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 2 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 qSV triplication,
but fits well elsewhere.