On anelliptic approximations for qP velocities in TI and orthorhombic media

Next: Examples Up: Proposed Approximations Previous: Proposed Approximations

### Moveout approximation

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:

 (54)

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

Next: Examples Up: Proposed Approximations Previous: Proposed Approximations

2017-04-14