The whole interpolation scheme can be divided into five discrete modules:

- Each trace is low-pass filtered. By filtering the data in time, the spatially aliased portion of the spectrum is removed.
- The low-pass filtered data are interpolated in space by performing a one-dimensional Fourier transform, zero padding, and performing the inverse transform.
- The low-frequency (LF) data are then cubed in the time domain in order to broaden the spectrum. This is done to both the original and interpolated LF data.
- The cubed LF traces ([
*f*_{low}(*t*)]^{3}) are then used to find a shaping filter. For each original trace, a filter*b*(*t*) is found such that*b*(*t*)*[*f*_{low}(*t*)]^{3}=*f*_{all}(*t*)*f*_{all}(*t*) is the wide-band data including high- and low- frequency. This is done using conjugate gradients with the subroutine`shp()`(Appendix). - Once the shaping filter is found, it is used to reconstruct the HF data on the interpolated traces.

11/18/1997