A Fast Optimal Deconvolution Algorithm for Real Seismic Data Using Kalman Predictor Model

Adaptive Seismic Deconvolution via the Canonical Variate Analysis

“…The role of this Hankel matrix in "system identification" is a well known one, as seen in the works of Tse and Wienert [19] and Mehra [20]. These techniques have also been earlier applied to the seismic deconvolution problem in [8]. However, the singular value based techniques arc generally known to be statistically more consistent and numerically more stable.…”

“…Since the actual reflection sequence Uk ustd for these studies is a scaler time sequence, the vector Wk of (7) and (30) can be written as (42) where g is an appropriately dimensioned column matrix. The wavelet shape used f01 calculating the 1 arameters of the model (7)(8) for the generation of the synthetic seismogram was taken to be given by f(t)=54.4 t e-100 '=1360 t e-5000 t as in [l]. Figure lh :-hows the resulting noise free synthetic seismogram.…”

“…?at recent interest and a number of efforts have been rt!ported which apply the modern estimation theory techniques to improve the performance over the classically used, simple predictive deconvolution techniques. Amongst some of the notable recent approaches to this problem for seismic applications are the "white-noise" B~rnoulli sequence estimationfdetection approach of Mendel and his co-workers [l-4] (see also [S]) and the adaptive predictive deconvolution approaches of Griffiths [6], Prasad and Mahalanabis [7] and their co-workers [8][9][10]. The state-variable formulation of the deconvolution problem (also called the input white-noise estimation problem) and its several solutions suggested in [I-S] are very elegant and should be very useful whenever sufficient information is available about the nature of the seismic wavelet to warrant such modelling.…”

“…The state-variable formulation of the deconvolution problem (also called the input white-noise estimation problem) and its several solutions suggested in [I-S] are very elegant and should be very useful whenever sufficient information is available about the nature of the seismic wavelet to warrant such modelling. The adaptive, tim~-varying op!rators either in the tapped-delay line or the !attic~ filter forms suggested in [6][7][8][9][10], on the other hand, are likely to prove effective on nonstationary seismic data as from offshore experiments.…”

Seismic data deconvolution using Kalman filter based on a new system model

“…For instance, Crump (1974) first uses the discrete Kalman filter successfully for the deconvolution of the seismic signals to generate an estimate of the reflectivity function. Mahalanabis et al (1981Mahalanabis et al ( , 1983 propose fast and adaptive Kalman filter algorithms. Using the Kalman filter with different dimensions applied to seismic traces, Sayman (1992) uses optimal fixed-interval smoothing filters to attenuate the unexpected high-frequency energy caused by the original Kalman filter.…”