Appraisal of the Magnetotelluric Galvanic Electric Distortion by Optimisation of the Relation between Amplitude and Phase Tensors

The introduction of the Phase Tensor marked a major breakthrough in the understanding, analysis and treatment of galvanic distortion of the electric field in the Magnetotelluric (MT) method. We build upon a recently formulated impedance tensor decomposition into the known Phase Tensor and an Amplitude Tensor that is shown to be complementary and algebraically independent of the Phase Tensor. This recent decomposition demonstrates that the Amplitude Tensor contains inductive and galvanic information of the subsurface and that the inductive information is physically coupled to the one contained in the Phase Tensor. In this work we present an algorithm that employs this last finding to show that the MT galvanic electric distortion tensor can be separated from the inductive Amplitude Tensor and hence, that this distortion can be recovered for any given data up to a single constant usually denoted as galvanic shift. Firstly, to illustrate distortion effects on the Amplitude Tensor, we manually apply distortion by matrix multiplication to synthetic impedance tensor data. Then, we use the observations of that analysis to define an objective function, which minimises when there is no distortion present in the Amplitude Tensor. Secondly, we describe our algorithm that employs a genetic algorithm to find the optimal distortion tensor needed to correct the Amplitude Tensor, and therewith the impedance tensor. Lastly, we test the performance of the proposed methodology on synthetic data of known distortion and random distortion, and on four real data sets. The real data sets, lit007/lit008 and lit901/lit902, demonstrate the utility of the proposed algorithm by revealing geological expected results in the impedance data for the first time, which could not be achieved before by alternative methods.