Chap. 9] SEISMIC METHODS 



where the substitutions may be made, 



a:23u[sin (t'l — (p) — sin {^ — (p)] = X23u'Vi — — — 



LV2u VsuJ 



and 



a:2M[sin (ii -\- (p) — sin (a + ip)\ = X23d-Vi — — — • 



LV2d VsdJ 



529 



(9-58c) 



Computation proceeds in the following steps: (1) Compute z'l and «p from 

 formulas (9-54). (2) Determine V2 = Vi/sin ii . (3) Calculate Hi and 



Fig. 9-66. Travel-time curves for two layers of same dip direction (after 



O. V. Schmidt). 



hi from eq. (9-55). (4) Find angles a and j8 from apparent velocities 

 Viu and V3d (formulas [9-57c]). (5) Compute «2 and (^ — <p) from (9-57a). 

 (6) Find ^ from {\p — <p) and <p. (7) Calculate V3 = V2/sin 12 . (8) Find 

 Hz , and (9) h^ from (9-58). 



Two examples are given below, one for boundaries of the same dip 

 direction, the other for boundaries of opposite dips. The corresponding 

 travel- time curves are shown in Figs. 9-66 and 9-67 and furnish the 

 following numerical values : 



