Traveltime approximations for transversely isotropic media with an inhomogeneous background

Tariq Alkhalifah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

A transversely isotropic (TI) model with a tilted symmetry axis 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 TI media with respect to the independent parameter θ, 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. 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 θ 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.

Original languageEnglish (US)
Pages (from-to)WA31-WA42
JournalGeophysics
Volume76
Issue number3
DOIs
StatePublished - May 2011

Bibliographical note

KAUST Repository Item: Exported on 2023-03-31
Acknowledgements: I am grateful to KAUST for its financial support. I also thank Andrej Bona, Ilya Tsvankin, Ivan Psencik, and Andres Pech for their critical and helpful reviews of the paper.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics

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