Forel (1988) shows how the DMO process can be split in a velocity independent shrinking of the input trace and a standard NMO step.
First an array of zero offset locations has to be designed. Each nonzero offset trace contributes to all zero offset traces whose combined source-receiver location lies in between the nonzero offset source and receiver. b is the distance between zero offset location and the midpoint of the nonzero offset experiment.
In the first step the nonzero offset trace time tn is transformed into t1:
|k2 = h2-b2||(17)|
After processing all nonzero offset traces a standard normal move out of the (k,t1) panels results into a zero offset data set. The final NMO step permits a traditional velocity analysis. Unlike conventional NMO processing, DMO does not assume any particular reflector dip.
The equation set (A-3), (A-4) and (A-5) can be solved for (x,z) instead of (tn,tz). The points P(x,z) which fulfill the described conditions for varying traveltimes are called the locus of constant replacement point (lcr). Each P is the actual tangential point of an ellipse tn and a circle centered at a fixed B. The two-way traveltime t(PB) is t0. The traveltime t(SPR) is tn. The lcr is a circle: