The Kjartansson constant Q model
||This article may be too technical for most readers to understand. (July 2013)|
The Kjartansson constant Q model uses Mathematical Q models to explain how the earth responds to seismic waves and is widely used in seismic geophysical applications. Because these models satisfies the Krämers-Krönig relations they should be preferable to the Kolsky model in seismic inverse Q filtering. Kjartanssons model is a simplification of the first of Azimi Q models  (1968).
Kjartansson constant Q model
The phase velocity is written:
If the phase velocity goes to infinity in the first term on the right, we simply has:
This is Kjartansson constant Q model.
Studying the attenuation coefficient and phase velocity, and compare them with Kolskys Q model we have plotted the result on fig.1. The data for the models are taken from Ursin and Toverud.
Data for the Kolsky model (blue):
cr=2000 m/s, Qr=100, wr=2π100
Data for Kjartansson constant Q model (green):
a1=2.5 x 10 −6, γ=0.0031
- Azimi S.A.Kalinin A.V. Kalinin V.V and Pivovarov B.L.1968. Impulse and transient characteristics of media with linear and quadratic absorption laws. Izvestiya - Physics of the Solid Earth 2. p.88-93
- Strick E. The determination of Q, dynamic viscosity and transient creep curves from wave propagation measurements. Geophysical Journal of the Royal Astronomical Society 13, p.197-218
- Ursin B. and Toverud T. 2002 Comparison of seismic dispersion and attenuation models. Studia Geophysica et Geodaetica 46, 293-320.