In exploration there are two kinds of horizontal truncation problems. The first, which is at the end of the geophone cable, affects mainly common-midpoint stacking. The second is at the geographical boundaries of the survey and affects mainly migration. In both migration and stacking, hyperboloids are collapsed to points. But the processes differ because of the data itself. With stacking, it is predictable that energy will dip downward toward the far-offset cable truncation. With migration, reflectors can dip either downward or upward at the ends of the section. The downward-dipping case is better behaved. There seismic events move smoothly from the boundary to the interior.
The troublesome case occurs with migration when the seismic events dip upward at the edges of the survey. Then downward continuation moves seismic energy toward the boundary. On arriving at the boundary, it bounces back with opposite dip, and interferes with energy still moving toward the boundary. The problem may be reduced by appending space to the sides of the dataset, thus providing the dipping energy with a place to go. (You have previously decided what initial data padding to put in this space).