DEPTHS FROM SEISMIC TIME-TRAVEL CURVES 125 
B-—A 
= 
2 

(19) 
where V,’ is the apparent velocity obtained from the slope of the 
time-travel curve shot up dip, V2” is the apparent velocity obtained 
from the slope of the time-travel curve shot down dip, 72’ and X2’ are 
coordinates of a point on the time-travel curve shot up dip, and 7’ 
HOT PON 7 ; SURFACE R 

Fic. 3.—A cross-sectional profile of a single dipping stratum with the Mintrop shortest 
time path from the shot point to the receiving station R. 
and X.” are the coordinates of a point on the time-travel curve shot 
down dip. The true velocity V2 of the inclined layer is obtained from 
the following relations: 

B A 
iiek auch (20) 
2D 
Wo = V,/sin a. (21) 
The equations (1)—(21) apply only where the velocities of the layers 
are all in an ascending order of magnitude from V, to V,, and these 
equations are essentially the ones given by D.C. Barton in a paper 
entitled ‘‘The Seismic Method of Mapping Geologic Structure.’ 
However, if the area under consideration yields strata of several subse- 
quent dips of different angles, the calculations become very compli- 
cated and it is quite laborious to determine the various dips, true 
velocities, and thicknesses of the beds from enlarging on the expres- 
sions (1)—(21). To simplify this problem, the following semi-graphical 
method was developed. 
In most cases the thickness of the first bed can be calculated by 
the straightforward formula for parallel beds. The result, of course, 
gives the depth of the surface of the second bed only in the immediate 
vicinity of the shot point at each end of the profile. In general it may 
be assumed that the surface of this bed extends across the profile in a 
linear variation from the two shot points, and that this bed has the 
5 D. C. Barton, Geophysical Prospecting for 1929, p. 572. 
785 
