Chap. 9] SEISMIC METHODS 535 



In the case of the double horizontal layer we have for the intercept 3:23 : 

 2rfi/vx + 0:23/ V2 = 2di/vi + 2(c?2 — rfi)/v2 + a;23/v3, which leads to 



d^^dr-^-^-^il--"). (9-596) 



V2 \ V3/ 



For the refraction path the corresponding depth 



(-3 



^23 . 



J , , \ V3/ , , COS Zi — COS a 



di = di -f- ^ : 1- rfi : : ~ , 



2 COS t2 Sin ii COS /3 



that is, the simple cosine ratio previously mentioned applies here only to 

 the first term. The error increases as more layers and less velocity con- 

 trast are involved. 



In the case of a dipping layer the underlayer travel time for vertical 

 propagation is given by 



fe = ?^^+^ 



Vi V2 



where the symbols have the same meaning as in formula (9-50a). Sub- 

 stituting e = s cos (p, Z = H cos <p, z = h cos ip, 



1 /OTT • >. , S„ COS ^ 



ku = - {2Hu cos (f — Su sm (p) + 



Vi V2 



1 /o7 , . s , Sd cos (p 



tid = - {2hd cos (p -\- Sd sm (p) + 



Vi V2 



By differentiation, 



dt2u _ _ sin ^ cos ^ _ 1 



ds Vi V2 V2u 



and 



so that 



dkd _ sin (p cos <p _ 1 

 ds Vt V2 V2d' 



H„_ V W a„d A, = — > ^-^. (9-59c) 



2 cos <p I cos (p 



These relations differ again by the factor cos i from those previously given 

 for the depths calculated for the refraction path. 



If in the case of the double incUned layer Z„ and Zd are the depths 



