I mentioned already the multiples elimination method, proposed by Hampson
(1986). The primaries should correspond to small values of *p*, while
the multiples (especially water-bottom multiples and peglegs) should
map to large values of *p*. However, when the primaries are too deep,
their peglegs tend to have also small *p*-parameters, since
*p*=1/(*t _{0}V*

Then, for land data, the ground-roll, having a very low velocity, should
map to regions of very large values of *p*. Consequently, canceling the
*U*(*t _{0}*,

Finally, as we will see on real marine data, the direct arrivals and
their low-frequency trend will also map to large values of *p*, because
they have a linear moveout. However, they actually cover a vast region
of the *t _{0}*-

However, the role of the mute is essential. After NMO correction, the
seismic events at far offsets are stretched, especially for small 0-offset
times. Then, they will map to a vast region of *p*, since they can be
described by several parabolas. If a mute is not sufficient, it is also
possible to give low weights to these far offsets, since the Toeplitz
structure makes weighting easy to use. Furthermore, the seismic events
at far offsets don't fit the parabolic modeling, which justifies in this
context the under-weighting in this region.

Actually, I will use for my examples two marine shot-gathers, known to
contain no dipping events, nor important diffractions. Consequently,
the NMO correction can be reliable. The first one contains very strong
long-period water-bottom multiples, and I will show on it the efficiency
of the multiples elimination. The second one will be used for
interpolation purposes. Some traces are missing : the mapping to
the *t _{0}*-

1/13/1998