546 EXPLORATION GEOPHYSICS 



and C. When the bridge is balanced, i.e., zero deflection of the indicating instrument 

 T, the following relation holds : 



Eab _ Ra + i?l 



EbO Rc I iV2 



In this equation, the resistances Ra and Ro are unknown. Hence, a compensation 

 process is introduced in order to obtain an expression for the potential drop ratio in 

 terms of measurable quantities. 



Fig. 334. — Potential drop ratio compensator. (After Lundberg and 

 Zuschlag, A.I.M.E. Geophysical Prospecting, 1932.) 



Suppose Ri is arbitrarily changed to Ri, thus destroying the bridge balance. 

 The bridge may be brought back to balance by adjusting R2 to R2'. The condition for 

 balance becomes 



Eab _ Ra + Ri' 

 Ebo Ro I Rt 



On combining this equation with the last equation, we obtain 



Eab _ Ri Ri. 

 Ebo R2 Ra 



Although the contact resistances are eliminated from the final expression for the 

 potential drop ratio, reliable results will be obtained only when contact resistances are 

 negligible. This is true because the contact resistance is not a constant but is dependent 

 on current flow and other factors which may change during a measurement. 



The apparent resistivity at any station is proportioned to the product of the 

 observed potential drop ratio and the resistivity of the surface layer. 



The instrument described above is not suitable for use with alternating fields. 

 A more recent form of the compensator is said to permit large phase adjustments 

 and cover a wide range of contact resistances. 



Low Frequency Potential Gradient Instruments 



Many other potential gradient instruments have been developed t which utilize 

 low frequency alternating current for energizing the ground. When low frequency 

 energizing is used, the relatively detailed phase determinations that are required in the 

 500 and 250 cycle Ratiometers or Racoms are unnecessary, and depth penetration is in- 

 creased. The circuit employed in a majority of these instruments corresponds to that of 

 a simple alternating current bridge. Usually the zero instrument for indicating balance 

 is a sensitive oscillograph galvanometer used with an amplifier. 



As with other potential gradient instruments, depths to formation boundaries 

 are indicated by zero gradients only if the layers are horizontal. 



t For example, see C. A. Heiland, "Improvements in Geophysical Equipment for Foundation 

 and Ground Water Research," presented at the A.I.M.E. meeting, New York City, February, 

 1937; "Method and Apparatus for Electrical Prospecting," U. S. Patent 2,189,377, issued Feb. 

 6. 1940. 



