SEISMIC METHODS 767 



Assume that the velocity F5 in the layer whose surface constitutes the 

 marker horizon is constant. Then 



and the expression for the travel-time T may be written in the form 



Introduce the quantities t,n and tn defined by the relations : 

 tj = toA-^ = delay time at M 



Also, set 



tn =tBs- -77- = delay time at N 



h = T — -zy = intercept time 

 K 5 



The intercept time may also be expressed in the form : 



b = tJ-\-tn' (118) 



Equation 118 is the basic relation of subsequent deductions. Since T, 

 X, and F5 are determinable from the observed data, the intercept time h 

 may be regarded as an observed quantity.* 



For a given velocity distribution in the geologic section, the delay 

 times tm and tn are dependent only on the depths Hm and f/„ respectively. 

 Furthermore, if the velocity distribution is known, it is theoretically 

 possible to deduce a relationship between the delay time t' and the depth 

 H and to portray this relationship graphically. Thus, if the delay times 

 can be determined from observed data, the corresponding depths may be 

 read from the graph. 



The relationships of delay times to depths and to offset distances may 

 be obtained from the geometry of the hypothetical path. In Figure 464, 

 a is the angle formed by the hypothetical wave path with the vertical at 

 a point in the depth interval AH; Aa denotes an increment of offset 

 distance ; A5 is the path length in the interval AH. The increment of delay 

 time corresponding to Aa will be denoted by Af'. From the geometry of 

 the figure, 



AH = A^ cos a, Aa = AH tan a 



and from Snell's law 



V 



sm a — ^pj- 



* To achieve accuracy in the final results, it is of course necessary that the value 

 of the observed travel-time be corrected for the low velocity or so-called "weathered" 

 layer. 



