ELECTRICAL METHODS 



515 



tigations on the propagation of electric current in anisotropic media have 

 been reported by Schlumberger and Leonardont and by Maillet and 

 Doll, t It is well known that in stratified rocks electric current is prop- 

 agated more easily along the strike than in a direction perpendicular 

 to the strike. This phenomenon may be treated quantitatively by intro- 

 ducing a coefficient of anisotropy A defined by the relation 



=V5 



where rt denotes the resistivity along the strike, "transverse resistivity," 

 and ri the resistivity perpendicular to the direction of the beds, "longi- 

 tudinal resistivity." 



Figure 312 shows a cross section of an equipotential surface on a 

 vertical plane that is perpendicular to the bedding plane and passes 

 through a point source of current located in a homogeneous medium. 

 If the medium is isotropic as well as homogeneous, the equipotential 

 surfaces surrounding the current source are spheres. (Compare p. 

 508.) If the medium is anisotropic and homogeneous, the equipotential 

 surfaces surrounding are ellipsoids of revolution around an axis 

 through perpendicular to the strike. It may be shown that the ratio of 

 the semi-axes of the ellipse {OA/ 

 OB) is equal to the coefficient of 

 anisotropy A. 



The ellipticity of the equipotential 

 surfaces in anisotropic media has 

 important consequences as regards 

 the interpretation of resistivity data. 

 One of these consequences, the so- 

 called paradox of anisotropy, is that 

 in the case of a stratified formation 

 tilted vertically, the observed, appar- 

 ent transverse resistivity is smaller 

 than the observed, apparent longi- 

 tudinal resistivity, while the inverse 

 proposition holds for the true resis- 

 tivities. Another consequence is that 

 formulas derived for a stratified 

 medium comprising several parallel, 

 homogeneous, isotropic layers hold for a medium comprising anisotropic 

 layers provided the resistivity of each layer is set equal to yjrirt, where 

 Yi and rt denote the longitudinal and transverse resistivities of the layer 



t C. and M. Schlumberger and E. G. Leonardon, "Some Observations Concerning Electrical 

 Measurements in Anisotropic Media, and their Interpretation," A.I.M.E. Geophysical Prospecting, 

 1934, pp. 159-181. 



t R- Maillet and H. G. Doll, "Sur un theoreme relatif aux milieux electriquement anisotropes, et 

 ses applications a la prospection electrique en courant continu," Ergansungshefte fiir angewandte 

 Geophysik, Vol. 3, No. 1, 1932. 



Fig. 312. — Cross section of equipotential 

 surface by a vertical plane passing through a 

 point source of current located in a homo- 

 geneous, horizontal stratum. (After Schlum- 

 berger and Leonardon, A.I.M.E. Geophysical 

 Prospecting, 1934.) 



