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Muir's trick is to turn the problem on its side and also look at the
*horizontal* paraxial approximating ellipse. This has all the
useful properties of the vertical ellipse, with the difference
that it fits the true horizontal velocity and the vertical NMO velocity
(not the same thing as the true vertical velocity).
Figure shows the vertical and horizontal
paraxial approximating ellipses, along with
Muir's double-elliptic approximation. Muir's approximation fits
four parameters, the vertical and horizontal true and NMO velocities.
Since it is single-valued, it cannot follow the *q*SV triplication,
but fits well elsewhere.

** Next:** in the dispersion-relation domain
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Stanford Exploration Project

12/18/1997