Characterization of the magnetotelluric tensor in terms of its invariants

Abstract

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.

Transverse Tectonics Feature Delineated by Modelling of Magnetotelluric Data from Garhwal Himalaya Corridor, India

“…The data recorded from GHC were corrupted to different degrees by distortion due to different types of geological and man-made noise sources. To deal with noisy data, we used impedance invariants and phase tensor-based techniques for the determination of geoelectric dimensionality and strike directions 21,22 . The basic philosophy of the technique is discussed here briefly.…”

“…Weaver et al 21 have developed dimensionality criteria based on seven rotational invariants (I 1 to I 7 ).…”

Interpreting the Eromanga and Georgina Basins from magnetotelluric data

“…This code calculates strike based on the phase tensor (Caldwell et al, 2004) and impedance tensor invariant (Weaver et al, 2000;Weaver and Lilley, 2004) methods and produces the mean, mode and median for consideration. The strike analysis used has a 90° ambiguity (Thiel, 2008), so the geological strike was used in concert with the strike analysis results to determine the strike of N160°E used for inversion.…”

Magnetotelluric Tensor Decomposition: Insights from Linear Algebra and Mohr Diagrams

“…There is an appeal in putting both in-phase and quadrature data on the same axes, as demonstrated by Szarka & Menvielle (1997) and Weaver et al (2000), but when showing a full frequency range separate sets of axes are practical. Also at times it is helpful to add axes for Z ′ yx and Z ′ yy as on Fig.…”

“…2a that the MT observations can be expressed in terms of seven invariants of rotation. From different sets which are possible, and evident from formal analysis (Szarka & Menvielle, 1997;Weaver et al, 2000), this chapter adopts the invariants shown in Fig. 3.…”