126 SIDON HARRIS 
seismic velocities at each end of the profile indicated by the time- 
travel curves. It must be remembered that the dip formulas can be 
used only where either the true velocity of the dipping bed is known 
or where the reversed profiles overlap. Suppose the surface of the third 
bed indicates a dip of 6; degrees with the horizontal surface. As the 
true velocities of the first two beds are known, and as the surface of 
the second bed is parallel to the surface of the ground, the true velocity 
and dip of the third bed may be determined from the following rela- 
tions: 
B—A 
6, = » where sin B = V2/V3” (22) 
2 
sin A = V2/V3' 

where V3” is the apparent velocity down dip, and V;’ is the apparent 
velocity up dip. 
V3; = true velocity = V2/sin (A + 4). (23) 
It now remains only to find the thickness of the second bed under 
each shot point. First, calculate the angles of refraction for the Mintrop 
path refracted along the surface of the third bed by using relations (6) 
and (7), and lay off the path accordingly for a station on the V3” and 
V3’ curves. Then, measure the path length through the first layer and 
determine the time required to traverse this layer by dividing the path 
length by the velocity V;. Subtract this time interval from the time 
coordinates of the chosen points on the V;’’ and V3’ curves and use the 
remainders as the values of T in relations (15) and (16). It must be 
remembered that the values of X used in the calculations of and kare 
the distances of the stations chosen from the respective shot points 
minus the mirage distances on the surface of the V2 layer. The mirage 
distance is illustrated by the distances ab and fq in Figure 4. 
Suppose the surface of the fourth bed has a dip. On account of 
the dip of the third layer, the slopes of the time-travel curves of the 
fourth bed will be affected whether the fourth bed has a dip or not. In 
order to remove this effect of the third bed the following procedure is 
taken. Assume a true velocity for the fourth bed; a mean value be- 
tween the velocities obtained from the up and down dip time-travel 
curves is usually a fair approximation. Calculate the angles of dif- 
fraction of the Mintrop path diffracted from the surface of the fourth 
bed, using the assumed velocity for V4 in the relations (8)—(10), and 
lay off the parts of the path through the first and second layers for at 
least two points on the up dip profile and the same number on the down 
dip profile. Calculate the time required in traversing the first and 
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