SEISMIC METHODS 655 



On setting, 



Vi ' di Vx V2 ' di Vi V2 



the boundary condition (3) becomes: 



—Mo sin 2a + Mi sin 2a + FM, cos 2c = — GMl sin 2b + J Mr cos 2d 



The boundary condition (3a) can be written in the form : 



, rr 2 ) I sing . cosa , \ < i sin a ,. . cos a ,. \ 



fli ^•^i ) I y~ ^0 sm o — Mo cos a I + I — Mi sm a jj— Mi cos a I 



( sin c ,, cose,. . \l ^j „/ sina,. . sino,, . 

 Mt cos c Ml sin c I > — 2c(i t/i I rj— Mo sm a r;— Ml sm o — 



sine ,, \ J T7 ■> ) I sin & ,, . , cos b.. ,\, 

 Ml cos c I = di V2-\\ f7~^^^ ^*" ^ v~^^ ^°^ ^ / "^ 



(sine? , , J cos d .. • j 1 ( oj 2 i sin & ,^ . , , sine? ,, ,1 

 Mt cos d — Mr sm c? I > — 2c?2 V2^ < 77- Ml sm b ■\ Mt cos d > 

 V2 Vz J ) y V2 V2 ) 



On simplifying in several steps, one obtains 



- di Vi Mo - di ViMi + 2d, -^ Mo sin'^ a + 2dx-^ Mi sin== a 



vi 

 + 2dx Vx Mt sin c cos c = — e?2 V2 Mi, + 2d2 -r^ Ml sin" b — 2d2 V2 Mt sin d cos d 



or 



-di VxMo { 1— 2-pi^sin'a j —dxViMi i 1— 2-^sin°a j + di z/i M, sin 2e 



= —d2V2ML ( 1— 2-^sin='&-c?2F2Mrsin2d j 



sin^o Vx^ 



or smce . . ■ = — r 



sm c Vx 



— dxVxMo (1 — 2sin''r) —dxVxMi (1— 2sinV) +dxVxM,sm2c 



= — d2 VsMl (1—2 sin^ d) — d2 V2 Mt sin 2d 

 or 



— dx Vx Mo cos 2e — dx Vx Mi cos 2c + dx vi M, sin 2c 



= — diVs Ml cos 2cf — d2 V2 Mr sin 2d 

 or 



—Mo cos 2c — Mj cos 2c + HMt sin 2c = — IMl cos 2d — KMt sin 2d 

 where 



TT__ V\ , _ C?2 Fa „ _ di V2 



Vx dx Vx dx Vx 



