EWING 



[chap. 1 



theoretical curve which most closely fits the observed values thus indicates 

 the velocity and thickness of Layer 2, These curves were computed assuming 

 uniform velocity in each layer. A similar method of comparing observed with 

 theoretical curves is used to handle models with velocity gradients. This is 

 discussed in detail in Chapter 5. 



0.3 



0.3 



0.05 



jm,' 



Fig. 2. Relationship of bottoin reflected and sub-bottom reflected waves for different 

 ratios of layer thicknesses, /i2/fii, ^nd velocities, C'2/C'i. (After Katz and Ewing, 1956.) 



3. Refracted Waves 



In seismic exploration, sound waves refracted at an interface between two 

 media with different velocities are of particular interest. In Fig. 1 the Rn ray 

 is refracted by the velocity change across the 1-2 interface such that it pro- 

 pagates in Layer 2 along a jiatli more nearly horizontal than that in Layer 1 . 

 The refraction is described by Snell's Law, 



sm 931 sm (po 



Ci 



O2 



When ip-i is 90°, equation (2) reads 



sin (pi = CijCo. 



n 



(:i) 



This defines the critical angle of incidence, 95c, , for which the ray is refracted 

 parallel to the 1-2 interface. Similarly, there is a value of (pz for which a ray 

 travelling in Layer 2 will be refracted along the 2-3 interface. The soimd wave 

 refracted at the critical angle travels along the interface at the speed of soiuid 

 in the higher velocity layer, and part of its energy is continually re-emergent 

 into the lower velocity medium at an angle equal to that of the incident ray. 



Fig. 3 shows the ray paths for direct, refracted and reflected waves for a 

 tiiree-layer model and their relationshi]) to each other on a time-distance 

 graph. 



