The output of predictive deconvolution

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The method of predictive deconvolution, with prediction distance greater than unity, is widely used in the oil industry to eliminate multiple reflections from seismic reflection data. When the prediction distance is unity the method corresponds to autoregressive modeling. In this case the output of the deconvolution becomes the reflectivity series of the subsurface for a minimum‐phase wavelet. For prediction distances greater than unity, prediction filters are related recursively (Ulrych et al., 1973). We show that another interesting relationship exists between the autoregressive prediction error operator and the prediction error operator with arbitrary prediction distance. This relationship can be used to investigate the output of predictive deconvolution applied to nonminimum‐phase wavelets. As a consequence, we can show that predictive deconvolution and the phase correction method for Vibroseis data (Ristow and Jurczyk, 1975) are nearly identical.