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Spectral factorization technique for estimation of an ARMA operator for multichannel deconvolution of seismic data [Note 1. Received October 1994, revision accepted May 1996. ...]
Author(s) -
Pathak R.K.,
Sengupta S.,
Sinha S.
Publication year - 1997
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1046/j.1365-2478.1997.3400263.x
Subject(s) - deconvolution , seismic trace , algorithm , blind deconvolution , matrix decomposition , seismogram , mathematics , computer science , geology , wavelet , physics , artificial intelligence , eigenvalues and eigenvectors , quantum mechanics , seismology
A new spectral factorization method is presented for the estimation of a causal as well as a causally invertible ARMA operator from the correlation sequence of seismic traces. The method has been implemented for multichannel deconvolution of seismic traces with the aim of exploiting the trace‐to‐trace correlation that exists within seismograms. A layered earth model with a small reflectivity sequence has been considered, and the seismic traces have been considered as the output of a linear system driven by white noise reflection coefficient sequences. The present method is the concatenation of three algorithms, namely Kung's method for state variable ( F , G , H ) realization using a singular value decomposition (SVD) algorithm, Faurre's technique for computation of the strong spectral factor and Leverrier's algorithm for ARMA representation of the spectral factor. The inverted ARMA operator is used as a recursive filter for deconvolution of seismic traces. In the example shown, two traces with a covariance sequence of 160 ms length have been considered for multichannel deconvolution of stacked seismic traces. The results presented, when compared with those obtained from a conventional deconvolution algorithm, have shown encouraging prospects.