Tensor de impedancias magnetotelúrico en álgebras de Clifford: signatura rerum del tensor de impedancias magnetotelúrico

Abstract

[eng] The Magnetotelluric tensor and its transformations are considered elements of the Clifford Algebra. In this way, not only are the already known procedures reproduced but also new concepts and relationships hidden in the tensor are now elucidated. In the frame of Clifford Algebra C/3, the magnetotelluric tensor is expressed in terms of its simplest geometric-algebraic components. In this way, seven irreducible independent rotation invariants are deduced. Galvanic distortion is represented in Cl2 Clifford Algebra. An analysis of the subalgebras in C/3 recognises a particular subalgebra as the one giving meaning to the independence of the phase tensor with the galvanic distortion. The Mohr diagrams and the phase tensor are analysed in the context of Clifford Algebra Cl2. The indexes Indexi, Index2 and the Phase Sensitive Strike are deduced from the phase tensor in Cl2. In particular, Indexi and Index2, which are independent of galvanic distortion and rotation, have enabled to introduce new criteria for the analysis of the dimensionality. In Clifford algebra Cl2, a number of relationships have been found, from which a method to determine the galvanic distortion in the 3D case, with the assumption that the regional tensor has a 2D or 1D (and certain 3D cases) behaviour at short periods, has been developed. The method is based on a constrained stochastic heuristic method, which consists of exploring randomly the full space of the distortion parameters twist, shear and anisotropy. A method to find the strike of the 2D short periods is developed. A different strike angle for each period can be obtained in a 2D case because of noise. In this way we expect to recover the strike direction perturbing the data for each period with a similar random Gaussian distribution to achieve a common strike for all the short periods. The program MITT (Magnetotelluric Impedance Tensor Tools) is carried out. The program is based on the methodology developed to determine the galvanic distortion in a regional 3D case. In addition, MITT offers different useful tools about the representations of the impedance tensor: Apparent resistivities and phases, Mohr diagrams and probability density functions. MITT can be downloaded from the Dip6sit Digital de la UB, http://hdl.handle.net/2445/668.