Geoscience Reference
In-Depth Information
Example: calculation of layer thickness and seismic velocity from a
normal-incidence reflection line
Avelocity analysis of reflection data has
6kms
−
1
t
0
,
1
=
1
.
0
s
,
α
1
=
3
.
0kms
−
1
t
0
,
2
=
1
.
5
s
,
α
2
=
4
.
Calculate a velocity-depth model from these values, assuming that there is a
constant velocity in each layer. Since
α
1
must be equal to
α
1
, the velocity of the top
layer,
z
1
, can be calculated from Eq. (4.90):
3
.
6
×
1
.
0
2
.
0
z
1
=
=
1
.
8km
Now
α
2
can be calculated from Eq. 4.88:
(4
.
0
2
×
1
.
5)
−
(3
.
6
2
×
1
.
0)
α
2
=
1
.
5
−
1
.
0
=
√
22
7kms
−
1
.
08
=
4
.
Finally,
z
2
is then calculated from Eq. (4.90):
4
.
7
×
0
.
5
2
z
2
=
=
1
.
175 km
.
0
Notice that the velocity
α
2
is larger than the RMS velocity
α
2
in this example.
Unfortunately, the interval velocities and depths frequently cannot be determined
accurately by these methods (see Problem 21). In exploration work the inaccuracy
of velocity-depth information can usually be made up for by detailed measurements
from drill holes. However, when reflection profiling is used to investigate structures
deep in the crust and upper mantle, such direct velocity information is not available.
There is an added problem in this situation: when the depths of horizons are much
larger than the maximum offset, the NMO correction is insensitive to velocity. This
means that any velocity that is approximately correct will stack the reflections
adequately, and so the interval velocities calculated from the stacking velocities will
not be very accurate. As an example, consider a two-layer model:
=
8kms
−
1
The reflection hyperbola (Eq. (4.65)) for this interface is
α
1
=
6kms
−
1
,
z
1
=
20 km
,
2
400
+
x
2
4
and the two-way normal incidence time
t
0
is 6.667 s. The NMO correction is
(Eq. (4.73))
1
3
t
=
x
2
480
The maximum offset used in deep reflection profiling is rarely greater than about
5km and often less. At this offset, the correct NMO correction for the reflection is
0.052 s. However, this correction has to be estimated from the data. Using the
t
NMO
=
