Hyperbolic stacking over offset may be the most important computer process in the prospecting industry. It is more important than migration because it reduces the data base from a volume in (s,g,t)-space to a plane in (y,t)-space. At the present time few people who interpret seismic data have computerized seismic data movies, so most interpreters must have their data stacked before they can even look at it. Migration merely converts one plane to another plane. Furthermore, migration has the disadvantage that it sometimes compounds the mess made by near-surface lateral velocity variation and multiple reflections. Stacking can compound the mess too, but in bad areas nothing can be seen until the data is stacked. In addition to its other drawing points, stacking gives as a byproduct estimates of rock velocity.
Historically, stacking has been done using ray methods, and it is still being done almost exclusively in this way. Migration, on the other hand, is more often done using wave-equation methods, that is to say, by Fourier or finite-difference methods. Both migration and stacking are hyperbola-recognition processes. The advantages of wave-equation methods in migration have been many. Shouldn't these advantages apply equally to stacking? It would seem so, but current industrial practice does not bear this out. The reasons are not yet clear. So the latter part of this section really belongs to a research monograph with the facetious title ``Theory That Should Work Out Soon.'' More advanced ideas of velocity estimation are later. Wave-equation stacking and velocity-determination methods are ingenious. Perhaps they have not yet been satisfactorily tested, or perhaps they are just imperfectly assembled. The reader can guess, and time will tell.
One possible reason why much of this theory is not in routine industrial use is that the issue of stacking to remove redundancy may be more appropriately a statistical problem than a physical one. To allow for this contingency I have included a bit on ``wave-equation moveout,'' a way of deferring statistical analysis until after downward continuation. Another possibility is that the problems of missing data off the ends of the recording cable and spatial aliasing within the cable may be more flexibly attacked by ray methods than by wave-equation methods. For this contingency I have included a brief subsection on data restoration. Whatever the case, the data-manipulation procedures in this chapter should be helpful.