652 



EXPLORATION GEOPHYSICS 



Both the energy and the ampHtude equations are derived on the 

 assumption that the velocities in the two layers differ by finite amounts 

 so that the boundary corresponds to a substantially abrupt discontinuity.* 



Amplitude of the Waves. — The densities of the two media will be denoted by 

 di and d^ respectively and the following notation will be used for the different waves. 



JVave 



Incident longitudinal . 

 Reflected longitudinal . 

 Reflected transverse . . 

 Refracted longitudinal 

 Refracted transverse . . 



Index 



Velocity 



Medium 



Fig. 407. — Sketch illustrating angles made by wave rays and displacements with the normal at the 



boundary between media 1 and 2. 



The positive axis of s is in the plane of the paper and is parallel to the normal at 

 the boundary directed from medium 1 to medium 2, and the positive axis of x is in the 

 plane of the paper and is directed toward the left. (Figure 407.) The positive direction 

 of displacement of the waves is assumed to be the direction from medium 1 towards 

 medium 2. 



* It is important to note that a continuous gradual change, sucn as that produced 

 by increase of pressure with depth, generally will not produce detectable reflections. 



