The first step in the interpretation of magnetotelluric (MT) data involves estimating 101−102 frequency-domain impedances, Z(ω), from the raw electric and magnetic field time series e(t), h(t) (approx. 106 real numbers/site) [e.g., Swift, 1967, Sims et al., 1971]. Superficially, this initial data reduction step is almost trivial. Making the usual MT assumptions that the external sources are spatially uniform, and allowing for noise in the simplest way, e and h are related in the frequency domain via the linear statistical model (1)e=Zh+ε, where ε represents noise. The impedance Z can then be estimated quite simply by Fourier transforming the time series, and using linear least squares (LS) to minimize the misfit to equation (1) [Sims et al., 1971]. Unfortunately, this simple approach can fail catastrophically for noisy data, producing estimates that are heavily biased or wildly oscillatory [e.g., Gamble et al., 1979a; Jones et al., 1989; Figure 1]. As a consequence a number of refinements to the simple LS approach have been proposed in an effort to guarantee impedance estimates that are useful for subsequent stages in the interpretation process.
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Egbert et al. (1996) studied this question.