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J.W. Thorbecke

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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 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. ...
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 data set. 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 minimize 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 2-D seismic reflection data set 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 subsequent subsurface imaging and monitoring studies. ...
Journal article (2024) - Jan Thorbecke, Mohammed Almobarak, Johno van IJsseldijk, Joeri Brackenhoff, Giovanni Meles, Kees Wapenaar
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. ...
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 are used to redatum wavefields to a deeper level in the subsurface. 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 elimination of the overburden and underburden. Our results indicate that this approach enhances the resolution of reflection data. These enhanced reflections can be utilised for imaging and monitoring applications. ...
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. To retrieve a response that is free from the 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. In addition, the method also reveals target-related multiples that probe the reservoir more than once, which further defines the changes in the reservoir. To verify the effectiveness of the method, a numerical example is constructed. This test finds 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 the potential to observe dynamic changes in the subsurface with increased accuracy. ...
Journal article (2023) - Johno van IJsseldijk, Joeri Brackenhoff, Jan Thorbecke, Kees Wapenaar
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 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 data set 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 estimate internal multiples outside the recording time. Both the primaries and the multiples can then be utilized 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. ...
Journal article (2022) - Jacob F. F. Bulmer, Bryn A. Bell, Ian A. Walmsley, Anthony Laing, Rachel S. Chadwick, Alex E. Jones, Diana Moise, Alessandro Rigazzi, J.W. Thorbecke, Utz-Uwe Haus, Thomas Van Vaerenbergh, Raj B. Patel
Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian boson sampling (GBS), in which photons are measured from a highly entangled Gaussian state, is a leading approach in pursuing quantum advantage. State-of-the-art GBS experiments that run in minutes would require 600 million years to simulate using the best preexisting classical algorithms. Here, we present faster classical GBS simulation methods, including speed and accuracy improvements to the calculation of loop hafnians. We test these on a ∼100,000-core supercomputer to emulate GBS experiments with up to 100 modes and up to 92 photons. This reduces the simulation time for state-of-the-art GBS experiments to several months, a nine–orders of magnitude improvement over previous estimates. Last, we introduce a distribution that is efficient to sample from classically and that passes a variety of GBS validation methods. ...

Implementation and examples

Journal article (2022) - Joeri Brackenhoff, Jan Thorbecke, Giovanni Meles, Victor Koehne, Diego Barrera, Kees Wapenaar
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 significant amount of computational cost. To limit the cost, we apply floating point compression to the reflection data to reduce their volume and the loading time from disk. We apply the Marchenko implementation to numerical reflection data to retrieve accurate Green's functions inside the medium and use these reflection data to apply imaging. This requires the simulation of many virtual source points, which we circumvent using virtual plane-wave sources instead of virtual point sources. Through this method, we retrieve the angle-dependent response of a source from a depth level rather than of a point. We use these responses to obtain angle-dependent structural images of the subsurface, free of contamination from wrongly imaged internal multiples. These images have less lateral resolution than those obtained using virtual point sources, but are more efficiently retrieved. ...
Journal article (2021) - Riaz Alai, Faqi Liu, Eric Verschuur, Jan Thorbecke, Gundogan Coskun, Shuqian Dong, Cosmin Macesanu, Bin Wang, Christopher Lee Slind, Eric Andersen
In our case studies, the success of subsalt exploration and development wells depended heavily on the characterization of highly heterogeneous lacustrine microbial carbonates. Acoustic and elastic inversions have proved to be a good proxy for identification of reservoir quality variation for exploration and development well placements. However, qualitative and quantitative usage of subsalt seismic amplitudes requires proper illumination and good signal-to-noise ratio. If properly imaged, mode-converted reflections and interbed multiples can be complementary to the P-wave image. But, in conventional P-wave-oriented imaging, both types of events cannot be imaged correctly. They appear as coherent noise and negatively impact the overall exploration and development project outcomes, especially in areas with poor illumination. This paper consists of two parts: first, we investigate the potential problems resulting from converted waves and interbed multiples in data from two different basins - the Gulf of Mexico and the Campos Basin in offshore Brazil - and show our approach to attenuate them to reveal the true structures. The second part focuses on advanced identification of interbed multiples in modeling and migration methods. To facilitate the various strategies to attenuate interbed multiples, "interpretation"of the various events plays a significant role. Vertical seismic profile (VSP) data are excellent for the purpose; however, these data are only available at well locations, if they are recorded. As a result of many years of technology advancement, pseudo VSP data can be constructed effectively from standard streamer survey data. Two methods are highlighted in this paper for building pseudo VSP data in a full two-way sense, based on a typical Brazil-type salt model: Marchenko-based processing and full-wavefield migration. Major subsalt plays in the Gulf of Mexico and emerging plays in Brazil should benefit significantly from elimination of these kinds of coherent noise. ...
Journal article (2021) - Jan Thorbecke, Lele Zhang, Kees Wapenaar, Evert Slob
The Marchenko multiple elimination (MME) 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 are similar to each other, but they use different time-domain truncation operators. The MME scheme retrieves a new data set without internal multiple reflections. The transmission-compensated Marchenko multiple elimination scheme does the same and additionally compensates for transmission losses in the primary reflections. Both schemes can be solved with an iterative algorithm based on a Neumann series. At each iteration, a convolution or correlation between the projected focusing function and the measured reflection response is performed, and, after each convolution or correlation, a truncation in the time domain is applied. After convergence, the resulting projected focusing function is used for retrieving the transmission-compensated primary reflections and the projected Green's function is used for the physical primary reflections. We have determined that internal multiples are removed by using time-windowed input data that only contain primary reflections. We evaluate both schemes in detail and develop an iterative implementation that reproduces the presented numerical examples. The software is part of our open-source suite of programs and fits into the Seismic Unix software suite of the Colorado School of Mines. ...
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 retrieved Green's functions form the input for redatuming by multidimensional deconvolution (MDD). The redatumed reflection response is free of internal multiples related to the overburden. Alternatively, the redatumed response can be obtained by applying a second focusing function to the retrieved Green's functions. This process is called Marchenko redatuming by double focusing. It is more stable and better suited for an adaptive implementation than Marchenko redatuming by MDD, but it does not eliminate the multiples between the target and the overburden. An attractive efficient alternative is plane-wave Marchenko redatuming, which retrieves the responses to a limited number of plane-wave sources at the redatuming level. In all cases, an image of the subsurface can be obtained from the redatumed data, free of artefacts caused by internal multiples. Another class of Marchenko methods aims at eliminating the internal multiples from the reflection data, while keeping the sources and receivers at the surface. A specific characteristic of this form of multiple elimination is that it predicts and subtracts all orders of internal multiples with the correct amplitude, without needing a macro subsurface model. Like Marchenko redatuming, Marchenko multiple elimination can be implemented as an MDD process, a double dereverberation process, or an efficient plane-wave oriented process. We systematically discuss the different approaches to Marchenko redatuming, imaging and multiple elimination, using a common mathematical framework. ...
Journal article (2021) - Joeri Brackenhoff, Jan Thorbecke, Kees Wapenaar
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 Green's function superposed with its time-reversal. Unlike the classical homogeneous Green's function representation, our approach requires no receivers on an enclosing boundary; however, it does require the source signal to be symmetric in time. We demonstrate that, in 3-D, the single-sided representation is an improvement over the classical representation by applying the representations to numerical data. We retrieve responses to virtual point sources with an isotropic and with a double-couple radiation pattern and compare the results to a directly modeled reference result. We also demonstrate the application of the single-sided representation for retrieving the response to a virtual rupture that consists of a superposition of double-couple point sources. This is achieved by obtaining the homogeneous Green's function for each source separately before they are transformed to the causal Green's function, time-shifted, and superposed. The single-sided representation is also used to monitor the complete wavefield that is caused by a numerically modeled rupture. However, the source signal of an actual rupture is not symmetric in time, and the single-sided representation can, therefore, only be used to obtain the causal Green's function. This approach leaves artifacts in the final result; however, these artifacts are limited in space and time. ...
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, that is by focusing energy at unphysical interfaces, and false negatives, that is by destructively interfering with primaries. Multiple prediction/primary synthesis methods are usually designed to operate on point source gathers and can therefore be computationally demanding when large problems are considered. A computationally attractive scheme that operates on plane-wave datasets is derived by adapting a data-driven point source gathers method, based on convolutions and cross-correlations of the reflection response with itself, to include plane-wave concepts. As a result, the presented algorithm allows fully data-driven synthesis of primary reflections associated with plane-wave source responses. Once primary plane-wave responses are estimated, they are used for multiple-free imaging via plane-wave reverse time migration. Numerical tests of increasing complexity demonstrate the potential of the proposed algorithm to produce multiple-free images from only a small number of plane-wave datasets. ...
Conference paper (2020) - M. Staring, L. Zhang, J.W. Thorbecke, K. Wapenaar
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 predict internal multiples. Therefore, the role of the adaptive filter has changed for these methods. Rather than needing an aggressive adaptive filter to compensate for inaccurate internal multiple predictions, only a conservative adaptive filter is needed to compensate for minor amplitude and/or phase errors in the internal multiple predictions caused by imperfect acquisition and preprocessing of the input data. We demonstate that a conservative adaptive filter can be used to improve the attenuation of internal multiples when applying a Marchenko multiple elimination (MME) method to a 2D line of streamer data. In addition, we suggest that an adaptive filter can be used as a feedback mechanism to improve the preprocessing of the input data. ...
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 assumptions, merits and limitations of these methods. ...

From Point-Source to Plane-Wave Datasets Applications

Conference paper (2020) - G.A. Meles, L. Zhang, J.W. Thorbecke, K. Wapenaar, E.C. Slob
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-related artefacts can be dealt with via Marchenko methods, either via Green’s functions redatuming or data domain schemes (i.e., multiple prediction / primary synthesis algorithms). Data domain Marchenko methods were originally designed to operate on point source gathers, and can therefore be computationally demanding when large problems are considered. However, computationally attractive schemes operating on plane-wave datasets were also derived, by adapting Marchenko point source gathers methods to include plane-wave concepts. As a result, current Marchenko algorithms allow fully data-driven synthesis of primary reflections associated with point and plane-wave source responses. Numerical tests show that while the best images are obtained when well sampled point source gathers are processed, using few multiple-free plane-wave gathers can be used as an unexpensive and effective processing step. ...
Journal article (2019) - Lele Zhang, Jan Thorbecke, Kees Wapenaar, Evert Slob
We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require any model information. It consists of convolutions and correlations of the data with itself. A truncation in the time domain is applied after each convolution or correlation. The retrieved data set can be used as the input to construct a better velocity model than the one that would be obtained by working directly with the original data and to construct an enhanced subsurface image. Two 2D numerical examples indicate the effectiveness of the method. We have studied bandwidth limitations by analyzing the effects of a thin layer. The presence of refracted and scattered waves is a known limitation of the method, and we studied it as well. Our analysis indicates that a thin layer is treated as a more complicated reflector, and internal multiple reflections related to the thin layer are properly removed. We found that the presence of refracted and scattered waves generates artifacts in the retrieved data. ...
In recent years, progress has been made in the field of virtual seismology. Using the novel data-driven Marchenko method, virtual sources and receivers can be created in the subsurface using only reflection data at the surface of the Earth and a background velocity model of the subsurface. Extensive studies have been performed on the application of the Marchenko method to 2D reflection data. This includes both synthetic reflection data and field reflection data. These studies have shown the potential improvements of the method for applications such as hydrocarbon imaging and wavefield monitoring. In the case of wavefield monitoring, a network of virtual receivers can be created in the subsurface to monitor the wavefield response of a subsurface source. This source response can be directly measured in the field, or it can be created from the reflection data, making it a virtual source response. Sensitivity studies have been performed to consider the acquisition limitations of the reflection data, as well as the influence of complex source signatures. This showed the potential of applying the Marchenko method for objectives such as monitoring complex induced seismicity signals and forecasting the responses of induced earthquakes. In this paper, we wish to present further studies for the creation of virtual sources and receivers from 3D reflection data. Similar studies for the application of the Marchenko method for hydrocarbon imaging have been performed, however, in these prior studies, both the source and receiver were virtual. In this paper, we also consider the case that the source is not created from the reflection data, but rather is recorded, and the influence of these types of sources on the monitoring. Furthermore, the limitations of the acquisition setup in the 3rd dimension are considered. ...