Quadratic solution for the 2-D magnetotelluric impedance tensor distorted by 3-D electro-galvanic effects

Abstract

Magnetotelluric observations over one or 2-D structures that are distorted by 3-D electrogalvanic effects, need to be corrected for their proper conversion into reliable images of the subsurface electrical resistivity distribution. One of the most widely used approaches for correcting the data is the Groom-Bailey decomposition of the impedance tensor in terms of the unknown parameters of strike, twist and shear, along with the also unknown 2-D impedances. The standard approach for recovering the 2-D impedances is to solve numerically for all the unknowns as a non-linear inverse problem. In thiswork,we pose the recovery of the undistorted impedances in terms of a quadratic equation whose solutions filter out the distortions after a final tune for the appropriate shear parameter. The formula relies on two known invariants of the impedance tensor, the series and parallel invariants that have special immunity to some of the distorting parameters. Compared with the standard numerical recovery, the analytical solution provides more accurate results; they are clear-cut for both amplitudes and phases. The recovered amplitudes of the impedance are independent of strike, twist and shear, and the phases, in addition, of static effects. The recovery formula is transparent to random noise; hence the data preserve the original uncertainties. The applications to individual soundings of the COPROD2S1 data set and to a profile over a seismogenic region in Baja California, illustrate the effectiveness of the approach. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.