(6) |

(7) |

(8) |

In both approximations, q represents the anelliptic factor and set equal to zero
gives hyperbolic moveout equation.
In the case of Byun's approximation, the anelliptic factor, q or *v*_{q}, directly represents the deviated velocity from the ellipse or the velocity at 45 degrees, respectively.
In the case of Muir's approach, the unit of q has no dimension, and the magnitude is controlled by the ratio of horizontal velocity to vertical velocity.

From a practical point of view, Muir's method is superior
because it can be used for surface common midpoint gather data by fixing time for some event
and applying semblance analysis as a function of q and *v*_{x}.
Byun's approach requires one more parameter, *v*_{z}, to calculate moveout. For a given event, therefore, semblance analysis can be performed by scanning over ranges of the three parameters, *v*_{z},*v*_{x} and *v*_{q}. If the average vertical velocity *v*_{z} is known, as may the case from VSP or check-shot data, then the semblance scan can be done over the two parameters, *v*_{x} and *v*_{q}.

1/13/1998