Attenuating orthorhombic models are often used to describe the azimuthal variation of the seismic wave velocity and amplitude in finely layered hydrocarbon reservoirs with vertical fractures. In addition to the P-wave related medium parameters, shear wave parameters are also present in the complex eikonal equation needed to describe the P-wave complex-valued traveltime in an attenuating orthorhombic medium, which increases the complexity of using the P-wave traveltime to invert for the medium parameters in practice. Here, we use the acoustic assumption to derive an acoustic eikonal equation that approximately governs the complex-valued traveltime of P-waves in an attenuating orthorhombic medium. For a homogeneous attenuating orthorhombic media, we solve the eikonal equation using a combination of the perturbation method and Shanks transform. For a horizontal attenuating orthorhombic layer, both the real and imaginary part of the complex-valued reflection traveltime have nonhyperbolic behaviors in terms of the source-receiver offset. Similar to the roles of normal moveout (NMO) velocity and anellipticity, the attenuation NMO velocity and the attenuation anellipticity characterize the variation of the imaginary part of the complex-valued reflection traveltime around zero source-receiver offset.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Q. Hao thanks the rock and seismic (ROSE) project for its support, and I. Pšenčík for valuable communication on seismic wave attenuation after the 17th International Workshop on Seismic Anisotropy held in Austin. T. Alkhalifah thanks KAUST for its support. We thank the associate editor Igor Ravve, Yanadet Sripanich and two anonymous reviewers for their critical reviews of the manuscript.