A method for making downhole electromagnetic logging measurements of a subterranean formation is disclosed. An electromagnetic logging tool is rotated in a subterranean wellbore. The tool includes a transmitter axially spaced apart from a receiver. The transmitter may include an axial transmitting antenna and at least one transverse transmitting antenna and the receiver may include an axial receiving antenna and at least one transverse receiving antenna. The transmitting antennas transmit corresponding electromagnetic waves into the subterranean wellbore. The receiving antennas receive corresponding voltage measurements which are processed to compute harmonic voltage coefficients. Ratios of the selected harmonic voltage coefficients are processed to compute gain compensated, azimuthally invariant measurement quantities.