Imaging Properties of Apparent Resistivities Based on Rotational Invariants of the Magnetotelluric Impedance Tensor

TL;DRAbstract

Apparent resistivity images of thin sheet like models having a complicated geometry are studied in a wide period-range by means of three-dimensional (3D) numerical modelling. Fifteen different definitions of the apparent resistivity are calculated using five different functions [¦f(Z)¦, Re f(Z), Im f(Z), f(Re Z), and f(Im Z)] of three rotational invariants f of the magnetotelluric impedance tensor [f(Z) = Z 1 2 = (Z xy − Z xy)2/4; f(Z) = det(Z) = Z xx · Z yy − Z xy · Z yx; f(Z) = ssq(Z) = Z xx 2 + Z xy 2 + Z yx 2 + Z yy 2]. A simple visual analysis of apparent resistivity maps and of sounding curves averaged over and around a conductive (and a resistive) heterogeneity embedded in a homogeneous half space is presented. The imaging properties appear to depend much more on the apparent resistivity definition than on the rotational invariant itself. Except for the very short period range corresponding to the oscillating section of the sounding curves, a robust and regular behaviour of the

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