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The first anelliptic approximation has a certain lack of symmetry.
There are two vertical control parameters,
*V*_{z} and ,but only a single horizontal control parameter
*V*_{x}.
If our data
includes sources and receivers separated both horizontally and
vertically, it makes sense
to use an approximation that is symmetric between *x* and *z*.
We can do this by generalizing to the following template:
| |
(14) |

If equation () reduces to
the first anelliptic form given by equation ();
if equation () reduces
to the original elliptical
form given by equation ().
Following this newer template,
equation () (the ray equation) becomes

| |
(15) |

where
,,and as before *M* indicates slowness squared
(*M*_{x} = 1/ *V*_{x}^{2},
,,and *M*_{z} = 1/ *V*_{z}^{2}).
Similarly,
equation () (the dispersion relation) becomes

| |
(16) |

where
,,and as before *W* indicates velocity squared
(*W*_{x} = *V*_{x}^{2},
,,and *W*_{z} = *V*_{z}^{2}).
Note that the subscript indicates
moveout velocity measured for near-vertical propagation; i.e.,
is the square NMO velocity we use
every day in surface-to-surface data processing.
(If an *x* subscript seems confusing for a paraxial measurement about
the vertical, remember that in an elliptic world it is a horizontal velocity
that surface moveout measures.)
The subscript indicates
moveout velocity measured for near-horizontal propagation, such
as might be found in a cross-borehole experiment.

** Next:** ANELLIPTIC PARAMETERS FOR TI
** Up:** Dellinger, Muir, & Karrenbach:
** Previous:** Consistency
Stanford Exploration Project

11/17/1997