Characterization of the magnetotelluric tensor in terms of its invariants

The magnetotelluric impedance tensor is defined in terms of seven independe nt 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 th e axes of reference. The invariants are algebraically related to but nevert heless 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 invarian ts define the properties of a 1-D earth when the next four invariants are n egligibly 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 in dicate 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 calculatio ns for a synthetic model consisting of a small conductive anomaly in the fo rm 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 da ta to which 2 per cent random Gaussian noise has been added. The theoretica l properties of the invariants are verified by the pure numerical data, and are confirmed statistically by the noisy data.