A method for making downhole electromagnetic logging while drilling measurements, the method comprising (a) rotating an electromagnetic logging while drilling tool in a subterranean wellbore, the logging tool including a plurality of transmitter antennas (52, 54) and a plurality of receiver antennas (56,58) symmetrically spaced along a logging while drilling tool body, the plurality of transmitter antennas (52, 54) including at least one axial transmitter antenna and at least one transverse transmitter antenna, the plurality of receiver antennas (56, 58) including at least one axial receiver antenna and at least one transverse receiver antenna; (b) applying a time varying electrical current to the at least one axial transmitter antenna and the at least one transverse transmitter antenna while rotating in (a) to produce corresponding time varying magnetic fields; (c) causing the at least one axial receiver antenna and the at least one transverse receiver antenna to receive corresponding time varying electromagnetic voltage measurements while rotating in (a) for each of the time varying magnetic fields produced in (b); (d) processing the voltage measurements acquired in (b) to compute harmonic voltage coefficients; characterized by (e) processing ratios of the harmonic voltage coefficients to compute gain compensated quantities including symmetrized and anti-symmetrized quantities, the symmetrized quantities being proportional to a difference between xz and zx values and the anti-symmetrized quantities being proportional to a sum of the xz and zx values, wherein transmitter and receiver gains are fully cancelled out of the gain compensated quantities. (a) rotating an electromagnetic logging while drilling tool in a subterranean wellbore, the logging tool including a plurality of transmitter antennas (52, 54) and a plurality of receiver antennas (56,58) symmetrically spaced along a logging while drilling tool body, the plurality of transmitter antennas (52, 54) including at least one axial transmitter antenna and at least one transverse transmitter antenna, the plurality of receiver antennas (56, 58) including at least one axial receiver antenna and at least one transverse receiver antenna; (b) applying a time varying electrical current to the at least one axial transmitter antenna and the at least one transverse transmitter antenna while rotating in (a) to produce corresponding time varying magnetic fields; (c) causing the at least one axial receiver antenna and the at least one transverse receiver antenna to receive corresponding time varying electromagnetic voltage measurements while rotating in (a) for each of the time varying magnetic fields produced in (b); (d) processing the voltage measurements acquired in (b) to compute harmonic voltage coefficients; characterized by (e) processing ratios of the harmonic voltage coefficients to compute gain compensated quantities including symmetrized and anti-symmetrized quantities, the symmetrized quantities being proportional to a difference between xz and zx values and the anti-symmetrized quantities being proportional to a sum of the xz and zx values, wherein transmitter and receiver gains are fully cancelled out of the gain compensated quantities.