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The prestack seismic input data are decomposed into input blocks for 5D interpolation. These blocks are extracted CMP
gathers that have NMO applied and all the necessary statics. The blocks are CMP super-gathers that overlap in time and
space. A typical size for a super-gather is 16 x 16 CMP bins, and 250 msec in length.

The program then interpolates each irregularly sampled input block to a regularly sampled output block. The
interpolation is performed on each frequency slice of the input data block. A forward, non-uniform, four
dimensional, Fourier transform is performed on the input frequency slice being operated upon.

Since the input data are irregularly spaced, the Fourier spectrum will contain what is referred to as spectral leakage.
To improve this spectrum for interpolation purposes, the Calcoulee Continuum uses the Anti Leakage Fourier
Transform (ALFT) as described by Xu et al., 2005. This is an iterative procedure. On each iteration, the most significant,
highest amplitude, spectral events are extracted from the four dimensional Fourier domain and saved. These
extracted spectral events are also reconstructed and removed from the input data being operated upon. The residual
input data are put through the forward, non-uniform Fourier transform again for the start of the next iteration.
This iterative process is continued until the amplitude of the extracted spectral events falls below the user-
specified level. The collected spectral events are put through a reverse four dimensional Fourier transform to
construct the regularly sampled output block. Finally, the interpolated regularized output CMP gathers are then
constructed from the interpolated output blocks.
5D Interpolation