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Among the possible forms of deviation from the ellipse, one probable function is which has zero value in the vertical and horizontal directions, and maximum value of 45 degrees.
In this approximation, the ray velocity equation becomes

| |
(2) |

where *q*^{-2} has four times the value of the deviated sloth from the besting fitting ellipse at 45 degrees and where the case *q*=0 corresponds to elliptically anisotropic velocity.
By using trigonometric identity, equation(2) becomes Byun's approximation :
| |
(3) |

where
*a*_{0}^{2}=*v*_{x}^{-2}

*a*_{1}^{2}=*v*_{z}^{-2}-*v*_{x}^{-2}+*q*^{-2}

*a*_{2}^{2}=*q*^{-2}

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** Up:** ANELLIPTIC APPROXIMATION
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Stanford Exploration Project

1/13/1998