A zero-offset signal is input to adjoint NMO to make synthetic data which is then NMO'ed and stacked. Notice that the end of one rectangle exactly coincides with the beginning of the rectangle at next larger offset. Thus, rectangle width increases with offset and decreases with time. You might fear the coding that led up to Figure 5 is a fussy and inefficient business because of all the short little summation loops. Luckily, there is a marvelous little formula that allows us to express the integral under any of the little rectangles, no matter how many points it contains, by a single subtraction.
Integration is the key.
It is only necessary to realize that the sums are, like a definite integral, representable by the difference of the indefinite integral at each end. Figure 5 is not fully consistent with Figure 1 . In Figure 5 notice that the last point in each rectangular area overlaps the next rectangular area by one point. Overlap could be avoided by shortening each rectangle by one point, but then rectangles near the apex of the hyperbola would have zero length which is wholly unacceptable. This would be better, but far from perfect.