Traveltime approximations for transversely isotropic media with an inhomogeneous background |

**Tariq Alkhalifah**

A transversely isotropic model with a tilted symmetry axis
(TI) is regarded as one of the most effective
approximations to the Earth subsurface, especially for imaging
purposes. However, we commonly utilize
this model by setting the axis of symmetry normal to the reflector.
This assumption may be accurate in many places, but deviations from this assumption
will cause errors in the wavefield description. Using perturbation theory and Taylor's series,
I expand the solutions of the eikonal equation for 2D transversely isotropic
media with respect to the independent parameter , the angle the
tilt of the axis of symmetry
makes with the vertical, in a generally *inhomogeneous* TI background with
a vertical axis of symmetry (VTI). I do an additional expansion
in terms of the independent (anellipticity)
parameter in a generally inhomogeneous elliptically
anisotropic background medium. These new TI traveltime solutions are
given by expansions in and
with coefficients extracted from solving linear first-order partial differential
equations. Pade approximations are used to enhance the accuracy of
the representation by predicting
the behavior of the higher-order terms of the expansion.
A simplification of the expansion for homogenous media provides
nonhyperbolic moveout descriptions of the traveltime for TI models
that
are more accurate than other recently derived approximations.
In addition, for 3D media, I develop traveltime approximations using Taylor's series type of expansions in the azimuth of the axis of symmetry. The
coefficients of all
these expansions can also provide us with the medium sensitivity
gradients (Jacobian) for nonlinear tomographic-based inversion for the tilt in the symmetry axis.

- Introduction
- The TI eikonal and expansion in
- Expansion in terms of and
- A homogeneous model test
- The vertical direction
- The symmetry-axis azimuth and the 3-D case
- Discussion
- Conclusions
- Acknowledgments
- Bibliography
- Appendix A: Expansion in
- Appendix B: Expansion in and
- Appendix C: The homogeneous medium case
- Appendix D: Expansion in 3D
- About this document ...

Traveltime approximations for transversely isotropic media with an inhomogeneous background |

2013-04-02