Magnetotellurics: the CBB or phase tensor and Bahr's 1988 analysis

The phase tensor of magnetotellurics is analysed in terms of its invariants with regard to axes rotation. These invariants are displayed as conic sections (ellipses), eigenvectors, and as Mohr diagrams. Attention is drawn to a supplementary ellipse which may be constructed to complement the usual phase tensor ellipse. The two ellipses together help convey the full information available from phase tensor analysis. For the cases of 1D and 2D regional structure, the ellipses, eigenvectors and Mohr diagrams show distinctive features, such as no preferred strike direction in the case of 1D, and a consistent strike (or across-strike) direction in the case of 2D. In the general case of 3D regional structure a "closest 2D strike" direction may be apparent, though there is a range of possibilities for this quantity. The range includes Bahr's regional strike estimates, which are shown to be given by the eigenvectors of the phase tensor. Generally in this paper, the phase tensor will be referred to as the CBB tensor, in recognition of its discoverers Caldwell, Bibby and Brown