An Improved Equivalent Circuit for Electric Field Sensors in Geophysical Exploration

In electromagnetic measurements, electric field sensors consist of two halves, with remote electrodes of negative and positive polarity coupled through wires and low pass filters to the differential inputs of an analogue-to-digital converter; the electrical ground of the analogue-to-digital converter is connected to the ground through a reference electrode. We present, analyse and evaluate improved equivalent circuits for such electric field sensors. This serves to identify the maximum contact resistances of the electrodes for which the recorded voltages are unaffected by system response effects over a given frequency range. In the first step, we verify a new equivalent circuit for one half of an electric field sensor by comparison to a previously published equivalent circuit. In contrast to the latter, our equivalent circuit accounts for the spatial variability of the electric field along an extended sensor cable, the finite impedance of the receiver input stage, the non-zero contact resistance of the reference electrode and residual cable on a winch. Furthermore, the cable is characterised by its resistance, self-inductance and capacitance to the ground and the ionosphere or the borehole fluid. Compared to the absolute value of the voltage, our results show that the system response affects the phase of the voltage at lower frequencies. In the next step, we develop an equivalent circuit for a complete electric field sensor connecting two sensor halves to an analogue-to-digital converter. We study both symmetric and asymmetric set-ups with identical and differing cable lengths, respectively, of the sensor halves. Over the whole frequency range, the amplitude gets the lower, the higher the sum of contact resistances of the remote electrodes is. In contrast, the phase is distorted only at higher frequencies. Generally, the contact resistance of the central reference electrode has little effect. For symmetric sensors, of the combinations of contact resistances of the remote electrodes that have the same sum, it is the combination of identical contact resistances that shows the lowest distortion. The distortion owing to different contact resistances of the remote electrodes is only slight and mostly in the amplitude at high frequencies. For asymmetric sensors, the benefits of using a differential analogue-to-digital converter input are no longer exploited. For instance, flipping the contact resistances of the remote electrodes leads to different responses at high frequencies. In borehole applications, it is of particular importance to account for the spatial variability of the electric field due to the skin effect, field propagation and the curvature of the borehole track. We consider an extended electric field sensor that is placed in a borehole at an inclination of $45{}^{\circ }$ in a homogeneous half-space. At high frequencies, the capacitive leakage of the wire in the borehole, parasitic self-inductance of residual cable on the winch, the electromotive force induced in the cable on the winch by an ambient magnetic field, and the low-pass filter in the input stage of the receiver complicate data interpretation and are strongly dependent on the set-up.