On anelliptic approximations for qP velocities in TI and orthorhombic media |

To convert the proposed group-velocity approximation (equation 47) to the corresponding moveout approximation, we apply again the general expression given in equation 31. Adopting the same notation rules, the moveout approximation takes the form:

where

(55) |

(56) | |||

(57) |

denotes the offset in direction, denotes the offset in direction, denotes the NMO-velocity in direction, denotes the NMO-velocity in direction, and denotes the hyperboloidal part of reflection traveltime squared given below,

(58) |

We apply the same strategy to reduce the number of parameters with an approximation on for as in equation 35.

For small offset, the Taylor expansion of equation 54 is

(59) | |||

The asymptote of this expression for unbounded offsets and is given by

and | (60) |

which denote the horizontal velocities squared along and directions respectively.

On anelliptic approximations for qP velocities in TI and orthorhombic media |

2017-04-14