I applied L1 deconvolution on this gather, with the L2 predictive filter as initial estimate; I computed one 50-sample filter for all traces. The residuals of this L1 deconvolution are presented in Figure , with also the difference between the L2 residuals and the L1 residuals. As I expected, the L1 residuals are a sharpened version of the L2 residuals: the largest amplitudes have been increased, the smallest have been decreased. This is not really obvious on the sections, but it appeared clearly when I computed the kurtosis of the traces in the central part of the gather (between 1.5 and 2.5 sec, to avoid the strong water-bottom reflections): the kurtosis of the L1 residuals were larger than those of the L2 residuals. It also appears on the difference section when we look at the water-bottom reflection. However, the estimation of the phase of the seismic wavelet has not been improved, and especially the precursor has not been removed, but accentuated.
This sharpening of the residuals presents the advantage of increasing the contrast between reflectors, and stressing the main reflectors. Moreover, as this gather presents some lateral variations of amplitude, these variations will be enhanced by the sharpening of the residuals.
I also tried a Lp deconvolution with p=0.1, though the objective function is no longer a norm. However, with the L2 filter as initial estimate, the algorithm converged. As expected, the result was once again a sharpening of the L2 residuals, but it was very similar to the result of the L1 deconvolution.