Magnitude-phase Relationship behind Controlled-source Electromagnetic Field Revealed by Nyquist Diagrams

We present a means of processing data from frequency-domain controlled-source electromagnetic method observations via a Nyquist diagram. For a controlled-source electromagnetic field in the frequency domain, the x component of the electric field and the y and z components of the magnetic fields were chosen for discussion. Typical 1-D models and a 3-D model, which have a single anomalous body embedded in a half space, have been used to calculate the complex electromagnetic fields. The corresponding Nyquist diagrams have been plotted and analyzed. The diagrams can reveal the magnitude-phase frequency characteristics of an electromagnetic field and can be used to guide data processing by considering the constraints of the intrinsic connection between amplitude and phase. The results further show that: (1) the Nyquist diagrams of both electric and magnetic responses, varying from low to high frequencies, are all characterized by continuous, single-direction, clockwise spiral curves; (2) for the magnetic field, the opening direction of the Nyquist curve is upward for the y and downward for the z components, regardless of the change in resistivity; (3) for the electric fields, the resistivity changes also lead the spiral structure to take on complicated shapes, such as a snail-like shape or a W, and the starting points of the Nyquist curves depend on the variations in the resistivity with depth. According to the aforementioned rules, we can obtain reliable and reasonably complex field data during the data processing of frequency-domain controlled-source electromagnetic method, which lays a foundation for 3-D frequency-domain data inversion.