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Postcoloring versus prewhitening

The output of a PE filter, as we know, is white (unless it is gapped), but people do not like to look at white signals. Signals are normally sampled at adequate density, which means that they are small anywhere near the Nyquist frequency. There is rarely energy above the half-Nyquist and generally little but marine noises above the quarter-Nyquist. To avoid boosting these noises, the ungapped PE filter is generally altered or accompanied by other filters. Three common approaches follow: The last process is called ``prewhitening'' for some complicated reasons: the idea seems to be that the prefilter removes known color so that the least-squares coefficients are not ``wasted'' on predicting what is already known. Thus the prefilter spectrum $S(\omega)^{-1}$is theoretically the inverse of the prior estimate of the input spectrum. In real life, that is merely an average of estimates from other data. If the desired output spectrum does not happen to be $S(\omega)$,it does not matter, since any final display filter can be used. Although this is a nice idea, I have no example to illustrate it.

There is also the question of what phase the postfilter should have. Here are some cautions against the obvious two choices:

Since the postfilter is broadband, its phase is not so important as that of the deconvolution operator, which tries to undo the phase of a causal and resonant earth.


next up previous print clean
Next: BLIND DECONVOLUTION Up: THE ERROR FILTER FAMILY Previous: Nonwhiteness of gapped PE-filter
Stanford Exploration Project
10/21/1998