Real and imaginary components of electromagnetic logging measurements

A method for making gain compensated electromagnetic logging measurements of a subterranean formation, the method comprising

• (a) rotating an electromagnetic logging tool in a subterranean wellbore, the logging tool including a transmitter axially spaced apart from a receiver, the transmitter including an axial transmitting antenna and at least one transverse transmitting antenna, the receiver including an axial receiving antenna and at least one transverse receiving antenna;
• (b) causing the axial transmitting antenna and the at least one transverse transmitting antenna to sequentially transmit corresponding electromagnetic waves into the subterranean formation;
• (c) using the axial receiving antenna and the at least one transverse receiving antenna to receive voltage measurements corresponding to the electromagnetic waves transmitted in (b);
• and
• (d) processing the voltage measurements received in (c) to compute harmonic voltage coefficients;
• and
• (e) processing ratios of selected ones of the harmonic voltage coefficients computed in (d) to compute real and imaginary components of a gain compensated measurement quantity.

A downhole logging while drilling tool comprising:

• a logging while drilling tool body;
• a transmitter including at least one transmitting antenna deployed on the tool body;
• a receiver including at least one receiving antenna deployed on the tool body, the receiver being axially spaced apart from the transmitter;
• a controller configured to (i) cause the at least one transmitting antenna to transmit electromagnetic waves;
• (ii) cause the at least one receiving antenna to receive voltage measurements corresponding to the electromagnetic waves transmitted in (i);
• and (iii) process the voltage measurements received in (ii) to compute real and imaginary directional resistivity measurements.