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The magnetotelluric impedance tensor through Clifford algebras: part II — a constrained stochastic heuristic method for recovering the magnetotelluric regional impedance tensor in 2D/3D case
- Source: Geophysical Prospecting, Volume 67, Issue 3, Mar 2019, p. 670 - 695
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- 31 Jul 2017
- 11 Jan 2019
- 22 Feb 2019
Abstract
A method for obtaining the galvanic distortion matrix is presented so that the regional impedance tensor (free of distortion) is recovered. The method is a constrained stochastic heuristic method, which consists in randomly exploring the space of the distortion parameters. Constraints are imposed on the shortest periods of the regional impedance tensor that, at these short periods, tends to be two dimensional (or one dimensional). Depending on the constraints used, two different methods to recover the regional impedance tensor in this 2D/3D case are presented. Method 1 needs to find the strike of the short periods and Method 2 applies to the measurement directions. Twist, shear and anisotropy parameters are obtained. Thus, the regional impedance tensor is recovered with the only exception being the vertical shift due to the gain, which is equal for all the components of the tensor. Examples with synthetic impedance tensors from 2D/3D models perturbed with galvanic distortion are presented to illustrate how the algorithm works. The presence of noise in data is considered and rules for proceeding are provided. The same examples perturbed by Gaussian noise together with experimental data illustrate the capabilities of the algorithm.