By Nicholas Rast
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Its projection on the horizontal plane is shown in Fig. 5, a, and the section of the vertical plane along the lines /—/, that is in the direction of the ray in Fig. 5, b. Since 10) 1 o 0^ S Jh Τ 200 400| 600 800 1000 1200 1330 1500 ----7- / 1/ / (b) F i g . 5. Projection of point where ray intersects interface, a—plan; vertical cross section along direction of incidence of ray; 1—structure contours of interface; I—I direction of incidence of ray. 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.
We can now pass immediately to the consideration of problems encountered in geometrical seismics. Problem 1. To determine on the net the plane which includes the direction of the ray and the normal to the boimdary. It is known that incident, reflected and refracted rays and the normal to an interface lie in one plane, which is also the plane of the rays. We shall use this property to find the plane of the rays. Imagine the centre of a stereo graphic net at the point of incidence of a ray; we now plot on the tracing paper, using the net, the direction of the incident ray and the normal to the interface.
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 Unes 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. 05s. As we might have expected the isochrones form smooth lines extending along the line of the Umits of the structure.