294 



EXPLORATION GEOPHYSICS 



A torsion balance placed in a distorted force field will be deflected and 

 twisted by the gravity forces acting on it, as illustrated in Figure 156. It 

 will be understood that the curvatures of forces and equipotential surfaces 

 are greatly exaggerated in the illustrations. The actual curvatures are 

 extremely small, on the order of 10~^^ radians per centimeter. 



LINES OF 



GRAVITATIONAL FORCE 



TORSION BALANCE 



\ 



X 



/ 



y" 



Fig. 156. — Showing the deflection of a tor- 

 sion system by the curvature of the_ lines of 

 force of gravity where a heavy mass is present 

 in the subsurface. 



EQUIPOTENTIAL 



Fig. 157. — Illustrating the effects on lines of 

 force of gravity and equipotential surfaces above 

 a salt dome. 



A mass of low density below the surface, such as a salt dome, would 

 create a dispersion of the force field or a warping in the direction of the 

 lines of force of gravity as illustrated in Figure 157. Such a low density 

 area produces a sag in the equipotential surfaces above it. A plumb line 

 at a station over a salt dome would be deflected toward the more dense 

 sediments surrounding the dome. 



Gravitational Potential and Equipotential Surfaces. — To under- 

 stand the forces acting on a torsion balance, it is necessary to examine the 

 nature of the potential function of the gravity field and, in more detail, the 

 concept of equipotential surfaces of gravity. If we consider the space 

 around a sphere of mass m, a mathematical function can be set up, called 

 the potential function, which expresses the gravity potential for every point 

 in this space. 



Referring to Figure 158, the force on a unit particle at Pi, due to the 



spherical mass, is F = —G ~ , where the minus sign denotes that the force 



is in the negative ri direction, or is toward m. 



The difference of potential between two points in a field is defined as 

 the negative of the work done by the field in carrying the particle between 

 the points. Physically, this means that a particle in a force field (force of 

 gravity, in this case) will move from a point of higher to a point of lower 

 potential. The potential is such that the magnitude of its space rate of 



