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The magnetotelluric impedance tensor through Clifford algebras: part I — theory
Author(s) -
RomeroRuiz Ivan,
Pous Jaume
Publication year - 2019
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12741
Subject(s) - tensor (intrinsic definition) , clifford algebra , algebra over a field , mathematics , distortion (music) , tensor calculus , tensor contraction , cartesian tensor , pure mathematics , tensor density , mathematical analysis , tensor field , physics , exact solutions in general relativity , tensor product , amplifier , optoelectronics , cmos
The magnetotelluric impedance tensor is analysed in the context of Clifford algebras. In this framework, the tensor is broken down into different parts, each one with a particular geometric algebra meaning, the simplicity of which allows us to deduce a number of known properties and opens up many other possibilities. As examples to show its capabilities, some of the algebraic relationships involving the impedance tensor, such as rotations, Mohr diagrams and phase tensor, are shown under this theory. Rotations are analysed in Clifford algebra C l 3and Mohr diagrams, and phase tensor are expressed in Clifford algebra C l 2 . The galvanic distortion matrix and its transformations are also seen in Clifford algebra C l 2 , where a number of relationships allow us to recognize the galvanic distortion in a measured two‐dimensional/three‐dimensional impedance tensor. These relationships are useful as constraints to determine the galvanic distortion parameters.