SPATIAL PROBLEMS IN GEOMETRICAL SEISMICS 65 



of this point on to the observation plane is denoted by the letter a. It must 

 be noted, however, that in this case the trace of the projection of the inter- 

 section of the ray surface with the inclined refracting boundary can be found 

 by purely geometrical constructions as an ellipse formed by the intersection 

 of the conical surface with the inclined plane. 



The line thus constructed is the geometric locus of the points of refrac- 

 tion of rays belonging to the 30° radial surface under consideration. At 

 these points the rays having been refracted pass into the second medium. 



Let us determine the direction of the rays in the second medium (after 

 they have been refracted). This is easily done with a Wulff net by the me- 

 thod described (Problem 3). 



Now let us see how to determine the direction of one of the refracted 

 rays, for example a ray with an azimuth in the first medium on emergence 

 from the source equal to 300°. Following the method described above we 

 set the centre of the net at the point of incidence of the ray and plot on the 

 net the direction of the normal to the interface and the direction of the 

 incident ray. Since the refracting interface is a plane the direction of the 

 normal will be the same for all points on this interface. The angle at which 

 the normal inclines to the vertical is equal to the angle of inclination of 

 the plane to the horizontal, namely 10°. The azimuth of the normal is 0°. 

 The direction of the normal (0° and 10°) is shown in Fig. 11 by the 

 letter iVj 2- 



Since the centre of the projection is placed at the point of incidence, in 

 plotting on the Wulff net the direction of an incident ray emerging from the 

 source with an azimuth of 300° we must take the inverse azimuth, that is 

 120°. The direction of the incident ray under consideration (120° and 30°) 

 is shown in the illustration by the point A. Using tracing paper we plot 

 points corresponding to both directions on one meridian, and then measure 

 the angle of incidence ij g? which is equal to an angle of 30°. 



We calculate the angle of refraction from the angle of incidence and the 

 velocity ratio vjv-^ according to the formula 



. . . . V2 



sm ic, 1 = sm 1-, o — , 



where i^ j^ is the angle of refraction. 



sin ig^i = 0.588 ij 2 = 0-705; i^^^ = 45°. 



We plot the angle of refraction we have found in the plane of the ray 

 from the normal in the direction of the incident ray, and mark the point B 



Applied geophysics 5 



