528 



SEISMIC METHODS 



[Chap. 9 



The travel times are: 



(a) For up-dip shooting: 



tsu = - {su sin (/3 - (p) + Hiuicos (a + ^) + cos (jS - <p)] 



Vi 



+ Hiu • 2 sin ii cos i^ cos ^ } 



(6) For down-dip shooting: 



1 



tzd = - {Sd sin (a + V?) + A]d[c0S (a + v?) + COS 03 — (f)] 

 Vi 



+ hid '2 ^in fi cos 12 cos ^} 



(9-576) 



and the apparent velocities are: 



t 



V3u = 



Vi 



Vsd = 



dtsu sin (/3 — <p) 

 ds Vi 



(9-57c) 



d^3d sin (a + «p) 



Depths may be calculated from intercepts Xi and xz (xn , X23) in the 

 up-dip and down-dip profile. As the relations for Xnu and xud have been 

 given before eq. (9-55), it is assumed that Hi , hi , and <p are known. For 

 the computation of H2 and h2 use is made of the intercepts a;23« and X23d ; 

 or the first and third parts of the travel-time curve may be extended to 

 the intermediate intercepts x^u and Xisd . Then the depths follow from: 



(a) The 0:13 intercepts: 



a:i3„[l — sin (/3 — <p)] — Hiu[cos (a -\- <p) -\- cos (jS — v?)]' 



Hiu = 

 and 



2 sin t'l cos 22 cos \^ 



Xi3d[l — sin (a + <p)] — /iid[cos (a -1- v?) -1- cos (jS — <p)] 



^ (9-58a) 



2 sin I'l cos t2 cos ^ 

 (6) The a:23 intercepts: 



a:23u[sin (t'l — v?) — sin (jS — ^)] — Hiu[cos {a -\- <p) -{■ cos (j8 — ^)] 



Hiu — 



2 sin z'l cos i^ cos ^ 



+ 



Hiu 2 cos ti cos <p 



hid = 



2 sin ii cos 22 cos \^ 



a:23<i[sin (ii + <p) — sin (a + v?)] — hu [cos (a -f v?) -1- cos (0 — <p)] 



2 sin ii cos ii cos ^ 



/lid 2 cos ii cos (p 



+ 



2 sin ii cos 12 cos ^ ' 



(9-586) 



