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Amplitude variations with offset (AVO) (view source)
Revision as of 17:09, 30 June 2015
, 17:09, 30 June 2015no edit summary
'''b) Aki, Richard and Frasier Approximation (1976)'''
'''b) Aki, Richard and Frasier Approximation (1976)'''
Bortfeld approximation then revised by Richard-Frasier (1976) and by Richard-Aki (1980). Approximation of Richard-Frasier is giving a simple equation because it is written in a clear three forms, namely the right-hand side includes the first P wave velocity, the second node density and the last wave velocity.
Bortfeld approximation then revised by Richard-Frasier (1976) and by Richard-Aki (1980). Approximation of Richard-Frasier is giving a simple equation because it is written in a clear three forms, namely the right-hand side includes the first P wave velocity, the second node density and the last wave velocity.
<math> R(\theta)= a\frac{\Delta Vp}{Vp}+ b \frac{\Delta \rho}{\rho}+ c \frac{\Delta Vs}{Vs} </math>
where <math> a = \frac{1}{2\cos^{2}\theta}, b = 0.5-\left [ 2\left ( \frac{Vs}{Vp} \right )^{2}\sin^{2}\theta \right ], c = -4\left ( \frac{Vs}{Vp} \right )^{2}\sin^{2}\theta </math>
and <math> \rho = \frac{\rho_2+\rho_1}{2}, \Delta \rho = \rho_2 - \rho_1 </math>
<math> Vp = \frac{Vp_2+Vp_1}{2}, \Delta Vp = Vp_2 - Vp_1 </math>
<math> Vs = \frac{Vs_2+Vs_1}{2}, \Delta Vs = Vs_2 - Vs_1 </math>
<math> \theta = \frac{\theta_2+\theta_1}{2} </math>
'''c) Hilterman (1983)'''
'''c) Hilterman (1983)'''