We'll need to know a wavelet in the time and space domain
whose amplitude spectrum is
(so its power spectrum is *k*_{r}).
Do not mistake this for the the helix derivative Claerbout (1998)
whose power spectrum is *k*_{r}^{2}.
What we need to use here is the square root of the helix derivative.
Let the (unknown) wavelet with
amplitude spectrum
be known as *G*.

- 1.
- Apply
*G*to the data. The prior spectrum of the modified data is now white. - 2.
- Estimate the PEF of the modified data.
- 3.
- The interpolation filter for the original data
is now
*G*times the PEF of the modified data.

Why is this more efficient?
The important point is that the PEF should estimate
the minimal practical number of freely adjustable parameters.
If *G* is a function that is lengthy in time or space,
then the PEF does not need to be.

How important is this extra statistical efficiency? I don't know.

4/27/2000