Predictive deconvolution: theory and practice

TL;DR: The least-squares prediction filter with unit prediction distance is equivalent within a scale factor to the zero-lag inverse filter as mentioned in this paper for deconvolution of seismograms, and it has been widely used in the last few decades.

Abstract: Least-squares inverse filters have found widespread use in the deconvolution of seismograms. The least-squares prediction filter with unit prediction distance is equivalent within a scale factor to the least-squares, zero-lag inverse filter. The use of least-squares prediction filters with prediction distances greater than unity leads to the method of predictive deconvolution which represents a more generalized approach to this subject.The predictive technique allows one to control the length of the desired output wavelet, and hence to specify the desired degree of resolution. Events which are periodic within given repetition ranges can be attenuated selectively. The method is thus effective in the suppression of rather complex reverberation patterns.