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Let's suppose the NMO-correction of a CMP gather is performed with the velocity
curve of the primaries (velocity *V*_{p}). A multiple with RMS velocity *V*_{m}
and 0-offset time *t*_{0} will be moved to the position:
| |
(1) |

Defining the residual slowness 1/*V*_{r} and the parameter *p* by:
a series expansion of *t*(*h*) will give:
| |
(2) |

*V*_{r}^{2} is guaranteed to be positive, since we expect the velocity of a
multiple to be smaller than the velocity of a primary at the same 0-offset
time. So, for ``not too large'' offsets, the shape
of a multiple turns out to be parabolic after NMO-correction.

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** Up:** WHY PARABOLIC TRANSFORMS?
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Stanford Exploration Project

1/13/1998