700 ELECTRICAL METHODS [Chap. 10 



However, in the case of dipping formations, equipotential-line surveys can 

 give useful information on dip and strike because of the electrical ani- 

 sotropy of stratified media. Schlumberger has designated the ratio of the 

 transverse and longitudinal resistivities as "anisotropy coefficient." For 

 vertically stratified ground, the influence of anisotropy on the shape of 

 the equipotential lines is most noticeable. The equipotential surfaces are 

 no longer spherical about one electrode but are ellipsoids of revolution with 

 the major axis in the direction of stratification. In plan view the trace 

 of the equipotential surface will likewise be an ellipse, with the major 

 axis in the direction of strike. The ratio of the axes is proportional to the 

 ratio of the square roots of the conductivity in the direction of strike and 

 that at right angles to the strike. 



When stratified ground is covered with glacial drift or other uncon- 

 formable layers, it is necessary that the equipotential surfaces reach deeply 

 into the stratified portion to make the deformations detectable. Hence, 

 large equipotential ellipses whose minor axes are at least twice as great as 

 the assumed cover thickness should be traced. Dips may also be deter- 

 mined directly from the displacement of the ellipses if contact can be made 

 underground with the formation under test. 



There occurs a refraction of the equipotential surfaces on formation 

 boundaries. If a given line approaches the boundary in a medium with 

 the resistivity p by the angle a, and if it is refracted into the second medium 

 (resistivity p') by the angle a', the relation obtains: 



p tan a = p' tan a'. (10-30) 



The maximum refraction is obtained if the bisecting direction makes an 

 angle of 45° with the formation boundary. Hence, it is advantageous to 

 lay out the electrode basis at an angle of 45° with the boundary to be 

 located. 



3. In virtually all electrical methods, model experiments play an im- 

 portant part because of difficulties encountered in the calculation of the 

 electrical anomalies of geologic bodies. These experiments are made on a 

 small scale in the laboratory where it is possible to simulate a number of 

 conditions difficult of evaluation, such as topography, irregular shape of 

 the ore body, and so on. In duplicating actual conditions on a small scale 

 it is necessary to pay close attention to the fundamental equations con- 

 trolling the electrical anomalies of subsurface bodies, since it may be 

 necessary to change the conductivity scale when the geometric scale is 

 changed. In accordance with formula (10-28e), the potential of a sphere 

 depends on the relative dimensions and on the conductivity ratio in refer- 

 ence to that of the country rock. Hence, if both are duplicated in the 

 laboratory, the observed potential anomalies may be expected to be dupli- 



