ASYMMETRY OF SOUND VELOCITY UU 
In the diagram, Fig. 4, layers of the above-the-average velocity are repre- 
sented at a-a. In shooting a line of stations in an up-dip direction, the time 
intervals between stations 1-2 and 2-3 will be short, while between stations 
3-4 and 4-5 the intervals will be longer, because these stations are beyond the 
zone of influence of the fast layer “a”. However, on advancing farther down 
the line, other laminations of higher-than-average velocity will be en- 
countered and the intervals will again be shortened. Conversely, when shoot- 
ing down-dip, many of the intervals will be lengthened by these same layers. 
Now it is expectable that the flatter the dip (until it becomes nearly 
horizontal), the more continuous will be the effect on the time intervals. 
Therefore, moderate dips, such as are usually found in practice, will show this 
type of velocity asymmetry to the best advantage, and those formations 
which exhibit the least uniform stratification will generally be the ones whose 
dip it will be easiest to determine. 

Fig. 4. 
It may be objected that the foregoing analysis is based on the slope- 
effect and not on dip. To a certain extent this is true. In extreme cases, like 
that shown in Fig. 4 where the high velocity layers are unusually thick and 
clearly defined, the interpretation can be based purely on the theory of 
refraction shooting. But in a majority of cases the layers of higher velocity 
are relatively thin, rather closely spaced, and seldom recognizable in the 
outcrops. Thus it seems to be the aggregate effect of many sloping layers 
which generally produces asymmetrical velocities such as those tabulated in 
the latter part of this paper. Consequently, there is no choice but to make the 
interpretation in terms of dip rather than in terms of slope. 
CASE 2 
In Fig. 5a the wave is shown traveling in an up-dip direction. Exaggerat- 
ing conditions somewhat for the sake of clearness, we may assume that the 
wave, taking the path of least time, descends fairly deeply into the shale and 
is steadily refracted on a curved path until the critical angle is reached, when 
it follows the bedding and finally emerges at the surface giving the time 
interval A¢,. In shooting down dip, the principle of reversibility of wave paths 
tells us that, between identical surface points, the path will be the same from 
either direction and there can be no difference in the recorded times. Simi- 
larly, if the subsurface dip is everywhere uniform, equal shooting distances 
will give identical paths even though the surface points are not the same. 
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