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Amplitude variations with offset (AVO) (view source)
Revision as of 17:31, 30 June 2015
, 17:31, 30 June 2015no edit summary
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>
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>
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> 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> Vs = \frac{Vs_2+Vs_1}{2}, \Delta Vs = Vs_2 - Vs_1 </math>
'''c) Hilterman (1983)'''
'''c) Hilterman (1983)'''
Hilterman simplified Bortfeld equations by separating the reflection coefficients into the form of acoustic and elastic :
Hilterman simplified Bortfeld equations by separating the reflection coefficients into the form of acoustic and elastic :
<math> R(\theta_1) = \frac{Vp_2\rho_2\cos\theta_1 - Vp_1\rho_1\cos\theta_2}{Vp_2\rho_2\cos\theta_1 + Vp_1\rho_1\cos\theta_2 }+ \left ( \frac{\sin\theta_1 }{Vp_1}\right )\left ( Vs_1+Vs2 \right )\left [ 3\left ( Vs_1-Vs2 \right ) + \frac{2\left ( Vs_2\rho_1 - Vs_1\rho_2 \right )}{\rho_2 + \rho_1} \right ] </math>
'''d) Shuey Approximation (1985)'''
'''d) Shuey Approximation (1985)'''
Shuey modified Aki and Richard equation by using variable of poisson ratio as follows:
Shuey modified Aki and Richard equation by using variable of poisson ratio as follows:
<math> R(\theta_1) = R_p + \left [ R_p A_o + \frac {\Delta\sigma}{1-\sigma^{2}} \right ]\sin^{2}\theta + \frac{\Delta\alpha }{2\alpha}\left ( \tan^{2}\theta-\sin^{2}\theta \right ) </math>
where
<math> \sigma =\frac{\left ( \sigma _1+\sigma _2 \right )}{2}, \Delta \sigma = \left ( \sigma _2-\sigma _1 \right )</math>
<math> A_o = B-2\left ( 1+B \right )\frac{1-2\sigma }{1-\sigma } </math>
<math> B = \frac{\frac{\Delta \alpha }{\alpha }}{\frac{\Delta \alpha }{\alpha }+ \frac{\Delta \rho }{\rho }}</math>