Minimum-Variance and Maximum-Likelihood Deconvolution for Noncausal Channel Models

This paper extends the previous works of Mendel and his students on the subject of deconvolution from causal channel (wavelet) models to noncausal channel models. Noncausal wavelets occur, for example, in seismic data processing when a land vibrator is used to excite the Earth. Minimum-variance and maximum-likelihood deconvolution algorithms are developed herein for symmetrical and/or nonsymmetrical time-invariant wavelets that are excited by stationary and/or nonstationary white noise inputs. Minimum-variance deconvolution algorithms for a noncausal wavelet turn out to be quite different than those for a causal wavelet; however, maximum-likelihood deconvolution algorithms for a noncausal wavelet, which involve event detection and amplitude restoration, are essentially the same as those for a causal wavelet. Examples are provided that illustrate the performance of the different deconvolution algorithms.