arXiv subjects

Kees Wapenaar

Publications and source records attributed to Kees Wapenaar.

At least 19 recordsLinked to original sources

arXiv2026

On the relation between time-reversed acoustics and Green's function retrieval in space-variant and in time-variant materials

The methods of time-reversed acoustics and Green's function retrieval are traditionally deployed for classical inhomogeneous, time-invariant materials. The mutual relation between these methods is well-established. Recently, similar methods have been proposed for homogeneous, time-variant materials. Here we investigate their mutual relation and their relation with the corresponding methods in classical materials. For this analysis we make use of the fact that the wave equations for both classes of material are similar, with the roles of time and space interchanged. However, the principle of causality holds for both classes of material, hence, here the roles of time and space are not interchanged. We find that: (1) whereas classical time-reversed acoustics involves emission of a time-reversed single-component wave field from a (ideally closed) boundary into the inhomogeneous material, its idealized counterpart involves emission of a sign-reversed two-component wave field, recorded in a time-reversed material, from a single time instant into the actual time-variant material; (2) whereas classical Green's function retrieval involves temporal crosscorrelation of wave fields at two space locations in response to single-component sources on a (ideally closed) boundary, its counterpart involves spatial crosscorrelation of wave fields at two time instants in response to two-component sources at a single time instant.

physics.app-ph↗

arXiv2025

Representations for multidimensional down-down deconvolution of ocean-bottom seismic data: theory and practical implications

Multidimensional up-down deconvolution effectively eliminates surface-related multiples from ocean-bottom seismic data. Recently, several down-down deconvolution methods have been introduced as attractive alternatives. Whereas multidimensional up-down deconvolution fully accounts for lateral variations of the medium parameters, the underlying theory of some of the down-down deconvolution methods is essentially based on the assumption that the medium is horizontally layered. Using reciprocity theory, this assumption is circumvented. This leads to representations for either receiver-side or source-side multidimensional down-down deconvolution. Compared with multidimensional up-down deconvolution, receiver-side down-down deconvolution only utilizes the downgoing part of the wavefield that better samples the shallow subsurface, but it is not entirely data-driven. Source-side down-down deconvolution benefits from the better sampled source array, but in the presence of sparsely sampled receivers it requires solving an underdetermined system of linear equations.

physics.geo-ph↗

arXiv2025

Reciprocity and representation theorems for rotational seismology

Recently, there has been an increasing interest in employing rotational motion measurements for seismic source inversion, structural imaging and ambient noise analysis. We derive reciprocity and representation theorems for rotational motion. The representations express the rotational motion inside an inhomogeneous anisotropic earth in terms of translational and rotational motion at the surface. The theorems contribute to the theoretical basis for rotational seismology methodology, such as determining the moment tensor of earthquake sources.

physics.geo-ph↗

arXiv2025

Multiple reflections on Huygens' principle

According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the waves emitted by the secondary sources are represented by Green's functions. In many present-day applications of Huygens' principle, these Green's functions are replaced by their time-reversed versions, thus forming a basis for backpropagation, imaging, inversion, seismic interferometry, etc. However, when the input wave field is available only on a single open boundary, this approach has its limitations. In particular, it does not properly account for multiply reflected waves. This is remedied by a modified form of Huygens' principle, in which the Green's functions are replaced by focusing functions. The modified Huygens' principle forms a basis for imaging, inverse scattering, monitoring of induced sources, etc., thereby properly taking multiply reflected waves into account.

physics.geo-ph↗

arXiv2025

Recursive Interferometric Surface-wave Suppression For Improved Reflection Imaging

High-resolution seismic reflections are essential for imaging and monitoring applications. In seismic land surveys using sources and receivers at the surface, surface waves often dominate, masking the reflections. In this study, we demonstrate the efficacy of a two-step procedure to suppress surface waves in an active-source reflection seismic dataset. First, we apply seismic interferometry (SI) by cross-correlation, turning receivers into virtual sources to estimate the dominant surface waves. Then, we perform adaptive subtraction to minimise the difference between the surface waves in the original data and the result of SI. We propose a new approach where the initial suppression results are used for further iterations, followed by adaptive subtraction. This technique aims to enhance the efficacy of data-driven surface-wave suppression through an iterative process. We use a 2D seismic reflection dataset from Scheemda, situated in the Groningen province of the Netherlands, to illustrate the technique's efficiency. A comparison between the data after recursive interferometric surface-wave suppression and the original data across time and frequency-wavenumber domains shows significant suppression of the surface waves, enhancing visualization of the reflections for following subsurface imaging and monitoring studies.

physics.geo-ph↗

arXiv2024

Application of Marchenko-based isolation to a land S-wave seismic dataset

The overburden structures often can distort the responses of the target region in seismic data, especially in land datasets. Ideally, all effects of the overburden and underburden structures should be removed, leaving only the responses of the target region. This can be achieved using the Marchenko method. The Marchenko method is capable of estimating Green's functions between the surface of the Earth and arbitrary locations in the subsurface. These Green's functions can then be used to redatum wavefields to a level in the subsurface. As a result, the Marchenko method enables the isolation of the response of a specific layer or package of layers, free from the influence of the overburden and underburden. In this study, we apply the Marchenko-based isolation technique to land S-wave seismic data acquired in the Groningen province, the Netherlands. We apply the technique for combined removal of the overburden and underburden, which leaves the isolated response of the target region which is selected between 30 m and 270 m depth. Our results indicate that this approach enhances the resolution of reflection data. These enhanced reflections can be utilised for imaging and monitoring applications.

physics.geo-ph↗

arXiv2024

Green's functions, propagation invariants, reciprocity theorems, wave-field representations and propagator matrices in 2D time-dependent materials

The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent materials, this relation is less straightforward for multi-dimensional materials. This paper discusses fundamental aspects of 2D electromagnetic and acoustic wave propagation and scattering in homogeneous, time-dependent materials. This encompasses a review of transmission and reflection at a single time boundary, a discussion of the Green's function and its symmetry properties in a piecewise continuous time-dependent material, a discussion of propagation invariants (including the net field-momentum density), general reciprocity theorems, and wave field representations. Analogous to the well-known expression for Green's function retrieval by time-correlation of passive measurements in a space-dependent material, an expression is derived for Green's function retrieval by space-correlation of passive measurements in a time-dependent material. The paper concludes with the discussion of the propagator matrix for a piecewise continuous time-dependent material, its symmetry properties and its relation with the Green's function.

physics.app-ph↗

arXiv2024

Waves in space-dependent and time-dependent materials: a systematic comparison

Waves in space-dependent and time-dependent materials obey similar wave equations, with interchanged time- and space-coordinates. However, since the causality conditions are the same in both types of material (i.e., without interchangement of coordinates), the solutions are dissimilar. We present a systematic treatment of wave propagation and scattering in 1D space-dependent and time-dependent materials. After formulating unified equations, we discuss Green's functions and simple wave field representations for both types of material. Next we discuss propagation invariants, i.e., quantities that are independent of the space coordinate in a space-dependent material (such as the net power-flux density) or of the time coordinate in a time-dependent material (such as the net field-momentum density). A discussion of reciprocity theorems leads to the well-known source-receiver reciprocity relation for the Green's function of a space-dependent material and a new source-receiver reciprocity relation for the Green's function of a time-dependent material. A discussion of general wave field representations leads to the well-known expression for Green's function retrieval from the correlation of passive measurements in a space-dependent material and a new expression for Green's function retrieval in a time-dependent material. After an introduction of a matrix-vector wave equation, we discuss propagator matrices for both types of material. Since the initial condition for a propagator matrix in a time-dependent material follows from the boundary condition for a propagator matrix in a space-dependent material by interchanging the time- and space-coordinates, the propagator matrices for both types of material are interrelated in the same way. This also applies to representations and reciprocity theorems involving propagator matrices.

physics.app-ph↗

arXiv2024

On acoustic space-time media that compute their own inverse

We derive time reflection and transmission coefficients for 1D acoustic waves encountering a time boundary at which the properties of the medium change instantaneously. The time reflection and transmission coefficients are shown to be identical to so-called reverse-space reflection and transmission coefficients which appear in the recursive computation of focusing wavefields used in seismology. We establish a bijectivity between the focusing wavefields and the wavefields produced by time scattering and show how this can be used to construct a space-time medium where the time scattering anticipates the space scattering and "computes" the exact inverse for the space scattering. The construction is shown to be independent of the boundary conditions chosen to compute the reflection and transmission coefficients. We demonstrate the construction with a simple numerical example of a single pulse encountering a series of time boundaries before reaching a spatial inhomogeneity. The time boundaries scatter the single pulse into a focusing wavefield that subsequently focuses through the spatial inhomogeneity. Under certain conditions, the transmitted wave has both the same wave shape and amplitude as the original pulse, yielding a transmission coefficient of unity. The reflection coefficient of the space-time medium is always non-zero however.

physics.geo-ph↗

arXiv2024

Target-oriented least-squares reverse-time migration with Marchenko redatuming and double-focusing: Field data application

Recently, the focus of reflection seismologists has shifted to applications where a high-resolution image of the subsurface is required. Least-Squares Reverse-Time Migration (LSRTM) is a common tool used to compute such images. Still, its high computational costs have led seismologists to use target-oriented LSRTM for imaging only a small target of interest within a larger subsurface block. Redatuming the data to the upper boundary of the target of interest is one approach to target-oriented LSRTM. Still, many redatuming methods cannot account for multiple scattering within the overburden. We apply a target-oriented least-squares reverse time migration algorithm that integrates Marchenko redatuming and double-focusing to a field dataset. This redatuming method accounts for all orders of multiple scattering in the overburden, thus improving the accuracy of target-oriented LSRTM. Moreover, we demonstrate the effectiveness of a double-focusing algorithm in reducing the data size by decreasing both spatial and temporal dimensions of the model and the data. The algorithm's performance is evaluated using field data acquired in the Norwegian Sea. The numerical results show that our target-oriented LSRTM algorithm can reduce the internal multiple effects and increase the resolution of the resulting image.

physics.geo-ph↗

arXiv2024

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 be resolved by an iterative or direct method. These focusing functions, when applied to reflection data, create virtual point-sources inside the medium. Combining individual virtual point-sources into a plane-wave leads to an efficient computation of images without internal multiples. In this study the internal multiples are eliminated in a redatuming step which is part of the imaging algorithm. To use the Marchenko algorithm with plane-wave focusing functions, the time window that separates the unknowns must be adapted. The design of the plane-wave Marchenko algorithm is explained and illustrated with numerically modeled and measured reflection data.

physics.geo-ph↗

arXiv2023

Time-lapse applications of the Marchenko method on the Troll field

The data-driven Marchenko method is able to redatum wavefields to arbitrary locations in the subsurface, and can, therefore, be used to isolate zones of specific interest. This creates a new reflection response of the target zone without interference from over- or underburden reflectors. Consequently, the method is well suited to obtain a clear response of a subsurface reservoir, which can be advantageous in time-lapse studies. The clean isolated responses of a baseline and monitor survey can be more effectively compared, hence the retrieval of time-lapse characteristics is improved. This research aims to apply Marchenko-based isolation to a time-lapse marine dataset of the Troll field in Norway in order to acquire an unobstructed image of the primary reflections, and retrieve small time-lapse traveltime difference in the reservoir. It is found that the method not only isolates the primary reflections but can also recover internal multiples outside the recording time. Both the primaries and the multiples can then be utilised to find time-lapse traveltime differences. More accurate ways of time-lapse monitoring will allow for a better understanding of dynamic processes in the subsurface, such as observing saturation and pressure changes in a reservoir or monitoring underground storage of hydrogen and CO2.

physics.geo-ph↗

arXiv2023

Wavefield Finite Time Focusing with Reduced Spatial Exposure

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 theorems. In heterogeneous media, Time-Reversal Focusing theoretically involves in- and output signals that are infinite in time and the resulting waves propagate through the entire medium. Recently, integral representations have been derived for single-sided wavefield focusing. Although the required input signals for this approach are finite in time, the output signals are not and, similar to Time-Reversal Mirroring, the resulting waves propagate through the entire medium. Here, an alternative solution for double-sided wavefield focusing is derived. This solution is based on an integral representation where in- and output signals are finite in time, and where the energy of the waves propagating in the layer embedding the focal point is smaller than with Time-Reversal Focusing. We explore the potential of the proposed method with numerical experiments involving a head model consisting of a skull enclosing a brain.

physics.class-ph↗

arXiv2023

A framework for subsurface monitoring by integrating reservoir simulation with time-lapse seismic surveys

Reservoir simulations for subsurface processes play an important role in successful deployment of geoscience applications such as geothermal energy extraction and geo-storage of fluids. These simulators provide time-laps dynamics of the coupled poro-mechanical processes within the reservoir and its over-, under-, and side-burden environments. For more reliable operations, it is crucial to connect these reservoir simulation results with the seismic surveys (i.e., observation data). However, despite being crucial, such integration is challenging due to the fact that the reservoir dynamics alters the seismic parameters. In this work, a coupled reservoir simulation and time-lapse seismic methodology is developed for multiphase flow operations in subsurface reservoirs. To this end, a poromechanical simulator is designed for multiphase flow and connected to a forward seismic modeller. This simulator is then used to assess a novel methodology of seismic monitoring by isolating the reservoir signal from the entire reflection response. This methodology is shown to be able to track the development of the fluid front over time, even in the presence of a highly reflective overburden with strong time-lapse variations. These results suggest that the proposed methodology can contribute to a better understanding of fluid flow in the subsurface. Ultimately, this will lead to improved monitoring of reservoirs for underground energy storage or production.

physics.geo-ph↗

arXiv2023

Extracting small time-lapse traveltime changes in a reservoir using primaries and internal multiples after Marchenko-based target zone isolation

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 over- and underburden effects, the data-driven Marchenko method is used. This method effectively isolates the target response, which can then be used to extract more precise time-lapse changes. Additionally, the method also reveals target-related multiples that probe the reservoir more than once, which further define the changes in the reservoir. To verify the effectiveness of the method, a numerical example is constructed. This test shows that when using the isolated target response, the observed time differences resemble the expected time differences in the reservoir. Moreover, the results obtained with target-related multiples also benefit from the Marchenko-based isolation of the reservoir. It is, therefore, concluded that this method has potential to observe dynamic changes in the subsurface with increased accuracy.

physics.geo-ph↗

arXiv2023

Target-Enclosed Least-Squares Seismic Imaging

Least-Squares Reverse-Time Migration (LSRTM) is a method that seismologists utilize to compute a high-resolution subsurface image. Nevertheless, LSRTM is a computationally demanding problem. One way to reduce the computational costs of the LSRTM is to choose a small region of interest and compute the image of that region. However, finding representations that account for the wavefields entering the target region from the surrounding boundaries is necessary. This paper confines the region of interest between two boundaries above and below this region. The acoustic reciprocity theorem is employed to derive representations for the wavefields at the upper and lower boundaries of the target region. With the help of these representations, a target-enclosed LSRTM algorithm is developed to compute a high-resolution image of the region of interest. Moreover, the possibility of using virtual receivers created by Marchenko redatuming is investigated.

physics.geo-ph↗

arXiv2023

Virtual plane-wave imaging via Marchenko redatuming

Marchenko redatuming is a novel scheme used to retrieve up- and down-going 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 similarly to standard migration methods, Marchenko redatuming only requires an estimate of the direct wave from the virtual source (or to the virtual receiver), illumination from only one side of the medium, and no physical sources (or receivers) inside the medium. In this contribution we consider a different time-focusing condition within the frame of Marchenko redatuming that leads to the retrieval of virtual plane-wave responses. As a result, it allows multiple-free imaging using only a one-dimensional sampling of the targeted model at a fraction of the computational cost of standard Marchenko schemes. The potential of the new method is demonstrated on 2D synthetic models.

physics.geo-ph↗

arXiv2023

Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions

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, source vectors and wave-field vectors. The matrix-vector formalism also allows the formulation of representations in which propagator matrices replace the Green's matrices. These propagator matrices, in turn, can be expressed in terms of Marchenko-type focusing functions. An advantage of the representations with propagator matrices and focusing functions is that the boundary integrals in these representations are limited to a single open boundary. This makes these representations a suitable basis for developing advanced inverse scattering, imaging and monitoring methods for wave fields acquired on a single boundary.

physics.app-ph↗