The use of Mohr circles in the interpretation of magnetotelluric data

Abstract

One of Ted Lilley?s many original contributions to electromagnetic geophysics was his introduction of the Mohr circle 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 usefulness of Mohr circles was virtually unrecognised by the MT 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. In his early treatments of MT data, Lilley bypassed this complication by concentrating solely on the real part of the MT tensor, and was able to identify various invariants of the real tensor geometrically on the Mohr circle diagram. In later discussions of the physical interpretation of the seven independent invariants of the complex MT tensor, however, it became necessary to consider both real and imaginary Mohr circles together when seeking a geometrical representation of all the invariants. A significant advance was made with the introduction of the (real) phase tensor by Caldwell, Bibby and Brown (2002). Although the phase tensor has only three independent invariants, they retain the important physical properties of the seven invariants of the MT tensor, and 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. An analysis of MT field data with error bars will be presented using the phase tensor and its Mohr circle representation in order to show when a two- or one-dimensional interpretation of the regional conductivity structure is appropriate and strike angles are calculated for two-dimensional structures.