SPECTRAL FACTORIZATION TECHNIQUE FOR ESTIMATION OF AN ARMA OPERATOR FOR MULTICHANNEL DECONVOLUTION OF SEISMIC DATA

A new spectral factorization method is presented for the estimation of a causal as well as a causally invertible ARMA operator from the corr elation sequence of seismic traces. The method has been implemented fo r multichannel deconvolution of seismic traces with the aim of exploit ing the trace-to-trace correlation that exists within seismograms. A l ayered earth model with a small reflectivity sequence has been conside red, and the seismic traces have been considered as the output of a li near system driven by white noise reflection coefficient sequences. Th e present method is the concatenation of three algorithms, namely Kung 's method for state variable (F,G,H) realization using a singular valu e decomposition (SVD) algorithm, Faurre's technique for computation of tile strong spectral factor and Leverrier's algorithm for ARMA repres entation of the spectral factor. The inverted ARMA operator is used as a recursive filter for deconvolution of seismic traces. In the exampl e shown, two traces with a covariance sequence of 160 ms length have b een considered for multichannel deconvolution of stacked seismic trace s. The results presented, when compared with those obtained from a con ventional deconvolution algorithm, have shown encouraging prospects.