Term by term gain calibration of triaxial propagation measurements

A method for obtaining a gain corrected triaxial electromagnetic antenna measurement, the method comprising:

• (a) rotating an electromagnetic logging tool in a subterranean borehole, the logging tool including at least first and second axially spaced triaxial transmitters and at least first and second axially spaced triaxial receivers, each of the triaxial transmitters including a plurality of mutually independent transmitting antennas and each of the triaxial receivers including a plurality of mutually independent receiving antennas;
• (b) applying a time varying electrical current to each of the plurality of transmitting antennas in each of the axially spaced transmitters to transmit corresponding electromagnetic waves while rotating in (a);
• (c) causing each of the plurality of receiving antennas in each of the axially spaced receivers to measure voltages corresponding to each of the electromagnetic waves transmitted in (b) to acquire a plurality of full tensor voltage measurements;
• (d) causing a downhole processor to remove a full tensor voltage offset from the full tensor voltage measurements acquired in (c) to obtain a corresponding plurality of offset corrected voltage tensors;
• and
• (e) causing the downhole processor to process the offset corrected voltage tensors tensor term by tensor term to compute a full tensor, gain corrected quantity.