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Amplitude variations with offset (AVO) (view source)
Revision as of 16:38, 30 June 2015
, 16:38, 30 June 2015no edit summary
Zoeppritz derived the amplitudes of the reflected and transmitted waves using the conservation of stress and displacement across the layer boundary.
Zoeppritz derived the amplitudes of the reflected and transmitted waves using the conservation of stress and displacement across the layer boundary.
<math> \begin{bmatrix}
R_p\\
R_s\\
T_p\\
T_r
\end{bmatrix} = \begin{bmatrix}
-\sin \Theta_1 & -\cos \Phi _1 & \sin\Theta _2 &\sin \Phi _2 \\
\cos \Theta _1 &-\sin \Phi _1 &\cos \Theta _2 &-\sin \Phi _2 \\
\sin 2\Theta _1 &\frac{Vp_1}{Vs_1}\cos 2\Phi _1 &\frac{\rho_2V_{s2}^{2}Vp_1}{\rho _1Vs_1^{2}Vp_2}\cos2\Phi _2 &\frac{\rho_2V_{s2}Vp_1}{\rho _1Vs_1^{2}}\cos2\Phi _2 \\
-\cos 2\Phi _1 &\frac{Vs_1}{Vp_1}\sin 2\Phi _1 &\frac{\rho_2Vp_2}{\rho _1Vp_1}\cos2\Phi _2 &-\frac{\rho_2Vs_2}{\rho _1Vp_1}\sin 2\Phi _2
\end{bmatrix}^{-1}\begin{bmatrix}
\sin \Theta _1\\
\cos \Theta _1\\
\sin 2\Theta _1\\
\cos 2\Phi _1
\end{bmatrix} </math>
Because Zoeppritz equations give four equations with four unknowns, there are some of approximations in order to perform physical interpretation and visualization of the effect of some parameters to reflection coefficient. Some of the approximations are:
Because Zoeppritz equations give four equations with four unknowns, there are some of approximations in order to perform physical interpretation and visualization of the effect of some parameters to reflection coefficient. Some of the approximations are:
'''Class 4 '''
'''Class 4 '''
Class 4 has negative reflection coefficient at zero offset and amplitude that is decreasing against the offset. There is a change in polarity at a certain angle and then amplitude will increasing proportionally to the offset.
Class 4 has negative reflection coefficient at zero offset and amplitude that is decreasing against the offset. There is a change in polarity at a certain angle and then amplitude will increasing proportionally to the offset.
== References ==
[1] ] Choliq, M. T. (2007). Pemodelan parameter elastic batuan degan inversi AVO untuk karakterisasi reservoir hidrokarbon karbonat formasi baturaja, Jawa Barat Utara.
[2] Young, Roger A. and LoPiccolo, Robert D. (2004). Conforming and Non-conforming Sands – An Organizing Framework for Seismic Rock Properties.