Gain-corrected measurements

An electromagnetic logging while drilling method to compute a property of a subterranean formation, the method comprising:

• (a) rotating an electromagnetic logging tool in a borehole penetrating the subterranean formation, the electromagnetic logging tool including one or more arrays, wherein the arrays comprise first and second co-located triaxial transmitters and first and second co-located triaxial receivers spaced apart from one another along a longitudinal axis of the electromagnetic logging tool;
• (b) applying an alternating electrical current to each of the transmitter antenna coils in each of the triaxial transmitters to transmit corresponding electromagnetic energy into the subterranean formation while rotating in (a);
• (c) causing each of the receiver antenna coils in each of the triaxial receivers to measure a voltage corresponding to the electromagnetic energy transmitted in (b) to obtain electromagnetic measurements of the subterranean formation;
• (d) forming impedance matrices from the voltages measured in (c), the impedance matrices including a first transfer impedance matrix z11 for the first transmitter and the first receiver, a second transfer impedance matrix z12 for the first transmitter and the second receiver, a third transfer impedance matrix z21 for the second transmitter and the first receiver, and a fourth transfer impedance matrix z22 for the second transmitter and the second receiver;
• (e) combining the impedance matrices formed in (d) to compute a matrix of gain-corrected measurements, wherein combining the impedance matrices comprises (i) computing a first product of an inverse of the first transfer impedance and the second transfer impedance and a second product of an inverse of the fourth transfer impedance and the third transfer impedance;
• and (ii) combining the first product with a transpose of the second product to compute the matrix of gain-corrected measurements;
• and
• (f) inverting the matrix of gain-corrected measurements computed in (e) to compute the property of the subterranean formation, wherein the property includes at least one of a horizontal resistivity, a vertical resistivity, a dip, an azimuth, and a bed thickness of the subterranean formation.