Methods and apparatus are disclosed for minimizing or eliminating an undesired axial electric current induced along a subsurface borehole in the process of subsurface measurements with transmitter and/or receiver antennas which are substantially time varying magnetic dipoles with their dipole moments aligned at an angle to the axis of the borehole. Some antennas are disposed within the borehole on instruments having a non-conductive support member. One instrument includes a conductive all-metal body with an antenna adapted for induction frequencies. Antenna shields adapted for controlled current flow are also provided with an all-metal instrument. Methods include providing an alternate path for the current along the instrument body. Another method includes emitting a controlled current to counter the undesired current. Another method corrects for the effect of the current using a superposition technique. An embodiment of the instrument includes an antenna disposed between a pair of electrically coupled electrodes. The antenna is disposed on the instrument such that it comprises a tilted or transverse magnetic dipole. Another embodiment of the instrument includes a non-conductive housing with a conductive segment disposed thereon. An antenna is disposed on the instrument about the conductive segment. Another embodiment includes an antenna disposed between two pairs of electrodes with means to measure a voltage at the electrodes when electromagnetic energy is transmitted within the borehole. Yet another instrument includes an antenna disposed between a first pair of electrodes and means to measure a voltage at the electrodes when electromagnetic energy is transmitted within the borehole. This embodiment also includes means to energize a second electrode pair in response to the voltage measured at the first electrode pair.