The use of the conjugate-gradient algorithm in the computation of predictive deconvolution operators

A number of excellent papers have been published since the introduction of deconvolution by Robinson in the middle 1950s. The application of the Wiener‐Levinson algorithm makes deconvolution a practical and vital part of today’s digital seismic data processing. We review the original formulation of deconvolution, develop the solution from another perspective, and demonstrate a general and rigorous solution that could be implemented. By “general” we mean a deterministic time‐varying and multichannel operator design, and by “rigorous” we mean the straightforward least‐squares error solution without simplifying to a Toeplitz matrix. Also we show that the conjugate‐gradient algorithm used in conjunction with the least‐squares problem leads to a satisfactory simplification; that in the computation of the operators, the square matrix involved in the normal equations need not be computed. Furthermore, the product of this matrix with a column matrix can be obtained directly from the data as a result of two cascad...