SECT. 1] 



SEISMIC REFRACTION AND REFLECTION MEASUREMENTS 



15 



Fig. 9 shows a two-layer case in which there is assumed to be a small velocity 

 discontinuity at the water-sediment interface, and in which the velocity in 

 the upper sediments is approximately equal to that of water at the sea floor, 

 increasing linearly with depth beneath the bottom. To demonstrate the full 

 effect of gradient, we first assume that the sediments are infinitely thick and 

 that velocity increases with dej)th at a constant rate K sec~i : 



C = Cq + KZ. 



(6) 



Time 

 4^ 



2"! 



■-I 



Distance 



Vsloclty 



Depth ' 



Fig. 9. Ray diagram and time-distance graph showing effect of velocity gradient in thick 

 sediments. 



With this velocity-depth structure, ray paths in the sediments are segments 

 of circles whose centers lie at a height of CqJK above the water-sediment 

 interface. For a particular depth of water and for a particular value of A', 

 there exists a critical distance, Dc, between shot and detector for which a ray 

 originating at the surface and penetrating into the sediments can be returned 

 to the surface. This ray is designated Re in Fig. 9. At ranges shorter than D^ 

 only reflected waves from the sea floor can retvirn to the surface. At any range 

 greater than Dc two arrivals are returned to the surface, one which penetrates 

 more deeply and one which penetrates less deeply into the sediments than the 

 arrival following the path of Re. Since much of its path is through the high- 

 velocity sediments, the deep ray, Rd, reaches the detector earlier than the 

 shallow ray, Rs. As shown in the time-distance graph in Fig. 9, the Rd curve 



