760 EXPLORATION GEOPHYSICS 



the expression for the travel-time T may be written in the form: 



_ 2li cos 6 + X sind 2h cos 6 sin (a + 6) xcosO .r sin ^ sin (a + ^) 

 Vl cos (a + e) F2C0s(a+e) ~~V~2 Fa COS (a + ^) 



Also, since (a + 6) is the critical angle, 



Vl 



sin (a + ^) = jy— 



y 2 



cos (a + 6) 



-^'-m 



Hence, 



2/z cos ^ /I Fi \ , ;ir sin ^ /I Fi \ , :tr cos ^ 



T = 



/J_ _ _F]_\ , xsm6 / 1 F]_\ , ;trco: 



or 



T=2/.cosW|^-pr5 + ^(^ + sinW^-7:;i) (US) 



Equation 115 is the equation of a straight line. 



The travel-time curve therefore consists of two straight line segments, 

 one corresponding to the direct wave and the other to the refracted wave. 

 The segment corresponding to the direct wave passes through the origin 



and has a slope -zy . The segment corresponding to the refracted wave has 

 Fi 



a slope ^^ + sin V 77^ - 77^ ^"^ ^ ^'^^ intercept 



K2 y \~ V 2" 



TO = 2h cos 6 \-rr^ - tti . 



If the seismometer is up dip from the shot-point, 6 must be replaced 

 by —6. In the usual procedure two shot-points are used, one at the up dip 

 end of the profile and the other at the down dip end. The vertical distance 

 to the boundary at the down dip shot-point will be denoted by h' and the 

 distance between the shot-points will be denoted by L. It is evident from 

 Figure 460 that h' = SS'' = h + L tan d. 



The travel-time curve for up dip shooting consists of two straight line 

 segments. The first segment has a slope 1/Fi and passes through the 

 point X = L. The second segment has a slope of magnitude ( cos 6/V2 — 

 sin 6 Vl/Fi^ — 1/F2^) and a time intercept with the line x = L oi magni- 

 tude Ti = 2h' cos e Vl/Fi^-l/Fa^. 



