Geoscience Reference
In-Depth Information
Now,
i
c
and
δ
can be obtained by adding and subtracting Eqs. (4.50) and (4.51):
α
1
1
2
α
d
+
α
1
sin
i
c
=
α
u
(4.52)
1
α
d
+
α
1
2
1
α
u
=
α
1
1
2 cos
i
c
α
d
−
α
1
δ
=
α
u
(4.53)
1
α
d
−
α
1
2 cos
i
c
1
α
u
=
For small dip angles
δ
,
α
2
is therefore given by
1
α
2
=
sin i
c
α
1
1
α
d
+
1
2
1
α
u
=
(4.54)
If the dipping interface is not the first but a deeper interface, the velocities and
thicknesses are determined exactly as above except that contributions from the
overlying layers must be included in Eqs. (4.42) and (4.44). (The algebra can be
somewhat tedious; see Slotnick (1959) for detailed derivations.)
4.3.4 Seismic record sections
When seismic-refraction travel-time data are plotted on a time versus distance
graph, straight-line segments can be fitted to the points, and then velocities and
layer thicknesses can be calculated. However, as has been mentioned, many struc-
tures are most unlikely to be detected by such a simple travel-time interpretation
alone.
A good way to display all the data available is to plot a record section such as
those shown in Figs. 4.18, 4.41, 9.6, 9.7, 9.27 and 10.12. The recording (
record
)
from each seismometer is plotted at its appropriate range on a time-distance
plot. The great advantage of plotting the data on a record section is that all
of the amplitude and travel-time information is then displayed together. Phases
can be easily correlated from trace to trace, which means that second arrivals
and reflections, which often do not have a clear starting time and so would not
necessarily be identified on a single record, stand out clearly. Hidden layers and
low-velocity zones, which cannot be detected from the first-arrival travel times
(Fig. 4.35), should be resolved when a record section is used in the interpretation
of a refraction line.
To avoid having to plot record sections on exceedingly large pieces of paper
or with a very small scale for time,
reduced record sections
are used. To do
this, the time (
t
) axis of the plot is replaced by a reduced time (
t
v
) axis,
where
x
is the offset distance (horizontal axis) and
v
is the
reduction velocity
.
This means that phases arriving with a velocity
v
line up horizontally on the
−
x
/
