A method for making downhole electromagnetic logging while drilling measurements includes rotating an electromagnetic logging while drilling tool in a subterranean wellbore. The logging tool includes a first transmitter and a first receiver deployed on a first sub and a second transmitter and a second receiver deployed on a second sub. Rotating the logging tool causes the first and second subs to rotate at different rates. A plurality of electromagnetic voltage measurements are acquired from the first and second receivers while rotating. The acquired voltage measurements are processed to compute harmonic coefficients which are mathematically rotated to obtain rotated coefficients. Ratios of selected ones of the rotated coefficients are processed to compute gain compensated measurement quantities.