Chap. 9] 



SEISMIC METHODS 



527 



The true dip is then calculated from eq. (9-56a). With the above 

 formulas, relations may readily be set down for two profiles making an 

 arbitrary angle with each other, 



10. Two dipping layers. Travel times 

 for two inclined layers are derived in the 

 same manner as for the single inclined 

 layer and the double horizontal layer.^ 

 Thicknesses of layers below the origin 

 will be designated by H for up-dip shoot- 

 ing and by h for down-dip shooting. 

 A profile shot up dip in reference to the 



upper formation boundary may be down ^ „ ^ , 



,. . , X ^u J u J Fig. 9-64c. Travel times for two 



dip m reference to the second boundary, p.^mes as in Fig. 9-646 (adapted 



In order to avoid ambiguity, the direc- from Gassmann). 



Fig. 9-65. Ray paths in two dipping layers. 



tion of shooting will be referred to the upper boundary. With the nota- 

 tions of Fig. 9-65, 



. . V2 . . Vi sin a sin /3 . . Vi 



sm ^2 = — ; sm ti = — ; - — = -; — ^ = sm i\ = — : 



V3 V2 sm 7 sm 5 V2 



7 = 12 + (^ — <p) and S = Z2 — (^ — i;^). 



Therefore, 



• ^ • r- /. \i sin jS 

 sm d = sm 1*2 — \w — ^)\ = — 



sin 7 = sin [«2 + (lA ~ v)] = 



sm ii 



sin a 



sin ii ' 



(9-57a) 



" For details see Schmidt, op. cit., 7(1/2), 37-56 (1931). 



