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I show with a 3-D field data example that the subtraction method
works better than the filtering approach. The dataset is also used in
Guitton (2003). Figure shows
the input data with an overwhelming amount of noise. For the
subtraction and filtering methods, I use 3-D non-stationary
prediction-error filters (PEFs) to approximate the modeling and inverse
covariance operators, respectively. These filters have been estimated
with a weighted PEF estimation scheme Guitton (2003)
to take into account the amplitude variations in the data. The PEFs
are estimated from a noise and signal model that I computed by
band-passing the data: 0. to 45 Hz filtering for the signal model and
35 to 125 Hz. filtering for the noise model. Note that with the subtraction method, the modeling
operators are computed with inverse PEFs. Unfortunately, these inverses are not
guaranteed to be stable Rickett (1999).
Therefore, with PEFs, the subtraction method might not be always feasible.
Figures and
show the noise attenuation results
for the filtering and subtraction method, respectively. Note that the PEFs and
the patches for the two methods are identical. In addition, the
convergence of both methods during the noise attenuation phase is
very similar.
It is interesting to notice that the subtraction method gives a cleaner
panel, with more continuous reflectors everywhere. The amplitudes are
also stronger with the subtraction method, as seen in the time slice
section.

**data3d
**

Figure 1 A near-offset section of
a 3-D land survey. Some signal is visible near 0.42 s. This section
is contaminated with ground-roll. The amplitude varies across time
and offset with missing traces as well.

**separ-ns-weight-AGC-3d
**

Figure 2 Estimated signal with
the filtering approach. The noise is well attenuated.

**separ-ns-weight-AGC-nemeth-3d
**

Figure 3 Estimated signal with
the subtraction method. The signal is stronger and more continuous
than in Figure .

** Next:** Conclusion
** Up:** Guitton: Signal/noise separation
** Previous:** Why is it working
Stanford Exploration Project

7/8/2003