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For the simple 1-D example under consideration, the filter coefficients
are now estimated with the norm approximated with the Huber function.
In Figure , I display the result of the adaptive subtraction
when the norm is utilized to estimate a single shaping filter
(equation () with a small ).
**1Dl1
**

Figure 5 (a) The signal estimated with the
norm. (b) The noise estimated with the norm.

The estimated signal in Figure a resembles the true signal
very well, and so does the estimated noise.
It is easy to check that the energy (in a sense) in Figure a (*e*_{1}=2) is less
than the energy (in a sense) in Figure a
(*e*_{1}=3.2).
Figure shows the shaping filter associated with the
norm. This filter is a spike at *lag*=0.
This simple 1-D example demonstrates that the norm should
be utilized whenever significant amplitude differences exist between
multiples and primaries. In the next section, a synthetic
example where internal multiples are attenuated illustrates the
properties of the subtraction.

** Next:** 2-D data example: attenuation
** Up:** Principles of norm and
** Previous:** Shaping filters and the
Stanford Exploration Project

5/5/2005