268 



EXPLORATION GEOPHYSICS 



(b) Gradient of Gravity 



Consider the ^.g"o for the granite ridge (Figure 126), which is also 

 the case for an antichne. As is brought out in Figure 130, the slope of 

 this curve at various points is a measure of the gradient of gravity at the 

 points. At point A of Figure 130, forming the quotient dg/dx gives a 



numerical value for the rate of 

 change of gravity force, or the gra- 

 dient of gravity, at point A. The 

 gradient at A can be assigned a di- 

 rection, namely, toward increasing 

 values of gravity, or what in this 

 case amounts to the same thing, to- 

 ward the crest of the granite ridge. 

 At the point of the maximum 

 value of ^g"o the gradient (rate of 

 change) would be zero. The direc- 

 tion of the gradient reverses as the 

 ridge is crossed. 



An analogy to the gradient of a 

 function, such as gravity, is the 

 reading of the speedometer of a 

 traveling automobile at a given in- 

 stant. If the momentary speed was 

 50 miles per hour, that value repre- 

 sents a function : namely, the ve- 

 locity or distance divided by time. The torsion balance measures, at each 

 station, the rate of change of gravity, or A^r'^^/distance. 



The gravity gradient may be represented by a vector, plotted with the 

 station at its origin. Torsion balance measurements give the gradient in 

 two components : the north-south and the east-west gravity gradients at 

 each station. These two vector quantities are used to plot the resultant, or 

 total gradient. The total gradient may be plotted as a vector at the map 

 position of the station, to show the magnitude and direction of the total 

 gravity gradient. 



The north vector* is the rate of 

 change of gravity in the north direc- 

 tion. The east vector is the compo- 

 nent of the horizontal gradient of 

 gravity in that direction. By combin- 

 ing these two vectors to obtain their 

 vector sum, the resultant is a vector 

 whose length represents the total 

 horizontal gradient, and whose ori- 



FiG. 130. — The gradient at point A equals 

 dg/dx, or the rate of change of gravity with 

 respect to distance x. 



N. OR X AXIS 



E. OR I) AXIS 



Fig. 131. — A plot of the N-S and E-W com- 

 ponents of gravity gradient, showing dg/ds, or 

 resultant gradient of gravity. 



* In a given case the components might of course be south and west, respectively. 



