Sharp Deconvolution in Elimination of Multiples

Introduction To remove effects of unwanted signatures such as a long seismic wavelet or multiples by deconvolving them from the seismic trace, classical methods of deconvolution (Robinson and Treitel, 1980), (Webster and Levin, 1978) are implemented very successfully: spiking and predictive deconvolution respectively. Herewith we would like to show that development of mathematical aspects of solving ill-posed problems enables to contribute into the practice of seismic data processing. Traditional multiple suppression is based on predictive deconvolution realized with the Wiener filter elaborated for stationary time series. We try to take into account that a. records of a pulse are highly non-stationary, b. information about reflections is contained not only in record cross-correlations but in autocorrelations as well: it is the starting point of the classical predictive deconvolution that the well-seen self-repetiti