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In addition, multiple removal is a classic long-standing problem. The inverse scattering series (ISS) free-surface multiple elimination Various methods (e.g., Carvalho, 1992; Verschuur et al., algorithm has certain prerequisites: (1) removing the 1992; Weglein et al., 1997, 2003; Berkhout and Verschuur, reference wavefield, (2) estimation of source wavelet and radiation 1999; Dragoset et al., 2008) have been developed to either attenuate pattern, and (3) source and receiver deghosting. In this or eliminate free-surface multiples, and each method abstract, the impact of prerequisites (2) and (3) on the ISS has different assumptions, advantages, and limitations. Among free-surface multiple elimination algorithm (Carvalho, 1992; these methods, the ISS free-surface multiple elimination algorithm Weglein et al., 1997) is discussed. To improve the ISS multiple (Carvalho, 1992; Weglein et al., 1997, 2003) is fully predication, the algorithm is also modified and extended data-driven and does not need any subsurface information, to accommodate the source radiation pattern. That radiation which is a big advantage, especially under conditions of complex pattern accommodation can provide added value compared to geology. Given its prerequisites, the ISS free-surface multiple previous methods that assumed an isotropic point source for elimination algorithm (Carvalho, 1992; Weglein et al., predicting amplitude and phase of free-surface multiples. All 1997, 2003) can, in principle, predict the exact amplitude and these prerequisites can be provided by Green's theorem methods phase of all free-surface multiples at all offsets and remove without requiring subsurface information. They are consistent them through a simple subtraction without adaptively subtraction with the ISS free-surface multiple elimination algorithm.

The eliminating all surface related multiples. For this method the data Q (zn) matrix can bc considered to be the overall reflection itself is used as the multiple prediction operator.

Abstract The simulation industry is rapidly moving towards the frequent use of complex reservoir models including such features as faults, implicit well terms, and thermal or compositional effects. All of these things can pose great difficulties for the standard direct elimination methods typically found in reservoir simulators. This paper takes a new look at sparse Gaussian elimination methods in the context of the current technology and trends in simulation and computing. A novel implementation is described, and numerical results are presented that indicate that this implementation can be a more effective tool for simulation than previous versions of sparse elimination. Introduction It is well known that the solution of linear equations can account for far more than half of the total computational effort in a numerical reservoir simulation. Because of this a great deal of attention has been given to the development of effective (i.e., accurate and efficient) methods for solving such equations. Major recent advances have been made in the technology of iterative methods, especially those based on conjugate-gradient-like iterations (cf., References 1, 8, and 12 for example). Despite this, however, there is still strong evidence that direct methods, based on Gaussian elimination, can play an important role. In addition to the moderate-size two-dimensional models on which such methods have traditionally been used, it appears that direct methods can also be useful for a variety of complex fully-implicit reservoir models incorporating such features as faults, implicit well models, or compositional or thermal effects. Such models, which are coming into increasingly-more-frequent use, can pose great difficulties for even the best iterative methods. Moreover, some of the newer iterative methods that may be capable of solving extremely difficult linear systems require the solution of certain submodels that seem most amenable to efficient solution by direct methods. Most direct methods traditionally used in reservoir simulators are based on band Gaussian elimination in combination with a clever re-ordering of the unknowns to exploit certain structural features of the linear equations. The most commonly-mentioned method is the D4-Gauss method due to Price and Coats. In the past ten years, however, there has been substantial interest in more general sparse Gaussian elimination methods that can more fully exploit the large number of zero entries in the coefficient matrices arising from reservoir simulation. Within the simulation industry, there have been a number of proposals for such methods and several papers have examined the performance of sparse Gaussian elimination in the context of reservoir simulation. By and large, the methodology of these studies has involved the application, with little modification, of high-quality general-purpose codes developed by specialists in numerical linear algebra. The usual conclusion has been that, especially for larger problems, sparse methods can offer some advantages over simpler alternatives such as band elimination or D4-Gauss, but that the gain does not warrant the significant increase in code complexity. This has seemed to be particularly true on the vector and array processors now so widespread in the industry; in fact, the sparse methods tested were often very uncompetitive on such machines.

The theory of surface-related multiple elimination has already An iterative approach is proposed to the process of surface-related been described in literature (Verschuur et al, 1992) but here some multiple elimination. If the original data is used as initial guess, the conventional expression is obtained (series expansion, Verschuur different formulations will be given. The theory is described in et al, 1992). If the output of the Radon multiple elimination the space-frequency domain, where all data can be treated per method is used as initial guess, very effective and efficient frequency component separately.

We explore feasibility of surface-related multiple elimination by two-step separation where primaries and multiples are separated in the latent space of autoencoder. First, we train a convolutional autoencoder to produce orthogonal embeddings of primaries and multiples. Second, we train another network to classify the latent space embedding of target data into respective wave types and decode predictions back to the data domain. Moreover, we propose an end-to-end workflow for generation of realistic synthetic seismic data sufficient for knowledge transfer from training on synthetic to inference on field data. We evaluate the two-step separation approach in synthetic setup and highlight strengths and weaknesses of using masks in encoder latent space for surface-related multiple elimination.