(25) 



678 EXPLORATION GEOPHYSICS 



i=vM 



Now the slope, or emergence angle, of the wave front is given by 



oi = cos~^» (26) 



or ai = sin~* "v/l ~ ^^ 



since P + m^ + n^=l 



then sin ai = s/W+w^ (27) 



Substituting Equations 25 into 27 



si„. = FW(f)%(fy (28) 



The equation of the wave surface at the origin is 



Ix + my + n2 = (29) 



and the intersection of the wave front with the surface, Z = 0, is the line 



lx + my = (30) 



The direction of the dip of the wave is in the direction of motion of the 

 wave and hence is at right angles to the direction of this line of intersection. 

 Let the angle between the direction of the dip and the x axis be designated 

 by }p. Now 



dx 

 From (30) tan i/' = — 



Hence tan,/r = ^ (32) 



qI 



"dx 

 From Equations 28 and 32 it follows that the sin a\ is a vector whose com- 



ponents are Fi •?— and Vi -r — 

 dx dy 



Thus the true direction and magnitude of the dip of the wave front can 

 be computed and plotted as the vector resultant of the components of the 

 sines of the emergence angles recorded by spreads crossing at right angles. 



