The advantage of common-midpoint analysis is that the effects of earth dip tend to show up mainly on the midpoint axis, and the effect of seismic velocity shows up mainly on the offset axis. Our immediate goal is to define an invertible, wave-equation approach to determination of interval velocity. The disadvantage of common-midpoint analysis is that it is nonphysical. A slant stack at common geophone simulates a downgoing Snell wave, and you expect to be able to write a differential equation to describe it, no matter what ensues, be it multiple reflection or lateral velocity variation. A common -midpoint slant stack does not model anything that is physically realizable.
Nothing says that a partial differential equation exists to extrapolate such a stack.
This doesn't mean that there is necessarily anything wrong with a common-midpoint coordinate system. But it does make us respect the Snell wave approach even though its use in the industrial world is not exactly growing by leaps and bounds. A new four-component system will now be defined. Next the surface offset h ' is defined. We will not use the old definition of offset.