# The magnetotelluric tensor: improved invariants for its decomposition, especially ‘the 7th’

Frederick E. M. LilleyResearch School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia.

Email: ted.lilley@anu.edu.au

*Exploration Geophysics* - https://doi.org/10.1071/EG17053

Submitted: 10 April 2017 Accepted: 22 September 2017 Published online: 27 October 2017

Journal Compilation © ASEG 2017 Open Access CC BY-NC-ND

## Abstract

A decomposition of the magnetotelluric tensor is described in terms of quantities which are invariant to the rotation of observing axes, and which also are distinct measures of the 1D, 2D or 3D characteristics of the tensor and so may be useful in dimensionality analysis. When the in-phase and quadrature parts of the tensor are analysed separately there are two invariants which gauge 1D structure, two invariants which gauge 2D structure, and three invariants which gauge 3D structure. A matrix method similar to singular value decomposition is used to determine many of the invariants, and their display is then possible on Mohr diagrams. A particular set of invariants proposed some seventeen years ago is revised to yield an improved set. Several possibilities for the seventh invariant are canvassed, and illustrated by examples from field data. Low values of Δ*β*, the invariant now preferred for ‘the 7th’, may indicate a particular simplification of otherwise complicated three-dimensional structure.

**Key words:** crustal structure, decomposition, electromagnetic methods, magnetotellurics, tensor.

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