A method is provided for determining an electric
conductivity of an earth formation formed of different earth
layers, which earth formation is penetrated by a
wellbore containing a
wellbore fluid, is provided. The method includes the steps of: lowering an
induction logging tool into the
wellbore to a location surrounded by a selected one of the earth
layers, the tool having a
magnetic field transmitter effective to induce magnetic fields of different frequencies in the earth formation, and a
magnetic field receiver effective to receive response magnetic fields and to provide a
signal representative of each response
magnetic field, at least one of the
transmitter and the
receiver having a plurality of
magnetic dipole moments in mutually orthogonal directions. At least two of the different frequencies are selected, and for each selected frequency, the
transmitter is operated so as to induce a magnetic field in the earth formation and the
receiver is operated so as to provide a
signal representing a response magnetic field, wherein the at least one of the transmitter and receiver is operated in the mutually orthogonal directions. The signals are combined in a manner so as to create a combined
signal having a reduced dependency on the electric
conductivity in the wellbore region. The formation resistivity and the relative orientation of the
logging tool with respect to the formation layering is determined from the combined signal.