In contrast to conventional acquisition practices, simultaneous source acquisition allows for overlapping wavefields to be recorded. Relaxing the shot schedule in this manner has certain advantages, such as allowing for faster acquisition and/or denser shot sampling. This flexibility usually comes at the cost of an extra step in the processing workflow, where the wavefields are deblended, that is, separated. An inversion-type algorithm for deblending, based on the focal transform, is investigated. The focal transform uses an approximate velocity model to focus seismic data. The combination of focusing with sparsity constraints is used to suppress blending noise in the deblended wavefield. The focal transform can be defined in different ways to better match the spatial sampling of different types of marine surveys. To avoid solving a large inverse problem, involving a large part of the survey simultaneously, the input data can be split into sub-sets that are processed independently. We discuss the formation of such sub-sets for ocean bottom node and streamer-type acquisitions. Two deblending experiments are then carried out. The first is on numerically blended ocean bottom node field data. The second is on field-blended towed streamer data with a challenging signal overlap. The latter experiment is repeated using curvelet-based deblending for comparison purposes, showing the virtues of the focal deblending process. Several challenges of basing deblending around the focal transform are discussed as well as some suggestions for improved implementations.

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Nearly-simultaneous-source (blended) acquisition differs from conventional acquisition in that seismic wavefields originating from different sources are allowed to overlap in the recorded seismic traces. This allows more flexibility in deciding the number of shots, the shot density and the effective acquisition time of a survey, but it adds the complication of having to handle blended wavefields. This thesis explores an inversion-based deblending method for wavefield separation in the marine setting. As deblending is usually an underdetermined problem, extra information in the form of additional constraints and regularization is needed to obtain a unique solution with minimal blending-noise leakage. To this end, the proposed method uses the focal transform in combination with sparsity-promoting regularization to discriminate against solutions to the blending equation that are valid, but contain excessive amounts of blending noise. The focusing operation provided by the focal transform will tend to focus the coherent signal to be extracted but will not focus equally well incoherent blending noise. Sparse solutions will tend to retain the high-amplitude focused events but not the lower-amplitude blending noise. A key feature that makes sparse solutions possible is the ability to describe curved events in a subsurface-consistent manner, using few focal domain coefficients. The focal transform can be defined in multiple ways, using one-way or two-way wavefield propagation operators. In the implementations described in this thesis, I use a crude velocity model, based on picked normal-moveout (NMO) stacking velocities, to construct focal operators that can focus surface data onto a set of depth levels where significant reflectors are found. This choice of velocity model is suboptimal for focusing purposes, but is a pragmatic compromise, given that a more detailed velocity model may not be available at the deblending phase of the processing workflow. In principle the focusing and defocusing operations involve the entire dataset, which makes the focal transform computationally expensive to evaluate. An investigated remedy is to use acquisition-specific subsets of the input data to split the problem in smaller chunks, combined with a suitable flavor of the focal transform and focal grid. Another method extension that I discuss is that of using a focal-curvelet hybrid transform for deblending. The main advantage is that events with linear moveout tend to be more sparsely represented in a curvelet basis. However, this comes at the cost of extra computational effort and some difficulty in balancing the contribution of the two transforms to the final solution. I test these approaches on both synthetic and field data, with examples on towed streamer and ocean-bottom-node acquisitions. While in most cases a perceptible amount of blending-noise leakage remains present in the results, a significant amount of blending noise is suppressed. In some cases the deblending process is able to uncover weak events previously masked by strong blending noise. When the hybrid transform is used, the results show a better recovery of events that are filtered out when the focal transform is used alone. Curved near offset events are in some cases also recovered with higher fidelity compared to using the curvelet transform alone. A significant challenge is the sometimes limited focusing for field data and synthetics as a result of trying to approximate the kinematics of complex 3D velocity models with flat-layered models and stacking velocities. The computational cost of the method is also a challenge. While working with data and focal domain subsets helps, additional measures are needed before applying focal deblending on realistically-sized field data. I make several suggestions for modifications of the method and propose extensions for future research.@en

Nowadays, using simultaneous source seismic acquisition is becoming popular in order to achieve a denser source spacing in an efficient manner. For further processing these data need to be deblended, meaning that they have to be separated in their non-overlapping constituents. In this work, we adopt a novel greedy inversion solver to design a faster version of the double focal transform, which we can use to eliminate blending noise in simultaneous source acquisition. The greedy inversion introduces a coherence-oriented mechanism to enhance focusing of the significant model space, leading to a sparse model space and fast convergence rate. Although the convergence rate of greedy inversion is larger than that of the Spectral Projected Gradient for ℓ₁ minimization (SPGL1) solver, the greedy solver is still not fast enough. We propose to use a relative tolerance strategy to speed up the greedy solver: the LSQR (Sparse Equations and Least Squares) algorithm in the inner loop of the greedy solver is stopped when the misfit change between inner iterations is less than a pre-defined relative tolerance value or when it reaches a maximum number of iterations. Synthetics and numerically blended field data examples demonstrate the validity of its application for deblending. We also investigate the effect of random noise on the deblending process, which shows that it is better to apply a denoising process before deblending in order to get an optimum result.

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In this work, we adopt a greedy inversion solver to design a fast version of the double focal transform that we can use to eliminate blending noise in simultaneous source acquisition. The greedy inversion introduces a coherence-oriented mechanism to enhance focusing of significant model space, leading to a sparse model space and fast convergence rate. Synthetics and numerically blended field data examples demonstrate the validity of its application for deblending. We also tested different inversion parameters (percentile value and weights) influencing the choice of the model subspace. The results indicate that by setting the percentile carefully and using weights it is possible to get better deblending results.@en

In this paper we examine the advantages of using a hybrid focal - curvelet transform for deblending. The focal transform is at best for curved events (typically at smaller offsets), while the curvelet transform is effective for linear events (e.g. at far offsets). Thus, the addition of the curvelet transform is very suited for events that cannot be easily reconstructed by the focal transform alone, such as linear events that are not in the range of the focal operators. The improved deblending capabilities of the hybrid focal - curvelet approach is demonstrated on both simulated and numerically blended field data.@en

Although theoretically straightforward, adapting focal deblending to realistic 5D acquisition scenarios can be challenging in practice. The two main issues that have to be dealt with are insufficiently sampled spatial dimensions and the computational effort needed for the deblending inversion. In order to deal with both issues, we propose dividing the data in 'smart' subsets, specialized for the acquisition type. Then, the deblending problem can be divided into a number of smaller problems that can be solved independently. The focal transform used for the deblending is also redefined to fit the geometry of the subsets. We examine the case of OBN acquisition and test the performance of the proposed scheme on numerically blended field data.

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The applicability of a deblending method is directly related to acquisition parameters, such as source and detector locations. We formulate focal deblending in two alternative ways. In the first case, the double focal transform is used, which relies on a well-sampled source and detector dimension. In the second case, the single-sided focal transform is used, which does not depend on a well-sampled source dimension. Comparing the deblending results, we find that although the double focal transform is superior, blending noise can be significantly attenuated using the single-sided focal transform, which allows application to more practical acquisition geometries. By combining with shot repetition, the deblending result can be further improved. @en

Blended data acquisition is gaining popularity, requiring - in most cases - a deblending process before further processing and imaging is applied. Recently, focal transform-based de- blending has been proposed. By applying subsurface-based fo- cal operators to both sources and receivers, reflection informa- tion can be sparsely represented and, thereby, separated in the focal domain from blending noise. Although focal deblending can be easily extended to handle 5D data, involving all four spatial axes in the focusing process will be computationally costly. Instead, we propose dividing the data in 'smart' sub- sets that emerge naturally from the acquisition type, and using focal operators designed for those subsets. In this way, each subset can be deblended independently from the rest. We de- fine such subsets for the case of a marine towed multi-streamer acquisition and test the deblending performance on a synthetic dataset.

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