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Cos1
Figure 4. Migrating impulses on a constant-offset section. Notice that shallow impulses (shallow compared to ![]() |
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Cos0
Figure 5. Forward modeling from an earth impulse. |
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It is not easy to show that equation (8.5) can be
cast in the standard mathematical form of an ellipse, namely,
a stretched circle.
But the result is a simple one,
and an important one for later analysis.
Feel free to skip forward over the following verification
of this ancient wisdom.
To help reduce algebraic verbosity,
define a new equal to the old one shifted by
.
Also make the definitions
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(10) |
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(11) |
Fixing , equation (8.9) is the equation for a circle with
a stretched
-axis.
The above algebra confirms that the
``string and tack'' definition of an ellipse
matches the ``stretched circle'' definition.
An ellipse in earth model space corresponds
to an impulse on a constant-offset section.
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![]() | Dip and offset together | ![]() |
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