![[*]](http://sepwww.stanford.edu/latex2html/cross_ref_motif.gif)
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
(http://www.delphi.tudelft.nl/SMAART/S2Breadme.htm).
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.