764 EXPLORATION GEOPHYSICS 



Hence, 



sin o = -^ = .727 a = 46M0' 



sin )8 = :^, = .600 p= 36°50' 



sin-i -^ = 1/2 (a + y8) = 41°45' 

 K2 



-^ = .666 F2 = 9000ft./sec. 77- = 1.11 x lO"* 



6 = 1/2 (/? - a) = 4°55' cos = .996 



Extending the segments back to the shot-points gives 



TO =.174 to' =.490 



so that 



h = J"" =700 ft.; h' = ^^= = 2000ft. 



2cos5V^-^ 2cos6yJy^-y^ 



From the third sections 



F3'= 1 5,500 ft./sec. 

 F3''= 14,600 ft./sec. 



sin ai = -^ = .387 ai = 22°45' 



y& 



sin/?i = ^ = .411 )&i = 24°15' 



F: 



The times along the segments OiOi', 5'26'2', ^S'l^S'i' and O2O2' may be 

 computed either trigonometrically or graphically by using the values of 

 ^1, h, h\ ai, and ;8i given above. The times are found to be 0.117, 0.191, 

 0.306 and 0,341 respectively. By subtracting the times along OiOi' and 

 SxSx from the time 1.698 along OxOiSxSi the time 1.275 is obtained 

 at the distance 12,000 feet as measured along Oi'^'i. The calculations 

 of the times along 0i'02' and 0i''02'' are carried out in the same way, and 

 the solution proceeds as already outlined. 



Limitations of Outlined Calculations 



By the methods just outlined, the thicknesses, dips, and velocities 

 of the subsurface strata can be calculated when these quantities satisfy 

 the assumptions upon which the methods of calculation are based. Strata 

 with velocities lower than the velocities of the overlying strata or strata 



