Using Mohr circles to identify regional dimensionality and strike angle from distorted magnetotelluric data

Mohr circles have recently been used as an aid in the analysis of the magnetotelluric (MT) impedance tensor. Although well known as a representation of the stress tensor in elasticity theory, the potential application of Mohr circles to MT data was virtually unrecognised by the geoelectromagnetic induction community until the pioneer paper of Lilley (1976). An important difference between the stress tensor and the MT tensor is that the former is real while the latter is complex, which means that the MT tensor must be represented by two Mohr circles rather than one. Although early discussions on the behaviour of MT data concentrated mainly on the real part of the MT tensor, it became necessary in more detailed treatments to consider both real and imaginary Mohr circles together. In particular, identification of seven independent invariants of the complex MT tensor as geometric invariants on a Mohr circle diagram, and their physical interpretation, required the two Mohr circles to be plotted together. A significant advance has been made with the introduction of the (real) phase tensor by Caldwell, Bibby, and Brown (2004). Although the phase tensor has only three independent invariants, it has been shown by Weaver, Agarwal, and Lilley (2003) that they retain the important physical properties of the seven invariants of the MT tensor introduced earlier but with the distinct advantage that they can be displayed graphically in a single Mohr circle diagram. In particular, identification of the dimensionality of the regional conductivity structure becomes a straightforward matter whether or not the data are distorted by near-surface conductivity anomalies.