Amplitude-phase decomposition of the magnetotelluric impedance tensor

The introduction of the phase tensor marked a breakthrough in the understanding and analysis of electric galvanic distortion effects. It has been used for (distortion-free) dimensionality analysis, distortion analysis, mapping, and subsurface model inversion. However, the phase tensor can only represent half of the information contained in a complete impedance data set. Nevertheless, to avoid uncertainty due to galvanic distortion effects, practitioners often choose to discard half of the measured data and concentrate interpretation efforts on the phase tensor part. Our work assesses the information loss due to pure phase tensor interpretation of a complete impedance data set. To achieve this, a new MT impedance tensor decomposition into the known phase tensor and a newly defined amplitude tensor is motivated and established. In addition, the existence and uniqueness of the amplitude tensor is proven. Synthetic data are used to illustrate the amplitude tensor information content compared with the phase tensor. Although the phase tensor only describes the inductive effects within the subsurface, the amplitude tensor holds information about inductive and galvanic effects that can help to identify conductivity or thickness of (conductive) anomalies more accurately than the phase tensor. Furthermore, the amplitude and phase tensors sense anomalies at different periods, and thus the combination of both provides a means to evaluate and differentiate anomaly top depths in the event of data unavailability at extended period ranges, e.g., due to severe noise.