SPATIAL PROBLEMS IN GEOMETRICAL SEISMICS 57 



according to the assumption this ray makes an angle of 20° with the 

 vertical, it will be projected onto the observation plane in a section Ax = Ah 

 tan 20°, when it penetrates to a depth Ah. If we now plot on the plan on the 

 scale of the constructions the section Ax in the direction of incidence of the 

 ray, we shall obtain on the projection of the ray a successive series of points 

 corresponding to certain definite depths of the ray: in our case Ah = 100m 

 and the points will be at 100, 200 and 300m. 



Let us suppose that we strike the point marked 1300m, that is at this 

 point the ray has penetrated to a depth of 1300m; while the structure contour 

 of the interface 1320m passes through this point, it is obvious that the 

 ray has not yet reached the interface. We plot the section once again and 

 obtain a point marked 1400m but the structure contour 1340m passes 

 through this point on the plan and consequently our ray has not 

 yet intersected the interface between the contours 1300 and 1400m, Inter- 

 polating values for the depths between the structure contours 1300 and 1400m 

 and also the depths of the section Ax 1300 — 1400m, we obtain a point c 

 in which the depths both along the structure contours of the interface and 

 along the ray are the same — 1330m. 



The point c is thus a projection of the trace of intersection of our chosen 

 ray with the interface. Having made such constructions for many rays of 

 the conic surface and having joined the points obtained in a smooth curved 

 line we shall obtain on the plan the trace of intersection between the interface 

 and our ray surface (hne 2 in Fig. 4). This line is also the projection on to 

 the horizontal plane of the hne on which the rejflection of the rays making 

 up our ray surface takes place. 



(b) Determination of the direction of the reflected rays. Having constructed 

 on the plan projections of the points of incidence of the rays under considera- 

 tion we find the direction of the rays after reflection. This is done by means of 

 a Wulff" net, in the manner indicated above (Problem 3). The centre of 

 the Wulfi" net is placed at the point of incidence of the ray and the direction 

 of the incident rays and the direction of the normal to the interface at the 

 point of incidence are plotted on the Wulff net. The direction of the nor- 

 mal is determined from the structure contour chart of the interface. 



The azimuth of the normal to the boundary at the point of incidence is 

 determined by the direction of maximum incHnation of the boundary at 

 this point. This direction corresponds on the plan (Fig. 6, a) to the direction 

 of the normal to the structure contour of the interface. The angle of incidence 

 of the normal to the vertical is determined from the value of the angle of 

 incidence of the interface at the point of incidence. 



The angle made by the normal with the vertical can be determined 



