314 



EXPLORATION GEOPHYSICS 



Since curvature = — where p = radius of curvature : 

 P 



1 -1 Z'^U _, 1 1 '^'U 



Px g ^x" py g 3/* 



The difference in these curvatures or the "R" line value is 



\py P' ) V^-^" ^y"/ \'^y' ^-^' / 



(54) 



(55) 



where g^ = — 



■dU 



which is the deviation of the equipotential surface from the spherical shape 

 (Pj,' =1 pmin, and px =p max, whilc for a sphere 

 p/ = Px' and 7? = 0) . 



If pi and pi are used in place of 

 ture: 



R 



Px' and Py as representing the principal radii of curva 



= a ( ^ ~ L\ = (^U _^u\ 

 ^Vpi pJ \dx'' dy'^J 



(56) 



Relation of the directions x' and y' to astronomic directions x and y or N-S and 

 E-W: 



We heretofore have designated x' and y as the N-S and E-W directions. Actually 

 the x' and y directions are those of maximum and minimum curvature of subsurface 

 equipotential surfaces and are not necessarily in the astronomic N-S and E-W. The 



strike of a subsurface anticline or 

 the strike of the section of minimum 

 curvature of the equipotential sur- 

 faces arising from such a feature 

 will deviate from the north by an 

 angle designated as \. 



Figure 176 shows the horizon- 

 tal plane touching an elliptical equi- 

 potential surface and the horizontal 

 components of gravity force acting 

 in this plane, together with the ast- 

 ronomic directions x or N-S, and y 

 or E-W. The direction x' lies as 

 before in the section of minimum 

 curvature of the equipotential sur- 

 face and the y direction is at right 

 angles thereto. The angle X as indi- 

 cated can be defined as the angle 

 that the x' direction (or direction 

 of the section of minimum curva- 

 5 ture) makes with the astronomic 



Fig. 176.— Showing the horizontal plane touching an north Tt i'q mpasnrprl in rlptrrppc 



elliptical equipotential surface at one point and the "Orm. It IS measured m aegrees 



gravity components in the plane. The angle X is the clockwise from the true north, 

 angle between the x' direction, or the section of mini- -r^ ^ • i, i 



mum curvature of the surface and the astronomic north. i* rom torsion balance measure- 



