Polarity preserving decon in ``N log N'' time

Symmetrical decon preserves polarity. Hooray!

The most primative deconvolution is a symmetrical filter, for example ${\rm FT}^{-1}(1/\vert D(\omega)\vert)$ where $\vert D(\omega)\vert$ denotes the amplitude spectrum of the data. The output ${\rm FT}^{-1}(D/\vert D\vert)$ of this filter is spectrally white. This decon filter converts a Ricker wavelet to an impulse at its center. Hooray! Notice this impulse will have the opposite polarity of that of predictive decon which attempts to spike the first lobe of the Ricker wavelet.

RickerAnnotated Figure 1. The non-causality needed is defined by the small backward distance from the center of the Ricker wavelet to its onset.