The relation between vertical and horizontal slownesses, better known as the dispersion relation, for transversely isotropic media with a tilted symmetry axis (TTI) requires solving a quartic polynomial equation, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of the perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the vertical slowness that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for a small tilt in the symmetry angle. © 2012 European Association of Geoscientists & Engineers.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Alexey Stovas would like to acknowledge the ROSE project for financial support. Tariq Alkhalifah would like to thank KAUST for its financial support. We would also like to acknowledge Ivan Psencik and anonymous reviewers for very instructive comments.
ASJC Scopus subject areas
- Geochemistry and Petrology