Multiples elimination

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(t₀,p), where t₀ and p are the parameters describing the parabolas previously defined. Once we have these values U(t₀,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(t₀,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(t₀,p), and vice-versa.