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reflectivity
Figure 1 The acoustic wave reflectivity and the transmission of a planar reflector in the case of zero incident angle
From Fig.1, and assuming that the density is constant, the normal reflectivity is defined as
| ![\begin{displaymath}
R\vert_{\theta =0} = \frac{v_{2}-v_{1}}{v_{2}+v_{1}},\end{displaymath}](img28.gif) |
(16) |
and the transmission coefficient is
| ![\begin{displaymath}
T\vert_{\theta =0} = \frac{2v_{2}}{v_{2}+v_{1}},\end{displaymath}](img29.gif) |
(17) |
where
is the incident angle. Therefore, defining the scattering potential as
, equation (16) and (17) can be rewritten as
| ![\begin{displaymath}
R\vert_{\theta =0}=\frac{1-\sqrt{1+a}}{1+\sqrt{1+a}},\end{displaymath}](img32.gif) |
(18) |
and
| ![\begin{displaymath}
T\vert_{\theta =0}=\frac{2}{1+\sqrt{1+a}},\end{displaymath}](img33.gif) |
(19) |
respectively.
If waves meet a reflector with a non-zero incident angle, the reflectivity and transmission coefficient are
| ![\begin{displaymath}
R\left( \theta_{1}\right) = \frac{v_{2}cos\theta _{1}-v_{1}cos\theta _{2}}{v^{2}cos\theta_{1}+v_{1}cos\theta _{2}},\end{displaymath}](img34.gif) |
(20) |
and
| ![\begin{displaymath}
T\left( \theta_{1}\right) = \frac{2v_{2}cos\theta _{1}}{v_{2}cos\theta _{1}+v_{1}cos \theta _{2}}.\end{displaymath}](img35.gif) |
(21) |
Similarly, they can be expressed with the scattering potential as
| ![\begin{displaymath}
R\left( \theta_{1}\right)=\frac{cos\theta_{1}-\sqrt{1+a}cos\theta _{2}}{cos\theta_{1}+\sqrt{1+a}cos\theta_{2}},\end{displaymath}](img36.gif) |
(22) |
and
| ![\begin{displaymath}
T\left( \theta_{1}\right)=\frac{2cos\theta_{1}}{cos\theta _{1}+\sqrt{1+a}cos\theta _{2}},\end{displaymath}](img37.gif) |
(23) |
respectively.
The angle reflectivity has a close relation to the scattering potentials. Generally, the angle reflectivity is estimated by amplitude-preserved imaging, and lithological parameter disturbances are evaluated from them by AVO/AVA inversion.
Next: Iterative inversion imaging algorithms
Up: wave propagator and its
Previous: [2] Scalar wave equation
Stanford Exploration Project
11/1/2005