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I will illustrate the properties of the *L*^{1} deconvolution on a synthetic
trace, first without noise (``pure trace''), then with noise (several random
spikes). Two kinds of deconvolution will be considered: deconvolution with a
known wavelet, and predictive deconvolution. Though spiky noise is not usual
in real data, it might be found for some kinds of acquisition (with a bad marine
streamer for example) and is representative of the robustness of *L*^{1}-norm
processes.
Figure is a plot of all the synthetic inputs I used. The time
sampling is *dt*=4 msec; the traces contain 512 samples. The first
trace represents the synthetic wavelet; I chose it minimum-phase, in order
to optimize the result of the standard *L*^{2}-Wiener predictive deconvolution,
which I will compare to the *L*^{1} deconvolution. Its frequency band is 10-70
Hz. The second trace represents a spiky sequence of reflection coefficients.
Next comes the convolution between the synthetic wavelet and this spiky
sequence. Finally, the fourth trace represents the noisy trace, formed
with five high-amplitude spikes added to the pure trace.

** Next:** Deconvolution with a known
** Up:** Gilles Darche: L Deconvolution
** Previous:** Stability of the IRLS
Stanford Exploration Project

1/13/1998