On the robust estimation of power spectra, coherences, and transfer functions

Robust estimation of power spectra, coherences, and transfer functions is investigated in the context of geophysical data processing. The methods described are frequency‐domain extensions of current techniques from the statistical literature and are applicable in cases where section‐averaging methods would be used with data that are contaminated by local nonstationarity or isolated outliers. The paper begins with a review of robust estimation theory, emphasizing statistical principles and the maximum likelihood or M‐estimators. These are combined with section‐averaging spectral techniques to obtain robust estimates of power spectra, coherences, and transfer functions in an automatic, data‐adaptive fashion. Because robust methods implicitly identify abnormal data, methods for monitoring the statistical behavior of the estimation process using quantile‐quantile plots are also discussed. The results are illustrated using a variety of examples from electromagnetic geophysics.