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I tried the same processing with exponential and gaussian noise. Unfortunately,
the *L*^{1} minimization is no more efficient. The noise samples now have various
amplitudes, about the same repartitions as the original trace, and cannot be
isolated from the seismic samples by the original criterion of small
weight: they have all kinds of weighting. The *L*^{1} norm itself does not
improve the result of the *L*^{2} deconvolution; the most usual way to suppress
the noise is to use large damping factors, which is not a typical
characteristic of the *L*^{1} norm. Moreover, even if the noise *n* is
gaussian, white, and uncorrelated with the seismic data, the *L*^{1} normal
equations cannot use these properties, because the correlations terms (*n*^{T}*n*,
*y*^{T}*n*) will be weighted by the matrix *W*, and replaced by *n*^{T}*Wn* and *y*^{T}*Wn*
(which may not vanish). I will suggest in the last part a method to
cope simultaneously with two kinds of noise, for example gaussian and spiky
noise, using *L*^{1} and *L*^{2} norms simultaneously.

** Next:** L norm and non
** Up:** SYNTHETIC EXAMPLE
** Previous:** Predictive deconvolution
Stanford Exploration Project

1/13/1998