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After NMO correction, the primaries are described by approximately
horizontal lines: their corresponding *p*-parameters are close to 0.
On the other hand, multiples, and especially long-period multiples, should
be characterized by large *p*-parameters.
Thus, the idea is to transform the NMO-corrected data set *d*(*t*,*h*) into
another set of values *U*(*t*_{0},*p*), where *t*_{0} and *p* are the parameters
describing the parabolas previously defined. Once we have these values
*U*(*t*_{0},*p*), the separation of the multiples and the primaries is
determined by the choice of a cut-off *p*-parameter: above this parameter,
we set all *U*(*t*_{0},*p*) to 0. To avoid truncation effects, the setting to 0
actually uses a tapering process.

Some restrictions apply. The multiples should be long-period, to have
large values of *p*. Also, the parabolic modeling is less valid at far
offsets. Finally, it is preferable to have only flat reflectors to
have this parabolic modeling. However, I haven't yet studied the effect of
dip on the parabolic transforms.

Finally, the problem is now how to transform the data *d*(*t*,*h*) into the
values *U*(*t*_{0},*p*), and vice-versa.

** Next:** EXPRESSIONS OF THE PARABOLIC
** Up:** WHY PARABOLIC TRANSFORMS?
** Previous:** Parabolic shape of the
Stanford Exploration Project

1/13/1998