356 EXPLORATION GEOPHYSICS 



is the relative density of the block, i.e., <t = ai — <t2 where o-i is the density 

 of the block and 0-2 that of the medium in which the block lies. 



(a) Infinite horizontal slab (Figure 207) bounded hy x = Xi and + 00, 

 y = ± CO, 2 = 2i and S2 {s2 > ^1) . 



Ua,,= GaXoge^^J-^^ (115) 



U^= -2Ga( tan-i -^ -tan-i |i j (116) 



U yz — U xy — 'J 



(b) Infinite horizontal slab bounded by an inclined face 



Uxz^ GcT rsin2</,loge^4^^- (^2-^1) sin2</>J (117) 



UA=-Ga \y2 sin 2c/, loge ^4x^ + 2(^2 - ^i) sin^ </>1(118) 



U yz — ty xy — 



(c) Infinite horizontal prism with vertical faces bounded by .r = Xi and xo, 

 3; = ±: (X), z = Z\ and Z2. 



Ux. - G.iog. \j^^r^2 • -^^IT^^) (119) 



[/a = - 2(7(7 ( tan-i -^ + tan-i ^ - tan-i ^ - tan-i -^ ) ( 120) 



V ^1 •*"2 •*■! X2 J 



U yg — 'J xy — '-' 



(d) Infinite horizontal prism with inclined faces 



Uxz = Ga Sm2 ,^1 loge ^2-L .,2 ~ ^m^ ^2 loge ^ g r ^ 2 



Ua = 



- (^2-^1 ) sin 2(/>i+ (^4-^3) sin 2<^2 (121) 



-Ga\y2 Sm 2<^i loge ^.24-^2 ~ ^ ^m 2(^2 loge ^ 2.^2 



+ 2(92- ex) sin2</,i-2(^4-^3)sin2</>2 J 



