This page provides links to several papers on on seismological Q, some of which are hitherto not published. As one reads it through, it may become apparent why some of this material may be difficult to publish. I critically reconsider several key points on which the models of seismological Q established over the past 50 years have been based, and show that:
In many observations, the reported frequency dependence of Q may be related to inaccurate corrections for geometric spreading. In fact, I have not yet found a case in which a frequency-dependent in situ Q would be required to explain the observations! This applies to numerous observations of body, surface, Lg, and coda waves in several frequency bands from ~1000 s to ~100 Hz. The concept of "scattering Q" also appears quite difficult for differentiating from the geometrical spreading or intrinsic Q in observations.
Looking into the theory of wave attenuation, the use of the 'quality factor' Q for describing the Earth's medium appears to be not well justified and mostly driven by imprecise analogies. In particular, I question the accepted interpretation of attenuation as related to elastic relaxation mechanisms and complex values of elastic moduli in the frequency domain. Similarly, the well-known 'correspondence principle' may be valid only for waves in uniform media.
In modeling wave propagation in anelastic media, I also question the 'viscoelastic' theories built on postulated complex-valued elastic moduli. Although perfectly self-consistent in themselves, they lead to incorrect representation of boundary conditions, resulting, for example, in wrong expressions for the acoustic impedance in the presence of anelasticity. This also leads to inaccurate predictions of the surface-wave Q. The equivalence of the velocity and Q-1 sensitivity kernels typically used in seismic attenuation tomography is also questioned.
Morozov, I. B. (2008). Geometrical attenuation, frequency dependence of Q, and the absorption band problem, Geophys. J. Int., 175, 239-252,
Morozov, I. B., Zhang, C., Duenow, J. N., Morozova, E.A., and Smithson, S. (2008). Frequency dependence of regional coda Q: Part I. Numerical modeling and an example from Peaceful Nuclear Explosions, Bull. Seism. Soc. Am., 98, 2615–2628, doi: 10.1785/0120080037
Morozov, I. B. (2009). Thirty years of confusion around 'scattering Q'? Seismol. Res. Lett., 80, 5-7. Also see a of this note by J. Xie and M. Fehler (Seism. Res. Lett., 80, 646-647), and my reply (Seismol. Res. Lett., 80, 648-649)
Morozov, I. B. (2009). More reflections on Q, CSEG Recorder, 34(2), 12-13.
Morozov, I. B. (2010a). On the causes of frequency-dependent apparent seismological Q. Pure Appl. Geophys., 167, 1131–1146, doi 10.1007/s00024-010-0100-6. This paper opened a dedicated forum on the frequency dependence of Q (Mitchell, B. (2010). Prologue and invitation to participate in a forum on the frequency dependence of seismic Q, Pure Appl. Geophys., 167, 1129; doi: 10.1007/s00024-010-0180-3), in which it was again extensively criticized by J.Xie (Xie, J. (2010). Can we improve estimates of seismological Q using a new "geometrical spreading" model?, Pure Appl. Geophys., 167, 1147-1162; doi: 10.1007/s00024-010-0188-8). Here is my detailed response, which was not included in the forum.
Morozov, I. B. (2010b) Attenuation coefficients of Rayleigh and Lg waves, J. Seismol., doi 10.1007/s10950-010-9196-5
Morozov, I. B. (2010c) Anelastic acoustic impedance and the correspondence principle. Geophys. Prosp., doi 10.1111/j.1365-2478.2010.00890.x.
On long-period body-wave attenuation (t*) (Journal of Seismology, 2012, doi: 10.1007/s10950-012-9315-6)
Measurement of attenuation and geometric spreading in a VSP (GEOPHYSICS, VOL. 78, NO. 6, C41-C52, 2013)
Taxonomy of Q (accepted by Geophysics)
Seismological Attenuation without Q, Trafford, 2010. A critical study of the concept of Q in seismology and systematic development of an alternative attenuation-coefficient model. Buy at Trafford.com, Amazon.co.uk, Amazon.com, Barnes & Noble
Formulation of attenuation without the Q concept This also includes a theoretical and numerical model of Love-wave Q
Mechanics of seismic attenuation in planets (Part I: Fundamentals)
Physical character of seismic viscoelasticity
On first principles of viscoelasticity
On geometrical spreading and explanation of positive frequency dependence of Q
New solid-viscosity model of Earth's free oscillations
On relation of bulk and shear Q factors
Dynamic moduil in poroelasticity
General Standard Linear solid: Part I and Part II