Skip to main content
SpringerLink
Log in

Trade-off of Elastic Structure and Q in Interpretations of Seismic Attenuation

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

The quality factor Q is an important phenomenological parameter measured from seismic or laboratory seismic data and representing wave-energy dissipation rate. However, depending on the types of measurements and models or assumptions about the elastic structure, several types of Qs exist, such as intrinsic and scattering Qs, coda Q, and apparent Qs observed from wavefield fluctuations. We consider three general types of elastic structures that are commonly encountered in seismology: (1) shapes and dimensions of rock specimens in laboratory studies, (2) geometric spreading or scattering in body-, surface- and coda-wave studies, and (3) reflectivity on fine layering in reflection seismic studies. For each of these types, the measured Q strongly trades off with the (inherently limited) knowledge about the respective elastic structure. For the third of the above types, the trade-off is examined quantitatively in this paper. For a layered sequence of reflectors (e.g., an oil or gas reservoir or a hydrothermal zone), reflection amplitudes and phases vary with frequency, which is analogous to a reflection from a contrast in attenuation. We demonstrate a quantitative equivalence between phase-shifted reflections from anelastic zones and reflections from elastic layering. Reflections from the top of an elastic layer followed by weaker reflections from its bottom can appear as resulting from a low Q within or above this layer. This apparent Q can be frequency-independent or -dependent, according to the pattern of thin layering. Due to the layering, the interpreted Q can be positive or negative, and it can depend on source–receiver offsets. Therefore, estimating Q values from frequency-dependent or phase-shifted reflection amplitudes always requires additional geologic or rock-physics constraints, such as sparseness and/or randomness of reflectors, the absence of attenuation in certain layers, or specific physical mechanisms of attenuation. Similar conclusions about the necessity of extremely detailed models of the elastic structure apply to other types of Q measurements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Aki, K. (1980). Scattering and attenuation of shear waves in the lithosphere. Journal of Geophysical Research, 85, 6496–6504. doi:10.1029/JB085iB11p06496.

    Article  Google Scholar 

  • Aki, K., & Chouet, B. (1975). Origin of coda waves: Source, attenuation, and scattering effects. Journal of Geophysical Research, 80, 3322–3342. doi:10.1029/JB080i023p03322.

    Article  Google Scholar 

  • Aki, K., & Richards, P. G. (2002). Quantitative seismology (2nd ed.). Sausalito: University Science Books. ISBN 0-935702-96-2.

    Google Scholar 

  • Bonar, D. C., & Sacchi, M. D. (2010). Complex spectral decomposition via inversion strategies. SEG Denver 2010 Annual Meeting, Denver. doi:10.1190/1.351310.

  • Calvet, M., & Margerin, L. (2013). Lapse-time dependence of coda Q: Anisotropic multiple-scattering models and application to the Pyrenees. Bulletin of the Seismological Society of America, 103, 1993–2010. doi:10.1785/0120120239.

    Article  Google Scholar 

  • Deng, W., & Morozov, I. B. (2016). Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies. Geophysics, 81(4), D395–D404. doi:10.1190/geo2015-0406.1.

    Article  Google Scholar 

  • Fuchs, K., & Müller, G. (1971). Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophysical Journal International, 23(4), 417–433.

    Article  Google Scholar 

  • Gardner, G., Gardner, L., & Gregory, A. (1974). Formation velocity and density—The diagnostic basics for stratigraphic traps. Geophysics, 39(6), 770–780.

    Article  Google Scholar 

  • Gochioco, L. M. (1991). Tuning effect and interference reflections from thin beds and coal seams. Geophysics, 56(8), 1288–1295. doi:10.1190/1.1443151.

    Article  Google Scholar 

  • Han, L., & Liu, C. (2015). Can we use wavelet phase change due to attenuation for hydrocarbon detection? In 85th Annual International Meeting, SEG, New Orleans, 2962–2966. doi:10.1190/segam2015-5890451.1.

  • Jackson, I., & Paterson, M. S. (1993). A high-pressure, high-temperature apparatus for studies of seismic wave dispersion and attenuation. Pure and Applied Geophysics, 141(2/3/4), 445–466. doi:10.1007/978-3-0348-5108-4_12.

    Article  Google Scholar 

  • Kjartansson, E. (1979). Constant-Q wave propagation and attenuation. Journal of Geophysical Research, 84, 4737–4748. doi:10.1029/JB084iB09p04737.

    Article  Google Scholar 

  • Lakes, R. (2009). Viscoelastic materials. Cambridge: Cambridge University Press. ISBN 978-0-521-88568-3.

    Book  Google Scholar 

  • Lines, L., Vasheghani, F., & Treitel, S. (2008). Reflections on Q. CSEG Recorder, 34, 36–38.

    Google Scholar 

  • Lines, L., Wong, J., Innanen, K., & Vasheghani, F. (2014). Research note: Experimental measurements of Q-contrast reflections. Geophysical Prospecting, 62, 190–195. doi:10.1111/1365-2478.12081.

    Article  Google Scholar 

  • Mashinskii, E. (2017). Dynamic microplasticity manifestation in consolidated sandstone in the acoustical frequency range. Geophysical Prospecting, 65, 266–279. doi:10.1111/1365-2478.12398.

    Article  Google Scholar 

  • Morozov, I. B. (2010). On the causes of frequency-dependent apparent seismological Q. Pure and Applied Geophysics, 167, 1131–1146. doi:10.1007/s00024-010-0100-6.

    Article  Google Scholar 

  • Morozov, I. B. (2015). Effective moduli and Poisson’s ratios in poroelasticity. Canadian Journal of Exploration Geophysics, 40, 21–34.

    Google Scholar 

  • Morozov, I. B., & Baharvand Ahmadi, A. (2015). Taxonomy of Q. Geophysics, 80(1), T41–T49. doi:10.1190/GEO2013-0446.1.

    Article  Google Scholar 

  • O’Doherty, R., & Anstey, N. A. (1971). Reflections on amplitudes. Geophysical Prospecting, 19(3), 430–458. doi:10.1111/j.1365-2478.1971.tb00610.x.

    Article  Google Scholar 

  • Pimienta, L., Borgomano, J., Fortin, J., & Guéguen, Y. (2016). Modelling the drained/undrained transition: Effect of the measuring method and the boundary conditions. Geophysical Prospecting, 64(4), 1098–1111.

    Article  Google Scholar 

  • Pimienta, L., Fortin, J., & Guéguen, Y. (2015). Experimental study of Young’s modulus dispersion and attenuation in fully saturated sandstones. Geophysics, 80(5), L57–L72.

    Article  Google Scholar 

  • Quan, Y., & Harris, J. M. (1997). Seismic attenuation tomography using the frequency shift method. Geophysics, 62, 895–905. doi:10.1190/1.1444197.

    Article  Google Scholar 

  • Richards, P. G., & Menke, W. (1983). The apparent attenuation of a scattering medium. Bulletin of the Seismological Society of America, 75, 1005–1021.

    Google Scholar 

  • Ricker, N. (1953). The form and laws of propagation of seismic wavelets. Geophysics, 18, 10–40. doi:10.1190/1.1437843.

    Article  Google Scholar 

  • Santos, L. T., & Tygel, M. (2004). Impedance-type approximations of the P–P elastic reflection coefficient: Modeling and AVO inversion. Geophysics, 69, 592–598.

    Article  Google Scholar 

  • Tonn, R. (1991). The determination of the seismic quality factor Q from VSP data: A comparison of different computational methods. Geophysical Prospecting, 39, 1–27. doi:10.1111/j.1365-2478.1991.tb00298.x.

    Article  Google Scholar 

  • Wang, S., Yang, D., Li, J., & Song, H. (2015). Q factor estimation based on the method of logarithmic spectral area difference. Geophysics, 80(6), V157–V171. doi:10.1190/geo2014-0257.1.

    Article  Google Scholar 

  • White, R. (1992). The accuracy of estimating Q from seismic data. Geophysics, 57(11), 1508–1511. doi:10.1190/1.1443218.

    Article  Google Scholar 

  • White, J. E., Mikhaylova, N. G., & Lyakhovitsky, F. M. (1975). Low-frequency seismic waves in fluid-saturated layered rocks. The Journal of the Acoustical Society of America, 57(S1), S30–S30. doi:10.1121/1.1995164.

    Article  Google Scholar 

  • Zhang, C., & Ulrych, T. J. (2002). Estimation of quality factors from CMP records. Geophysics, 67, 1542–1547. doi:10.1190/1.1512799.

    Article  Google Scholar 

Download references

Acknowledgements

W. Deng was supported by the Scholarship Council, P. R. China. We are grateful to Dr. Alexander Minakov and anonymous reviewers whose questions and comments have helped improving this manuscript.

Author information

Authors and Affiliations

  1. University of Saskatchewan, Saskatoon, SK, S7N5E2, Canada

    Wubing Deng & Igor B. Morozov

Authors
  1. Wubing Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Igor B. Morozov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wubing Deng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, W., Morozov, I.B. Trade-off of Elastic Structure and Q in Interpretations of Seismic Attenuation. Pure Appl. Geophys. 174, 3853–3867 (2017). https://doi.org/10.1007/s00024-017-1581-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-017-1581-3

Keywords

Search

Navigation