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The first-anelliptic example in Figure
would have been more realistic if we had simply omitted
the depth scale entirely.
Mathematically this means rewriting
equation () explicitly in terms of vertical traveltime,
finding the first-anelliptic equivalent of equation ().
To do this,
replace *M*_{z} *C* by *T*(0)^{2},
*S* by *x*^{2},
and
*M*_{x} by ,obtaining the first-anelliptic processing-NMO equation:
| |
(25) |

The anellipticity parameter *F*_{W} controls the deviation from
normal moveout; if the moveout is exactly hyperbolic.
Note that one should not try to define
using a measured value for *M*_{x}.
*F*_{W} and are both vertical paraxial measurements;
there is no reason to suppose
they should be strictly related to *M*_{x}, a horizontal measurement.

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Stanford Exploration Project

11/17/1997