contained energy decreases. The mechanism by which this modification develops 

 has been a matter of study by numerous investigators, notably Sharpe (1942), 

 Ricker (1953), Born (1941), and McDonal, Mills, Sengbush, and White (1955). 

 Agreement among their conclusions is lacking, and we can only state that with 

 very limited exceptions (Pickett, 1955), the longer the path the less the high 

 frequency content. 



6 2 > Kz > ^T2 



Figure 26-3. Four wavelets result from an incident longitudinal 

 plane wavelet impinging upon an interface between media of 

 different elastic constants and densities. The directions of propa- 

 gation are shown by — > and the directions of particle displace- 

 ment by <-> . The angles relate as sin aJ'S^ = sin o^l/Vl^ 

 = sin a T r r/Yj l = sin a t L/VL, 2 = sm a \X\^'^2- ^L and Vt are 

 the longitudinal and transverse velocities respectively and 5 is the 

 density. The subscripts L and T represent "longitudinal" and 

 "transverse" respectively; r and t stand for "reflected" and "trans- 

 mitted." 



When in its travel through the layered crust a wavelet encounters an 

 interface between media of different elastic constants and densities, it divides 

 into several parts. When for instance, as in Figure 26-3, a longitudinal plane 

 wavelet reaches a plane interface between such extended media in angularity 

 with its direction of propagation, it splits into four wavelets: two longitudinal 

 and two transverse. One longitudinal and one transverse are reflected and one 



562 



