A field profile consists of the seismograms of one shot and many receivers along a line. Migration of a single profile, or of many widely separated profiles, demands a conceptual basis that is far removed from anything discussed so far in this book, namely, exploding-reflector and survey-sinking concepts. Such a conceptual basis exists, predates (Claerbout ), and seems more basic than that of exploding reflectors or survey sinking. I call this older imaging concept the U/D imaging concept.
The sinking concept seems to demand complete coverage in shot-geophone space. Exploding reflectors requires many closely spaced shots. On the other hand, profile imaging with the U/D concept has no requirement for density along the shot axis. An example of a dataset that could only be handled by the older concept is a sonobuoy. A sonobuoy is a hydrophone with a radio transmitter. It is thrown overboard, and a ship with an air gun sails away, repeatedly firing until the range is too great. The principle of reciprocity says that the data is equivalent to a single source with a very long line of geophones.
While improving technology is leading to greater sampling density on the geophone axis, we are unlikely to see increasing density in shot space. There are only twenty-four hours in a day, and we must wait ten seconds between shots for the echoes to die down. So, given a certain area to survey and a certain number of months to work, we end out with an irreducible shotpoint density. Indeed, with three-dimensional geometries proving their worth, we may see less spatial sampling density. Poor sample density in shot space is a small impediment to profile methods.
Unlike the exploding-reflector method and the survey-sinking method, U/D concepts readily incorporate modeling and analysis of multiple reflections. Indeed, an ingenious algorithm for simultaneous migration and de-reverberation is found in FGDP. In principle it can be applied to either field profiles or slant stacks.
Wave equation methods have been suggestive of new ways of making weathering-layer corrections. Yet none have yet become widely accepted in practice, and it is too early to tell whether a DSR approach or a profile approach will work better.
All these considerations warrant a review of the profile migration method and the U/D imaging concept. We could easily see a revival of these in one form or another.