The seismic convolutional model describes seismic wave propagation as a linear system. A seismic trace then consists of a wavelet or pulse convolved with the reflection response or reflectivity series plus additive noise.

An important problem in seismic data processing is the removal of the effect of the wavelet (spiking deconvolution or inverse filtering) in order to estimate the reflectivity series. When the wavelet is known, designing an optimal spiking filter by a least-squares approach is straightforward. For a mixed-delay wavelet, we must delay the position of the desired output spike. This delay can later be removed so that the...

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