The whole process of *de-migration* and depth migration is carried out
using GOCAD which is a software for handling 3-D surfaces. The initial
data are the time migrated surfaces and a velocity model that will be used
during the depth migration. We assume that there exists or that we can
obtain a *V*_{rms} velocity at each point of the triangulated time migrated
surface.

Provided with the initial data, one can perform the first step: the (time)
*de-migration*, in order to obtain the observed time surfaces. In the
second step, we have to do the ``exact'' inverse work of zero offset
acquisition, that is to say, map migration is a process that uses
ray-tracing to compute the path of a ray between the *de-migrated*
surface, equivalent to a free surface, and the future depth migrated surface.
From each atom of the *de-migrated* surface a ray is sent with an imposed
initial direction of shooting. This ray is computed taking into account the
refractions at each interface cut by the ray (and previously depth migrated)
and the consumption of the time *t _{0}* given by

To check the accuracy of the method described above, I have used several
examples of synthetic data: horizontal layers, dipping layers, multi-layered
time models and time syncline (that produces a triplication as a time
*de-migrated* surface). All these examples have produced good results.
In particular, I had the opportunity to observe the inverse effect of
time migration produced by *de-migration* in the case of a dipping
reflector model: the generated surface is moved down dip, is less steep and
elongated Yilmaz (1987).

11/17/1997