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Dip filtering is conveniently incorporated
into the wave extrapolation equations.
Instead of initializing the Muir expansion
with
we use
.(Recall from chapter
that r0 is the cosine
of an exactly fitting angle).
For the 15
equation we have
| ![\begin{displaymath}
i\,k_z^{ (15) }\,v \eq -\,i\, \omega \ +\
{v^2 \, k_x^2
\over \epsilon\ -\ i\, \omega \, ( r_0 \ +\ 1 ) }\end{displaymath}](img35.gif) |
(6) |
For the 45
equation we have
| ![\begin{displaymath}
i\,k_z^{ (45) }\,v \eq -\,i\, \omega \ +\
{v^2 \,k_x^2 \over...
...2 \, k_x^2
\over \epsilon\ -\ i\, \omega \, ( r_0 \ +\ 1 ) }
}\end{displaymath}](img36.gif) |
(7) |
Figures 5 and 6 show
hyperbolas of diffraction for
the 15
and 45
equations
with and without the dip filtering parameter
.
hyp15
Figure 5
Diffraction hyperbolas of the 15
equation
without dip filtering (left),
and with dip filtering (right).
hyp45
Figure 6
Diffraction hyperbolas of the 45
equation
without dip filtering (left),
and with dip filtering (right).
Next: Gain control does dip
Up: COSMETIC ASPECT OF WAVE
Previous: Accentuating faults
Stanford Exploration Project
10/31/1997