Abstract
Backus and Wyllie equations are used to obtain average seismic velocities at zero and infinite frequencies, respectively. Here, these equations are generalized to obtain averages of the seismic quality factor (inversely proportional to attenuation). The results indicate that the Wyllie velocity is higher than the corresponding Backus quantity, as expected, since the ray velocity is a high-frequency limit. On the other hand, the Wyllie quality factor is higher than the Backus one, following the velocity trend, i.e., the higher the velocity (the stiffer the medium), the higher the attenuation. Since the quality factor can be related to properties such as porosity, permeability, and fluid viscosity, these averages can be useful for evaluating reservoir properties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Backus, G. E. (1962). Long-wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research, 67, 4427–4440.
Carcione, J. M. (1992). Anisotropic Q and velocity dispersion of finely layered media. Geophysical Prospecting, 40, 761–783.
Carcione, J. M. (2014). Wave fields in real media. Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media, 3rd edition, Elsevier.
Carcione, J. M., Kosloff, D., & Behle, A. (1991). Long wave anisotropy in stratified media: a numerical test. Geophysics, 56, 245–254.
Mainardi, F. (2010). Fractional calculus and waves in linear viscoelasticity. London: Imperial College Press.
Pride, S. R., Berryman, J. G., & Harris, J. M. (2004). Seismic attenuation due to wave-induced flow. Journal of Geophysical Research, 109, B01201. doi:10.1029/2003JB002639.
Stovas, A., & Ursin, B. (2007). Equivalent time-average and effective medium for periodic layers. Geophysical Prospecting, 2007(55), 871–882.
Wyllie, M. R. J., Gregory, A. R., & Gardner, L. W. (1956). Elastic wave velocities in heterogeneous and porous media. Geophysics, 21, 41–70.
Zhu, Y., Tsvankin, I., Dewangan, P., & van Wijk, K. (2007). Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media. Geophysics, 72, D1–D7.
Acknowledgements
This research is supported by the “Distinguished Professor Program of Jiangsu Province, China”, the “Fundamental Research Funds for the Central Universities, China”, and the open fund of the State Key Laboratory of the Institute of Geodesy and Geophysics, CAS (SKLGED2017-5-2-E). KACST has partially funded the research. We thank Editor Andrew R. Gorman for useful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qadrouh, A.N., Carcione, J.M., Ba, J. et al. Backus and Wyllie Averages for Seismic Attenuation. Pure Appl. Geophys. 175, 165–170 (2018). https://doi.org/10.1007/s00024-017-1676-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-017-1676-x