Wiener spiking deconvolution and minimum-phase wavelets; a tutorial

While working on the problem of enemy missile fire prediction at MIT during World War II, Norbert Wiener developed a statistical process which separated radar signals from noise. The process was originally known as smoothing or Wiener prediction filtering. The inverse process of unsmoothing, or prediction error filtering, was called decomposition and was later termed deconvolution. Today, prediction error filtering is the most commonly used technique for processing reflection seismic data. Prediction error filtering can be classified as either spiking or predictive deconvolution. This tutorial explains spiking deconvolution and elucidates how the abstract mathematics used to design spiking filters are actually easy to understand. First, the convolution model upon which deconvolution theory is based is briefly reviewed. This model breaks down the seismic trace into individual components. Spiking deconvolution makes assumptions concerning each of these components. It is clearly shown how the required assumptions are interwoven with the mathematical development of spiking filter design. Finally, a few examples illustrate the importance of minimum phase wavelets for acceptable filter performance.