point-Spread-Functions to reconstruct the original data. The subsampled, original and reconstructed reflection data are used to image the medium of interest with the Marchenko method. The image obtained using the subsampled data shows artifacts caused by internal multiples, which...

Acoustic inversion in one‐dimension gives impedance as a function of travel time. Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the other...

We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in opposite directions along the preferred axis. This decomposition is not unique. We discuss flux-normalised and f...

Marchenko imaging is based on integral representations for focusing functions and Green's functions. In practice the integrals are replaced by finite summations. This works well for regularly sampled data, but the quality of the results degrade in case of imperfect sampling. Here we introduce discrete representations that account for imperfect samp...

To enhance monitoring of the subsurface, virtual sources and receivers inside the subsurface can be created from seismic reflection data at the surface of the Earth using the Marchenko method. The response between these virtual sources and receivers can be obtained through the use of homogeneous Green's function retrieval. A homogeneous Green's fun...

Wavefield focusing can be achieved by Time-Reversal Mirrors, which involve in- and output signals that are infinite in time and waves propagating through the entire medium. Here, an alternative solution for wavefield focusing is presented. This solution is based on a new integral representation where in- and output signals are finite in time, and w...

The Marchenko method retrieves Green’s functions between the acquisition surface and any arbitrary point in the medium. The process generally involves solving an inversion starting with an initial focusing function, e.g., a direct-wave Green’s function from thedesired subsurface position, typically obtained using an approximate velocity model. We f...

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, i.e. by focusing energy at unphysical interfaces, and false negatives, i.e. by destructively interfering with primaries. A pletora of algorithms have been...

We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are t...

The wavefields resulting from the Time Reversal Mirroring have infinite support in time, which could be not ideal for various applications. Things are different in Finite Time Focusing, where wavefields are theoretically confined in time and space by the direct propagation path from the boundary to the focal point. As can be observed in these movie...

Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where multiple scattering is strong. Marchenko imaging has recently been introduced as a data-driven way to deal with internal multiple scattering. Given the increasing interest in non-reciprocal materials, both for acoustic and electromagnetic applicatio...

We compare three data-driven internal multiple reflection elimination schemes derived from 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 second scheme doe...

The elastodynamic Marchenko method removes overburden interactions obscuring the target information. This method either relies on separability of the so-called focusing and Green's functions or requires an accurate initial estimate of the focusing and Green's function overlap. Hitherto, F1- and G-+ have been assumed separable, whereas F1+ and (G--)...

Wavefield focusing is often achieved by time-reversal mirrors, where wavefields emitted by a source located at the focal point are evaluated at a closed boundary and sent back, after time-reversal, into the medium from that boundary. Mathematically, time-reversal mirrors are derived from closed-boundary integral representations of reciprocity theor...

We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in opposite directions along the preferred axis. This decomposition is not unique. We discuss flux-normalised and f...

Seismic interferometry allows one to turn a receiver into a so-called virtual source. Conventionally, simple cross correlations suffice to retrieve a virtual-source response. This approach, however, has limitations in case of irregularities of in the distribution of the illuminating sources (e.g., noise, earthquakes). Seismic interferometry by mult...

The earthquake seismology and seismic exploration communities have developed a variety of seismic imaging methods for passive- and active-source data. Despite the seemingly different approaches and underlying principles, many of those methods are based in some way or another on Green's theorem. The aim of this paper is to discuss a variety of imagi...