The relationship between the magnetotelluric tensor invariants and the phase tensor of Caldwell, Bibby, and Brown

We examine the relationship between the seven invariants of the complex MT tensor, which we previously proposed as a vehicle for testing the dimensionality of the regional conductivity structure prior to an analysis of MT data, and the three invariants of the real 'phase tensor', recently introduced as an innovative aid in the treatment of MT data. It is found that the relevant invariants, and the necessary conditions on them for galvanically distorted data to be consistent with 1D, 2D, or 3D regional structures, agree in almost every detail for the two approaches. The new method does lead, however, to an improved normalisation of the eighth (dependent) invariant previously introduced. It is shown that the phase tensor can be expressed as a sum of three simple matrices, clearly associated with 1D, 2D and 3D regional conductivity structures respectively. It is further shown that it can be depicted graphically as a single Mohr circle that retains the principal properties of the separate real and imaginary Mohr circles associated with the MT tensor. The simplicity and elegance of the phase tensor method is achieved by dispensing with the capability of distinguishing between galvanically distorted and undistorted data in 1D and 2D regions, a distinction that is ultimately unimportant and unnecessary with real data. The paper concludes with a simple illustrative example of the theory applied to a real MT dataset from NE Australia. A shallow 1D regional conductivity structure associated with a sedimentary basin is revealed, and a 2D anomaly with calculated strike angle is also identified.