Shot continuation is an obvious task for a data cube extrapolation program. There are two applications of shot continuation. First is the obvious one of repairing holes in data in an unobtrusive way. Second is to cooperate with reflection tomographic studies such as that proposed by Mattias Schwab Schwab (1993).
Offset continuation is a well-developed topic because of its close link with dip moveout (DMO). DMO is heavily used in the industry. I do not know how the data-cube extrapolation code I am designing here would fit into DMO and stacking, but because these are such important processes, the appearance of a fundamentally new tool like this should be of interest. It is curious that the DMO operator is traditionally derived from theory, and the theory requires the unknown velocity function of depth, whereas here I propose estimating the offset continuation operator directly from the data itself, without the need of a velocity model.
Obviously, one application is to extrapolate off the sides of a constant-offset section. This would reduce migration semicircles at the survey's ends.
Another application is to extrapolate off the cable ends of a common midpoint gather or a common shot point gather. This could enhance multiple prediction or reduce artifacts in velocity analysis.
The application that drove me to putting the code in its present form is extending Kjartansson-style tomography.