Determining a full electromagnetic coupling tensor using multiple antennas

An apparatus, comprising:

• two or more antenna groups spaced along a longitudinal axis of an electromagnetic logging tool disposed in a wellbore penetrating a formation, each antenna group having one antenna or multiple antennas proximately located or collocated, each antenna group having at least one antenna having a dipole moment that is tilted relative to the longitudinal axis of the logging tool, at least one antenna group having at least one other antenna having a dipole moment that is transverse or tilted relative to the longitudinal axis of the logging tool, and any given pair of antenna groups comprising at least four antennas with at most three of those antennas having dipole moments that are tilted relative to the longitudinal axis of the logging tool;
• a logging tool rotation angle measuring device;
• and
• a processor capable of:
• controlling the transmission of electromagnetic energy from at least one antenna group;
• controlling the reception of electromagnetic energy by at least one other antenna group;
• controlling the measurement of a tool rotation angle by the tool rotation angle measuring device;
• obtaining from the received electromagnetic energy and the measured tool rotation angle sufficient information to determine all of the elements of an electromagnetic coupling tensor;
• determining some or all of the elements of the electromagnetic coupling tensor;
• and
• inferring petrophysical properties of the formation using the elements of the electromagnetic coupling tensor.

A non-transitory, computer-readable storage medium, which has stored therein one or more programs, the one or more programs comprising instructions, which when executed by a processor, cause the processor to perform a method comprising:

• controlling the transmission of electromagnetic energy from at least one antenna group;
• controlling the reception of electromagnetic energy by at least one other antenna group, wherein each antenna group has one antenna or multiple antennas proximately located or collocated, each antenna group has at least one antenna having a dipole moment that is tilted relative to the longitudinal axis of a logging tool, at least one antenna group having at least one other antenna having a dipole moment that is transverse or tilted relative to the longitudinal axis of the logging tool, and any given pair of antenna groups comprising at least four antennas with at most three of those antennas having dipole moments that are tilted relative to the longitudinal axis of the logging tool;
• controlling the measurement of a tool rotation angle by a tool rotation angle measuring device;
• obtaining from the received electromagnetic energy and the measured tool rotation angle sufficient information to determine all of the elements of an electromagnetic coupling tensor;
• determining some or all of the elements of the electromagnetic coupling tensor;
• and
• inferring petrophysical properties of the formation using the elements of the electromagnetic coupling tensor.