Geoscience Reference
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where the shot spacing is in units of receiver spacing. In the example of Fig. 4.40,
the number of receivers is eight and the shot spacing is one. This results in a
four-fold coverage. Reflection-profiling systems usually have 48 or 96 recording
channels (and hence receivers), which means that 24-, 48-, or 96-fold coverage
is possible. The greater the multiplicity of coverage, the better the system is for
imaging weak and deep reflectors and the better the final quality of the record
section. In practice, receiver spacing of a few tens to hundreds of metres is used,
in contrast to the kilometre spacing of refraction surveys.
In order to be able to add all these recordings together to produce a signal
reflected from the common depth point, one must first correct them for their
different travel times, which are due to their different offset distances. This cor-
rection to the travel times is called the normal-moveout (NMO) correction .
The travel time for the reflected ray in the simple two-layer model of Fig. 4.34
is given by Eq. (4.65). The difference between values of the travel time t at two
distances is called the moveout ,
t . The moveout can be written
z 1 +
x b
4
2
α 1
x a
4
2
α 1
t =
z 1 +
(4.69)
where x a and x b ( x a >
x b ) are the distances of the two geophones a and b from
the shotpoint. The normal moveout
t NMO is the moveout for the special case
when geophone b is at the shotpoint (i.e., x b =
0). In this case, and dropping the
subscript a, Eq. (4.69) becomes
z 1 +
2
α 1
x 2
4
2 z 1
α 1
t NMO =
(4.70)
If we make the assumption that 2 z 1
x ,which is gene rally appr opriate for
reflection profiling, we ca n use a b inomial expansion for z 1 +
x 2
/
4:
1 +
z 1 +
x 2
4 = z 1
x 2
4z 1
z 1 1
2 1 / 2
x
2 z 1
=
+
= z 1 1 +
x
2 z 1
2
x
2 z 1
4
x
2 z 1
6
1
2
1
8
1
16
+
+ ···
(4.71)
Toafirst approximation, therefore,
z 1 +
4 = z 1 1 +
2
x
2 z 1
x 2
1
2
(4.72)
Substituting this value into Eq. (4.70)gives a first approximation for the normal
moveout
t NMO .
1 +
2
x
2 z 1
2 z 1
α 1
1
2
2 z 1
α 1
t NMO
=
x 2
4 α 1 z 1
=
(4.73)
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