Geology Reference
In-Depth Information
Figure 13.8
Reciprocal time interpretation. The geometry of the triangles
GQR and GRS is identical to that of the 'magic triangle' of Figure 13.4. The
sum of the travel times from S
1
and S
2
to G differs from the reciprocal time,
t
R
, taken to travel from S
1
to S
2
by the difference between the times taken to
travel QS at velocity
V
2
and QGS at velocity
V
1
.
In Figure 13.8, the difference between
t
R
and the sum of the travel times
t
A
and
t
B
from the two long shots to any geophone,
G
,is:
t
A
+
t
B
−
t
R
=
2
d
/
V
1
,
2
where
d
is the thickness of the upper layer. If there are multiple interfaces,
d
in this equation is replaced by
D
, the depth of the refractor beneath G,
and
V
1,2
is replaced by a
depth conversion factor
,
F
, which is a function of
all the velocities involved, weighted according to the layer thicknesses. At a
short shot 2
D
t
i
(the intercept time) and the
F
value can be calculated.
The ways in which
F
varies between short shots may be very complicated,
but linear interpolation is usually adequate in the field (see Example 13.1).
Although
t
R
can be measured directly, it is more convenient to calculate
it by applying the equations at the short-shot locations, where 2
d
/
V
1,2
(or
its multi-layer equivalent) is the intercept time. Geophones are therefore
located at the short-shot points when the long shots are fired, allowing
t
A
and
t
B
at these points to be measured. The two estimates of
t
R
should agree
to within about 3 ms, and if they do not, the raw data and the calculations
should be thoroughly checked to find the reason for the discrepancy.
Short-shot reciprocal times are measured directly if short-shots are fired
from the end-geophone positions, and the fact that they should be equal
may help in picking arrivals. However, they have little interpretational
significance.
/
F
=
Example 13.1
Field interpretation of a four-shot refraction spread with long-shot (LS) and
short-shot (SS) arrivals from west (W) and east (E) ends plotted on same set
