S U M M A R YThe rotational invariants of the magnetotelluric impedance tensor Z may serve as the most compact 3-D interpretational parameters, since they do not depend on the direction of the inducing field, and they may have various morphological characteristics over 3-D bodies. Their complete system is reviewed for the first time in this paper. It is demonstrated that the complex Z-having eight real-valued independent elements-has seven independent rotational invariants. The complex determinant det(Z) contains three independent real-valued invariants: det(%Z), det(9mZ) andand not two, as is usually assumed from its complex character. The same is true for the sum of the squares of the elements of Z, ssq(Z) = Z:, + Z2 + ZjX + Z$ Its real-valued invariants are ssq(%Z) = and 9m ssq(Z) = 2(%Zxx 9mZ,, + %Z,, 9mZxy + %Z,, 9mZy, + %Zyy YmZ,,) where 9% ssq(Z) = ssq(%Z) -ssq(XmZ), and ssq(%Z) + ssq(9iZ) = IIZllT; here llZ1lf is the Frobenius norm of Z. The sets of seven independent rotational invariants can be selected in many different ways. In the classical magnetotelluric set, %Zl, 9mZl[where Z1= (Zxy -2,,)/2], %Z2, 9mZz (where the trace Z,, + Z,, = 2 2 2 ) and the three determinant-based real-valued invariants, det (%Z), det (9mZ) and 9 % det(Z), are suggested for use. If the trace, the determinant and ssq(2) are accepted as basic scalar functions (we call them the mathematical selection of invariants), eight different sets of independent invariants can be selected, The geometrical meaning of rotational invariants is illustrated using two different graphic representations: complex-plane ellipses and Mohr circles. For electromagnetic imaging purposes it is suggested that some of those parameters that are derived from the real tensor %Z should be used, since at realistic periods the model geometry of thin-sheet-like 3-D models is much better reflected in, for example, %Zl, det(%Z) and ssq(%Z) than in any other invariants.Key words: electrical resistivity, electromagnetic methods, magnetotellurics. 9%22xx + %2zxy + %2Z,, + 9 4 % 2xy zyy; ssq(9mZ) = 9m22,, + 9m2zxy + 9*2zy, + 9m2zyy;

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In the first part of the paper a brief introduction is given (a) to the magnetotelluric (MT) and magnetovariation (MV) soundings, (b) to electrical resistivity of minerals and rocks, and their dependence on temperature and fluid content. The basic geoelectric model in the Pannonian Basin is a (linear) tectonic zone ("dike") and a series of dikes.In the second part the main crustal and mantle conductivity anomalies observed in the Pannonian Basin (PB) are summarized: (a) deep conductive crustal fractures and their relation to the occurrence of the earthquakes, boundary of the megablock(s) etc., (b) middle crustal conductors as indicators of decrease in stress and seismic activity depending on thermal regime, (c) the conductive asthenosphere and its lateral change in the PB in connection with the heat flow and tectonics. The general relation between the depth of the conductive asthenosphere and the regional heat flow is also presented, (d) MT anisotropy of the resistivity distribution in the PB and its tectonic explanation based on Haas's tectonic map (2001, Fig. 1). All these observations and conclusions are considered as results for further investigations.