Abstract: The invention relates to a method and apparatus for studying the resistivity of a geological formation around a borehole fitted with metal casing. An electric current is applied to the casing so as to cause current to leak into said formation at a given level, and said current is shunted by a feedback circuit in contact with the casing on either side of the measurement level, said circuit being organized to ensure that the current flowing along the casing at said level is less compared with the shunt current, the difference between the voltage drops on the adjacent sections of casing situated on either side of the measurement level is determined, and the leakage current (Ifor) is deduced therefrom.