MULTIPLE REFLECTED WAVES 



87 



boundary. We give below formulas to describe the vertical component 

 of displacement JF at the front of a double reflected wave. 



U < o < arcsm —^ , 



^=ir.^. 



(3) 



With angles of incidence 



B 



/^\*ii_ 



^1 = 



Q2 



A{D^+^BC sin a) 



^'y-l -r^ + ^(i)2+45Csin2a) 



?2 



W.= 



A^ 



2n Ha^^ ^ q^ 



= E,: 



(4) 



Here IV^ is the vertical component of displacement at the front of a single 

 reflected wave; a^, a^, b^ are the velocities of longitudinal and transverse 

 waves in the overlying (1) and underlying (2) media; q^ and Q2 are the densities 

 in these media, and H is the depth of the lower reflecting boundary; 



^=|/l-sin2a; B = 



-Wl 



Vii)'-'--- 





sm'^'cc 



D 



<h 



2 sin^ a. 



For angles of incidence arcsin — - < a< arcsin -r^ 



02 02 



W 



A^ 



471 Ha^ |/^i 



= ]/[Re{E2^)? + [Im{E2^)\^F, 



(5) 



where 



^2 = 



B[^V^i-AiD^- 4BCi sin^a) 

 62/ ^2 



i = V — 1; Re and /^ indicate respectively the real and imaginary parts of 

 the quantity £"2^; F expresses the form of the oscillation. 



