The Estimation Of Magnetotelluric Impedance Tensor Elements From Measured Data

Abstract

Abstract Six different estimates of the magnetotelluric impedance tensor elements may be computed from measured data by use of auto-power and cross-power density spectra. We show that each of the estimates satisfies a mean-square error criterion. Two of the six estimates are relatively unstable in the one-dimensional case when the incident fields are unpolarized. For the remaining four estimates, it is shown that two are unaffected by random noise on the H signal, but are biased upward by random noise on the E signal. The remaining two estimates are unaffected by random noise on the E signal, but are biased downward by random noise on the H signal. Computation of all of the estimates provides a measure of the total amount of noise present, as indicated by a stability coefficient for the estimates. In the absence of additional information as to the relative signal-to-noise ratios of the E and H signals, we suggest that a mean estimate be used. A numerical example is included.