756 EXPLORATION GEOPHYSICS 



the horizontal distance x between the shot-point and a seismometer station 

 may be obtained directly from the basic ray equations 37 and 39; that is, 





^^ (106) 



and 



^=2X„ = 2\"-^^^^^^ (107) 



For the case under discussion, the parameter p = ^ has the follow- 



ing important properties 



1. The maximum depth H is that at which au = an = 90°. Hence, 



sin 90° _ 1 



That is, the parameter p is equal to the reciprocal of the velocity of the 

 medium at the point of maximum penetration of the refracted ray. 



2. The parameter p is equal to the slope of the travel-time curve cor- 

 responding to the path ORS. This may be proved as follows : The slope 



dT 



of the travel-time curve at any point is — . But— = —j — . Hence, the 



dp 

 slope may be evaluated by differentiating Equations 106 and 107 with 

 respect to the parameter p and forming the quotient. 



dP~ ), V\h)[l-pW^{h)-\ d"-^P^^ [1- 



pWih)Y^' 



V(h) [l-/>^F^(/t)]^+/>^F^(/0 [l-/>"F^(/0]-^ ,. 

 [1-pW^ih)] 



-i> 



^^ — dk 



Hence, 





^^ ^" =p (109) 



*> 



'' '■■ ^^ — dh 



-p-y'W]^ 



