Constrained robust estimation of magnetotelluric impedance functions based on a bounded-influence regression M-estimator and the Hilbert transform

Abstract. Robust impedance estimation procedures are now in standard use in magnetotelluric (MT) measurements and research. These always yield impedance estimates which are better than the conventional least square (LS) estimation because the 'real' MT data almost never satisfy the statistical assumptions of Gaussian distribution upon which normal spectral analysis is based. The robust estimation procedures are commonly based on M-estimators that have the ability to reduce the influence of unusual data (outliers) in the response (electric field) variables, but are often not sensitive to exceptional predictors (magnetic field) data, which are termed leverage points.

This paper proposes an alternative procedure for making reliably robust estimates of MT impedance functions, which simultaneously provide protection from the influence of outliers in both response and input variables. The means for accomplishing this is based on the bounded-influence regression M-estimation and the Hilbert Transform operating on the causal MT impedance functions. In the resulting regression estimates, outlier contamination is removed and the self consistency between the real and imaginary parts of the impedance estimates is guaranteed. Using synthetic and real MT data, it is shown that the method can produce improved MT impedance functions even under conditions of severe noise contamination.