Summary The magnetotelluric impedance tensor is defined in terms of seven independent parameters that are invariant under a rotation of the horizontal axes on the surface of the Earth, plus an angle that defines the orientation of the axes of reference. The invariants are algebraically related to but nevertheless different from those recently proposed by Szarka & Menvielle (1997). They have been chosen in such a way as to have clear representations on a Mohr circle diagram and also to reveal geoelectric properties of the Earth near the site where the impedance data are measured. The first two invariants define the properties of a 1‐D earth when the next four invariants are negligibly small. If the next two are also non‐negligible, the earth is 2‐D with a strike direction that can be recovered. The last three invariants indicate different degrees of three‐dimensionality and the discussion of them with reference to small‐scale galvanic distortion in an otherwise 1‐ or 2‐D structure largely retraces the insightful pioneering work of Bahr (1988). The properties of the invariants are illustrated with numerical calculations for a synthetic model consisting of a small conductive anomaly in the form of a cube at the surface of an otherwise 2‐D earth that is divided by a vertical fault into regions with a strong resistivity contrast. Results are presented for synthetic data that contain only numerical noise, and for data to which 2 per cent random Gaussian noise has been added. The theoretical properties of the invariants are verified by the pure numerical data, and are confirmed statistically by the noisy data.

The Mohr circle, most commonly met in the analysis of mechanical stress, is used to depict magnetotelluric impedance information, taking the real and quadrature parts of magnetotelluric tensors separately. The magnetotelluric concepts of two-dimensionality, three-dimensionality, skew and anisotropy are then all given quantitative expression on a diagram, as are various magnetotelluric invariants. In particular, a new invariant, the "central impedance," becomes evident in a discussion of effective impedances. Some insight is gained into impedance rotations, and an anisotropy angle is defined, analogous to skew angle.Mohr circles are also tested to depict the effects of the shear and twist operations on a regionally twodimensional structure. Generally, the application of shear or twist results in an impedance tensor with a Mohr circle of typical three-dimensional form.

The problem of expressing a general 3-D magnetotelluric (MT) impedance tensor in the form of a 2-D tensor that has been distorted in some way is addressed first in terms of a general theorem. This theorem shows that when the real and quadrature parts of a tensor are analyzed separately as distinct matrices, all that is necessary to make a matrix with 2-D characteristics from one with 3-D characteristics is to allow the electric and magnetic observing axes to rotate independently. The process is then examined in terms of the operations of twist and pure shear (“split”) on such matrices. Both of two basic sequences of split after twist, and twist after split, produce a typical 3-D matrix from one initially 1-D, with the parameters of split contributing 2-D characteristics to the final matrix. Taken in reverse, these sequences offer two basic paths for the decomposition of a 3-D matrix, and are seen to be linked to the initial theorem. The various operations on matrices are expressed diagrammatically using the Mohr circle construction, of which it is demonstrated two types are possible. Mohr circles of an observed MT tensor display all the information held by the tensor, and the two types of circle construction respectively make clear whether particular data are well suited to modeling by either split after twist, or twist after split. Generally, tensor decompositions may be displayed by charting their progress in Mohr space. The Mohr construction also displays the invariants of a tensor and shows that tensor decomposition can be viewed as a process of determining an appropriate set of invariants. An expectation that the origin of axes should be outside every circle categorizes as irregular any tensors which, in either the real or quadrature part, do not satisfy a [Formula: see text] criterion. The theory of the present paper applies equally to procedures for distorting 1-D and 2-D model calculations for the purpose of matching observed 3-D data.

The Carpentaria Conductivity Anomaly of western Queensland is a major element in the electrical conductivity structure of the Australian continent. Investigation of it is significant both for its own sake, and as a case history in the general understanding of continental conductivity structure. Following its earlier discovery by reconnaissance magnetometers arrays, detailed magnetotelluric observations were carried out in 1997 along a transect crossing the anomaly between Cloncurry and Julia Creek. The magnetotelluric results define a good conductor within the crust beneath the sediments of the Eromanga Basin. The conductor extends over a depth range of tens of kilometres. This structure, evidently shown also by aeromagnetic and gravity data, is interpreted as the eastern boundary of the Mt Isa Block at a plate suture, which was later covered by the sediments of the Eromanga Basin. Seismic tomographic results show a major gradient in seismic-wave speed in the region. It appears the potential-field, electromagnetic and seismic methods have detected different characteristics of the same geologic structure, with complementary results. The electromagnetic results, new to this paper, define horizontal position well, and give evidence of highly conducting material from the crust to a depth of tens of kilometres. The seismic results extend the depth of the boundary into the upper mantle. The case history supports the hypothesis that the major conductivity anomalies of the geomagnetic deep-sounding method mark continental sutures of fundamental significance in recording the creation of continents.

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