### Abstract

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 [ζf(Z)ζ, Ref(Z), Imf(Z), f(ReZ), and f(ImZ)] of three rotational invariants f of the magnetotelluric impedance tensor [f(Z) = Z_{1}^{2} = (Z(xy) - Z(yx))^{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 imaging parameters is observed. In this so called 'normal' period range the 3D imaging properties seem to be the best if the apparent resistivity is derived when using the function ReZ, i.e. when computing the rotational invariant with the real parts of the four impedance tensor elements. For apparent resistivities derived from ReZ, a rapid convergence over lateral resistivity contrasts and oscillations with small amplitude over homogeneous areas are actually observed in the apparent resistivity maps. In the period domain, they are characterised by a maximum rate of convergence to the underlying resistivity at longer periods and by a reasonably small standard deviation, even in presence of a near-surface disturbing body.

Original language | English |
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Pages (from-to) | 149-175 |

Number of pages | 27 |

Journal | Acta Geodaetica et Geophysica Hungarica |

Volume | 35 |

Issue number | 2 |

Publication status | Published - Jan 1 2000 |

### Keywords

- Electrical resistivity
- Electromagnetic methods
- Magnetotellurics

### ASJC Scopus subject areas

- Building and Construction
- Geophysics
- Geology

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## Cite this

*Acta Geodaetica et Geophysica Hungarica*,

*35*(2), 149-175.