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Will it work? I do not know. What I do know is that it will fail for
a well-defined class of model traces, those with the so-called *Bussgang
Property*, which was defined and discussed by Rocca &al (1979). The class
includes all stationary sequences (of any color) that have a Gaussian
distribution of amplitudes, so it seems reasonable to expect that the method
will work increasingly well as the traces depart from Gaussian. A trace
consisting of a few, well-defined compact wavelets is a good example of
a far-from-Gaussian model.
How do they fail? Simply put, the Bussgang property is that if two sequences
have zero correlation, then any memoryless non-linear transformation of
either of them leaves them uncorrelated. In the present case, the HF and LF
partitions are uncorrelated, and the amplitude cubing is a memoryless,
non-linear mapping. Thus there is no prediction of the high frequencies from
the low.

I have found Thomas' textbook (1969) to be a useful introduction to
non-linear filtering.

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Stanford Exploration Project

12/18/1997