12 EWING [CHAP. 1 



segment of the path above the interface minus the travel time along the 

 interface. For example the intercept time for Layer 2 at A is 



t = 

 reducing to 



2hi 2hi tan iiz 



Ci cos ii2 Cs 



, 2hi 



t = -p^ cos li2. 

 ^1 



Similar relationships can be derived from the deei:)er interfaces giving the 

 following set of equations : 



h& = -p7- cos li2 



2/i2a • "la 



ha = -PT- COS t23 + 7^ (cOS ai3 + COS ^13) (5) 



02 Oi 



2A3a . A2a . . n \ ^la , n . 



Ma = -7^— COS t34 + 77- (cOS a24 + COS ^824) + 77- (cOS ai4 + COS ^14). 



03 02 Ci 



These equations give the time-intercept formulae for point A. A. similar set 

 exists for point B. With (4) and (5) and the slopes and intercepts taken from 

 the time-distance graph, true velocities, inclinations and thicknesses can be 

 computed. 



5. Shear Waves and Complex Refracted Waves 



In Fig. 8 are shown the ray paths and refraction lines for the most com- 

 monly observed arrivals in seismic work at sea. This model is typical of the 

 structure on the continental rise of the east coast of the United States. The M 

 discontinuity and the mantle are not shown because doing so would have 

 unduly complicated the picture with additional lines. 



Of the compressional wave arrivals shown, the least commonly observed is 

 that in Layer 2, In fact, it is seldom seen in deep-water areas and is shown here 

 mainly to indicate its relationship to other arrivals. Layer 4 (see Raitt, Chapter 

 (i) is observed in all but some of the deepest areas, where the arrivals are 

 masked and are difficult to see as second arrivals. 



Of the shear-wave arrivals, i.e. those which propagate as compressional 

 waves in Layers 1-3 and as vertically polarized shear waves (»SV) in the high- 

 velocity layers, the one which travels in Layer 5 (designated by open circles) is 

 most commonly observed. Though relatively common, its strength is markedly 

 variable from one profile to another, indicating an appreciable variation in 

 the conditions essential to efficient transformation from compressional to shear 

 propagation. 



Note that the shear waves in both Layers 4 and 5 are transformed at the 

 3-4 interface. Transformation from compressional to shear waves at the 4-5 



