62 E. I. Gal'perin et al. 



25°, 30°, 35°, 40°, 45°, 50°. Using such constructions we can now pass 

 on directly to calculating the travel times along the rays. The length of the 

 ray's segment required for this is determined from the difference in depth 

 AH of the initial and terminal points of the segment of the ray and its angle 

 with the vertical from the formula 



cos 9? 



The times for any ray are calculated separately for each segment in the 

 broken line and then the travel times are summed. The travel time obtained 

 is entered on the plan at the emergence point of the appropriate ray. The 

 chart of isochronous lines is obtained by interpolating the travel time values for 

 all emergence points of the rays under consideration. Fig. 9 shows an 

 isochrones chart constructed by the method described. The isochrones 

 are plotted on this chart at 0.05s. As we might have expected the isochrones 

 form smooth hnes extending along the line of the Umits of the structure. 



We now consider a problem for a three -layered medium. 



CONSTRUCTING THE SURFACE HODOGRAPH FOR REFLECTED 

 WAVES IN THE CASE OF A THREE-LAYERED MEDIUM 



By way of example we shall analyse in detail an isochrone chart for waves 

 reflected from a dome, making allowance for intermediate refraction on an 

 incHned plane*. The construction of the medium is shown in Fig. 10, b^ 



The velocity ratio — in the first and in the second layers is equal to 1.2. 



The source of excitation is in both cases above the slope of the dome. 



The general scheme for solving the problem is the same as for problem 1. 

 The difference is that it is necessary to make allowance for an intermediate 

 interface. We do this by constructing projected traces of the intersections 

 of the ray surfaces with the intermediate interface both before and after 

 its reflection when we are tracing the ray surfaces. 



Let us examine the tracing of several ray surfaces. Fig. 10, a, show.^ 

 constructions for a ray surface formed by rays which emerge from a source 

 and make an angle 9? = 30° with the vertical. It can be seen from the plan 

 that the source is set in relation to the top of the dome. Radial lines emerging 

 from the source are produced at every 10° and correspond to the direction^ 

 (azimuths) of the rays in the first medium which were used in tracing the 

 ray surfaces. 



* The solution of this problem is given in(^). 



