264 



GRAVITATIONAL METHODS 



[Chap. 7 



using the distance between the extremes in gradients and curvatures have 

 been constructed by Jung. The dip angle may also be calculated from 

 the ratios of gradient maxima and minima. The direct interpretation 

 of torsion balance anomalies of vertical and inclined dikes has been dis- 

 cussed in detail by H. Shaw.^^° 



By letting i = 90° in eq. (7-93c), the gradient and curvature anomalies 

 of*a step with a vertical face (fault, escarpment, or the like) are obtained. 

 With the notation of Fig. 7-98/, 



U^'z = 2k8 log 



ri 



— C/a' = 2k8(<p2 — <pi). 



' (7-94a) 



The upper and lower depths follow, therefore, from the amplitudes and 

 abscissas of the extremes in gradients and curvatures, thus: 



d.D = (xc._ 

 d 



= (xo,)' 



logio ^ = 0.438Gn,,,. 



(7-946) 



The anomalies of a block with vertical faces, as in Fig. 7-9Sg, may be ob- 

 tained by subtracting two faces, as in eq, (7-94a) or by letting i = 90° 

 in formula (7-93/i). Then 



C/x'. 



2/c5 log, 



Virs 



— Ua' = 2kd((p2 — <pi 



<Pi + <P3) 



(7-94c) 



For direct interpretation, it is helpful that the curvature at the symmetry 

 point, X = 0, is equal to twice the angle subtended by the upper and 

 lower edges. Hence, Cmax. = 2<po , where (po = i<pi — (^2)x=o = (<Pi — <pz)x^ . 

 The complete determination of depth and outline is possible by means of 

 diagrams constructed by Jung. " 



When the dike is of infinite depth extent, r4 ■;^ r^ and (^4 ?^ (^2 , so that 

 with the notation of Fig. 7-98/i, 



U:,', = 2k8 log< 



Ua' = -2k8^. 



(7-94d) 



1" Ibid. 



'21 Zeit. Geophys., 3, 257-280 (1927); 5, 238-252 (1929). 



