654 EXPLORATION GEOPHYSICS 



^ I d. v." V. - 2d. v.^ (^ } " Sl ^^ ^'^ ^' ~ ^^^ ''^^ (5) } ^^^^ 



where the bar above the various components and operators denotes values taken at 

 the boundary. 



On substituting the values given by the system of equations (1) into the boun- 

 dary conditions, one obtains 



Mo + Mi + Mj — Ml + Mr 



W0 + W1 + ZVt — VOL + Wt 



^^^^ IVij-*- 37; + (,^+-37; + v^+-37;/-^^^^-\V-37+-97; 



, / 3Mr , 3wr \ I 



3s 3^ / j 



J TT 2 J I 3mo , 314/0 I I / 3m t I 3w; I I I 3m t , 3wt \ I 



''■'^'\V3^ + "3F^"^l^"37 + ^7'^ V^aJ"^ &"y/~ 

 ^*-' (t + t + t) =". V' {(¥^) + (¥^)} 



The boundary conditions (2) and (2a) can thus be written in the form: 

 Mn sin o -}- Mi sin a + Mi cos c = Ml sin & — Mr cos d 

 Mo cos o — Mi cos o + M« sin c = Mx, cos b + Mr sin d 



The boundary condition (3) becomes: 



J ail cos a - , . sing , . \ , / cos a . sino \ 



rfi ^1)1 77"" Mo sm a 77— Mo cos o I + I ^^ Mi sm o + "TT" Mi cos a I 



, /cos c,, sine,, . il—j 2J1 cos ^ ,, . , 

 + I Mt cos c — Mi sm c f > = dz ^2)1 77— Ml sm b 



Ml cos & I + ( Mr cos d Mt sin d ) >• 



sin & 



V: 



On simplifying, one obtains 



di Vx Mo sin 2a , rfi t^i' Mi sin 2a , c ?i t^i^ Mi cos 2c _ _ rfa vi Ml sin 26 



Fi Fi t'l F2 



<f2 z's^ Mt cos 2rf 



+ 



r^s 



Mo sin 2a + Mi sin 2a +~^' cos 2c dTliJTI '' 



ds v^ Vx ,, „, 



— ; ; Mt COS 2o 



d\ v^ Vi 



