New acoustic approximation for transversely isotropic media with a vertical symmetry axis

Shibo Xu, Alexey Stovas, Tariq Ali Alkhalifah, Hitoshi Mikada

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Seismic data processing in the elastic anisotropic model is complicated due to multiparameter dependency. Approximations to the P-wave kinematics are necessary for practical purposes. The acoustic approximation for P-waves in a transversely isotropic medium with a vertical symmetry axis (VTI) simplifies the description of wave propagation in elastic media, and as a result, it is widely adopted in seismic data processing and analysis. However, finite-difference implementations of that approximation are plagued with S-wave artifacts. Specifically, the resulting wavefield also includes artificial diamond-shaped S-waves resulting in a redundant signal for many applications that require pure P-wave data. To derive a totally S-wave-free acoustic approximation, we have developed a new acoustic approximation for pure P-waves that is totally free of S-wave artifacts in the homogeneous VTI model. To keep the S-wave velocity equal to zero, we formulate the vertical S-wave velocity to be a function of the model parameters, rather than setting it to zero. Then, the corresponding P-wave phase and group velocities for the new acoustic approximation are derived. For this new acoustic approximation, the kinematics is described by a new eikonal equation for pure P-wave propagation, which defines the new vertical slowness for the P-waves. The corresponding perturbation-based approximation for our new eikonal equation is used to compare the new equation with the original acoustic eikonal. The accuracy of our new P-wave acoustic approximation is tested on numerical examples for homogeneous and multilayered VTI models. We find that the accuracy of our new acoustic approximation is as good as the original one for the phase velocity, group velocity, and the kinematic parameters such as vertical slowness, traveltime, and relative geometric spreading. Therefore, the S-wave-free acoustic approximation could be further applied in seismic processing that requires pure P-wave data.
Original languageEnglish (US)
Pages (from-to)C1-C12
Number of pages1
Issue number1
StatePublished - Nov 22 2019

Bibliographical note

KAUST Repository Item: Exported on 2021-02-17
Acknowledgements: We would like to thank editor J. Shragge, associate editor S. Hestholm; reviewers I. Ravve, P. Golikov, U. Waheed; and three anonymous reviewers for their comments and helpful suggestions.


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