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.

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Current developments in the field of surface multiple removal often aim at estimating primaries in a large-scale inversion process. The advantage of redefining surface multiple removal as a closed-loop process is that certain pre-processing steps can be included in the inversion process, such that an optimum multiple removal is guaranteed. One example is the receiver ghost, as the surface-related multiple elimination process requires deghosted data as input. In this chapter the receiver ghost effect is included in the closed-loop primary estimation process. Thus, primaries are directly estimated without the ghost effect such that its multiples and the ghost effect of all these wavefields add to the observed data with ghost. The proposed method including the ghost is validated on simulated and field data with a slanted cable.

In this chapter we will present the 3D Closed-Loop SRME algorithm (CL-SRME).
The fundamental theory will still be the same as the 2D algorithm presented in the previous chapter, but now practical considerations (regarding the data volume) will produce a different processing strategy. We will start with an introduction and a literature review on the field of 3D multiple separation. Then we will introduce the GSMP (’Generalized Surface Multiple Prediction’) method. This method will allow the efficient calculation of large matrix products. Two type of products will be discussed, the ’correlation product’ and the ’convolution product’. Once all tools are in place, we can describe our scheme for the 3D CL-SRME method. Without any loss of generality, we will make constant emphasis on the shallow reflector geologies, as this ones are the most relevant for the current work.

Surface-related multiple elimination (SRME) is one of the most commonly used methods for suppressing surface multiples. However, in order to obtain an accurate surface
multiple estimation, dense source and receiver sampling is required. The traditional approach to this problem is performing data interpolation prior to multiple
estimation. Though appropriate in many cases, this methodology fails when big data gaps are present or when relevant information is not recovered, e.g. near-offset data in shallow-water environments. We propose a solution in which multiple estimation is performed simultaneously with data reconstruction, such that data reconstruction helps obtaining better multiple estimates and in which the physical primary-multiple relationship helps constraining the data interpolation. To accomplish this we propose to extend the recently introduced Closed-Loop SRME (CL-SRME) algorithm to account for primary estimation in the case of coarsely sampled data. This is achieved by introducing a focal domain parameterization of the primaries in a sparsity-promoting CL-SRME method. Results proof that the method is capable of reliably estimating primary data in case of shallow water and with large undersampling factors.

Surface-related multiple elimination (SRME) is one of the most commonly used methods for suppressing surface multiples. However, in order to obtain an accurate surface multiple estimation, dense source and receiver sampling is required. The traditional approach to this problem is performing data interpolation prior to multiple estimation. Though appropriate in many cases, this methodology fails when big data gaps are present or when relevant information is not recovered, e.g. near-offset data in shallow-water environments. We propose a solution in which multiple estimation is performed simultaneously with data reconstruction, such that data reconstruction helps obtaining better multiple estimates and in which the physical primary-multiple relationship helps constraining the data interpolation. To accomplish this we propose to extend the recently introduced Closed-Loop SRME (CL-SRME) algorithm to account for primary estimation in the case of coarsely sampled data. This is achieved by introducing a focal domain parameterization of the primaries in a sparsity-promoting CL-SRME method. Results proof that the method is capable of reliably estimating primaries data in case of shallow water and with large undersampling factors.

Recently, a new approach to multiple removal has been introduced: estimation of primaries by sparse inversion (EPSI). Although based on the same relationship between primaries and multiples as in surface-related multiple elimination (SRME), it involves quite a different process. Instead of the traditional prediction and subtraction of multiples, in EPSI the unknown primaries are the parameters of a large-scale inversion process. The downside is its long calculation times, involving the equivalent of about 100-200 SRME processes. For improving the accuracy and efficiency in multiple removal a hybrid SRME+EPSI is proposed, which makes use of the strongest points of both SRME and EPSI methodologies. It appears that the final result is better than either the SRME or the EPSI algorithm alone and where the calculation time is limited to the equivalent of 10-20 SRME processes.