A method for obtaining fully gain compensated propagation measurements includes rotating an electromagnetic logging while drilling tool in a subterranean wellbore. The tool includes first and second transmitters and first and second receivers axially spaced apart from one another in which each of the transmitters and each of the receivers include an axial antenna and collocated first and second transverse antennas. The first and second transverse antennas in the first receiver are rotationally offset by a predefined angle from the first and second transverse antennas in the first transmitter. A plurality of electromagnetic voltage measurements are acquired at the first and second receivers while rotating and processed to compute harmonic coefficients. The harmonic coefficients are mathematically rotated through at least the predefined angle to obtain rotated coefficients. Ratios of selected ones of the rotated coefficients are processed to compute fully gain compensated measurement quantities.