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Multiple attenuation with the Sigsbee2B dataset

The Sigsbee2B dataset was designed to generate strong surface-related multiples, the surface being the water surface. Figure [*] shows the true stratigraphic interval velocity model for this dataset. The data were created with a 2-D acoustic finite difference modeler with constant density. Two datasets were generated: one with a free surface in Figure [*]a (FS) and one without a free surface in Figure [*]b (NFS). Both receiver and source ghosts are included in the modeling with or without free surface ( We can then directly subtract the two datasets to obtain a very accurate prestack model of the surface-related multiples, without the need for SRMP.

In complex geology, multiple attenuation results should be assessed after migration; then, the effects of the multiple attenuation technique on the amplitudes of the primaries in angle domain common-image gathers or on migrated images at zero offset (Figure [*]) can be inspected. For the Sigsbee2B dataset, a split-step double square-root (DSR) migration code with three reference velocities is used Popovici (1996); Stoffa et al. (1990). It is interesting to see that in Figure [*]a the multiples are very weak after migration below the salt compared to the constant offset sections in Figure [*]a. In particular, the water bottom multiple seems to disappear. This is because the multiples are extremely distorted by the migration process in the vicinity of the complex salt structure. Compared with the migration of the primaries only in Figure [*]b, the multiples in Figure [*]a are masking a lot of primaries in the deepest part of the model and need to be removed.

Two important tests are carried out in this section. Firstly, because the true primaries and multiples are known, the noise and signal PEFs can be ideally estimated without SRMP or the Spitz approximation and used for the separation. Secondly, in the more realistic case where only the model of the multiples is known, noise attenuation results are shown with 2-D or 3-D filters. The next section demonstrates that when an accurate model of the noise and signal is available, the signal can recovered with minimum distortion.