Geology Reference
In-Depth Information
Source S
x
Detector
T
0
= 2
d
/
V
T
2
= (4
d
2
+
x
2
)/
V
2
T
2
-
T
0
2
=
x
2
/
V
2
d
Velocity =
V
(hyperbolic equation)
T
-
T
0
=
∆
T
=
x
2
/2
T
0
V
2
(parabolic approximation)
Figure 12.1
Derivation of the normal moveout equation for a horizontal
reflector.
T
0
, normal incidence time;
d
, depth;
x
, distance from source.
12.1.2 Normal moveout
The true normal-incidence ray cannot be used in survey work, since a geo-
phone at a source point would probably be damaged by the source and would
certainly be set into such violent oscillation that the whole record would be
unusable. Detectors are therefore offset from sources and geometric correc-
tions must be made to travel times.
Figure 12.1 shows reflection from a horizontal interface, depth
d
,toa
geophone at a distance
x
from the source. The exact
hyperbolic
equation
linking the travel time
T
and the normal incidence time
T
0
is established by
application of the Pythagoras theorem. For small offsets, the exact equation
can be replaced by the
parabolic
approximation, which gives the
normal
moveout
(NMO),
T
−
T
0
, directly as a function of velocity, reflection time
and offset:
x
2
2
V
2
T
0
T
=
T
−
T
0
=
/
Since
V
usually increases with depth and
T
0
always does, NMO decreases
(i.e. NMO curves flatten) with depth.
Curved alignments of reflection events can be seen on many multi-channel
records (Figure 12.2). Curvature is the most reliable way of distinguishing
shallow reflections from refractions.
12.1.3 Dix velocity
If there are several different layers above a reflector, the NMO equation will
give the
root-mean-square
(RMS) velocity defined as:
V
RMS
=
V
1
t
1
+
V
2
t
2
···+···
V
n
t
n
/
T
n
