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 *t*_{n} is transformed
into *t _{1}*:

(16) |

k = ^{2}h-^{2}b
^{2} |
(17) |

(18) |

After processing all nonzero offset traces a standard normal move out of the
(*k*,*t _{1}*) 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 *t*_{n} and
a circle
centered at a fixed *B*. The two-way traveltime *t*(*PB*) is *t _{0}*.
The traveltime

(19) |

11/18/1997