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Bounds and averages of seismic quality factor Q

Abstract

An elastic two-phase composite, with no restriction on the shape of the two phases, has stiffness bounds given by the Reuss and Voigt equations, and a narrower range determined by the Hashin-Shtrikman bounds. Averages are given by the Voigt-Reuss-Hill, Hashin-Shtrikman, Gassmann, Backus and Wyllie equations. To obtain stiffness bounds and averages, we invoke the correspondence principle to compute the solution of the viscoelastic problem from the corresponding elastic solution. Then, seismic velocities and attenuation are established for the above — physical and heuristic — models which account for general geometrical shapes, unlike the Backus average. The approach is relevant to the seismic characterization of solid composites such as hydrocarbon source rocks.

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Acknowledgements

We are grateful to Petr Jílek and anonymous reviewers for a detailed review of our work. The authors are also grateful to the Jiangsu Innovation and Entrepreneurship Plan, Specially-Appointed Professor Plan of Jiangsu Province, and the National Natural Science Foundation of China (Grant No. 41974123).

Author information

Correspondence to Jing Ba.

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Qadrouh, A.N., Carcione, J.M., Alajmi, M. et al. Bounds and averages of seismic quality factor Q. Stud Geophys Geod 64, 100–113 (2020). https://doi.org/10.1007/s11200-019-1247-y

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Keywords

  • seismic attenuation
  • Voigt and Reuss bounds
  • Hashin-Shtrikman bounds
  • Reuss-Voigt-Hill average
  • Gassmann-Krief-Ciz-Shapiro average
  • Backus and Wyllie average
  • Q bounds