It is well known that source deghosting can best be applied to common-receiver gathers, whereas receiver deghosting can best be applied to common-shot records. The source-ghost wavefield observed in the common-shot domain contains the imprint of the subsurface, which complicates source deghosting in the common-shot domain, in particular when the subsurface is complex. Unfortunately, the alternative, that is, the common-receiver domain, is often coarsely sampled, which complicates source deghosting in this domain as well. To solve the latter issue, we have trained a convolutional neural network to apply source deghosting in this domain. We subsample all shot records with and without the receiver-ghost wavefield to obtain the training data. Due to reciprocity, these training data are a representative data set for source deghosting in the coarse common-receiver domain. We validate the machine-learning approach on simulated data and on field data. The machine-learning approach gives a significant uplift to the simulated data compared to conventional source deghosting. The field-data results confirm that the proposed machine-learning approach can remove the source-ghost wavefield from the coarsely sampled common-receiver gathers.@en

Common-receiver gathers with a dense source sampling are well suited for source-side deghosting based on wavefield propagation. However, often sources are sparsely sampled, which introduces aliasing artifacts for source deghosting based on wavefield propagation. The common-shot domain is often denser sampled. However, in the common-shot domain the source-side ghost wavefield is no longer determined by the water only. Instead, it will be affected by the complexity of the subsurface. Therefore, a data-driven estimation of the effect of the subsurface on the source ghost wavefield is integrated into our deghosting algorithm. The algorithm is based on wave field propagation operators that take into account the effect of the subsurface on the source-side ghost wavefield. To handle the effect of the subsurface on the source-side ghost wavefield, which is depth dependent, a multi-window implementation is used. A field data example is provided to demonstrate that source-deghosting in a well-sampled common-receiver domain gives an accurate ghost-free result. Then a comparison of the source-side ghost wavefield in the common-shot domain is made for two models: the Marmousi model (complex) and a horizontally layered model (simple). The source-side ghost wavefield is affected by the complex model, whereas the source-side ghost wavefield is unaffected by the simple model. The deghosting algorithm that takes into account the effect of the subsurface results in a more accurate deghosting result for the complex model compared to the deghosting algorithm that neglects the effect of the subsurface.@en

The sea surface is a strong reflector that results in a ghost wavefield at the source and the detector side. Consequently, a interference pattern occurs in the wavenumber-frequency domain. For a flat sea surface deep notch areas in the spectrum appear where there is destructive interference. The SNR (signal-tonoise ratio) is low in these areas. A rough and dynamic sea surface affects the propagation of the ghost wavefields and will distort the notch areas. If a rough and dynamic sea surface is present it should be taken into account in the process of deghosting. When the rough and dynamic sea surface is neglected the estimated ghost-free data will contain more noise. Often there are no additional measurements available that provide the exact shape of the rough and dynamic sea surface to model its corresponding ghost effect. Therefore, we introduce an adaptive deghosting method that takes into account a rough and dynamic sea surface without any prior information of this sea surface.@en

The sea surface is a strong reflector that results in a ghost wavefield at the source and the detector side. Consequently, a interference pattern occurs in the wavenumber-frequency domain. For a flat sea surface deep notch areas in the spectrum appear where there is destructive interference. The SNR (signal-tonoise ratio) is low in these areas. A rough and dynamic sea surface affects the propagation of the ghost wavefields and will distort the notch areas. If a rough and dynamic sea surface is present it should be taken into account in the process of deghosting. When the rough and dynamic sea surface is neglected the estimated ghost-free data will contain more noise. Often there are no additional measurements available that provide the exact shape of the rough and dynamic sea surface to model its corresponding ghost effect. Therefore, we introduce an adaptive deghosting method that takes into account a rough and dynamic sea surface without any prior information of this sea surface.@en

Uncertainties in the water velocity, receiver location and sea surface state introduce noise and ringing after deghosting. Therefore, a shot-based deghosting method is discussed that includes a constraint to reduce this effect of inaccuracies in the ghost model. First, we show results for a flat cable with an accurate ghost model. After that, the deghosting method is applied to a shot with a slanted cable. Finally, an inaccurate ghost model is applied to a shot, that is modelled with a variable sea surface.@en

Uncertainties in the water velocity, receiver location and sea surface state introduce noise and ringing after deghosting. Therefore, a shot-based deghosting method is discussed that includes a constraint to reduce this effect of inaccuracies in the ghost model. First, we show results for a flat cable with an accurate ghost model. After that, the deghosting method is applied to a shot with a slanted cable. Finally, an inaccurate ghost model is applied to a shot, that is modelled with a variable sea surface.@en

Accurate surface-related multiple removal is an important step in conventional seismic processing, and more recently, primaries and surface multiples are separated such that each of them is available for imaging algorithms. Current developments in the field of surface-multiple removal aim at estimating primaries in a large-scale inversion process. Using such a so-called closed-loop process, in each iteration primaries and surface multiples will be updated until they fit the measured data. The advantage of redefining surfacemultiple removal as a closed-loop process is that certain preprocessing steps can be included, which can lead to an improved multiple removal. In principle, the surface-related multiple elimination process requires deghosted data as input; thus, the source and receiver ghost must be removed. We have focused on the receiver ghost effect and assume that the source is towed close to the sea surface, such that the source ghost effect is well-represented by a dipole source. The receiver ghost effect is integrated within the closed-loop primary estimation process. Thus, primaries are directly estimated without the receiver ghost effect. After receiver deghosting, the upgoing wavefield is defined at zero depth, which is the surface.We have successfully validated our method on a 2D simulated data and on a 2D subset from 3D broadband field data with a slanted cable.@en

In exploration geophysics, seismic measurements are used to obtain information about the subsurface. A large proportion of these measurements take place in oceans, seas and lakes, where the sources and the receivers are generally located somewhere between the water bottom and the water surface during data acquisition. The sources emit an acoustic signal into the subsurface and the receivers measure, amongst other things, the reflections of this signal. Some of these signals only reflect within the subsurface, but others may reflect at the water surface one or more times. The signals that reflect at the water surface disturb the reflections from the subsurface and have a destructive effect on the bandwidth. In this thesis the focus is on the removal of signals with the first reflection and/or the last reflection at the water surface. Correctly removing these so-called ghost reflections will improve the bandwidth. In this thesis, three methods are covered, that aim to integrate the removal of ghost reflections into another process, or to improve the removal of ghost reflections under specific conditions. The first method integrates the removal of the receiver ghost into closed-loop surface-related multiple estimation. The results on modeled data and field data show that this is an efficient approach and provides a significant improvement over a sequential workflow. This first method, like many other methods that remove ghost reflections, requires accurate information about the depth of the receivers relative to the surface of the water. Due to a dynamic sea surface or movement of the cables this information about the depth of receivers is often not accurate, limiting the removal of the receiver ghost. The second method optimizes the removal of the ghost reflections by estimating and incorporating the depth of receivers relative to the dynamic water surface in this ghost removal process. On modeled data and field data, we show good results for cases where accurate information about the depth of the receivers relative to a dynamic water surface is not available. The first two methods address the removal of the receiver ghost, and it is well known that the receiver ghost should be removed in the shot domain. This is different when removing the source ghost, which has to be done in the receiver domain. However, in practice, the receiver domain is often coarsely sampled, complicating the removal of the source ghost in this domain. The third method handles the removal of the source ghost in the coarsely sampled receiver domain by training a convolutional neural network. The training data consist of coarsely sampled shot records with and without the receiver ghost that can be obtained relatively easy because the corresponding densely sampled shot records are available as well. Using reciprocity, these training data are a representative data set for removing the source ghost in the coarsely sampled receiver domain. The modeled data and field data results show that this machine learning approach is able to accurately remove the source ghost in the receiver domain. The modeled data results also show that this approach significantly improves the removal of the source ghost compared to its removal in the densely sampled shot domain.@en

In marine seismic the ghost wavefield results in deep notches in the broadband frequency spectrum corresponding to the depth of the sources and detectors with respect to the sea surface. An inverse filter is used to remove these ghost effects. Application this filter has the consequence that the notch areas are amplified. In the presence of noise, the signal as well as the noise are amplified, which can lead to an unfavourable signal-tonoise ratio. Three methods are compared with respect to signal reconstruction and effect on noise. The first method, the non-causal method is exact for the signal outside the notches and inside the notch areas the noise is controlled with a ceiling applied to the inverse filter. The second method minimizes an objective function in order to indirectly calculate the ghost-free result without explicitly using the inverse filter. Finally, the hybrid method is a combination of these two. The methods are separately applied to a shot with and without noise. In order to quantify which method is most suited with respect to both signal reconstruction and noise suppression, a quantitative analysis is carried out. A constrained closed-loop method is the most accurate for this particular case. @en

In marine seismic the ghost wavefield results in deep notches in the broadband frequency spectrum corresponding to the depth of the sources and detectors with respect to the sea surface. An inverse filter is used to remove these ghost effects. Application this filter has the consequence that the notch areas are amplified. In the presence of noise, the signal as well as the noise are amplified, which can lead to an unfavourable signal-tonoise ratio. Three methods are compared with respect to signal reconstruction and effect on noise. The first method, the non-causal method is exact for the signal outside the notches and inside the notch areas the noise is controlled with a ceiling applied to the inverse filter. The second method minimizes an objective function in order to indirectly calculate the ghost-free result without explicitly using the inverse filter. Finally, the hybrid method is a combination of these two. The methods are separately applied to a shot with and without noise. In order to quantify which method is most suited with respect to both signal reconstruction and noise suppression, a quantitative analysis is carried out. A constrained closed-loop method is the most accurate for this particular case. @en

A rough and time-variant sea surface can cause uncertainties of the source and detector locations with respect to the sea surface. Deghosting of pressure data that ignores the rough and time-variant character of the sea surface will result in noise and ringing. The effect of a rough and time-variant sea surface at the source is different from the detector side. At the source side an effective rough and time-invariant sea surface is considered, where at the detector side a rough and time-variant sea surface is considered. For both sides a deghosting method is proposed that on-the-fly will optimize the actual detector and/or source locations. The method uses wavefield propagation to take into account a rough and timevariant sea surface. In order to account for the time-variant effects the method is applied for specific windows of the data. An extreme case with a rough and time-invariant sea surface will show that the adaptive source deghosting method is able to improve the SNR after deghosting compared to a non-adaptive deghosting method. The next extreme case will show that at the detector side the window-based adaptive deghosting method will further improve the perfomance in the case of a time-variant surface.@en