Anomalous phases in TE-mode magnetotellurics

We examined the transverse electric mode of 2D magnetotelluric sounding for a simple system comprising a laterally variable thin sheet over an insulator terminated by a perfectly conducting base. We found, by asymptotic analysis and a numerical example, that the phase of the c response, or that of the corresponding entry in the impedance tensor, is completely unrestricted. This behavior is unlike that of 1D systems or transverse magnetic mode induction, where the phase is confined to a single quadrant.