or 



In triangle BSS" 

 or 



But 

 Hence 



Also, 

 and 



SEISMIC METHODS 759 



- . 7 cos ^ 



OA = h 



cos (a + $) 



BS sin (90 - d) 



SS"~ sin [90 -{p- 6)1 



BS = SS" ^°^ ^ 



cos (/? - e) 

 ^-^-'^ = SM'' + M''^'' = /i + ;r tan e 



55-=(/. + ^tan^) ^^^ 



cos (j8 — 0) 



AB = 0''y ' - 0''A - BS' - 5'5"'" 



0"y =;fCOS^ 



h sin a 



0"^ = 



cos (a + ^) 



COS e sin (^ - g) 



5^'= B6'sin (/3-^) = (/7+;irtan^) ,^ ^, 



cos (/? — 6) 



S'S''' = M'M" = hsm9 



Hence, 



.„ - ^sina /, 1 ^ -. cos ^ sin (;ff — ^) , • /, 



^5 = ;r cos ^ z — —TT- - (/z + jtr tan 9) .^ .. - h sin ^ 



cos (a + ^) cos {f3 — 6) 



If one substitutes the values of OA, BS and AB into Equation 114 and 

 makes use of the relation (a + ^) = (^ — 6) and collects similar terms, 

 Equation 114 becomes 



_ 2/i cos ^ + ;tr sin ^ , ^fcos^ h , • ■ • /i / a. a\ 



T = -^ , , .. + — p7 77 7TZ~T sm a + sm 5 cos (a + 6) 



FiCOS(a + ^) V2 VoCOS (9 + a) 



1 /, • / , /,sn .r sin ^ sin (a + ^) 

 + cos 9 sm (a + ^) J 77 7 — 1 -. 



F2 cos (a + 9) 



On making use of the trigonometric identities 



cos (a+ 9) = cos a COS ^ — sin a sin 9 

 sin (a + ^) = sin a cos 9 + cos a sin 9 

 cos^ ^ = 1 — sin^ 9 



