Comments On ‘Concerning dispersion relations for the magnetotelluric impedance tensor’ By E. Yee and K. V. Paulson

Abstract

SUMMARY Yee & Paulson (1988) derive an integral representation and some dispersion relations for a general magnetotelluric impedance tensor measured at a single point on the surface of the 3-D Earth. These results derive from the assumption that the impedance tensor defines a linear system which is causal and passive. We give a more careful discussion of the justification for causality and passivity and show that they do not follow from simple physical arguments; at the very least, there is a substantial gap in the mathematical derivation given by Yee & Paulson (1988). In fact, both conditions can almost certainly fail for physically realizable 3-D conductivities. We present a qualitative analysis of some simple examples which illustrate how this could occur, and give examples of estimated impedance tensors which are clearly not consistent with the passivity condition. We thus conclude that the relevance to real data of many of the results derived by Yee & Paulson must be seriously questioned. Key word: magnetotellurics.