Dereverberation by an adaptive lattice filter

The commonly used non-adaptive deconvolution methods (e.g. predictive, homomorphic, frequency domain) are all variations on the same idea. In different ways they derive from the spectrum of the seismic trace an estimate of the basic wavelet. This wavelet is then compressed to improve the resolution and to reduce the reverberations. However, this type of wavelet estimation is statistical, and this is, at the same time, both its strength and its weakness. We know that the greater the statistical weight, the better is the estimate of the seismic wavelet, particularly when the signal-to-noise ratio is poor. On the other hand, if the wavelet is estimated from an excessive amount of data it becomes difficult to follow the variations in space and time of the seismic signal. This limitation is one of the reasons for the study of adaptive and time-varying deconvolution methods. Among the various adaptive techniques (e.g. Widrow's, Kalman's), that which involves lattice filters attempts most faithfully, from a physical point of view, to reproduce and eliminate the short period reverberations in the uppermost layers and the intrabed multipies. These reverberations, together with the waveform induced by the source, the receiver response and the absorption, tend to broaden the wavelet and so reduce the resolution.