SEISMIC METHODS 



665 



of / and the velocity in the second medium ; that is, 



Hence 



A' A" = tV2 



A'A' 



B'B' 



V2 Fi 



Elementary trigonometry shows that 



A' A" = A'B" sin ao 



and 

 so that 



B'B" = A' B" sin ax 



sin 02 V2 sin a\ sin 02 



~" or ~~ 



sin a\ Vi Vi F2 



(10) 



which is the relation desired. 



Reflection or the turning back of the seismic wave occurs when it 

 encounters a boundary separating media of different seismic velocities. 

 The energy of the reflected wave and its phase relative to the initial wave 

 encountering the boundary depend upon degree of contrast of the elastic 

 properties of the two media separated by the surface of discontinuity. 



The law of reflection states (a) that the incident ray and the reflected 

 ray lie in the same plane and (b) that the angle of incidence (angle between 

 the incident ray and the normal to the reflecting surface) equals the angle 

 of reflection (angle between the reflected ray and the normal to the reflecting 

 surface.) 



Critical Angle of Incidence 



From a consideration of Snell's law we find a unique case where the 

 angle of refraction is 90 degrees and the corresponding sine is numerically 

 equal to unity. By definition the angle of the incident ray which results in 

 a refracted angle equal to 90 degrees is called the critical angle of incidence. 

 Consider now the case of two strata separated by a horizontal boundary 

 at a depth h. (Figure 410.) Let the velocity of the elastic wave in the 

 upper stratum be Fi and that 

 in the lower stratum be V2 

 and assume that V2 is greater 

 than Vi by a finite amount. 



In the general case, a ray 

 starting at the source and 

 reaching the boundary at the 

 point B will produce a re- 

 flected ray BS and a refracted 

 ray BP. The ray BS which is 



^^fl«^4-«^ U„^l, ;„4.^ 4.U^ C_„4. Fig. 410. — Sketch illustrating refraction and reflection 

 reflected back mtO the first of rays at a horizontal boundary. 



