116 Symposium on Microseisms 



T zz : p + Rp = D x Pl cos 26 + D t Pl sin 26 



sin 2a cos 28 



T 7X : = Di D t — ■ 



zx x a 2 b 2 



where p and p^re the densities of the liquid and solid respectively. 

 The solution is: 



(b 2 pc cos a \ 

 cos 2 26 + — sin 2a sin 28 - | 

 a 2 p x a cos Y/ 



2p cos 26 2pb2 sin 26 

 D = -t -, D t = — 



Pi A P! Aa 2 



b 2 pc cos a 

 with: A = cos 2 28 + — sin 2a sin 28 + 



a 2 pja cos y 



Arriving at the surface z = the reflected wave <£, gives rise to a new wave <!>■> in the + y 

 direction ; as the normal pressure caused by <f>, and $■• has to disappear at z = we have 



/x sin y + z cos y + 2 h cos Y \ I 

 2 =-RA exp-^ ivf ! ! - -tj > 



Thus the twice reflected wave <f>- 2 is equal to <£„ multiplied by — R exp (2 iq), with q = (vh 

 cos v)/c; it follows that the wave *, travelling in the v direction is given by 



S\<t>zn, or 0o y\ -B exp (2iq)f Hence 



n=o n=o 



( (x sin y + Z cos y \\ 

 iXP ( iV l c ''J/ 



* =A ^ — (1) 



+ 1 + R exp (2iq) 



