340 



EXPLORATION GEOPHYSICS 



Plotting Corrected Torsion Balance Results. — After the observed 

 results at a station have been corrected for the normal value and terrain 

 (and for topography, if necessary), the final results are plotted on a map 

 showing the stations of the survey. The conventional method of plotting 

 is as follovv^s : a cross is draw^n through the station parallel to the N-S and 

 E-W astronomic coordinates of the map. A suitable scale for the gradient 

 and curvature values is chosen, usually 1 mm. = 1 Eotvos unit. The amount 

 of the N-S gradient Uxg is plotted on the N-S axis, to the N. if positive ( + ) 

 and to the S. if negative ( — )• The E-W gradient Uyz is plotted on the E-W 

 axis to the E. if ( + ) and to the W. if (-). (See Figure 189.) The 

 resultant of these two components represents the magnitude and direction 

 of the gradient. 



dg. 



The total gradient ^= V ([7^^)^ + {Uy,y 



Using the values from station 3 at Wild Horse Park, previously pre- 

 sented, the plotted gradient would be as shown in Figure 190. From this 

 station the (corrected) final value of Ux- = -(-8.9 E., and Uy. = —17.6 E. 



',z 



Uxz 



'HI 



Fig. 189. — Plotting gradient of 

 gravity. 



STATION 3 



Fig. 190. — Gravity gradient at 

 Station 3, Wild Horse Park, 

 Pueblo County, Colorado. Scale: 

 1 mm. = 1 £. 



In plotting the curvature quantity or R-line value, it is necessary to 

 determine first the magnitude of R, representing the deviation of the equi- 

 potential surface from the spherical shape, and second the angle A which 

 gives the direction of the section of minimum curvature of this surface 

 from the north. From equations, 



\R\=y/ (UAy+ (2Uxyy andtan2A = 



-Ua 



A second small cross is drawn showing the N-S and E-W directions. (See 

 Figure 191.) On this pair of axes, using the same scale as for the gradient 

 values, the amount Ua is plotted to the N. if ( — ), and to the S. if ( + ). The 

 amount of ZUa^y is plotted to the E. if ( + ) and to the W. if ( — ). The 



