INTERPOLATION

We'll need to know a wavelet in the time and space domain whose amplitude spectrum is $\sqrt{k_r}$(so its power spectrum is k_r). Do not mistake this for the the helix derivative Claerbout (1998) whose power spectrum is k_r². What we need to use here is the square root of the helix derivative. Let the (unknown) wavelet with amplitude spectrum $\sqrt{k_r}$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.