Chap. 9] SEISMIC METHODS 509 



In another method of depth computation, the second part of the travel- 

 time curve is extended to the intersection with the abscissa, obtaining the 

 distance D. Then 



d = - tan i. (9-44c) 



A third method uses the time intercept ^o on the ordinate: 



d = tv2-tant = 1^. (9-44d) 



2 2 cos t 



A fourth method of depth calculation is based on the time ix of the 

 intercept: ^ 



2 K V2 + vi 



The determination of depth is as accurate as the measurement of dis- 

 tance between shot point and receiver, other things being equal. It de- 

 pends, further, on the relief (ac- 

 curacy of elevation correction), on 

 the accuracy of timing of the im- c^ ,ix . 

 pulses, and on the difference in ' ' ' ' 



velocities. Other refraction meth- i\ / \/, 



ods for the two-layer case, using 

 different interpretation methods ' ^ 



and different field technique, are Fig. 9-47. Wave paths, two-layer case, 

 discussed on pages 533 and 546. 



5. Two horizontal layers. In the single-layer case impulses past the first 

 break in the travel-time curve arrive by the path AGHF (see Fig. 9-47). 

 If a third layer is within range, these will be overtaken by waves traveling 

 along the path ABCDEF, and the travel-time curve will now have two 

 breaks. Let the velocities of the three media be Vi , V2 , and Vs , and the 

 respective depths of their lower surfaces di and da . Then sin j8 = V2/V3 , 

 since the angle at C is 90°. For the remainder of the path in the upper 

 layer, sin a/sin /3 = V1/V2 . Substituting sin j3, sin a = Vi/vs . 



In the expression for the underlay er travel time, (9-43), the first term 

 represents the underlayer effect and the second that of the overburden. 

 By analogy, the time for the path ABCDEF is composed of one under- 

 layer time and two overburden times, so that 



, s , 2(d2 — di) „ . 2di fn AK ^ 



is = 1 — ^ — cos /3 H cos a. (9-45a) 



V3 V2 Vi 



The second part of the travel-time curve gives the velocity through the 

 second layer, and the third part gives that through the third layer. By 



