** Next:** Predictive deconvolution
** Up:** SYNTHETIC EXAMPLE
** Previous:** SYNTHETIC EXAMPLE

Figure shows the results of the *L*^{2} and *L*^{1} deconvolutions for
the pure trace. Because the original wavelet lacked very low and very high
frequencies, I used a damping factor for both deconvolutions: 1/1000 of the
autocorrelation in the *L*^{2} algorithm, and 1/1000 of the
weighted autocorrelation at each iteration of the *L*^{1}
algorithm. The results are similar, as no noise was introduced. The ringing
around the main peaks comes from the lack of high frequencies in the data,
which forces the output to be convolved with a ``sinc'' function (impulse
response of a high-cut filter).
Then I did the same process with the noisy trace. The results are presented
on Figure . Even with a damping factor, the *L*^{2} deconvolution
cannot avoid the influence of the noise, because a damping factor is adapted
to gaussian noise. By giving the same weights to all the residuals (*W*=*Identity*
*matrix*), it overestimates the importance of the noise bursts, and damages
the output around these bursts. On the contrary, as expected, the *L*^{1}
deconvolution is insensitive to this noise.

** Next:** Predictive deconvolution
** Up:** SYNTHETIC EXAMPLE
** Previous:** SYNTHETIC EXAMPLE
Stanford Exploration Project

1/13/1998