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29)
In case of uniform scaling of velocity,
| ![\begin{eqnarray}
\frac{\partial z_{\tilde{\gamma}}}{\partial \rho_V}
=
\frac{z_\...
...{\cos(\alpha_x+\gamma)}
+
\frac{1}{\cos(\alpha_x-\gamma)}
\right).\end{eqnarray}](img80.gif) |
(46) |
The quantity
can be written
| ![\begin{eqnarray}
\frac{1}{\cos(\alpha_x+\gamma)}
+
\frac{1}{\cos(\alpha_x-\gamma...
...)}
&=&\frac{2\cos\alpha_x\cos\gamma}{\cos^2\alpha_x-\sin^2\gamma}.\end{eqnarray}](img82.gif) |
(47) |
| (48) |
| (49) |
| (50) |
Using equation (50), equation (46)
simplifies to
| ![\begin{eqnarray}
\frac{\partial z_{\tilde{\gamma}}}{\partial \rho_V}
&=&
z_\xi
\...
...2\alpha_x-\sin^2\gamma}
\tan \gamma
\tan \widehat{\gamma}
\right).\end{eqnarray}](img83.gif) |
(51) |
| (52) |
| (53) |
Next: Derivation of equation (30)
Up: Derivation of the derivative
Previous: Derivation of equation (26)
Stanford Exploration Project
4/6/2006