“Response of a normal resistivity tool in a borehole crossing a bed boundary,” Geophysics, Vol. 49, No. 2, pp. 142-149, February 1984.
The fundamental boundary-value problem involving a current electrode in an inhomogeneous medium is solved. Two integral equations are obtained by imposing the condition of conservation of electric currents. Solution of one of the integral equations involves potentials in a step-wise inhomogeneous medium. Two examples: the first is concerned with a normal tool in a well with mud conductivity sigma m in a thick bed of conductivity sigma 1 ; in the second, the response of a 16 inch normal tool is calculated when it is in a well with mud conductivity sigma m crossing a boundary separating two beds with conductivities sigma 1 and sigma 2 , respectively. Results agree with other theoretical data for the first case. For the second case they agree well with experimental data obtained from Schlumberger's resistor network model.