ELECTRICAL METHODS A67 



steps : (a) deriving theoretical curves for various assumed subsurface con- 

 ditions ; (b) comparing the theoretical curves with the actual field curves; 

 (c) inferring from an evaluation of all available data the combination of 

 assumed subsurface conditions which would produce electrical anomalies 

 that approximate the observed anomalies. The field procedure and inter- 

 pretative technique of these methods are applicable for relatively simple 

 subsurface conditions only. 



In (2), a quite different type of field procedure and interpretative 

 technique is employed. The field work is conducted primarily to obtain 

 general resistivity-depth relationships from which a characteristic or type 

 curve may be obtained for some sequence of subsurface conditions, what- 

 ever they may be. If approximately similar subsurface conditions exist at 

 two localities in a given area, the type curves will generally exhibit recog- 

 nizable similarities ; if the geological conditions are different, the type 

 curves will generally show variations which may be correlated with the 

 geological variations. This type of analysis may be applied best in areas 

 where lateral variations in geology are restricted largely to changes in the 

 depth to certain characteristic beds or "markers." Due to the complexity of 

 beds forming a sedimentary series, deep structural investigations may be 

 handled more successfully by this method than by method (1). 



Derivation of Fundamental Formulas 



Ohm's Law. — The elementary and familiar form for Ohm's law is 



where / = current in amperes 



E = electromotive force in volts 

 R = resistance in ohms 



For a conductor (such as a wire) 



where A = cross-sectional area 

 L = length 

 p = resistivity or the resistance of a cube of unit length. 



By combining these two equations, it is evident that 



LI , EA 

 — r or / = —r- 



A pL 



E= p-T or / = — T" 



The application of Ohm's law to the measurement of the electrical 

 resistance of a wire is illustrated in Figure 278, wherein the current is 

 measured by the ammeter / and the voltage by the voltmeter E. 



The last equation is the starting point for determining the laws gov- 



