The magnetotelluric impedance tensor through Clifford algebras: part Ⅰ - theory

摘要

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 Cl3 and Mohr diagrams, and phase tensor are expressed in Clifford algebra Cl2. The galvanic distortion matrix and its transformations are also seen in Clifford algebra Cl2, 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 distortionparameters.