Geology Reference
In-Depth Information
It is then necessary only to remember that sin i c = V 1 / V 2 to show that the
intercept time is:
t i = 2 d / V 1 , 2 where V 1 , 2 = V 1 V 2 / V 2 V 1
The quantity V 1,2 has the units of a velocity and is approximately equal to
V 1 if V 2 is very much larger than V 1 . The critical angle is then almost 90
and the delay suffered by the refracted ray in travelling between the surface
and the refractor is roughly equal to twice the vertical travel time. If the
difference between V 1 and V 2 is small, V 1,2 can be very large.
Intercept times can be estimated on T-D plots by drawing best-fit lines
through the refracted arrival times (Figure 13.3), but even a very good fit is
no guarantee that the depth of the refractor does not change in the region near
the shot-point, from which no refractions are observed. If, however, a long
shot is used as well, there should be a constant difference between long-shot
and short-shot travel times at points towards the far end of the spread (Figure
13.5). An intercept time can then be obtained by subtracting this difference
from the travel time between the long-shot and the short-shot locations,
which can be done exactly if there is a geophone in the short-shot position
when the long shot is fired. Otherwise, using the long-shot arrival at the geo-
phone closest to the short-shot at least reduces the distance over which ex-
trapolation must be made. Strictly speaking, the method will work only if the
travel time from B to S 1 in Figure 13.5 is the same as the travel time from S 1 to
D, but in practice the errors introduced by this assumption are usually small.
13.2.2 Multiple layers
The intercept-time equation can be extended to cases involving a number of
layers. The intercept time associated with the n th refractor is:
t n = 2 d 1 / V 1 , n + 1 + 2 d 2 / V 2 , n + 1 ···+··· 2 d n / V n , n + 1
Figure 13.5 Long-shot and short-shot travel paths for a three-layer case.
The paths for energy travelling to any given geophone from S 1 and S 2 are
identical once past the point D, and the long-shot/short-shot travel-time
differences will therefore be the same at all detectors from G 1 onwards.
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