Mode separation of magnetotelluric responses in three-dimensional environments

Abstract

SUMMARY Magnetotelluric (MT) responses in complex, 3-D terrains are in general characterized by (i) elliptical polarization states of horizontal electric and magnetic fields; (ii) the non-orthogonality of electric and magnetic fields and (iii) a coupling of the anomalous tangential-electric (TE) and tangential-magnetic (TM) modes, giving rise to a mode-mixed anomalous electric field at the surface. These 3-D effects are propagated into the MT impedance tensor, which is derived from horizontal electric and magnetic fields, recorded at the earth’s surface. The 2 × 2 impedance tensor is in general fully occupied, and each of its elements is a mode-mixed quantity. To study 3-D effects of MT (impedance) data, the TE and TM mode contributions must be separated. This becomes possible with the inclusion of the single-mode vertical magnetic transfer function (the ratio of vertical to horizontal magnetic fields). Then, the individual modes can be resolved without prior knowledge of the underlying 3-D conductivity structure. For this purpose, we consider (i) the spatial relations between electromagnetic field components recorded in an array of sites (Faraday’s law) and (ii) that the magnetic TE mode and electric TM mode fields are potential fields within the insulating air half-space above the earth’s surface. Based on these two dependencies, it is possible to reconstruct the entire electromagnetic field from (measured) mixed-mode impedances and vertical magnetic transfer functions and to separate it into TE and TM modes, and into normal and anomalous parts. Hereby, we cannot only study the contribution of the two modes on the observed impedance tensor but also quantify the influence of 3-D effects at each location and frequency of a particular data set. Results of a modelling study suggest, that (i) none of the elements of a 3-D impedances tensor can be regarded as favourable for a 2-D interpretation (only 3-D models can explain 3-D data), (ii) a heterogeneous crust can strongly obscure identification of responses originating from the lower crust or upper mantle even at very long periods and (iii) the TE mode magnetic transfer functions are most important for sensing deep anomalies.