72 E. I. Gal'perin et al. 



faces required for solving the problem as a whole can be traced in space in 

 a similar way. 



The projections of the rays onto the observation plane can be traced on 

 Fig. 10, and the directions (azimuth and angle with tlae vertical) of the 

 rays at any point on the observation plane determined. This could be used 

 to construct the field of lines of equal azimuthal deviations and the field 

 of lines of equal angles of emergence' ' '*\ 



One tracing paper can be used to determine the direction of the refracted 

 rays in the given case for all the radial surfaces, since the boundary is a plane 

 boundary and the direction of the normal is the same for all points on the 

 boundary. 



It is convenient to determine the direction of the rays after refraction on 

 a separate sheet of tracing paper for each ray surface, since the direction of 

 the normal varies at different points of the interface. From an examination 

 of the constructions for different ray surfaces, it follows that the azimuthal 

 deviations of rays emerging from a source with the same azimuth increase 

 in inverse proportion to the angle 9? of inclination with the vertical. When 

 cp = 10°, for example, rays with azimuths near to 180° suffer azimuthal 

 deviations of very nearly 180° on reflection. This, in particular, explains 

 the fact that the projections of the intersection traces of the 10° radial sur- 

 face with the reflecting interface and with the refracting boundary intersect 

 after reflection. 



Calculating the time field— The, time field is constructed by interpola- 

 ting travel time values for each of the rays under consideration. The travel 

 times along the rays are calculated from their various sections in each layer 

 separately, from the length of the section and the velocity value in the layer. 

 The length of the section is determined from the value of its horizontal 

 projection and from the angle of inclination with the vertical as determined 

 from the Wulff net. 



To determine the travel time of a wave along the ray we sum the values 

 for the travel times along its separate links. 



The chart of isochrones constructed for our case is shown in Fig. 16. The 

 points of emergence of the ray surfaces which we examined when we were 

 tracing are indicated by small circles. The chart of isochrones is constructed 

 from the values for the travel times at these points. The isochrones are 

 given at 0.05s. intervals. 



In this paper we have examined the solution for ray problems in seismic 

 prospecting only for reflected waves. The method is equally applicable to 

 head waves (^). 



The accuracy of the solution depends primarily on two factors— accuracy 



