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 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 (1968). Kjartanssons model is a simplification of the first of Azimi Q models. Azimi proposed his first model together with 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 Strick (1967) and has the attenuation proportional to |w| 1-γ | and is: 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.Ursin B. and Toverud T. 2002 Comparison of seismic dispersion and attenuation models. Studia Geophysica et Geodaetica 46, 293-320. cr = 2000 m/s, Qr = 100, wr = 2π100 a1 = 2.5 x 10 −6, γ = 0.0031
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 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. pp. 88–93 (1968). Kjartanssons model is a simplification of the first of Azimi Q models. Azimi proposed his first model together with Strick E. The determination of Q, dynamic viscosity and transient creep curves from wave propagation measurements. Geophysical Journal of the Royal Astronomical Society 13, pp. 197–218 Strick (1967) and has the attenuation proportional to |w| 1 − γ | and is: 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.Ursin B. and Toverud T. 2002 Comparison of seismic dispersion and attenuation models. Studia Geophysica et Geodaetica 46, 293–320. cr = 2000 m/s, Qr = 100, wr = 2100 a1 = 2.5 × 10 −6, γ = 0.0031
R
Mathematical
mathematical
R
Krämers-Krönig
Krämers–Krönig
R
-
–
R
p.88-93
pp. 88–93
R
p.197-218
pp. 197–218
R
1-γ
1 − γ
R
293-320.
293–320.
R
2π100
2100
R
x
×