68 E. I. Gal'perin et al. 



is now 305° and the angle with the vertical 39°. In order to make the follow- 

 ing discussion clear we show the ray under consideration and the structure 

 contours of the reflecting interface (Fig. 13) on the plan (constructions for 

 all the rays are usually shown on one drawing). The point a lies in the plane 

 of the inclined interface and has a depth of 356 m. Knowing the angle the 

 ray makes with the vertical (39°) we calculate the amount of projection of 

 the ray onto the observation plane during its penetration at some depth Ah 

 (in our case Ah = 50 m) as Ax =^ 50 tan 39°. We plot the segment Ax 

 from the point a along the direction of incidence of the ray. We now exam- 

 ine the two points on the projection of the ray which we have thus obtained: 

 706 and 756 m. At the first point the ray has not yet reached the reflecting 

 boundary, since the 742 ra contour passes through this point; at the second 

 point it has intersected the interface since the depth of this point along 

 the 756 m ray is greater than its depth along the 748 m contours. Conse- 

 quently, the projection of the point of incidence of the ray on to the refle- 

 cting boundary lies between the points 706 and 756 m along the ray and 

 between the contours 740 and 750 m and is found by interpolating the 

 depths. Similar constructions can be made for all rays. After joining by 

 a smooth Hne the trace projections of the intersection of the radial surface 

 with the reflecting interface, along which the rays belonging to our radial 

 surface are reflected (Fig. 10, line 4), we must next find the direction of the 

 reflected rays. 



This again is done by means of a Wulff" net. For this purpose the centre 

 of the net is set at the point of incidence of the ray, and the directions 

 of the incident ray and of the normal to the interface are plotted on the 

 grid. 



Let us trace the direction, after reflection, of the ray in which we are interested. 

 The ray has emerged from the source with an azimuth of 300° and has been 

 refracted on the inclined interface at a depth of 356 m at a point the pro- 

 jection of which on the plane is denoted by point o, and which has struck 

 the reflecting boundary at a point 746 m deep. The projection of the point 

 of incidence on the observation plane is denoted by the point h. We have 

 already described how to determine the direction of the reflected ray; we 

 shall now briefly recapitulate this method as it applies to our data. 



We imagine the centre of the net placed at the point of incidence, and 

 plot on it the directions of the incident ray and the normal to the interface. 

 The direction of the incident ray is determined as ^ve have sho^vn above, 

 by the co-ordinates (305° and 39°). The point B (see Fig. 11) mth the re- 

 verse azimuth characterizes the direction of the incident ray. The direction 

 of the normal to the interface is in our case determined by the values (318° 



