SEISMIC METHODS 



679 



RESULTANT SINE OF Oi 



Figure 420 illustrates the method of plotting these results in the usual 

 form of geological dip and strike symbols in horizontal plan. It also may 

 be noted that the direction of the resultant of the components of the emer- 

 gence angle corresponds to the true direction of the dip and strike of the 

 reflecting interface. 



It has been shown by Equation 17 

 that at any point of its path, a given 

 ray forms an angle with the vertical 

 conforming to the equation 



sin a = — sin ai (17) 



We may determine the numerical value 

 of ax as the resultant of its measured 

 components. Since the ray path in 

 question is the so-called "normal ray," 

 i.e., that ray which reverses its path, it 

 follows that at the point of reflection the angle of incidence a is equal to 

 the dip of the reflecting interface 6. Making use of Equation 17 and substi- 

 tuting B for a, we may write the expression for the dip ^ of the reflecting 

 interface 



Fig. 420. — Vector magnitude of sine and 

 direction of the dip of emerging wave front. 



V . 

 sm B = -rr sm ax 

 yi 



(20) 



Having determined the direction and magnitude of the dip of the 



reflecting interface by measurements at the surface of the ground, the next 



process is to find the position of the dip of the 



interface in space. 



For the purpose of simplification, let the 



horizontal distance measured in the plane of 



incidence be given the coordinate h. Let the 



sin ai , - . , , 

 constant parameter —^ — be designated as p. 



Vi 

 Then from Equation 17 



sin a = pV 



{2,2,) 



In Figure 421 is shown an element ds of 

 the ray path with component elements dh 

 and ds. 



The wave moves the distance ds in the incre- 

 ment of time dt. 



Fig. 421. — Component elements 

 of wave path. 



ds=V dt 



(34) 



