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In this section I attenuate in the poststack domain
surface-related multiples with shaping filters
that I estimate with the and norm. These filters are
non-stationary. Figure a shows the multiple-infested data.
Figure b displays the multiple model computed with
a data-driven modeling approach Kelamis and Verschuur (2000). Note that for this
gather, the amplitude differences between the primaries and the multiples
are not very strong.
My goal is to illustrate the use of the norm
in a more general case when surface-related multiples are present in the data.
I specifically focus on the event at 1.6s in Figure a.
This event is a primary that needs to be preserved by the subtraction procedure.
The amplitude of the primary at 1.6s is well preserved
with the norm in Figure a. Again,
gave a satisfying result. However, the amplitude
of this primary is attenuated with the norm as displayed
in Figure b. Figure shows a comparison
between the subtracted multiples with the (Figure a)
and the norm (Figure b). I conclude that
the norm tends to subtract too much energy.

**win3
**

Figure 10 (a) Stack infested
with multiples. (b) The multiple model computed with the Delft modeling
approach. The subtraction is done poststack.

**win
**

Figure 11 (a) The estimated primaries
with norm adaptive subtraction. (b) The estimated primaries
with norm subtraction. The primary at 1.6s is very attenuated with
the norm. The technique preserves its amplitude
better.

**win2
**

Figure 12 (a) The estimated
multiples with the norm subtraction. (b) The estimated multiples
with the norm subtraction. The norm tends to over-fit some
multiples that creates some leaking of primaries in the estimated noise.

This last example proves that the estimation of shaping
filters can always be done with the norm. An advantage of
the inversion scheme with the Huber norm is that only one parameter
(i.e., ) controls the behavior. Thus it is easy
to switch from one norm to another.
Of course, it remains difficult to assert if the subtracted multiples
with the norm are more similar to the actual multiples than
the subtracted multiples with the norm. This judgment is
only based on qualitative considerations for few known primary
reflectors that need to be preserved.

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Stanford Exploration Project

5/5/2005