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Performing the substitutions of Table
.1
into equation (10) gives dispersion
relationships for comparison to the exact expression (8).
These are shown in Table
.2.
Table:
As displayed in Figure 1,
the dispersion relations
tend toward a semicircle.
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![$5^\circ$](img28.gif) |
![$k_z \eq \displaystyle {\strut\omega\over v}$](img37.gif) |
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![$15^\circ$](img12.gif) |
![$k_z \eq \displaystyle {\strut\omega\over v} -
\displaystyle {\strut v k_x^2\over 2\omega}$](img38.gif) |
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![$45^\circ$](img15.gif) |
![$k_z \eq \displaystyle{\strut \omega\over v}
-{\displaystyle {\strut k_x^2}\over
\displaystyle {2\,{\omega\over v} -
{\strut v k_x^2\over 2\omega}}}$](img39.gif) |
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Next: Depth-variable velocity
Up: WAVE-EXTRAPOLATION EQUATIONS
Previous: Muir square-root expansion
Stanford Exploration Project
10/31/1997