A model reduction algorithm by spline approximation in the deconvolution of seismic signals

This paper presents a new method for obtaining ap - proximate low-order recursive (ARMA) realizations of convolution models. It is based upon optimum piecewise linear or cubic spline approximation of the convolution kernel. The method may be efficiently used in the deconvolution of seismic signal. The basic seismic wavelet is approximated by splines and a fixed-lag smoothing state-space representation, equivalent to the resulting ARMA model, is derived. Use of Kalman filtering gives fixed-lag smoothed estimates of the so-called reflection coefficient sequence. Adaptive estimation is used in the case when the seismic wavelet is not known apriori. Simulation results using a Ricker wavelet are presented, which illustrate the performance af the proposed method.