Dipole approximation of the solution for an electrode configuration in two-layer resistivity problem

An electrode configuration which consists of a pair of current electrodes, spaced at a unit apart, being kept at a great distance r from a pair of potential electrodes also spaced at a unit apart, has been investigated. Two theoretical apparent resistivity formulae were derived by applying Kelvin\u27s theory of images to the problem of two-layer case. One formula is obtained by the exact method of solution, the other being obtained by considering the pair of current electrodes as a single dipole. Results of numerical calculations show that the greater the spacing r in comparison to the spacing a, the better the dipole approximation will be and that the dipole approximation is valid only under condition that r must be at least equal to 20a or greater. Theoretical analysis shows that the configuration possesses several limitations which render it useless as a method for locating horizontal discontinuities in conductivity --Abstract, page i