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A little geometry gives simple expressions
for the horizontal and vertical position errors on the zero-offset section,
which are to be corrected by migration.
Figure 5.2 defines the
required quantities for a reflection event recorded at
corresponding
to the reflectivity at
.
reflkine
Figure 2.
Geometry of the normal ray of length and the vertical ``shaft''
of length for
a zero-offset experiment above a dipping reflector.
|
|
|
---|
The two-way travel time for the event is
related to the length
of the normal ray by
 |
(1) |
where
is the constant propagation velocity.
Geometry of the triangle
shows
that the true depth of the reflector at
is given by
 |
(2) |
and the lateral shift between true position
and false position
is given by
 |
(3) |
It is conventional to rewrite equation (5.2) in terms of two-way
vertical traveltime
:
 |
(4) |
Thus both the vertical shift
and the horizontal shift
are seen to vanish when the dip angle
is zero.
Next: Hand migration
Up: MIGRATION DEFINED
Previous: A dipping reflector
2009-03-16