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. ... Read more

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 have developed a two-step, amplitude- and phase-preserving, inversion-based workflow that addresses these problems. We apply robust estimation of primaries by sparse inversion (R-EPSI) to solve simultaneously for the surface-related primaries Green’s function and the source wavelet. A significant advantage of the inversion approach of the R-EPSI method is that it does not rely on an adaptive subtraction step that typically limits other demultiple methods such as surface-related multiple elimination. The resulting Green’s function is used as the input to a Marchenko equation-based approach to predict the complex interference pattern of all overburden-generated internal multiples at once. In this approach, no a priori information about the subsurface is needed. In theory, the interbed multiples can be predicted with correct amplitude and phase and, again, no adaptive filters are required. We illustrate this workflow by applying it on an Arabian Gulf field data example. It is crucial that all preprocessing steps are performed in an amplitude-preserving way to restrict any impact on the accuracy of the multiple prediction. In practice, some minor inaccuracies in the processing flow may end up as prediction errors for which corrections will be needed. Hence, we conclude that the use of conservative adaptive filters were necessary to obtain the best results after interbed multiple removal. The obtained results indicate promising suppression of surface-related and interbed multiples. ... Read more

In recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on two-dimensional synthetic data and applied to two-dimensional field data, but only little is known about their behaviour on three-dimensional synthetic data and three-dimensional field data. Particularly, it is not known whether Marchenko methods are sufficiently robust for sparse acquisition geometries that are found in practice. Therefore, we start by performing a series of synthetic tests to identify the key acquisition parameters and limitations that affect the result of three-dimensional Marchenko internal multiple prediction and subtraction using an adaptive double-focusing method. Based on these tests, we define an interpolation strategy and use it for the field data application. Starting from a wide azimuth dense grid of sources and receivers, a series of decimation tests are performed until a narrow azimuth streamer geometry remains. We evaluate the effect of the removal of sail lines, near offsets, far offsets and outer cables on the result of the adaptive double-focusing method. These tests show that our method is most sensitive to the limited aperture in the crossline direction and the sail line spacing when applying it to synthetic narrow azimuth streamer data. The sail line spacing can be interpolated, but the aperture in the crossline direction is a limitation of the acquisition. Next, we apply the adaptive Marchenko double-focusing method to the narrow azimuth streamer field data from the Santos Basin, Brazil. Internal multiples are predicted and adaptively subtracted, thereby improving the geological interpretation of the target area. These results imply that our adaptive double-focusing method is sufficiently robust for the application to three-dimensional field data, although the key acquisition parameters and limitations will naturally differ in other geological settings and for other types of acquisition. ... Read more

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. ... Read more

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. ... Read more

Curiosity regarding what we cannot see has always driven research. Science has helped us to uncover many of those hidden secrets. In particular, geophysics has helped us to image the inside of the Earth. By sending a seismic signal into the Earth and recording the signal that comes back, geophysicists can characterize the layers of the subsurface. Nowadays, geophysics is used for many purposes, for example, the localization of fossil fuels, the characterization of the subsurface for the construction of wind farms and the evaluation of reservoirs for geothermal energy. In order to decrease the risk and cost involved in these activities, we need images of the subsurface that are as accurate as possible.

These images can only be obtained if we fully understand the propagation of the seismic signal in the subsurface. A long-standing problem in geophysical imaging is the presence of internal multiple reflections. When imaging the subsurface, we assume that the signal only reflects once when there is a contrast in velocity and/or density (for example, when changing from sand to rock). However, in reality, the signal can reflect many times inside the subsurface before being recorded at the surface. When treating the arrivals that have reflected many times as arrivals that have only reflected once, we incorrectly image the subsurface and create ghost reflectors that do not exist. This problem is particularly strong in geological settings that have a complex structure with many strong velocity and/or density contrasts above an area of interest. This may happen, for example, when there is a reservoir of oil below a thick stratified salt layer. In such cases, the image of the area of interest is unreliable due to the presence of many ghost reflectors. Therefore, we have to use knowledge of wave propagation to predict and attenuate the internal multiples in the data prior to imaging.

In this thesis, I further develop the data-driven and wave-equation-based Marchenko method to make it suitable for the attenuation of internal multiples in seismic field data. In addition, I evaluate the performance of suitable methods by applying them to field datasets recorded in different geological settings. I start this evaluation by demonstrating that what we call the conventional Marchenko method is perhaps not the most suitable Marchenko method for the application to field data. I develop an alternative Marchenko method instead: the adaptive double-focusing method. I show that this method indeed produces improved results compared to the conventional Marchenko method when applying it to a line of 2D data of the Santos Basin, Brazil.

Since the 2D results show promise, I continue with the extension to 3D applications. I first identify the key acquisition parameters that affect the result of our Marchenko method on 3D synthetic data and conclude that the limited crossline aperture and the coarse sail line spacing have the strongest effect on the quality of the result. Based on this evaluation, I interpolate the sail line spacing on 3D field data acquired in the Santos Basin and use the adaptive double-focusing method to predict and subtract internal multiples. I conclude that 3D Marchenko internal multiple attenuation seems to be sufficiently robust for the application to narrow azimuth streamer data in a deep marine setting, provided that there is sufficient aperture in the crossline direction and that the sail lines are interpolated. In addition, the adaptive double-focusing method is suitable for the attenuation of internal multiples generated by a complex overburden and for simultaneously redatuming to a level below this overburden.

Next, I modify the adaptive double-focusing method to obtain an adaptive double dereverberation method that is suitable when only aiming to attenuate internal multiples generated in an overburden without redatuming. Moreover, this method does not require a velocity model. I apply this method to a 2D line of data acquired in the very shallow Arabian Gulf. Also, I assess how to meet the data requirements for the Marchenko method in shallow water environments (e.g., the removal of surface-related multiples, the deconvolution of the source signature) and demonstrate that the state-of-the-art Robust Estimation of Primaries by Sparse Inversion (R-EPSI) method is capable of producing the correct input data for the Marchenko method in such settings.

Subsequently, I discuss the role of the adaptive filter in the application of the Marchenko method to field data. I argue that developments in seismic data processing allow us to predict internal multiples with more accuracy, such that only a conservative adaptive filter is needed to correct for the unavoidable minor amplitude and phase discrepancies between the internal multiples in the data and the predicted internal multiples. I demonstrate this by using a conservative adaptive filter to subtract internal multiples that were predicted by applying an adaptive Marchenko multiple elimination method to a 2D line of field data acquired in the Norwegian North Sea.

Finally, based on the results presented in this thesis, I conclude that the Marchenko method is an effective, data-driven and robust method for the prediction of internal multiples in marine seismic data. Different Marchenko methods are suitable for different purposes. There are two key elements for the successful application of a Marchenko method to field data: 1) the acquisition geometry needs to be sufficiently dense and 2) a careful processing workflow needs to be constructed that accounts for the specifics of the geological setting at hand, with significant emphasis on amplitude and phase preservation. ... Read more

We apply Marchenko redatuming using an adaptive double-focusing method to 3D field data of the Santos basin, Brazil. This method was already successfully applied to 2D field data and we now study the acquisition geometry and preprocessing requirements in 3D. We start from 3D synthetic data modeled on a dense grid of colocated sources and receivers and decimate down to a realistic NAZ streamer acquisition. The synthetic tests show that the sail line spacing and the missing outer cables are the acquisition parameters with the strongest effect on Marchenko redatuming. We can interpolate for the sail line spacing and the near offsets, but the missing outer cables are unfortunately a limitation of the acquisition. After applying the proposed interpolation to 3D field data, interbed multiples are successfully predicted and subtracted from the target area, resulting in a significant improvement in the geological interpretation. Naturally, the pre-processing requirements and challenges strongly depend on the acquisition geometry and the geology of the area under investigation (e.g. water depth, shape of the overburden, maximum dip). Hence, these tests only give a general idea about the limitations of 3D Marchenko redatuming ... Read more

In seismic monitoring, one is usually interested in the response of a changing target zone, embedded in a static inhomogeneous medium. We introduce an efficient method that predicts reflection responses at the Earth's surface for different target-zone scenarios, from a single reflection response at the surface and a model of the changing target zone. The proposed process consists of two main steps. In the first step, the response of the original target zone is removed from the reflection response, using the Marchenko method. In the second step, the modelled response of a new target zone is inserted between the overburden and underburden responses. The method fully accounts for all orders of multiple scattering and, in the elastodynamic case, for wave conversion. For monitoring purposes, only the second step needs to be repeated for each target-zone model. Since the target zone covers only a small part of the entire medium, the proposed method is much more efficient than repeated modelling of the entire reflection response. ... Read more

Marchenko imaging is a methodology to image the subsurface with two important properties: (1)accurate amplitude and (2)free from free-surface and internal multiple artefacts. It requires an estimate of the first arrival of the focusing function which is commonly obtained from a macro velocity model. Inspired by this limitation, a projected Marchenko scheme has been introduced from which an internal multiple reflection elimination scheme has been derived. This internal multiple reflection elimination scheme requires an estimate of the two-way travel time surface of a selected horizon in the subsurface instead of a macro model. In order to make it totally model free we have rewritten the scheme by replacing the estimate of the two-way travel time surface by a fixed truncation for all traces. The output of the current scheme contains primary reflections without contamination from internal multiple reflections. We apply this scheme to a 2D numerical example to illustrate the procedure of this method and show how the internal multiple reflection eliminated data set can be retrieved and the migration image is improved. ... Read more

Recent developments in exploration seismology have enabled the creation of virtual sources and/or virtual receivers in the subsurface from reflection measurements at the earth's surface. Unlike in seismic interferometry, no physical instrument (receiver or source) is needed at the position of the virtual source or receiver. Moreover, no detailed knowledge of the subsurface parameters and structures is required: a smooth velocity model suffices. Yet, the responses to the virtual sources, observed by the virtual receivers, fully account for multiple scattering. This new methodology, which we call virtual seismology, has led to a breakthrough in hydrocarbon reservoir imaging, as is demonstrated in a companion paper (Staring et al., Marchenko redatuming for multiple prediction and removal in situations with a complex overburden). The aim of the present paper is to discuss applications of virtual seismology beyond exploration seismology, in particular induced earthquake monitoring, and to highlight the connections between these applications. The ability to retrieve the entire wave field between (virtual or real) sources and receivers anywhere in the subsurface, without needing a detailed subsurface model, has large potential for monitoring induced seismicity, characterizing the source properties (such as the moment tensor of extended sources along a fault plane), and forecasting the response to potential future induced earthquakes. This will be demonstrated with numerical models and preliminary real-data results. ... Read more

Internal multiples can create severe artefacts in seismic imaging, especially when our zone of interest is overlain by a complex overburden. These artefacts can mask structures, which has a strong effect on the interpretation of the image. Therefore, multiple prediction and removal is of significant importance for correct imaging and interpretation in settings with a complex overburden.
We propose an adaptive double-focusing method to predict and subtract the internal multiples that were generated in the overburden. This method is a form of the Marchenko method, that can retrieve the directionally-decomposed Green's functions between virtual sources and virtual receivers anywhere inside the subsurface. The retrieved Green's functions contain all orders of multiple scattering. The method only requires the single-sided reflection response and a smooth velocity model as input. Instead of conventional imaging methods, that assume that the wavefield only consists of single-scattered waves (and thus create imaging artefacts when multiple scattering is present), we now use the multiple-scattered Marchenko wavefields for correct redatuming and imaging.

We apply our method to 2D and 3D field data that were recorded in settings where imaging and interpretation is hindered by a complex overburden. First, we create virtual sources and virtual receivers directly above our zone of interest. Next, we use the retrieved Marchenko wavefields to predict and subtract the internal multiples that were generated in the overburden. Masked structures become visible after multiple removal, which significantly improves the geological interpretability. Therefore, we conclude that the adaptive double-focusing method (Marchenko redatuming) is capable of correctly predicting and removing internal multiples generated in the overburden. ... Read more

The Santos basin in Brazil suffers from strong internal multiples that overlap with primaries from the pre-salt reservoirs. We propose an adaptive double-focusing method for the removal of these multiples to obtain a correct image of the target area. The proposed method applies a form of source-receiver Marchenko redatuming to the reflection response. The Marchenko method is used to achieve single-focusing, after which we convolve the retrieved downgoing focusing function and the upgoing Green’s function to create double-focusing. This results in a base image that contains both primaries and internal multiples, and two models that predict the strongest internal multiples. Next, adaptive subtraction in the curvelet domain is used to remove these multiples from the base image. Some multiple interactions between the target area and the overburden remain, but we gain a robust method that is capable of dealing with a sparse acquisition geometry and imperfections in the (pre-processed) data. Also, this method is straightforward to implement and can be parallelized over pairs of focal points. These properties make adaptive double-focusing particularly suitable for the application to large volumes of field data. Tests on 2D field data and 3D field data show that the proposed method correctly predicts and removes the strongest internal multiples from the overburden, resulting in a clear improvement of the geological interpretability in the target area. ... Read more

We have developed an adaptive double-focusing method that is specifically designed for the field-data application of source-receiver Marchenko redatuming. Typically, the single-focusing Marchenko method is combined with a multidimensional deconvolution (MDD) to achieve redatuming. Our method replaces the MDD step by a second focusing step that naturally complements the single-focusing Marchenko method. Instead of performing the MDD method with the directionally decomposed Green's functions that result from single-focusing, we now use the retrieved upgoing Green's function and the retrieved downgoing focusing function to obtain a redatumed reflection response in the physical medium. Consequently, we only remove the strongest overburden effects instead of removing all of the overburden effects. However, the gain is a robust method that is less sensitive to imperfections in the data and a sparse acquisition geometry than the MDD method. In addition, it is computationally much cheaper, more straightforward to implement, and it can be parallelized over pairs of focal points, which makes it suitable for application to large data volumes. We evaluate the successful application of our method to 2D field data of the Santos Basin. ... Read more

We present an adaptive double-focusing method for applying source-receiver Marchenko redatuming to field data. Receiver redatuming is achieved by a first focusing step, where the coupled Marchenko equations are iteratively solved for the oneway Green’s functions. Next, source redatuming is typically performed by a multi-dimensional deconvolution of these Green’s functions. Instead, we propose a second focusing step for source Marchenko redatuming, using the upgoing Green’s function and the downgoing focusing function to obtain a redatumed reflection response in the physical medium. This method makes adaptive processing more straight-forward, making it less sensitive to imperfections in the data and the acquisition geometry and more suitable for the application to field data. In addition, it is cheaper and can be parallelized by pair of focal points. ... Read more

We propose an adaptive approach for the removal of internal multiples caused by an overburden using source-receiver Marchenko redatuming. Typically, a multi-dimensional deconvolution using the one-way Green’s functions is performed to achieve redatuming, after these functions have been retrieved by solving the coupled Marchenko equations. However, this processing step is sensitive to imperfections in the data and the acquisition geometry as well as computationally expensive. We propose an adaptive redatuming method that is less sensitive to such imperfections and as such should be beneficial when attempting source-receiver Marchenko redatuming with field data. We show this using 2D synthetic data from the Santos basin offshore Brazil. As an added bonus, it is also computationally less expensive. A disadvantage of the proposed method is that the obtained reflection response exists in the physical medium, causing some interactions with the overburden to remain. ... Read more

We compare the coupled Marchenko equations without free-surface multiples to the coupled Marchenko equations including free-surface multiples. When using the conventional method of iterative substitution to solve these equations, a difference in convergence behaviour is observed, suggesting that there is a fundamental difference in the underlying dynamics. Both an intuitive explanation, based on an interferometric interpretation, as well as a mathematical explanation, confirm this difference, and suggest that iterative substitution might not be the most suitable method for solving the system of equations including free-surface multiples. Therefore, an alternative method is required. We propose a sparse inversion, aimed at solving an under-determined system of equations. Results show that the sparse inversion is indeed capable of correctly solving the coupled Marchenko equations including free-surface multiples, even when the iterative scheme fails. Using sparsity promotion and additional constraints, it is expected to perform better than iterative substitution when working with incomplete data or in the presence of noise. Also, simultaneous estimation of the source wavelet is a potential possibility. ... Read more

In this paper, we focus on the field data application of source-receiver Marchenko redatuming. Conventionally, a source-receiver redatumed reflection response is obtained by first applying the Marchenko method for receiver-redatuming and then performing a multi-dimensional deconvolution (MDD) for sourceredatuming (Wapenaar et al. (2014)). The obtained reflection response is free from any interactions with the overburden. However, the MDD solves an ill-posed inverse problem (van der Neut et al. (2011a)), which makes it sensitive to imperfections in the data and the acquisition geometry. This is a problem for the field data application, since neither the data nor the acquisition geometry are ever perfect. In addition, MDD is computationally expensive. ... Read more

We present a one-dimensional lossless scheme to compute an image of a dissipative medium from two single-sided reflection responses. One reflection response is measured at or above the top reflector of a dissipative medium and the other reflection response is computed as if measured at or above the top reflector of a medium with negative dissipation which we call the effectual medium. These two reflection responses together can be used to construct the approximate reflection data of the corresponding lossless medium by multiplying and taking the square root in time domain. The corresponding lossless medium has the same reflectors as the dissipative medium. Then the constructed reflection data can be used to compute the focusing wavefield which focuses at the chosen location in subsurface of the dissipative medium. From the focusing function and constructed reflection response the Green’s function for a virtual receiver can be obtained. Because the up- and downgoing parts of the Green’s function are retrieved separately, these are used to compute the image. We show with an example that the method works well for a sample in a synthesized waveguide that could be used for measurements in a laboratory. ... Read more

We present an interferometric interpretation of the iterative Marchenko scheme including both free-surface multiples and internal multiples. Cross-correlations are used to illustrate the combination of causal and acausal events that are essential for the process of multiple removal. The first 4 steps in the scheme are discussed in detail, where the effect of different contributions on the result is displayed and the formation of individual events is illustrated. We highlight the events that are necessary to understand the process that removes both internal multiples and free-surface multiples from the data. We demonstrate that additional contributions are needed to correct for the presence of free-surface multiples. ... Read more