We present an acoustic eikonal equation governing the complex-valued travel time of P-waves in attenuating, transversely isotropic media with a vertical symmetry axis (VTI). This equation is based on the assumption that the Pwave complex-valued travel time is independent of the Swave velocity parameter v in Thomsen's notation and the attenuation coefficient A in the Thomsen-type notation for attenuating VTI media. We combine perturbation theory and Shanks transform to develop practical approximations to the attenuating acoustic eikonal equation, capable of admitting analytical description of the attenuation in homogeneous media. For a horizontal, attenuating VTI layer, we also derive non-hyperbolic approximations for the real and imaginary parts of the complex-valued reflection travel time.
|Original language||English (US)|
|Title of host publication||SEG Technical Program Expanded Abstracts 2016|
|Publisher||Society of Exploration Geophysicists|
|Number of pages||6|
|State||Published - Sep 2016|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Q. Hao thanks A. Stovas for helpful discussion on attenuation anisotropy. Q. Hao also thanks the rock and seismic (ROSE) project for support. T. Alkhalifah likes to thank KAUST for its support.