734 



EXPLORATION GEOPHYSICS 



Fig. 447. — Records from three collinear shot- 



The effect of spread length, i.e., the spread length correction, may be 

 evaluated by using curved wave fronts. Furthermore, the spread is 

 assumed sufficiently short that the wave front striking the spread approxi- 

 mates an arc of a circle of radius p. Specifically, it is assumed that the 

 reflected rays impinging on the end seismometers of the spread originate 

 in a portion of the reflecting horizon which is sufficiently small that it may 

 be regarded as approximately spherical in shape. 



It is a well-known law of geometrical optics that when a wave is 

 reflected from a curved surface, the radii of curvature, pj and pr, of the 

 incident and reflected wave fronts are related to the radius of curvature 

 of the reflecting surface, ps, by the equation 



Pi Pr Ps 



In using the equation, convex upward curvature will be reckoned posi- 

 tive and convex downward curvature negative. Let the path length from 

 the origin to the point of reflection be 1/2, then the radius, pi is —1/2. (The 

 effect of refraction on curvature of the wave front is neglected.) The 

 reflected wave starts back with a radius of curvature 



1 



Pr 



Ps J__ 



2 



Ps 



2(l + Ps) 



