Viscoacoustic anisotropic wave equations

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8 Scopus citations


The wave equation plays a central role in seismic modeling, processing, imaging and inversion. Incorporating attenuation anisotropy into the acoustic anisotropic wave equations provides a choice for acoustic forward and inverse modeling in attenuating anisotropic media. However, the existing viscoacoustic anisotropic wave equations are obtained for a specified viscoacoustic model. We have developed a relatively general representation of the scalar and vector viscoacoustic wave equations for orthorhombic anisotropy. We also obtain the viscoacoustic wave equations for transverse isotropy as a special case. The viscoacoustic orthorhombic wave equations are flexible for multiple viscoacoustic models. We take into account the classic visocoacoustic models such as the Kelvin-Voigt, Maxwell, standard-linear-solid and Kjartansson models, and we derive the corresponding viscoacoustic wave equations in differential form. To analyze the wave propagation in viscoacoustic models, we derive the asymptotic point-source solution of the scalar wave equation. Numerical examples indicate a comparison of the acoustic waveforms excited by a point source in the viscoacoustic orthorhombic models and the corresponding nonattenuating model, and the effect of the attenuation anisotropy on the acoustic waveforms.
Original languageEnglish (US)
Pages (from-to)C323-C337
Number of pages1
Issue number6
StatePublished - Sep 3 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We are grateful to the assistant editor J. Etgen, the anonymous associate editor and four anonymous reviewers for their reviews and comments. Most of the research work was accomplished when the first author was employed as a research consultant at KAUST. We thank KAUST for its support. The first author also appreciates the support from the College of Petroleum Engineering and Geosciences at KFUPM, and valuable suggestions from Prof. Stewart Greenhalgh.


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