152 GRAVITATIONAL METHODS [Chap. 7 



With X — x' = b, and 



d -\- X = ri X = d tan <pi 



D^ + x^ = rl X = D tan ^2 



d^ -{- {x — hY = rl X — b = d tan <pz 



D^ + (x - bf = r\ X - b = D tan <pi , 

 the anomaly in gravity is 



Ag = 2k8 \x loge — ' + 6 log, -* + Z)(^ - ^4) - d(<^i - ^s)] . (7^26) 

 L nn n J 



If a vertical dike has a considerable extent in depth, rz — u and 

 Z)(v92 — ^4) = 6. The anomaly in gravity then becomes 



A^ = 2k8 [x log, ^' + b Hoge ^' + 1) - d{<pi - <P3) J. (7^2c) 



It is seen that (contrary to the corresponding torsion balance anomalies) 

 the attraction of a vertical dike cannot possibly be calculated without 

 making some assumption about the depth to its lower end. Formula 

 (7-426) may be used to calculate the effect of a fault or buried escarpment 

 (Fig. 7-44c). Then rz = u, D<pi = d^pz, and 



Ag = 2kb Ix loge - + Z)^ - dipA . (7-42d) 



At a station far removed from the edge, rz/n = 1 and ^2 ^ ^1 — ^ so that 

 A^ = 2Trk8{D — d). This is identical with the formula for an infinite 

 disk or with Bouguer's formula. The Bouguer effect is twice as great as 

 the gravity anomaly directly over the edge of the escarpment, li x = 0, 

 then <p2 = <pi = t/2 or 



A^ = Tk8{D - d). (7-42e) 



If the section of a horizontal two-dimensional prism is triangular (Fig, 

 7-44d), the gravity anomaly is 



Ag = 2k8 < — [x sin i -\- d cos i] sin i loge — + cos t(«p2 — <pi) 



-x\oge-+D(<p2-<p,)]. (7-43a) 

 n J 



